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	The area of a lot		2022-12-31
		From Brian: To calculate lot size, do you use arc length or chord length? Lot Survey shows: Length 1 = 120.0' Length 2 = 120.0' Width 1 = 61.0' Width 2 = ARC Length 125.58' / CHORD Length 124.10' / Radius = 236.0' Answered by Harley.
	Velocity and acceleration		2021-01-09
		From yen: The motion of a stone projected upward is given by the relation s=112t - 16t^2. What are the values of velocity and acceleration when t=3 sec? Answered by Penny Nom.
	Running around a circular track		2020-10-31
		From kaylee: Keiko and Kendra are training for an international track competition. Kendra is running one lap on the outside of a circular track with a diameter of 1000 feet. Her constant rate of speed is 12 mi/h. Keiko is running one lap on the outside of a nearby circular track with a diameter of 1125 feet. She is also running at 12 mi/h. Find the time, in minutes, each runner needs to complete one lap. Answered by Harley Weston.
	Two equations with fractions		2020-10-22
		From mia: I am supposed to look for x and y. my teacher didn't explain very well. please help : (( 2x - y = 5 x/4 + y/3= 2 Answered by Penny Nom.
	Factoring an interest formula		2020-09-29
		From Kenneth: Hello P + Pr has a common factor of P so it can be expressed as P(1 + r) after the P is factored out.. How does the "P" get in front of (1 + r)? P/P + Pr/P = 1 + r What step is used to show that P is added in front of (1 + r)? I thank you for your reply. Answered by Harley Weston.
	Simultaneous equations		2020-09-05
		From Paa: a+b=8 a+c=13 b+d=8 c-d=6 find the value of each letter Answered by Penny Nom.
	The angular speed of a wheel		2020-09-03
		From Catrina: A car is moving at a rate of 75 miles per hour, and the diameter of its wheels is 2.6 in. Find the angular speed of the wheels in radians per minute. Answered by Penny Nom.
	4sin(2x)cos(2x)+1=0		2020-07-02
		From Sheila: 4sin(2x)cos(2x)+1=0 Answered by Penny Nom.
	A triangular garden		2020-05-24
		From yoonji: the 3 sides of a triangular garden measure 200 ft., 250 ft., and 300 ft., respectively. the garden is to be divided by a line bisecting the longest side and drawn from the opposite vertex. what is the length of the bisecting line? Answered by Penny Nom.
	A system of equations.		2020-04-27
		From solomon: xy + x =28 x + y +4 Answered by Penny Nom.
	A rectangular garde		2020-04-10
		From Denise: In a rectangular garden a person says "if I made that bed 2 feet wider and 3 feet longer it Would have been 64 sq,ft bigger. But if it had been 3 feet wider and two feet longer It would have been 68 sq.ft bigger. What is the length and width of the garden bed? Answered by Penny Nom.
	Form a square and a triangle from a wire		2020-04-08
		From Raahim: 2. A 2 meter piece of wire is cut into two pieces and once piece is bent into a square and the other is bent into an equilateral triangle. Where should the wire cut so that the total area enclosed by both is minimum and maximum? Answered by Penny Nom.
	A times table in base 5		2020-03-11
		From Felix: Design a time table for numbers 1-10 in base 5 Answered by Penny Nom.
	Multiplication base 8		2020-02-19
		From Tamesha: Let’s count with the symbols 0,1,2,3,4,5,6,7 (base 8) A). Create a multiplication table for this base B). Compute the following products using the multiplication algorithm I). 7605 times 3713 II). 63725 times 40627 Answered by Penny Nom.
	Sipping juice from a Tetra Pak		2020-02-11
		From Anjhelic: Karen is sipping juice from a 1 in. by 3 in. by 6 in tetra pack at the rate of 0.5in³/sec. How fast is the height of juice in the pack decreasing? Answered by Harley Weston.
	Investigating y = (-2)^x		2020-01-13
		From Gonzalo: This is not precisely a maths question, but it is formulated based on my maths curiosity. Fidgetting with my new graphic calculator, I started graphing things and had the idea to graph $y=(-2)^x.$ The result surprised me, and I thought a little bit about it, stored it on the back of my brain, and promised myself to look deeper into it someday. Answered by Harley Weston.
	Two people are clapping their hands		2019-12-06
		From Yukti: Two people are clapping their hands, but with different frequencies. Ramya claps her hands 17 times per 3 minutes, and Kumar claps his hands 31 times per 5 minutes. They start clapping at the same time. How many times does each one clap before they clap together at the same time again? Answered by Penny Nom.
	cos (3pi/2 -x)		2019-11-20
		From sam: 1. express the following as a trigonometric function of angle x for cos (3pi/2 -x) the answer in the textbook is -sin x but i am unsure of the process to get the answer. Answered by Penny Nom.
	Simultaneous equations		2019-10-16
		From deepak: This is too complicated please help me 8/x - 10/y = 1 and x+y=9 Answered by Penny Nom.
	Packing chocolates in boxes		2019-07-22
		From CHESKA: 1.levy can pack the chocolate bars either with 35 bars in a box,with 42 in a box, or with 49 in a box. what is the least number of chocolate bars that he has? 2. the blue light of a Christmas light blinks every 2 second. the red light blinks every 3 second and the yellow light blinks every 5 second. how many times will the three lights blink at the same tims in one hour? 3.a wooden straightedge can exactly measure an 825 cm rope, a675 cm rope, and 375 cm rope. what is the least possible length of the straightedge? how many times will it measure each rope? Answered by Penny Nom.
	The area of a triangle in acres		2019-06-23
		From Karen: if I have a triangle that measures 78 ft x 54 ft x 50 ft, how do I figure out what part of an acre that is?? Answered by Harley Weston.
	Maximize monthly revenue		2019-05-23
		From a student: A real-estate firm owns 100 garden type apartments. At RM400 per month, each apartment can be rented. However, for each RM10 per month increase, there will be two vacancies with no possibility of filling them. What rent per apartment will maximize monthly revenue? Answered by Penny Nom.
	Constructing a hexagonal pyramid		2019-04-25
		From REBECCA: I'm doing a project for my Honors Geometry class and I have to build a regular hexagonal pyramid. I was given the volume of .75 gallons, but I don't know how to figure everything else out. Please help? Thanks, Rebecca Answered by Harley Weston.
	A circle with a circular hole		2019-03-11
		From Sue: My little one is wondering if a circle with a circular hole could be described as an irregular semicircle. As it has 2 sides but is not the standard shape. Could you share your thoughts ?? Answered by Penny Nom.
	Running around a circular track in opposite directions		2019-02-24
		From carmi: how many times will lita and rose pass each other in 15 minutes if lita and rose start jogging on a 110 meters circular track. they begin at the same point but in opposite direction. lita at 8/3 meters per second and rose at 7/3 meters per second. Answered by Penny Nom.
	Loan payment formula		2019-02-24
		From Kenneth: I have a question regarding the loan payment formula shown below. Calculating the Payment Amount per Period The formula for calculating the payment amount is shown below. Simple Amortization Calculation Formula A = P X r(1 + r)n over (1 + r)n - 1 where A = payment Amount per period P = initial Principal (loan amount) r = interest rate per period n = total number of payments or periods Is this formula/calculation a condensed version of a longer calculation? I am curious to know how the (1 +r)n - 1 was developed from the longer calculation. For example, r(1 + r)n may have been (r + rn)n. The n's are exponents. I thank you for whatever helpful explanation that may be provided. Kenneth Answered by Harley Weston.
	cos(2x) = sin(x)		2018-12-18
		From Liz: Determine all values of x in [0,2pi] that solve the equation Cos(2x)=sinx Answered by Penny Nom.
	Simultaneous equations with fractions		2018-12-14
		From zaheer: solve simultaneous equations and give answer in fractional form 3x - 2 = 4y +5/3 y + 7 = 2x + 4 would really appreciate some help on this please Answered by Penny Nom.
	Angular velocity		2018-12-05
		From Kolade: Krusty the Clown and Sideshow Bob have covered themselves in velcro, and shot themselves out of a large cannon so that they stick to a huge rotating velcro wheel (don’t try this at home). As shown in Figure 1(a), Krusty is now stuck to a point 3.00 m from the center of the wheel while Bob is stuck to another point 5.00 m from the center. The wheel is rotating counterclockwise at 10.0 rpm. Conveniently a set of axes is suspended just in front the wheel (Krusty asked for axes, like the ones you would use to chop wood, so that he and Bob could chase each other with them in the usual wholesome entertainment he is known for. Unfortunately, the set designer misunderstood.) The axes do not rotate with the wheel. (a) Find Krusty’s and Bob’s angular velocities, in radians per second. Answered by Penny Nom.
	Two cones formed from two circular sectors		2018-11-30
		From APARNA: The central angles of two sector of a circle are 60° and 120° . Using these sectors two cones are made. If the radius of the smaller cone is 5 cm, find the radius and base area of the larger cone. Answered by Penny Nom.
	Angular speed		2018-10-18
		From Akidima: A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 seconds . What is the average angular speed of the wheel Answered by Penny Nom.
	The volume of a hotel soup pan		2018-09-15
		From Melanie: If the hotel pan measures 12 inches long x 5 inches wide x 6 inches tall, how many quarts of soup will the hotel pan hold? Answered by Penny Nom.
	Working with percentages		2018-08-26
		From Kenneth: 16 is 4% of what amount? The answer can be determined by the following unusual manner: 4% = 16 1% = 4 100% = 400 Can the following solutions for the following be determined by using the same type of calculation? 16 is ?% of 400 ? is 4% of 400 I thank you for your reply. Answered by Penny Nom.
	Amy and Joey on a circular track		2018-08-13
		From Zoe: Amy and Joey are situated on a circular track 400 feet around. Joey starts running at a rate of 10 feet per second. Amy waits for a full minute, then starts running from the same point (in the same direction) at 12 feet per second. How many seconds elapse before Amy passes Joey on the track? Answered by Penny Nom.
	A sulphuric acid solution		2018-07-12
		From Tan: How much 96% h2so4 to add into sulphuric acid 30% in order to make it to 50% sulphuric acid? Answered by Penny Nom.
	A circle inscribed in a regular polygon		2018-07-12
		From Naveen: The radius of inscribed circle for n sided regular polygon of a side a is? Please with proof Answered by Penny Nom.
	The base for a circular pool		2018-06-10
		From Adam: How many sheet of 4ft by 8ft foam would I need to lay under a pool 15dt in diameter Answered by Penny Nom.
	Subdividing a rectangle into squares		2018-05-13
		From jeverzyck: A rectangular board is 108cm wide and 156 cm long Equal squares as large as possible are ruled off this board.Find the size of the square.How many squares are there? Answered by Penny Nom.
	A rectangular prism with rounded corners		2018-04-25
		From Jackie: Rectangular prism that is 40 by 20 with rounded corners with a radius of 2.5. What would the surface area be? Answered by Penny Nom.
	A cone formed from a circular sector		2018-04-18
		From Jessica: A circle has a radius of 7.5cm. A sector with an angle of 240 degrees is cut out from the sector. If the sector is folded to form a cone. Find the length of the cone. Answered by Penny Nom.
	Covering a region with mulch		2018-04-13
		From Roberta: I have a fall zone area of approx. 700 sq ft. that I have to cover with a 6in depth of mulch. How much mulch would I need to purchase? Answered by Penny Nom.
	0.366 x cos square (02 degree 17 mins 27 seconds)		2018-03-12
		From michael: what is 0.366 x cos square (02 degree 17 mins 27 seconds) what is 0.366 x cos square (88 degree 26 mins 45 seconds) Answered by Penny Nom.
	The limit of (e^x-1)^(1/x) as x tends to 0		2018-02-27
		From ARGHA: Find the limit of (e^x-1)^(1/x) as x tends to 0. Answered by Penny Nom.
	Multiplies and factors		2018-02-24
		From Lil: Is a multiple the same as a factor? Answered by Penny Nom.
	Dividing a region in half		2018-02-24
		From mandy: There is a line through the origin that divides the region bounded by the parabola y=4x−5x2y=4x−5x2 and the x-axis into two regions with equal area. What is the slope of that line? Answered by Penny Nom.
	3 yards 6 inches times 7		2018-02-08
		From Tamara: 3 yards 6 inches × 7 Answered by Penny Nom.
	Simplify 1/2^i		2018-01-28
		From Deepak: How do I simplify this complex equation: z=1/(2^i) Answered by Penny Nom.
	The equation of a line		2018-01-23
		From Gloria: Write the equation of a line in standard form through the point (1, 6) and perpendicular to the line 2x –y = 9. Answered by Penny Nom.
	When are the hands of a clock perpendicular?		2018-01-11
		From Nazrul: How many times in a day are the hands of a clock perpendicular to each other? How can I find the times? Please help me. Answered by Penny Nom.
	Needing the area of an irregular Pentagon		2017-12-06
		From Dale: I'm needing to find the square footage of an irregular pentagon. I've seen the other questions similar to this one, but without a great deal of difficulty can't get you the angle degrees, or the length between opposing angles. I'm hoping that a different bit of information can help. So here goes: The longest side is 67ft long. One of its legs is 39ft long, and the other is 18ft long. The leg off of the other end of the 39ft leg is 35ft long. The leg off of the other end of the 18ft is 49ft long, and meets the other end of the 35ft side. The information that I DO have, which I'm hoping makes the difference, is that the 39ft and the 18ft sides are parallel. Also, while the angles at each end of the 67ft side are not right angles, they are fairly close to it, approximately 80 degrees at the 39 ft side corner, and 100 degrees at the 18ft side corner. Dale. Answered by Harley Weston.
	Formula when i know the GST total		2017-10-31
		From Duncan: HI - I've added up the GST from a pile of receipts and would like to know what the total cost of goods would be without GST. I don't want to add up 100's of receipts again with the cost before GST but I do need this total cost. i.e.) I know I paid $400 GST, what would the formula be to find out the cost of what I purchased before taxes? Your help is much appreciated! Answered by Penny Nom.
	formula when i know the GST total		2017-10-31
		From Duncan: HI - I've added up the GST from a pile of receipts and would like to know what the total cost of goods would be without GST. I don't want to add up 100's of receipts again with the cost before GST but I do need this total cost. i.e.) I know I paid $400 GST, what would the formula be to find out the cost of what I purchased before taxes? Your help is much appreciated! Answered by Penny Nom.
	A tangent to a curve		2017-10-22
		From Jasem: Suppose that f(x)=(3x-3)^1/2. (A) Find an equation for the tangent line to the graph of f(x) at x=2 (B) Find all values of xx where the tangent line is horizontal, and enter them as a comma-separated list (e.g., 2,-3,6). If there are none, enter none. Values of x Answered by Penny Nom.
	The distance between the origin and a moving point on a graph		2017-10-16
		From Paulina: Find the rate of change of the distance between the origin and a moving point on the graph of y=x^2 +1 if dx/dt=2 centimeters per second Answered by Penny Nom.
	An enclosure for some remote control boats		2017-10-03
		From Roberto: I am trying to build a "ring" for our remote control boats, using irrigation pipe. I'd like to use full 20' long sticks for the long sides and use eight of what we call 45s, which are actually 135' fittings to make the six short sides. If I know the length of the two long sides, what would be the formula to find the exact lengths of the short sides? Thank you. Answered by Penny Nom.
	The volume of a cone without calculus		2017-10-02
		From Akash: How to find the volume of a cone without the knowledge of calculus? Answered by Penny Nom.
	Four multiples of 10		2017-09-23
		From Laudacir: Four multiples of 10 are added together.the total is a 3 digit number with three consecutive digits. What could the four number be? Answered by Penny Nom.
	Simultaneous equations with fractions		2017-09-09
		From Farah: Hi, my name is Farah. I hope you can help me with this question . X/2 + g/5= 3 and 2g - f = 10 Answered by Penny Nom.
	The volume of an attic		2017-09-07
		From paul: trying to determine volume of an attic base is rectangular 29 ft by 37 ft peak runs parallel to longest base side and is 7 ft long roof lines run from each end of the peak to the respective corners the peak is 3.5 ft above the base (so seen from above there are 5 visible lines: the peak and 1 line to each of the 4 corners) Answered by Harley.
	Simultaneous equations		2017-09-02
		From keto: x-y=2,x^2+xy=12 Answered by Penny Nom.
	A rectangle and a circle		2017-08-12
		From Ramzan: a diagram shows the shape of rectangular framework with length (2x+20)cm and with (y+10)cm . The outline is made of wire . If a circle with diameter 56 cm is to be made from the wire and the area of the rectangle is 420 square centimeter ,find the possible lengths and width of the rectangle Answered by Penny Nom.
	An arched window		2017-07-24
		From Gerry: Looking to make a full size template for an arched window. Need increments every 16". The radius is 138' 0 9/16" , the chord is 226" and the rise at center of chord is 43" Answered by Penny Nom.
	3 consecutive multiples of 11		2017-07-22
		From nisha: using the multiples formula shown at ypur site how can we solve finding 3 consecutive multiples of 11 whose sum is 363 Answered by Penny Nom.
	Parallel and Perpendicular lines		2017-07-17
		From Karen: Find an equation for the line with the given properties. Perpendicular to the line 7x + 2y = -6; containing the point (-2, -1) Find an equation for the line with the given properties. Parallel to the line 5x - 3y =-6; x intercept = 3 Answered by Penny Nom.
	Simultaneous equations with fractions		2017-06-02
		From Jamal: 1/x + 1/y =5 and 1/y - 1/x =-1 Answered by Penny Nom.
	What is the regular price?		2017-05-11
		From Saira: If the sale price is 55.50$ and the discount is 12% what is the regular price Answered by Penny Nom.
	Canada's population as a percentage		2017-05-11
		From bethmarie: What percentage of the world population (7.5 billion) is Canada's population (36 million). Thank you very much! Answered by Penny Nom.
	Why does 10x10x10 give 1,000.0000000000001?		2017-04-12
		From Randolph: Hi, On your calculator I found that a box 10 by 10 by 10 inches has a volume of 1,000.0000000000001 cubic inches. Can you explain the numeral 1 thirteen places past the decimal? Thanks, Randy Answered by Penny Nom.
	Quadratic Equations		2017-03-28
		From Natalie: Hi Maths Central, I am having trouble with quadratic equations. The question is: Calculate the length 'l' of a rectangular pool by creating and solving a quadratic equation. 1. The rectangular pool is of equal area to a square pool, and a circular pool (5.70m^2). 2. The length of the rectangular pool must be 2m longer than the width 'w'. Thank you so, so much for your help, Maths Central! Answered by Penny Nom.
	Differentiate y = x^x^x		2017-03-19
		From Nafis: differentiate y = x^x^x Answered by Penny Nom.
	A regular tetrahedron		2017-03-12
		From Jeramie: When we have a regular tetrahedron, is it always true that all the angles of the triangles measure 60 degrees? Answered by Penny Nom.
	A block base for a plywood rectangle		2017-02-18
		From Joe: How many cinder blocks 16x8 would i need to build a solid base for a plywood base 54inches wide and 30 inches deep Thank you Answered by Penny Nom.
	Vinculum		2017-01-27
		From Dick: What is the line or bar over a Roman Numeral called? Eg. V with the bar over it representing 5,000 . Answered by Penny Nom.
	The volume of a slab		2017-01-21
		From Russell: Working with a segment of a circle. The O.D. is 3.440" the length of the chord is 3.130 I need information on the volume of the largest area. I would like to know (in thousands of an inch) how tall would the largest area need to be to equal .1143 cubic inches If you need more info I can send it Thanks in advance Answered by p.
	Angular speed		2017-01-21
		From Kenzi: A wheel of radius 14 inches is rotating 45°/sec. What is the linear speed in in/sec and the angular speed in RPM? (Round your answers to three decimal places) I already found the linear speed. I got 10.996 in/sec. I don't know how to find the angular speed. Answered by Penny Nom.
	The average rate of change of cot(t)		2017-01-18
		From Brianna: Hello! It's been a while since I've taken a math course, and I'm stuck on a problem in my calculus course. The question is this: Find the average rate of change of the function over the given interval. h(t)=cot(t) a) [5pi/4, 7pi/4] Answered by Penny Nom.
	Five equations		2017-01-16
		From Muhammed: A x 4 = E B ÷ 4 = E C + 4 = E D - 4 = E ___________ & A + B + C + D = 100 what is the value of E Answered by Penny Nom.
	8^3/2(2+2)		2017-01-13
		From Mary: 8^3/2(2+2) Answered by Penny Nom.
	Simultaneous equations with fractions		2016-12-21
		From Kimi: I am stuck on this,can someone please help me???? 1/2x+1/3y=11 8x+2/5y=102 Can someone please explain how to solve questions like these?? Or else I will never learn... Thank you Answered by Penny Nom.
	Two concentric circles		2016-12-21
		From shrestha: Two concentric circles have radii of 14 cm and 7 cm respectively. Find the area of space between them. Answered by Penny Nom.
	Two boys on the same route		2016-12-06
		From Abbey: Starting from the same spot, one boy completed a route in 9 minutes and another boy completed it in 15 minutes. When will both boys be at the same starting point at the same time again? Answered by Penny Nom.
	Simultaneous equations		2016-11-25
		From Rohan: x-2/3 + y - 1/4 = 13/12 2-x/2 + 3 + y/3 = 11/6 Answered by Penny Nom.
	Multiplication and repeated addition		2016-11-23
		From Anandmay: Hello I was looking closely at early arithmetic where I found how we discovered properties of Arithmetic. Like:2 x 3 = 3 x 2. This can be proved by considering a 2-D figure(actually,quadrilateral) having length consisting of 2 boxes of 1-by-1 dimensions and breadth of 3 boxes of the same dimensions. Now,consider it again,but,this time,length of 3,and breadth of 2 of such 1 by 1 boxes. We now notice that we can fit the 2 types of rectangles formed on each other precisely. So the multiplicative property of commutativity is true for all natural numbers as we can generalize the result(in our mind,for self satisfaction). Now,can you find me a nice satisfactory reason of why a fraction times a natural number equals the number times the fraction? I mean, for example,i can understand the meaning of 3 x 2/3 to be three times 2-3rd,that is, 2/3+2/3+2/3.Fair enough. But here is the problem:By definition and actual meaning of multiplication, a x b means the repeated sum of b,done 'a' times. So what is the meaning of doing 2/3 x 3?The repeated addition of 3 how many times??2/3 times??Not making sense,right?And even we have not proved yet the commutative property of numbers INCLUDING fractions.So how can we resolve this problem and make these things meaningful? Thanks Answered by Penny Nom.
	Volume of liquid remaining in a tilted cylinder		2016-11-08
		From Brian: I am trying to determine the amount of a liquid remaining in a 55 gallon drum when it is tilted at 45 degrees and the liquid level is low enough so that the liquid does not completely cover the bottom of the drum. Your help is greatly appreciated. Answered by Harley Weston.
	A pattern rule for a sequence		2016-10-28
		From Grace: Here's a Grade 7 question, we need to find the pattern rule: 1 - 1 2 - 3 3 - 6 4 - 10 ...... It may involve exponents, but we can't seem to figure it out. thank you. Grace. Answered by Penny Nom.
	An airplane schedule		2016-10-14
		From Stephanie: Starting at 8:00a.m., a passenger plane leaves from an airport every 6 minutes and a cargo plane leaves every 7 minutes. When is the next time these kinds of planes will leave at the same time? Answered by Penny Nom.
	Hexagonal pyramid bevel angles		2016-09-30
		From Peter: I have seen your response to a similar question from Steve which Chris and Harley responded to, however I am not familiar with some of the terms. Is there a formula that I can enter my details in which will give me the specific angles I require. The item I am constructing is much larger than the one you responded to previously. Thank you for any assistance you are able to provide. Answered by Penny Nom.
	2,006-1-2-3-4-...-48-49-50		2016-09-24
		From Mimi: Compute the following: 2,006-1-2-3-4-…-48-49-50 Answered by Penny Nom.
	The width of a 300 foot long rectangular acre		2016-09-21
		From Debbie: If 2 sides of a 1 acre plot is 300 feet each what are the other 2 sides? The acre is a rectangle. Answered by Penny Nom.
	The distance around a warehouse		2016-09-21
		From Chuck: How far do I walk when I walk around a 751,000 sq. ft. warehouse? Answered by Penny Nom.
	Integrate (x^2 - 4x + 4) ^4/3		2016-09-15
		From Ifah: Hi i have questions please answer Integral 2 sampai 3 dari (x² - 4x + 4) ^4/3 dx Answered by Penny Nom.
	The modulus of a complex number		2016-07-29
		From Cheyenne: There's a question on my Summer Assignment I cant figure out. Here it is: Find the absolute Value of the complex number. -5i Please help? Answered by Penny Nom.
	Two equations with fractions		2016-07-22
		From kanesh: p/2+q/3=3 p/4+2q/3=3 Answered by Penny Nom.
	Simultaneous equations		2016-06-25
		From sena: 2x/3+3y/2=-1 4x-5y=22 simultaneous equation Answered by Penny Nom.
	The difference between the ares of two rectangles		2016-06-09
		From Ingrid: I am trying to help my son with an area question. I have the answer, from the solutions, but I cannot figure out how to teach him. Question: Two rectangles have lengths 13cm and 19cm respectively. Their total area is 376cm squared. If both their widths are whole numbers, what is the difference in their areas? I know that this is solvable once I determine the widths of the rectangles , but how do I go about finding that? Thanks for your help Answered by Chris Fisher and Harley Weston.
	Implicit differentiation		2016-06-06
		From Pranay: Is a circle x^2+y^2=2 a function? If it is not a function, why is it possible to do implicit differentiation on it? Thanks. Answered by Penny Nom.
	A barn roof		2016-05-29
		From Joe: Is it possible to build a barn roof (irregular pentagon?) with a 12' base and the other 4 sides 4' each? Thanks. Answered by Penny Nom.
	Two pieces of rope		2016-05-21
		From Render: Fred cuts a 12- inch piece of rope. Then he cuts a second piece of rope that is 3/2 longer than the first piece. Is the second piece shorter or longer than the first piece? Explain. Answered by Penny Nom.
	A trough with a triangular cross section		2016-05-21
		From Clarice: A trough having an equilateral triangle end sections has sides equal to 0.4 m and 7m long.what is the volume of the liquid in the container if the depth of the water is one half the depth of the trough? Answered by Penny Nom.
	Euler's polyhedron formula		2016-05-20
		From Antonia: why does not cylinders follow Euler's polyhedron formula ( V-E+F=2) ?? if a cylinder has 3 faces, 2 edges and 0 vertices it doesn't follow Euler's formula??? Answered by Penny Nom.
	The volume of a truncated rectangular pyramidal pond		2016-05-13
		From Paul: How do you calculate a partially filled truncated rectangular pyramid if you always know the bottom rectangle, the maximum height top rectangle perimeter, but have a varying height. Similar to filling up a pond you know the current height and dimensions at the max rectangle how do you calculate it half full i.e. 10x30 outside perimeter with a 2x8 base and a max height of 6ft how do you calculate it at 3ft without re-measuring the top perimeter. Thanks, Paul Answered by Harley Weston.
	A pair of equations with fractions		2016-05-11
		From tiya: hello, i want to know how to solve this question. m/6+2n/3=6 -m/10=2n/5=2 Answered by Penny Nom.
	A rectangular field		2016-05-07
		From Jan: A rectangular field is 63m long and 21m wide. A fence of 2m in height is needed to fence the field and fencing is also required to divide the field in three square sections. There are three wooden gates measuring at 1.5m to the three sections of the field. What is the total surface area of the fence needed for fencing and diving the field? Answered by Penny Nom.
	Solve 2^2x + 3(2^x) - 4 = 0		2016-04-27
		From Lloyd: Solve the equation 2^2x + 3(2^x) - 4 = 0 Answered by Penny Nom.
	sin 2x - sin x = 0		2016-04-24
		From lilly: sin 2x - sin x = 0 0 Answered by Penny Nom.
	600(1+0.05)^7		2016-04-21
		From chelsey: I am unsure on how to solve this problem, 600(1+0.05) 7 ? Answered by Penny Nom.
	15.86 acres		2016-04-21
		From Ronald: If a rectangular piece of land is 1320 ft. on one side, how many feet would be required on the other side to equal 15.86 acres? Answered by Penny Nom.
	External and interior angles of a regular polygon		2016-04-19
		From pearl: a polygon has n sides.The exterior angle is 8 times the interior angle find the value of the interior angle find the value of n Answered by Penny Nom.
	Heights at various points along an arc		2016-04-15
		From Isiah: So I am working on a problem with a few friends; you have an arc with the center of its chord at 0,0. We also have a known sagitta and a known radius of curvature. How do we calculate the height extending in both the positive and negative directions? Central sag: 2.48 Chord length: 9.6 Answered by Penny Nom.
	Sloping my yard away from my house		2016-04-15
		From Harold: I need to slope a area of my yard away from my house and garage. The length of my house is 80 feet long and i need to slope it 22 feet away. I want to raise the dirt at the foundation by 6 inches and slope it down to nothing at the width of 22 feet. How much soil would i require? Answered by Penny Nom.
	Pizza delivery		2016-04-03
		From Andrew: Suppose you own a local pizza restaurant, Pizza with Pizzazz, and in order to compete with the big pizza chains in your area you are considering an advertising campaign offering customers a free pizza if their pizza is not delivered in 30 minutes or less. Even though your pizza restaurant is known for its fast and friendly delivery service, you are not sure if you can afford to give away too many pizzas for free. Looking over your past 12,421 pizza deliveries you find out 97% of the pizzas were delivered in 30 minutes or less. Calculate the probability that all 100 randomly selected pizza deliveries will have been made in 30 minutes or less? Hint: Use the multiplication rule. (Round 4 decimals) I'm really stumped on how exactly to do this problem. I don't need the answer just the steps broken down to show me how to get it! It would be gladly appreciated if you could help! Answered by Penny Nom.
	Maximizing the area of a two lot region		2016-04-03
		From yousef: A man wishes to enclose two separate lots with 300m of fencing. One lot is a square and the other a rectangle whose length is twice its width. Find the dimensions of each lot if the total area is to be a minimum. Answered by Penny Nom.
	A rotating schedule for a softball team		2016-03-25
		From Caroline: I couldn't find a similar question, hopefully there isn't one! I have a softball team of 18 people (7 girls and 11 boys), but am limiting each game to 13 players (6 girls and 7 boys). The season is 10 games long. How do I create a rotating schedule which allows members to play evenly? I tried separating the boys and girls to create rotation for each but I got confused. Some are unable to attend all games but for the simplicity of a rotation schedule can you please help? Answered by Robert Dawson and Victoria West.
	A percentage problem		2016-03-02
		From jehanzaib: if x is a percentage: e.g. 40% than what does "x/(1+x)" = 29%. what is the explanation. Answered by Penny Nom.
	A rectangular prism		2016-03-02
		From Paula: Trying to help with a math problem. I don't know how to set up the equation for this. A rectangular prism has a volume of 7.875m3rd and a height of 3.5 m. What is the area of the base of the prism? Thanks for your help! Answered by Penny Nom.
	Solve for x and y		2016-02-27
		From ntshidi: Y=1/2x+4and1/4x-6 Answered by Penny Nom.
	The sum of the angles of a triangle		2016-02-24
		From Sophia: Does every triangle add up to 180 degrees? (Such as a unique triangle) Answered by Penny Nom.
	The interior and external angles of a regular polygon		2016-02-17
		From percy: a regular polygon has n sides .The size of each interior angle is eight times the size of each exterior angle . 1.find the size of each exterior angle 2.calculate the value of n Answered by Penny Nom.
	Perpendicular lines		2016-02-14
		From Brendon: points A (-4; 6) , B (1;-2), C (5;-3) and D (4; 1) are given prove that AC and BD are perpendicular to each other Answered by Penny Nom.
	Calendar arithmetic		2016-02-14
		From Jenalee: January 1, 2001 is Julian Day 2 451 911 (the number of days that have passed since Day 0, January 1, 4713 BC). If Julian Day 0 was a Monday, what day of the week was January 1, 2001? Answered by Victoria West.
	Two equations in two unknowns		2016-02-13
		From Anumba: 4x + 2y = 4 7x - y = -11 Answered by Penny Nom.
	I was paid 67% of the total owed		2016-01-25
		From Julie: I was paid $27000. This is 67% of the Total Owed. The Total Owed is unknown. How do I calculate the amount of the Total Owed? Answered by Penny Nom.
	A system of linear equations		2016-01-24
		From kareem: my name is kareem and i am a student i have a math puzzle and i tried to solved it but it always have same mistake x-y=9 x+z=12 z-n=14 y+n=2 Answered by Penny Nom.
	A Max/Min problem with an unknown constant		2016-01-17
		From Guido: Question: The deflection D of a particular beam of length L is D = 2x^4 - 5Lx^3 + 3L^2x^2 where x is the distance from one end of the beam. Find the value of x that yields the maximum deflection. Answered by Penny Nom.
	A rectangular enclosure		2016-01-15
		From Amber: A rancher wants to use 300ft of fencing to enclose a rectangular area of 4400 square feet. What dimensions should the rectangle be? Answered by Penny Nom.
	A triangular shaped garden		2016-01-13
		From Demetrie: Dwayne's garden is triangle-shaped with two equal sides and a third side that is 4 ft more than the length of an equal side. If the perimeter is 49 ft, how long is the longest side? Answered by Penny Nom.
	The perimeter of a triangular plot of land		2016-01-11
		From Janelle: I need to fence off 6.5 acres. The plot is triangular shape. How many feet would I be fencing off? Answered by Penny Nom.
	Water flowing through a rectangular drain		2016-01-08
		From Tiffany: the cross section of drain is a rectangle 30 cm wide. If water 3.5 cm deep flows through the drain at a rate of 22 cm/s, how many litres of water will flow through in one minute? Answered by Penny Nom.
	Integration of dx/(x^2+1)^3		2016-01-07
		From Ishank: Integration of dx/(x^2+1)^3 Answered by Penny Nom.
	A relative maximum and a relative minimum		2015-12-28
		From kemelo: show for the following function f(x)=x+1/x has its min value greater than its max value Answered by Penny Nom.
	Constructing simultaneous linear equations		2015-12-28
		From Deborah: Linda thinks of a two-digit number. The sum of the digits is 8. If she reverses the digits, the new number is 36 greater than her original number. What was Linda's original number? Thank you! Answered by Penny Nom.
	Linear equations in two variables		2015-12-13
		From priya: I have problem in solving these equations please help me today itself very urgent: I)2x+y=y II)pie*x+y=9 Answered by Penny Nom.
	Constructing a cross country district schedule		2015-12-13
		From David: Retired math teacher trying to help son-in-law schedule a cross country district schedule. The would like to have four tri-meets each week for five weeks and one week of dual meets. The score the tri-meets as three duals, i.e. 1v2, 2v3, 1v3 constitutes one tri-meet. After many hours, not sure its possible, but I have forgotten a great deal! Thanks Answered by Victoria West.
	A schedule for a league with 15 teams		2015-12-05
		From Zac: Hello, I have a league schedule question. We have a league where we have say have 15 teams. Each team is to play each other twice during a 10 week session. However each team tries only to play 3 matches(teams) per night(week). How would we set up a random schedule for the 10 week session? Answered by Victoria West.
	A tangent line to a parabola		2015-12-02
		From pei: Given that the line y=mx-5 is a tangent to the curve y=2x^2+3 find the positive value of M. Answered by Penny Nom.
	Archimedes, Euclid and "Circular Reasoning"		2015-11-15
		From Ron: I have read about Archimedes and his work with sphere in cylinder and cone in cylinder and the volume relationships. Did he or any others also extend this to regular based polygon based regular like pillars, and columns? The ratio of 1/3 to 1 whole holds true with all regular based columns as example: a regular pyramid having a regular hexagon base inside a regular hexagon column of equal height. Answered by Chris Fisher.
	The area of a domed roof		2015-11-13
		From Brandon: I have a tank with a 13' radius that has a domed roof of 3.5' tall How do I figure out the area in SQFT? Answered by Penny Nom.
	Fencing around a rectangular field		2015-11-11
		From Darlene: Question from Darlene, a parent: A farmer has 10,000 meters of fencing to use to create a rectangular field. He plans on using some of the fencing to divide the rectangular field into two plots of land by constructing a fence inside the rectangle that is parallel to one of the sides. Let X be the width of the rectangular field. Write an equation to express the area of the field as a function of X. Find the value of X that maximizes the area of the field. Answered by Penny Nom.
	An 8 Team Basketball League Schedule		2015-10-28
		From Janice: We have an eight team league that play at four time slots each week. It's a seven week season. How do we schedule so that each teams plays each other at least once? Answered by Victoria West.
	A schedule for a pool league		2015-10-21
		From Hazel: I have to make a schedule for my pool league. I have twenty teams each of which must play all other teams. I have ten tables which must also be rotated to all teams play on all tables. Answered by Victoria West.
	Simplify -3(x-7)		2015-10-21
		From geraldine: simplify: -3(x-7) Answered by Penny Nom.
	Scheduling a social curling league		2015-10-20
		From Tyler: I'm scheduling a social curling league where all skips will play with all thirds, all seconds, all leads. And all thirds will do the same and so on. We have 6 teams of 4 and will be doing 6 rotations. Is it possible that all skips will play with all other players from other positions without anyone doubling up? My initial thoughts were (1,1,1,1) (2,2,2,2) (3,3,3,3) (4,4,4,4)(5,5,5,5)(6,6,6,6)... then rotate the thirds up and seconds down but don't know what to do with the leads and even with just 3 positions there's doubling (1,2,6,x)(2,3,5,x)(3,4,4,x)...4s have doubled (4,5,3,x)(5,6,2,x)(6,1,6,x) as you can see I'm having problems If you could let me know if this is even possible it would be greatly appreciated Answered by Victoria West.
	6 teams randomly arranged in groups of 3		2015-10-19
		From Anthony: im trying to make a game scheduled for 6 teams using a 1vs2vs3 ; 4vs5vs6 format. all 6 teams randomly arranged in groups of 3. each team will play all teams at least twice, im trying to see how to make the number of times each team play another the same. schedule should be arranged as such 1vs2vs3 4vs5vs6 so that (1vs2, 1vs3, 2vs3) and (4vs5, 4vs6, 5vs6) i am limited to having only 2 sets of 3 at a time with 6 teams. Answered by Victoria West.
	An 8 team schedule		2015-10-19
		From Dean: I need an 8 team schedule for 2 time slots where 3 teams are on the ice per slot. I understand that there will be 2 teams on a bye per day. How do make sure that the byes are fair? Can you help me out? Answered by Victoria West.
	A six team league to play a 20 game schedule		2015-10-19
		From Kelly: Hi there. Some of your posts are close, but my problem is evening out the home and away games. We have 6 teams in our league and we are going to play a 20 game schedule, playing everyone 4 times. We will play Fridays and Saturdays, each weekend. Of course the ideal would be to have each team have a home and an away game each weekend, but I realize that is impossible, but I would like it as close as possible. Any help would be much appreciated!! We also were considering opening with a home and away - Friday then Saturday with the same teams. Then carrying on with playing everyone else and then possibly finishing up with the same home and home Answered by Victoria West.
	Six teams playing five games		2015-10-18
		From Aidan: I have six teams that will be playing five games. I want each team to play each game once and each team to play each other team once. Is this possible or should I add an extra round and let some teams play each other twice? Answered by Victoria West.
	4 games in 4 time slots with 8 teams		2015-10-16
		From Paul: I'm trying to set up a game matrix for my kids that will have 4 games in 4 time slots with 8 teams. And every team is playing a different game in a different time slot. I provided the initial matrix and I am trying to ensure that no 2 teams play each other more than once. That's my problem.        8 pm 9 pm 10 pm 11 pm Crokinole 1 vs 2 Trivial Pursuit 3 vs 4 Darts 5 vs 6 Pictionary 7 vs 8 Please help, I've been at it for hours. Answered by Robert Dawson and Victoria West.
	Squash scheduling		2015-10-01
		From Ed: I have 5 teams and 2 courts. Every Thursday we play at four different times (6,7,8,9 o clock) Each team will play each other 5 times over 25 weeks. Everyone should get to play evenly at the best time (6:00) and the worst time (9:00) Answered by Victoria West.
	A 6-person team that has 9 players		2015-09-21
		From Sheri: I am organizing a 6-person team that has 9 players. How do I schedule them fairly over a 9 week league? Answered by Victoria West.
	A hockey roster of 19 kids		2015-09-21
		From Brian: We have a hockey roster of 19 kids. We only want to play 15 kids for each game. 4 players will not play each game. There are 16 games total. We want to rotate who doesn't play evenly. Can this be done? How many games will each player sit during the season? Answered by Robert Dawson and Victoria West.
	20 golfers for 6 days		2015-09-11
		From Dave: have 20 golfers for 6 days. Each player should pair with 18 golfers used a system on your website which is good for 5 days, but cannot get the 6th day. Thanks for your help Dave Answered by Victoria West.
	Scheduling for a bridge club		2015-09-09
		From margot: Can you help me with scheduling our bridge club? 8 rounds are played with four teams together. There are 16 teams in total, so our schedule should look like eight 4x4 boxes. (Each round the four teams play each other over the course of the evening) Answered by Victoria West.
	A schedule for eight teams and four stations		2015-09-04
		From Joel: We are having a youth activity where we have eight teams and four stations. At each station there will be two teams competing against each other. We need each team to go through all four stations, but without ever competing against the same team, and, of course, without ever doing the same station twice. If this possible? Thank you! Answered by Victoria West.
	A schedule for an 8 person team		2015-08-27
		From Julie: We have 8 people on our team, but only 4 can play every week. We have 32 weeks, total. How can we divide this so everyone plays evenly ? Answered by Robert Dawson.
	Reinforced steel mesh in a circular foundation		2015-08-22
		From Padmesh: in a circular foundation we are laying a reinforced steel mesh . i.e., like chords in both ways. the circle diameter is 2.91m and rods are placed 0.1m spacing. so I want to find the number of rods present in that circle. here by I am attaching an auto cad drawing for your reference Answered by Penny Nom.
	Rotating speakers through a 10 week schedule		2015-08-03
		From Timothy: I want 15 students to speak 7 times each over the course of 10 weeks. They each will have 5 minutes. Thanks Answered by Victoria West.
	1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 x 0 + 1 = ?		2015-06-18
		From Sharon: 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 x 0 + 1 = ? I got 1 as my answer despite BODMAS making it 12 because logic tells me I ought to place brackets around the first set of repeated addition. Could you please clarify this for me? Thank you 😊 Answered by Harley Weston.
	The surface area of a round bar		2015-06-06
		From chirag: Please tell me the formula for finding round bar surface in square inches/ mm Answered by Penny Nom.
	Manipulating an equation		2015-06-05
		From Leigh: Hi, I'm having trouble trying to find out how the equation y=mx+b for b comes up with the answer b=y-mx. Could you please assist me with this Answered by Penny Nom.
	The surface area of a triangular prism		2015-06-03
		From Alex: Find the surface area of a triangular prism with Isoceles triangles and dimensions 4 feet by 6 feet Answered by Penny Nom.
	A tangent to y = x^3		2015-05-31
		From Brayden: Show that a tangent line drawn to the curve y=x^3 at the point (d,f (d)), where d>0, forms a right triangle with the x and y axes in quadrant 4 whose area is (2/3)d^4. Answered by Penny Nom.
	A pentagon inscribed in a circle		2015-05-30
		From Victoria: find the area of a regular pentagon inscribed in a circle with radius 3 units Answered by Penny Nom.
	A pile of mulch		2015-05-15
		From Justin: I have a pile of mulch that measures 19 feet wide at the bottom and has a height of 6 feet. I need to know how many yards of mulch I have. Please help and help with the formula for further use. Thank you! Answered by Penny Nom.
	Two lorries approaching an intersection		2015-05-15
		From Nuraini: Two straight roads intersect at the right angles. Lorry A, moving on one of the roads, Approaches the intersection at 50mi/h and lorry B, moving on the other roads, approaches the intersection at 20mi/h. At what rate is the distance between the lorry changing when A is 0.4 mile from the intersection and B is 0.3 mile from the intersection? Answered by Penny Nom.
	A calculus optimization problem		2015-05-14
		From Ali: Given an elliptical piece of cardboard defined by (x^2)/4 + (y^2)/4 = 1. How much of the cardboard is wasted after the largest rectangle (that can be inscribed inside the ellipse) is cut out? Answered by Robert Dawson.
	The method of elimination		2015-05-01
		From oreanna: Question from oreanna, a student: How do u solve 2x+9y=3 7x-4y=-25 in elimination Answered by Penny Nom.
	Constructing a box of maximum volume		2015-04-14
		From Margot: I need to do a PA for maths and I'm a bit stuck. The PA is about folding a box with a volume that is as big as possible. The first few questions where really easy but then this one came up. 8. Prove by differentiating that the formula at 7 does indeed give you the maximum volume for each value of z. Answered by Penny Nom.
	Team selection		2015-04-13
		From Peter: I manage a football team with a list of 28 players. Only 24 can play each game. The season is 16 games. How do I fairly select 24 players each week. Answered by Robert Dawson.
	A word problem with fractions		2015-04-09
		From Lorraine: If the numerator of a certain fraction is doubled and the denominator is increased by 1, the fraction becomes 1/2. If the numerator of the original faction is squared and the denominator is decreased by 2, the fraction becomes equal to 1. Let x be the numerator and let y be the denominator of the original fraction. Write down two simultaneous equation in x and y. Solve these equations to find two possible values for the given fraction. Answered by Penny Nom.
	The area of the ring between two concentric circles		2015-04-08
		From Conner: The area of the ring between two concentric circles is 25pi/2 square inches. The length of a chord of the larger circle tangent to the smaller circle is? Answered by Robert Dawson.
	n^2 is a multiple of 100		2015-03-30
		From Rahul: I have to prove that n^2 is a multiple of 100 is necessary or Sufficient condition (or both) for n being multiple of 10 Answered by Penny Nom.
	A lot on a cul-de-sac		2015-03-06
		From ana: Julie lives on a cul-de-sac and wants to know if the city calculated the area of her plot of land correctly (see diagram below). We can assume the cul-de-sac is a circle and it has radius 40 feet.The boundary of the lot along the cul-de-sac (the arc from A to B) is 78.21 feet. The city found the area to be 7012.5 square feet–are they correct? Answered by Penny Nom.
	Two equations with fractions		2015-02-26
		From Pulane: Hi math centre I've been trying to solve these equations for days now please help (6/x)-(1/y)=4 (9/x)+1=(-2/y) Please help me solve them simultaneously Thank you Answered by Penny Nom.
	f(x)=(x^2-1)/(x-1)		2015-02-21
		From Ahmed: Is f(x)=[(x^2-1)/(x-1) and x=2 at x=1] differentiable at x=1 ? Why ? Answered by Penny Nom.
	Two equations		2015-02-16
		From nigel: 2x+1/2y=1 6x-3/2y=21 Answered by Penny Nom.
	Bearings and a rectangular plot		2015-02-14
		From Mubashir: A,B,C,D are the four corners of a rectangular plot marked on level ground. Given that the bearing of B from A is 040 degrees and that the bearing of C from A is 090 degrees. Calculate the bearing of (a)B from C (b)A from C (c) D from C Answered by Penny Nom.
	A parallelogram inscribed in a circle		2015-02-04
		From narendra: how can we prove that a circular parallelogram is a rectangle? Answered by Chris Fisher.
	128/(-16)/(-2)		2015-01-28
		From jackie: 128/(-16)/(-2) I was wondering if you can show me how to work this question out Answered by Harley Weston.
	A schedule for observing our peers		2015-01-23
		From Jennifer: I am a sales trainer. Each month we need to observe one of our peers and give feedback. What this means is every month, not only am I observing someone, but someone is also observing me. For example, in January, Amy observes Tracy, Tracy observes Rachel, Rachel observes Ryan, and so on. The last person would then observe Amy, bringing it full circle. There are 10 trainers on my team. How do I set it up to where each trainer observes another trainer only once over the course of the year (and in return, each trainer is only being observed once by each person)? I know they will eventually repeat but would that start in the 10th month? Answered by Robert Dawson.
	A schedule for 5 employees working 2 at a time		2015-01-23
		From Cynthia: We have 5 employees and need only 2 to work on Saturdays. what is the best way to fairly schedule everyone. PS. from time to time a sixth person will be thrown in to make things really interesting. Answered by Victoria West.
	Scheduling meetings with pairs of people		2015-01-22
		From Jacey: I am trying to figure out a formula/system to pair up a list of people so they meet with each other every month, but they rotate who they meet with. Right now I have 13 people and I would like to just type in their names and then have the system put each person with someone else every month and rotate so no one gets the same person twice. Can this be done? Answered by Victoria West.
	Scheduling 12 for lunch		2015-01-05
		From Sabrina: I have 12 staff members that need to have lunch together 1 time each week. I am trying to pair them in a way that we each have the same amount of lunches in the same amount of weeks. Please Help! Thanks! Answered by Victoria West.
	Revolutions per minute		2014-10-24
		From Edward: Hello; I have a 28.2 inch diameter tire; do not worry about engine RPM or gear ratios, please tell me what the RPM of that tire is at 8 MPH and 64 MPH. Thank you. Sincerely; Edward Answered by Penny Nom.
	A linear system		2014-10-14
		From pheter: 4/x - 1/y = 3 .... equation (1) 6/x - 2/y = 5 .... equation (2) Answered by Penny Nom.
	A fact family containing 4, 4 and 16		2014-10-14
		From Leslie: I am helping my son and the question is 4,4,16 in fact family what does that mean Answered by Penny Nom.
	A tennis ball in a triangular prism		2014-10-06
		From Anna: Hi, I need to find the the base and the height of a triangular prism, but I only know the diameter of a tennis ball that fits exactly in the triangular container.. The diameter for the ball is 8.50cm. Can you help me find the formula? Thank you! Answered by Penny Nom.
	Two equations in x and y		2014-09-25
		From seyilogo: solve y=2x - 3 and (4x - 2y) / x + y = 1 simultaneously Answered by Harley Weston.
	Continuity on a closed interval		2014-09-21
		From Pragya: The trouble I'm having is as follows : a continuous function is most of the times defined on a closed interval, but how is it possible to define it on a closed interval ,because to be continuous at endpoints of the interval the function's limit must exist at that endpoint,for which it has to be defined in its neighborhood,but we don't know anything about whether the function is always defined in the neighborhood. Please help... Answered by Penny Nom.
	Meetings for 77 students		2014-09-18
		From Adam: We have a new group of students starting, and would like to set up a series of small group meetings so each student meets each other, hopefully without meeting the same people twice. We have 77 students. In theory I would like to have 11 meeting slots, with 10 groups in each slot, with up to 8 students in each group. Is there a way to do this? I have wondered if it might be easier to do 9 meeting slots, with 9 groups per slot, with 9 students per group. Thanks! Answered by Victoria West.
	Two equations in two variables		2014-09-18
		From Susan: (28x + 36y) - [20000 - .75(28x + 36y) + 60000] = 5000 x + y = 10000 solving two equations involving variables Answered by Penny Nom.
	A tangent to a curve passing through a point not on the graph		2014-09-15
		From Aquilah: For the curve y = x2 + 3x, find the equations of all tangent lines for this graph that also go through the point (3, 14). Answered by Penny Nom.
	A six team track schedule		2014-09-15
		From Paul: I need to make a six (6) team track schedule. It needs to be five (5) triangular (3 team) meets with each team playing each team twice Answered by Victoria West.
	A barge of triangular cross section		2014-08-18
		From tushar: a barge of triangular cross section is 20m long 12 m wide and 6m deep.its floats in SW at a draft if 4m find its displacement Answered by Penny Nom.
	Multiplication in base five		2014-08-07
		From Alise: Hi Maths Central! I was wondering if you could help me with multiplying in base 5. I have read a question previously answered by you in regards to this but got fairly confused by it and was hoping you could help me with my question. My question is: Multiply 1422 base 5 by 21 base 5 keeping these numbers and answer in base 5. Would you also be able to explain how to get to the answer? Thanks! Answered by Penny Nom.
	A 6 team sports schedule		2014-08-02
		From Daniela: Hello, My husband and I are volunteering at our church's Jrs camp and we were given the task of making the schedule for sports. There will be 6 teams and a total of 3 games for two days. We would like for every team to play each other but we cannot figure it out. Pls help! Thanks. Answered by Victoria West.
	60% as much as $30.		2014-07-18
		From Kenneth: Question from Kenneth: Hello: Do you know why some "as...as" phrases indicate multiplication? For example, ? is 60% as much as $30. This is equivalent to 60% X $30 = $18. How does this make sense? I saw this example in an old textbook on business mathematics, but the author did not explain why it is equivalent to multiplication. I thank you for your reply. Answered by Robert Dawson.
	A rotation schedule for 14 teams		2014-07-08
		From Daniel: I am organizing team activities for a summer camp. We have 14 teams and 7 rotations and 7 different games. every team will play a different game each rotation. Where I am having trouble is I would like each team to play a different team each rotation without a repeat. Is that possible? if so what is the formula? Answered by Victoria West.
	The method of elimination		2014-07-05
		From leo: please explain how can i solve this problem 3x-6y=-38 6x-9y=44 using elimination and simultaneous method thank you :) Answered by Penny Nom.
	Angular speed		2014-06-29
		From andrea: a wheel having a radius of 10cm rotates such that the linear speed at its rim is 30mls. what is the angular speed of the wheel in rpm? Answered by Penny Nom.
	Differentiate ln[x(2x-4)^1/2]		2014-06-28
		From Igwe: If y=In[x(2x-4)^1/2],find dy/dx at x=3 Answered by Penny Nom.
	Simultaneous equations		2014-06-20
		From rana: solve the simultaneous equations a)3x=7y 12y=5x-1 Answered by Penny Nom.
	20 teams and 10 competition stations		2014-06-04
		From Joel: I have 20 teams. There are 10 competition stations. Each station will accommodate exactly 2 teams to compete with each other at a time. Each of the 20 teams needs to compete at each of the 10 stations exactly one time. Here's the catch I cannot solve: how to schedule it so that each team plays EVERY OTHER TEAM once and only once, while never repeating a station. Answered by Victoria West.
	10 golfers, playing 7 rounds in 2 x 3balls and 1 x 4ball		2014-06-04
		From adrian: Hi, We are off to Scotland on our yearly golfing trip soon. Question is we have 10 golfers, playing 7 rounds in 2 x 3balls and 1 x 4ball. I would like to ensure that each golfer plays with the other guys an equal amount of times, guess 3ish? and we share the amount of times each player plays in the 4ball. Hope you can help? Answered by Victoria West.
	A rotating schedule for 9 individuals		2014-05-29
		From Josh: I need to set up a rotating schedule for 9 individuals. The individuals will be pairing each week in groups of two. Thus, every week there will be 4 groups of two individuals and one individual not paired with anyone (i.e. a "bye week"). The rotating schedule should not repeat any pairing and it will continue until each individual has been paired with every other individual once. Thank you Answered by Victoria West.
	A hexagon with different side lengths		2014-05-16
		From Grace: Sorry if this is a simple question, but I can't seem to understand how to solve it. I am Trying to find the area of a hexagon with measurements 6x7x6x6x7x6, or 2 sets of opposing sides with 6, and one set with 7. Thank you. Answered by Penny Nom.
	A 12 week poker tournament		2014-05-12
		From Jamie: Looking to schedule a 12 week poker tournament with 18 players ...playing 2 separate 9 person tables...I'm looking to have a balanced schedule where everyone player with each other an equal amount of time Answered by Victoria West.
	A schedule for 2 teams of 10		2014-05-07
		From John: How can I set up a schedule for 2 teams of 10 on a team to play each individually against each other over a 10 day span at 10 different course with 10 different start times each day. I was looking to not repeat any competition. As an example, Team A would consist of players 1-10, Team B would consist of players 11-20. I would want to have 10 start times a day for 10 days where a member of team A plays a member of team B each day without repeating any matches and any of the same courses and not repeating any of the same start times. Any help in this would be GREATLY appreciated!!!! Answered by Victoria West.
	The derivative of sin(x)		2014-04-26
		From Lucky: f(x)=Sin(x), by first principle its f'(x)...show me how to solve such problem. Answered by Penny Nom.
	A schedule for 9 teams on 3 fields for 18 days		2014-04-25
		From Scott: I need to schedule 9 teams on 3 fields for 18 days with no buys. Two teams play while other practices in field(little guys). Two fields have backstops and other is open field. Would like to have even time on each diamond if possible. Thank you Answered by Victoria West.
	Solve for theta		2014-04-25
		From ALASTAIR: Hi, The question asks Solve for 'theta' cos2theta=sintheta x costheta. Substituting for cos2th either 1-2sin^2th or 2cos^2th does not give an equation in either sine or cosine alone how do I solve this please? Answered by Penny Nom.
	Two 9 hole golf leagues		2014-04-23
		From Sally: I need help scheduling two 9 hole leagues. Here are the variables: - Leagues alternate each week starting on the front and back - League A starts at 4:30 with 7 groups and League B starts at 5:15 with 8 groups (all use carts and must be teed off by 5:30) - Regular play must continue, customers who have started before league play begins have preference to continue their round whether they are playing 9 or 18 holes. Thank you!!! Answered by Victoria West.
	Golf with 3 teams of 20		2014-04-21
		From Joshua: Thank in advance for this great service Golf - new - 3 teams of 20 - to create 20 unique groups of 3 For example use 3 teams of 3 1a 2a 3a 1b 2b 3b 1c 2c 3c So groups are 1a 1b 1c 2a 2b 2c 3a 3b 3c Groups can only have one a, one and one c - and that combo should be unique Answered by Victoria West.
	Golf League Schedule for 15 weeks and three flights		2014-04-21
		From bigdog: I need help setting up a 12 team (3 flights with 3 teams in each flight) 15 week league play schedule. Each team must play teams in there perspective flight twice during the 15 week season. Answered by Victoria West.
	Simultaneous equations with fractions		2014-04-19
		From Maryam: I looked at your example of simultaneous equations with fractions and applied it to my question from an educate exam papers but I couldn't get it to work. The question is: x/8 - y = -5/2 3x + y/3 = 13 Answered by Penny Nom.
	The area bounded by the X-axis and y=x^(2)-4 from -5 to 0		2014-04-15
		From Lexie: Determine the area that is bounded by the following curve and the x-axis on the interval below. (Round your answer to three decimal places) y=x^(2)-4, -5 ≤ x ≤ 0 The answer is 32.333 but I have no idea how to get there. Answered by Penny Nom.
	A tangent of the curve (x/a)^n+(y/b)^n =2		2014-04-15
		From sudhir: the equation of tangent of the curve (x/a)^n+(y/b)^n =2. at(a,b) is Answered by Penny Nom.
	The surface area of a circular dome		2014-04-10
		From Shafiqah: Is this a dome's surface area formula?? {{2 × π r × h square units}} Is the surface area of the floor for the dome is calculate too in this formula? Thanks for answering. =) Answered by Robert Dawson and Penny Nom.
	Two rectangular prisms		2014-04-10
		From hannah: two rectangular prisms have a combined volume of 432 cubic feet Prism A has half the volume prism b has what are the volumes of prism a and prism Answered by Penny Nom.
	The surface area of a rectangular prism		2014-04-08
		From Manraj: Find the surface area of a rectangular prism with dimensions 4, 5, and 7 units. Answered by Penny Nom.
	A schedule for 6 people		2014-03-29
		From John: How do I set up a schedule where six people are here for ten of twenty days. Arranged in rotating groups of three, so everyone works with everyone else. Everyone works with everyone else at least once and everyone works ten days. Answered by Victoria West.
	Percentage increase of the population of a town		2014-03-28
		From hunter: The population of a certain town in 1984 was 2900 people. The percent increase was 2.5% each year. What is the town's population in 2002? Answered by Penny Nom.
	14 teams divided into two equal divisions		2014-03-18
		From C: We have 14 teams divided into two equal divisions. We want each team to play each team in their division one time and four teams from the other division one time. What is the schedule Answered by Victoria West.
	A circle which is tangent to two perpendicular lines		2014-03-09
		From MJ: I'm a College Student taking up Bachelor of Secondary Education on Math Subject. And I'm struggling for my research about Circles. I done solving the said topic particularly on this question: "What are the possible equations of a circle being tangent to a pair of perpendicular lines, having the origin as the Point of Intersection and the C (h, k), where h, k ∈ℤ" But I can't get what would be the process that I must do in order to jive to my idea/goal for that problem. Please check my idea that the numerical coefficients of the equation is equal to the radius of the circle. Thanks in advance! :) Answered by Penny Nom.
	A schedule for 6 teams over 12 weeks		2014-03-09
		From Paul: So I have a question. I noticed you came up with ways to create schedules and we are having a really hard time making our lineup correctly. Basically we have 6 teams that will play over a 12 week period every Monday night. The time slots are 1 hr each playing at 6, 7 and 8. We would like each team to play 3 games at each time slot over the 12 weeks. Is this something that can actually be accomplished? Thanks so much for your help! Answered by Eric Venables.
	8 team schedule over 7 days		2014-02-21
		From Andrea: I need to organize 8 teams. Each team has to go through 8 games against another team, but not against the same as before. Answered by Victoria West.
	A 7 person golf schedule		2014-02-21
		From Claude: Golf Holiday: 7 guys, play a 4-some and a 3-some each day for 10 days. Want to have the best balance of each player playing with every other player the same number of times and each player playing in an equal number of 4-somes and 3-somes. Answered by Victoria West.
	Simultaneous fractional equations		2014-02-15
		From benjamin: hi math central. benjamin here. during class, i had problem with this topic. normally i wont have problems with math but this topic i just too hard for me. please help i am having exam and test next week on this topic here is the question: using substitution method, solve the simultaneous equation. (x+1)/(y+2)=0.5 (x-2)/(y-1)=1/3 Answered by Penny Nom.
	Can a cylinder be considered a circular prism?		2014-02-08
		From Davina: Can a cylinder be considered a circular prism? Answered by Penny Nom.
	Two nonlinear equations		2014-01-26
		From Naryn: (1÷x) + (1÷y) = (7÷12) xy = 12 Answered by Penny Nom.
	A rectangular shaped property		2014-01-17
		From Donna: If I I have property that is rectangle shaped. I I know the ends are 100 feet how many feet would the sides be to make 5.4 acres Answered by Penny Nom.
	When would one flip the inequality sign?		2014-01-09
		From Natasha: Would one flip the inequality symbol in this equation: (explain why) (-9a)/(-9) > 81 And please explain in what circumstances one would flip the inequality sign THANKS! Answered by Penny Nom.
	Schedule for a 4 team basketball league		2013-12-08
		From Sommer: I need a schedule for my kids basketball league. There are 4 teams. We will play every Saturday for 4 weeks with 4 games per Saturday. Week 5 will be the playoffs where 1st will play 4th and 2nd will play 3rd. Week 6 will be winners of week 5. Please help!! Answered by Victoria West.
	Problem solving with fractions		2013-12-03
		From Jennie: Paul has 2/3 as many postcards as Shawn. Shawn has 3/5 as many postcards as Tim. If the 3 boys have 280 postcards, how many more postcards does Tim have than Paul? Answered by Penny Nom.
	Base 5 arithmetic		2013-11-27
		From samuel: Good day sir, please i don't understand when you say 4x4=13 in base five? In fact, am always having difficulties in addition, subtraction, division and multiplication of number in the same base other than base ten. Please can you give me one example each with details explainations? Answered by Penny Nom.
	A schedule for 32 golfers		2013-11-22
		From Scott: I would like a schedule for 32 guys playing in 8 foursomes for 13 week. I would like it so that no one plays in the same foursome more than once or twice. Is this possible to do??? Can you let me know at bogeysm@yahoo.com if you can do it and if you will do it. Answered by Victoria West.
	Admiring handblown glass ornaments		2013-11-21
		From Ruby: We are admiring hand blown glass ornaments 5% are unmarketable due to defects what is the probability the 3rd ornament is the first defective one Answered by Penny Nom.
	Scheduling 10 people for 5 rounds		2013-11-20
		From Keith: Using golf as an example, I would like to schedule 10 people for 5 rounds with 2 groups of 4 and 1 twosome each round. I would like to minimze the number of times any one player plays with another. Can you provide an optimal schedule? Thank you for your help. Answered by Victoria West.
	The area of an irregular octagon		2013-11-18
		From zafar: if i have a rectangular octagon then how i can find its area 1. The length of rectangle is 42 and the width is 21 and and the base length is 42-12 =30 i mean the length of base =30 Answered by Penny Nom.
	A lever		2013-11-09
		From Durgesh: A farmer uses a 2 m long lever to lift large rocks from the ground of his field . He places a fulcrum 20cm from the rock end of the lever and then stands on the other end, levering out the rock. If the farmer weighs 100 kg , what is the heaviest mass of the ro ck that he can lift using this method? (how to solve) Answered by Penny Nom.
	The popcorn box problem		2013-11-07
		From Dave: We know that calculus can be used to maximise the volume of the tray created when cutting squares from 4-corners of a sheet of card and then folding up. What I want is to find the sizes of card that lead to integer solutions for the size of the cut-out, the paper size must also be integer. EG 14,32 cutout 3 maximises volume as does 13,48 cutout 3. I have done this in Excel but would like a general solution and one that does not involve multiples of the first occurence, as 16, 10 cutout 2 is a multiple of 8,5 cutout 1. Answered by Walter Whiteley.
	Substitution type simultaneous equations		2013-11-03
		From Kayla: I am having problems with substitution type simultaneous equations, when the variable you are substituting is a algebraic one: y=x^2-3x+4 and 3x-2y=1 I have rearranged 3x-2y=1 to get x=(1+2y)/3 but when I substitute this x value into the other equation, I get the wrong answers! Would appreciate any help! Thank you. Answered by Penny Nom.
	Water flowing out of a tank		2013-11-03
		From Carolyn: The flow of water out of a hole in a tank is known to be proportional to the square root of the height of water above the hole. That is, dV/dt (proportional to) sq root (h) The tank has a constant cross-sectional area A, show that the height of water in the tank is given by h = ((-kt+C)/2)^2 If the tank is 9 metres high, and it takes 5 hours for it to drain from full to half full, how much longer will we have to wait until it is completely empty? Answered by Penny Nom.
	Is-5/-11 a positive rational number?		2013-10-30
		From tazneem: Is-5/-11 a positive rational number Answered by Penny Nom.
	A square inscribed in a circle		2013-10-14
		From Jenn: Hello! I am about to buy a 7'9" round rug, but I want to have it cut down into a square. What's the largest square I can obtain from this? Thank you! Answered by Penny Nom.
	Maximize the volume of a cone		2013-10-09
		From Conlan: Hi I am dong calculus at school and I'm stumped by this question: A cone has a slant length of 30cm. Calculate the height, h, of the cone if the volume is to be a maximum. If anyone can help me it would be greatly appreciated. thanks. Answered by Penny Nom.
	A schedule for 2, 7 team divisions		2013-09-24
		From Sampson: I'm looking to set up a weekly schedule within a 22 week segment of 2 7 team divisions where every team plays every other team in their divison 3 times and have 4 cross over games with 4 of the other 7 teams in the other division. I've yet to figure this out. Thanks for your time. Answered by Victoria West.
	25 people are attending a 5 day meeting.		2013-09-20
		From Lisa: 25 people are attending a 5 day meeting. There are 5 tables, with each table seating 5 (or 6). I want each person to sit at a different table every day with completely different people. Is this possible. Can do I figure this out? I have each of the people a letter designation from A to Y. Each table have a number from 1 to 5. Thank you! Answered by Victoria West.
	A rectangular hyperbola		2013-09-19
		From Soumya: Is the graph of an inverse variation a RECTANGULAR HYPERBOLA? If it is, then how can be the equation of a rectangular hyperbola be xy=constant , whereas in the books it is written that the graph of a rectangular hyperbola is- x^2-y^2=a^2? Answered by Chris Fisher.
	The volume of an attic		2013-09-18
		From David: I have small equipment hut that has a small attic space that I want to blow insulation into it. The attic size is shaped like a triangle that is about 8 feet by 10 feet by 7 inches at the highest point. I need to estimate the volume in square feet or cubic feet to know how many bags of insulation to blow into the space. Thanks Answered by Penny Nom.
	Intersection points and diagonals		2013-09-11
		From Kenneth: I was wondering, is there a relationship between the number of sides of a regular n-gon and the number of times its diagonals intersect? Ie: 4 sides=1 intersect (center, diagonals form an 'X' ) 5 sides=5 intersects (diagonals form a star) 6 sides=13 intersects And so on. Answered by Chris Fisher.
	A schedule for 18 golfers		2013-08-29
		From Brian: After searching the data base which helped me solve at least 3 other issues I have one more un answered question. I have 18 golfers split into 6 threesomes for 4 days of golf. What is my best option for a schedule mixing them all up as much as possible over the course of the 4 days Answered by Victoria West.
	Euclid's Parallel Postulate		2013-08-20
		From Justin: Hello there, I was wondering is Euclid's Fifth Parallel Postulate of parallel lines never intersecting, undecidable or essentially undecidable? Thank you so much for any help you can provide! Answered by Robert Dawson.
	Equal ordinate and abscissa		2013-08-15
		From sonit: the slope of tangent to the curve y=(4-x^2)^1/2 at the point, where the ordinate and abscissa are equal, is Answered by Penny Nom.
	Two perpendicular lines		2013-08-15
		From Hanna: The problem says, "Write the equation in standard form for the line that is perpendicular to the graph of y=5x+1 with a y-intercept of 4." I have no clue how to do this. Please help me! Answered by Penny Nom.
	Differentiate x^x - 2^sinx		2013-08-09
		From tarun: derivative of x^x - 2^sinx Answered by Penny Nom.
	16 golfers		2013-07-31
		From Pat: 16 golfers...3 nine hole rounds a day...for 4 days. what are the best pairings for the fewest repeats of partners? Answered by Victoria West.
	What is the value of |2((i)^(1/2))|?		2013-07-22
		From Delilah: What is the value of |2((i)^(1/2))| ? i.e. absolute value of 2 multiplied by square root of i. Answered by Penny Nom.
	10 guys playing 8-9 hole rounds		2013-07-19
		From Jason: I have 10 guys playing 8 9 hole match-play rounds. I need to have everybody play the other 9 men, but need to limit them to only a 9 hole match between them. If we need to go 3-3-4 or 2-4-4 for a better solution, that may be possible. Answered by Victoria West.
	Simultaneous equations		2013-07-10
		From Warren: solve this simultaneous equation: xy=4 2x+3y=14 Answered by Penny Nom.
	Scheduling a 12 person fishing		2013-07-09
		From Don: Greetings Math Central! I searched the index, but could not find a similar quandary. Here's my predicament: I am seeking help in scheduling a 12 person fishing outing. We have four boats. I would like to schedule three fishermen to a boat. We fish 2 1/2 days, split into morning and afternoon sessions. Thursday afternoon, Friday morning, Friday afternoon, Saturday morning, and Saturday afternoon We switch boats after lunch, with each fisherman moving to a different boat, with different partners. I would like to have each fisherman fish with as many others in the group as possible, with a minimum of partner duplication. I would like to have each fisherman fish in all of the four different boats over the course of the trip at least once. Would you please suggest a boat / fishing partner schedule that fits my parameters as closely as possible. Thank you! Don Answered by Victoria West.
	4 couples golfing		2013-07-06
		From Brian: We have 4 couples going on a 4 day golf vacation playing 4 rounds of golf. I have spent hours trying to set up a schedule that allows the 4 spouse to play together, and then each spouse to play with one of the other spouses (men with women) for the] other 3 rounds. I would like the foursomes to be different as possible. Also, no-one should RIDE in a cart with the same person more than once. I am not a math guy so I try to do this by working it out on paper, over and over again. It ain't working!! If you can help, I am very thankful. Brian Answered by Victoria West.
	8 golfers playing 8 games		2013-07-03
		From Johan: We have 8 golfers playing 8 games, and we want to schedule them so that they play together equal amount of times, or as close as you can get to that. They will be playing in two four balls each day. Anyone sorted this one out yet, I will really appreciate a solution? Thanks Johan Answered by Victoria West.
	13 golfers playing 5 rounds		2013-07-03
		From Alan: i have 13 golfers playing 5 rounds. want everyone to play together at least once. Answered by Victoria West.
	A league schedule for 6 hockey team		2013-07-02
		From Giovanni: Hello, I try to make a league schedule for 6 hockey team. Each team will play 36 games during the regular season. I cannot find a proper schedule generator. Can you help me please? Thank you Answered by Victoria West.
	Fantasy football league		2013-06-18
		From Chris: Hello, I am the commissioner of a fantasy football league. In this week, we play all 17 weeks of the season. It's a 12 team league, and we play each team twice. To do that, we have 5 "double header" weeks, which means you play 2 different teams. I am struggling to come up with a schedule to make this work. Does anyone have a solution? Answered by Victoria West.
	Compound interest		2013-05-10
		From Kyla: I am doing correspondents and cannot figure out how to explain the solution to this question, I do not understand how they came to this answer and need it explained step by step so I can complete the following questions in this unit, please help!!! Calculating compound Interest Johnny invest $800 that pays 8% compounded quarterly for 5 years. How much is the investment worth at the end of the 5th year? Answered by Penny Nom.
	The rings of a bull's eye		2013-04-28
		From Math: The bull’s eye of a target is a circle 20 cm in diameter. It is surrounded by four rings, each 15 cm wide. Find the area of each ring. Answered by Penny Nom.
	How do i reverse this formula?		2013-04-20
		From MK: I have 22,000,000 worth of gold and wants to want to resell the gold back with a profit. Each transaction of gold will have a transaction fee of 15%, so if i resell the gold back at 22,000,000, I will only get back 18,700,000 after 15% transaction cut. The current formula is X-15%X = Y where X = 22,000,000 and Y = 18,700,000 Will u be able to come up with a new formula if we don't know the value of X but we know the value of Y Something like this X-15%X = 22,000,000. How do i reverse this formula to find the value of X Thanks Answered by Penny Nom.
	4 linear equations with 3 unknowns		2013-04-12
		From Marian: how to solve for 3 unknowns in 4 simultaneous equations Answered by Penny Nom.
	A gravel pile in the shape of a triangular pyramid		2013-04-04
		From Casey: Hello Right now I am stuck and I feel embarrassed because I feel like the answer is so easy I should know it. I am working on a project and need to find a volume of gravel it will take to occupy this triangular prism like area. I am not sure what formulas I should use whether it be that for the volume of a pyramid or something more complex? Basically it forms a right triangle at one side then from there all points slope to one singular point about 10412mm away. I am attaching a picture drawn up in paint with the actual dimensions to clear up any confusion. Thank you for any help. Casey Answered by Penny Nom.
	Question		2013-04-04
		From Casey: Hello Right now I am stuck and I feel embarrassed because I feel like the answer is so easy I should know it. I am working on a project and need to find a volume of gravel it will take to occupy this triangular prism like area. I am not sure what formulas I should use whether it be that for the volume of a pyramid or something more complex? Basically it forms a right triangle at one side then from there all points slope to one singular point about 10412mm away. I am attaching a picture drawn up in paint with the actual dimensions to clear up any confusion. Thank you for any help. Casey Answered by Penny Nom.
	Simultaneous equations with fractions		2013-03-31
		From Terence: 5/x-6/y=1 17/x+30/y=16 I been spending whole day to solve this question. Would be very grateful if you can help I try The denominator value is a equations term which make is simultaneous equations so hard. Answered by Penny Nom.
	Tangents to the curve y = x^3		2013-03-24
		From Ethan: How many tangent lines to the curve y = x^33 pass through the point (2, 4)? For each such line, and the exact coordinates of the point of tangency on the curve. Answered by Penny Nom.
	Cumulative Frequency Math Question		2013-03-20
		From Primadonna: Hi, Please help me solve this question. Thank you so much. The cumulative frequency table below shows the length of time that 30 students spent text messaging on a weekend. Minutes Used Cumulative Frequency 31-40 2 31-50 5 31-60 10 31-70 19 31-80 30 Which 10-minute interval contains the first quartile? (1) 31–40 (2) 41–50 (3) 51–60 (4) 61–70 Answered by Penny Nom.
	Five players in a 4-player partnership game		2013-03-19
		From Dee: I have 5 players who are playing in a 4-player partnership game & want to rotate the 5th person in in such a way that each person is each other person's partner for a game. How can such a rotation be done? Answered by Penny Nom.
	Six-digit passwords		2013-03-19
		From Judy: Hello: Can you please explain why the answer to the following question is 10^6? What is the number of possible six-digit passwords when using the digits 0 through 9, with repetition allowed. Thank you. Answered by Penny Nom.
	Related rates		2013-02-17
		From Ishaak: A hemispherical bowl is filled with water at a uniform rate. When the height of water is h cm the volume is π(rh^2-1/3 h^3 )cm^3, where r s the radius. Find the rate at which the water level is rising when it is half way to the top, given that r = 6 and the bowl fills in 1 minute. Answered by Penny Nom.
	A word problem involving toys		2013-02-14
		From sandy: Each boy gets 5 toys.Each girl gets 3 toys.There are 150 pupils. The boys had 74 more toys than girls. How many boys? How many girls? Answered by Penny Nom.
	Simultaneous equations		2013-02-10
		From Michael: 2P + 1/3V =8 3P - 2/V=5 Answered by Penny Nom.
	We have 10 golfers and four rounds of golf in two days		2013-02-05
		From Steve: We are having a golf tournament. We have 10 golfers and four rounds of golf in two days. We are going to break the group of 10 into two flights. Flight A and Flight B. We would like all members in Flight A to play one nine hole match against each other. All players in Flight B to play one nine hole match against each other. Could we play in groups of 4,3 and 3? What is the best way to make the pairings work? Answered by Robert Dawson.
	Integration from 0 to 2pi of 1/(3cos x + 2) dx		2013-02-04
		From ankit: Integration from 0 to 2pi of 1/(3cos x + 2) dx Answered by Harley Weston.
	Multiplication in base two		2013-02-01
		From Michael: multiply in the indicated base 110two*11two Answered by Penny Nom.
	The fourth side of an irregular polygon		2013-02-01
		From Emran: I have a irregular polygon. I know 3 of the 4 sides, and 2 of the angles. A-B is 285, B-C is 149, and C-D is 310. Angle B is 135 degrees. and Angle C is 45 degrees. Is there a formula to solve for the final side? Thanks. Answered by Penny Nom.
	The multiplication table for the different bases		2013-02-01
		From sylvia: I am having a difficult time trying to figure out how to fill in the multiplication table for the different bases. i don't know how to get the numbers. Answered by Penny Nom.
	We have 2 teams of 6 couples each that play 6 games		2013-01-25
		From Denise: We put together a game night where we have 2 teams of 6 couples each that play 6 games. We haven't been able to figure out an arrangement that allows each couple to play each game with a different couple from the opposite team (i.e. Team A couples play every game with a different couple from Team B). Is this possible? It works with 2 teams of 5 couples each. Answered by Chris Fisher.
	A railroad embankment		2013-01-22
		From clint: the pennsylvania railroad found it necessary,owing to land slides upon the roadbed,to reduce the angle of inclination of one bank of certain railway cut near pittsburgh,pa.,from an original angle of 45 degrees to a new angle of 30 degrees. the bank as it originally stood was 200 ft.long and had a slant length of 60 ft.. find the amount of the earth removed, if the top level of the bank remained unchanged. Answered by Penny Nom.
	Maximize profit		2013-01-19
		From Chris: A firm has the following total revenue and total cost function. TR=100x-2x^2 TC=1/3x^3-5x^2+30x Where x=output Find the output level to minimize profit and the level of profit achieved at this output. Answered by Penny Nom.
	The weight of a pipe full of water		2013-01-16
		From joe: how do you figure out the weight of a pipe full of water Answered by Harley Weston.
	A large ditch		2013-01-11
		From steve: hi i have a large ditch to make a road entrance accross, the ditch is a green field on one side and a highway on the other side the ditch depth is 1.8m on the field side and 3.2 on the highway side the culvert pipe is 1,2m in diameter are you with me so far? the entrance from the highway will be 26m wide tapering in to 6m - ,20 m in from the highway there will be a concrete slab of 150mm over the top the fall from highway to field must not exceed 1/8 any ideas how much stone it will need Answered by Harley Weston.
	A trig identity		2013-01-04
		From Tehmas: Prove sinC+sinD=2sin(C+D/2)cos(C-D/2) Answered by Harley Weston.
	The quadratic formula		2013-01-03
		From itsel: Find the discriminant ans use it to determine the use the quadratic formula to solve the equasion -2x^2+3x+2=0 Answered by Penny Nom.
	Mod versus Rem in Turing		2013-01-01
		From Eric: I am a teacher teaching computer science using Turing. I am having difficulty understanding why one would use the mod operator versus the rem remainder operator. Mod seems to make the resulting sign depend on the sign of the divisor, whereas rem makes the resulting sign depend on the dividend. Examples: 11 mod 5 = 1 and 11 rem 5 =1 -11 mod 5 = 4 and -11 rem 5 = -1 11 mod -5 = -4 and 11 rem -5 =1 -11 mod -5 = -1 and -11 rem -5 = -1 What I can't understand is why this would matter. For example, -11 / 5 = -2.2 and 11 / -5 = -2.2 get the same result. So how is a remainder dependent on the sign of one of the parts? What benefit would using one over the other have? Any insight would be most helpful! Eric Answered by Harley Weston.
	An integral		2012-12-16
		From Slavena: integration of (lnx)^2 / x dx Answered by Penny Nom.
	An area bounded by lines		2012-12-16
		From sidra: find area bounded by functions: y=x y=2x and y=5-x Answered by Penny Nom.
	A max/min problem		2012-12-14
		From bailey: A right angled triangle OPQ is drawn as shown where O is at (0,0). P is a point on the parabola y = ax – x^2 and Q is on the x-axis. Show that the maximum possible area for the triangle OPQ is (2a^3)/(27) Answered by Penny Nom.
	The derivative of y = sin (30º + x)		2012-11-07
		From Saskia: derivative of y = sin (30º + x) Answered by Harley Weston.
	birdhouse in the shape of a rectangular prism		2012-10-29
		From Tiffany: Hello, I am Tiff M. from NYC. I was solving a math problem about adding,subtracting,multiplying or dividing fractions and mixed numbers. I am not getting this question below. * Laura is building a birdhouse in the shape of a rectangular prism. The base of the birdhouse has an area of 5 square inches. The height of the birdhouse is 2 7/12 inches. Laura calculated the volume of the bird house to be 10 7/12in. Is she correct? If not, what did she do wrong? Answered by Robert Dawson.
	An implicit differentiation problem		2012-10-26
		From Katie: find y' of x^2y-2y^3=3x+2y Answered by Harley Weston.
	How fast is the distance between the aircraft and the car increasing?		2012-10-24
		From Steven: At a certain instant an aircraft flying due east at 240 miles per hour passes directly over a car traveling due southeast at 60 miles per hour on a straight, level road. If the aircraft is flying at an altitude of .5mile, how fast is the distance between the aircraft and the car increasing 36 seconds after the aircraft passes directly over the car? Answered by Penny Nom.
	Differentiation rules		2012-10-23
		From Morgan: Use the derivative rules to differentiate each of the following: 1. f(x)=1/x-1 2. f(x)= sqrt(x) Answered by Penny Nom.
	Revolutions per second		2012-10-18
		From Crystal: Suppose a car wheel is 26 inches in diameter. a) If the tire completes one rotation, how far would the car travel? b) If the car is traveling at 60 miles per hour, how fast is the car wheel spinning in revolutions per second? Answered by Penny Nom.
	A word problem involving a fraction		2012-10-12
		From Derrick: If the numerator and denominator of a fraction are both decreased by 1 the fraction becomes 2/3. If the numerator and denominator are both increased by 1 the fraction will be 3/4. Find the original fraction. How to do? Answered by Penny Nom.
	Changing the sign of an inequality		2012-09-19
		From Bryauna: Why do you change the signs in inequalities?! Answered by Penny Nom.
	An equilateral triangle and a regular hexagon in a circle		2012-09-11
		From Heidemarie: The vertices of an equilateral triangle with side length of 10 sqrt 3 cm lie on a circle. Find the side length of the regular hexagon whose vertices lie on the same circle. Answered by Penny Nom.
	Angular velocity		2012-09-05
		From Kyra: A belt connects a pulley of radius 8cm to a pulley of radius 6cm. Each point on the belt is travelling at 24 cm/sec. Find the angular velocity of each pulley. Answered by Penny Nom.
	A tangent to f(x) = 1/x		2012-09-04
		From Steven: Consider the graph of the function f(x) = 1/x in the first quadrant, and a line tangent to f at a point P where x = k. Find the slop of the line tangent to f at x = k in terms of k and write an equation for the tangent line l in terms of k. Answered by Penny Nom.
	12 golfers, 4 rounds		2012-08-29
		From Paul: We have 12 golfers who will play four rounds of golf - how can we organize the foursomes so that each player has the most exposure to the other 11 players? Answered by Victoria West.
	A schedule for 6 teams and 37 games		2012-08-29
		From Giovanni: Hello, i try to prepare a schedules for 6 teams, and every teams will play 37 games before the playoff. How to make a schedules? thanks Answered by Victoria West.
	A rotating schedule		2012-08-16
		From Dusty: Ok, Im trying to create a rotating schedule. There are four jobs and four people but, one of four people cant preform one job. How can I figure out a rotating schedule for this issue? Answered by Victoria West.
	A volume of revolution		2012-07-15
		From Tewodros: Let f(x) = e^x and g(x) = x^1/2 both be defined on [0,1]. Consider the region bounded by f(x), g(x), x = 0, x = 1. Rotate this region about the y-axis and determine the volume using the shell method. Answered by Harley Weston.
	Scheduling an academic competition		2012-06-12
		From Mike: I need to schedule 18 high school teams to play each other in a "Jeopardy!"-like academic competition. Teams compete against each other 6 at a time (simultaneously) in 3 different rooms. What will the minimum amount of matches (I believe 6 ?) we would have to play to ensure that each team plays every other team exactly twice? And more importantly: what would that schedule look like? The best I've come up with is having most teams playing twice, but with 2 pairs of teams having to play either only once or sometimes 3 times. Thanks in advance for any help you can give! :-) Mike Answered by Chris Fisher.
	A multinomial theorem		2012-06-08
		From Anuj: if (1+x+xsquare) whole raise to 20 is a0 + a1x + ........ + a20xraise to 40, then find a0 + a2 + a4 + .......... + a38. How do you solve this??????? Answered by Robert Dawson.
	The volume of a wedge		2012-05-28
		From olwethu: volume of wedge that have side 3,3 cm and 6,2 cm and 20 cm long? Answered by Penny Nom.
	Multiples		2012-05-28
		From Kenneth: If I understand correctly , a multiple is a product of two numbers. For example some of the multiples of 6 are 6, 12, 18, 24, 30, etc. I just multiplied 6 by 1, 2, 3, 4, 5, etc. Are the multiples of a fraction, for example, 2/3, determined in the same way? Are they 2/3, 4/3, 6/3, 8/3, 10/3, etc., or are they instead, 2/3, 4/6, 6/9, 8/12, 10/15, etc.? Or do fractions have no multiples? Answered by Penny Nom.
	Multiplying binomials		2012-05-14
		From Jordan: How do I solve the equation: 3(x+4)(x-6) Answered by Penny Nom.
	A 25% sulfuric acid solution		2012-05-03
		From Scott: In order to make a 25% solution with 96% Sulfuric Acid, how much of the Sulfuric do I add to DI water to make up 2000ml?? Answered by Penny Nom.
	The area of a quadrilateral		2012-04-21
		From Rajat: calculate the area ABCD in which AB is 48'1'',BC is 98'4'',CD is 61'4'',DA is 102'10'',AC is 110'3'',BD is 116'9''. Answered by Penny Nom.
	16 golfers		2012-04-20
		From steve: i have 16 golfers, 4 in "A" flight , 4 in "B" flight , 4 in "C" and 4 in "D" We are playing 4 rounds (4 teams of 4) and every group must have a player from the A B C an D flight, and in no round may 2 people have already played together! Answered by Victoria West.
	Golf for 12		2012-04-18
		From Brent: I have a golf group that is set up as follows: 12 players, broken into 2 teams of 6. I am looking for a formula to have one player from team A play against one player for team B each round, not repeat the match, and ride with as little duplication as possible. I know that it is not statistically possible with these numbers and will have at least one round that has duplication. Answered by Robert Dawson.
	Two cars approach a right-angled intersection		2012-04-10
		From Michael: Two cars approach a right-angled intersection, one traveling south a 40km/h and the other west at 70km/h. When the faster car is 4km from the intersection and the other case if 3km from the intersection, how fast is the distance between the car cars changing? Answered by Penny Nom.
	Golf for 28		2012-04-10
		From EARL: HI, I HAVE 28 GOLFERS AND I NEED A SCHEDULE FOR 5 DIFFERENT DAYS THERE WILL BE 7 GROUPS OF 4 PLAYERS EACH DAY. ALL PLAYERS WOULD LIKE TO PLAY WITH ONE ANOTHER ONCE AND NOT PLAY WITH EACH MORE THAN ONCE IF POSSIBLE OR LIMIT THE TIMES A GOLFER PLAYS WITH ANOTHER TO A MINIMUM IF POSSIBLE. (PLEASE SEND AN EXAMPLE OF THE SCHEDULING OF THE GROUPS FOR THE TEE OFF ORDER) THANKS FOR ANY SOLUTIONS YOU CAN PROVIDE. EARL Answered by Robert Dawson.
	A semi-circular roof gutter		2012-04-09
		From Kyle: A semi-circular roof guttering contains some water. The cross-section of the guttering has a diameter of 10 centimetres. The surface of the water collected in the guttering is 8cm. What is the depth of water in the gutter? Answered by Penny Nom.
	A maximization problem		2012-04-09
		From Nancy: After an injection, the concentration of drug in a muscle varies according to a function of time, f(t). Suppose that t is measured in hours and f(t)=e^-0.02t - e^-0.42t. Determine the time when the maximum concentration of drug occurs. Answered by Penny Nom.
	The spread of a rumor		2012-04-09
		From Roohi: The function f(t) = a/(1+3e^(-bt)) has also been used to model the spread of a rumor. Suppose that a= 70 and b=3 0.2. Compute f(2), the percentage of the population that has heard the rumor after 2 hours. Compute f'(2) and describe what it represents. Compute lim t approaches infinity and describe what it represents. Answered by Penny Nom.
	A rectangular prism		2012-04-05
		From Tori: How do you find the base height if the base width is 10ft. The height is 7ft. And the volume is105ft. Answered by Penny Nom.
	Golf for 17		2012-03-29
		From Richard: Hi Guys, I have a scheduling problem which I don't think you have covered before. Apologies if you have! I have 17 golfers due to play 4 rounds of golf. Each round will consist of 3 threeballs and 2 fourballs (ie. 17 golfers in 5 groups)! Is it possible to come up with a schedule where each golfer plays with different partners in each round? Answered by Robert Dawson.
	The period T of a pendulum		2012-03-27
		From Ashley: The period T of a pendulum is given in terms of its length, l, by T=2pi sqrt(l/g) where g is the acceleration due to gravity(a constant) a. find dT/dl b. what is the sign of dT/dl c. what does the sign of dT/dl tell you about the period of the pendulums? Answered by Penny Nom.
	The area of an irregular hexagon		2012-03-20
		From Jacob: I am having trouble finding the area of an irregular hexagon with 5 right angles. It has 5 given sides, with the lengths as follows: 8.2 ft. 6 ft. 4.5 ft. 2.2 ft. 6 and one third ft. Answered by Chris Fisher.
	The volume of an irregular tetrahedron		2012-02-22
		From Brittany: If I am given an irregular tetrahedron with the coordinates of the 4 points how do I find the volume? For example I am asked to find the volume and only given the points A(-4,-3,5), B(2,-1,2), C(0,-5,0), and D(-2,0,0) can you shown me the working and formular to find the volume? Answered by Robert Dawson.
	Dt[sin t tan (t^2+1)]		2012-02-21
		From Ayu: Ayu Dt[sin t tan (t^2+1)] derivatives Answered by Harley Weston.
	36 golfers		2012-02-15
		From Steve: We will have 36 golfers playing 4 rounds of golf and would like to have different foursomes each round. In other words, no player will play with another more than once. Answered by Harley Weston.
	The derivative of x^-(1/2)		2012-01-14
		From Eric: I have an problem figuring out the derivative of the negative square root of x i.e. x^-(1/2) using the first principle. Could someone please show me? Thanks in advance! Answered by Harley Weston.
	Lost in the woods		2012-01-12
		From Liz: I am lost in the woods. I believe that I am in the woods 3 miles from a straight road. My car is located 6 miles down the road. I can walk 2miles/hour in the woods and 4 miles/hour along the road. To minimize the time needed to walk to my car, what point on the road should i walk to? Answered by Harley Weston.
	A volume of revolution		2012-01-11
		From john: find volume of solid generated by revolving the region in the first quadrant bounded by the curve y squared=x cubed, the line x=4 and the x-axis about the line y=8. The answer in the back of the book is 704 pi divided by5 Answered by Penny Nom.
	Triangular numbers that are square		2011-12-27
		From Luke: The “TnS” is a positive integer which is both Triangular number and Square number. For example, 36 is a “TnS” number since 36=1+2+3+4+5+6+7+8 (Triangular number) and 36=6x6 (Square number). What is the next “TnS” which is greater than 36? Answered by Penny Nom.
	Three sides of a triangle		2011-12-24
		From saba: the three sides of a triangular lot have lengths 10,11and 13cm,respectively. find the measure of its largest angle and the area of the lot? Answered by Penny Nom.
	Water is flowing into a cup		2011-12-19
		From Tim: A cup has a radius of 2" at the bottom and 6" on the top. It is 10" high. 4 Minutes ago, water started pouring at 10 cubic " per minute. How fast was the water level rising 4 minutes ago? How fast is the water level rising now? What will the rate be when the glass is full? Answered by Penny Nom.
	A cube of ice is melting		2011-12-05
		From Emily: a cube of ice (i.e.) each side is of the same length) is melting at a rate such that the length of each side is decreasing at a rate of 5cm per hour. how fast is the volume of the cube decreasing (in cubic cm per hour) at the instant the length of each side is 25cm? Answered by Penny Nom.
	The average age of 300 cars		2011-11-22
		From Jason: I have 300 used cars built from 1970 to 1980, I would like to know the average age by total volume. If I provide the qty built per year, can I determine the average age of the lot (300) by total volume? Total built 50 56 30 10 30 25 64 9 12 14 Year built 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 Thanks Answered by Penny Nom.
	Water pouring into a conical tank		2011-11-21
		From Patience: Hi my name is patience and I'm having a problem with this question. Water pours into a conical tank of semi vertical angle 30 degrees at the rate of 4 cm^3/s, where h is the depth of the water at time t. At what rate is the water rising in the tank when h = 10 cm? Thank you Answered by Penny Nom.
	I started with Euler's identity and manipulated it		2011-11-14
		From anonymous: I started with Euler's identity and manipulated it e^i*pi=-1 e^-i*pi=(-1)^-1 e^-i*pi=-1 e^-i*i*pi=(-1)^i e^--pi=(-1)^i e^pi=(-1)^i type it in in a calculator and you get e^pi=23.1406926... and (-1)^i=0.0432139183... What did I do wrong? Answered by Robert Dawson.
	Lines tangent to y^2=4x		2011-11-11
		From Reuchen: Find equations of the lines tangent to y^2=4x and containing (-2,1). Answered by Penny Nom.
	Modular arithmetic		2011-10-30
		From Kim: Hello, I am editing a resource for students, and I think some of the answers may be incorrect. The text I was given and my questions are in the attachment. Any help you could give would be appreciated. Thanks, Kim Answered by Harley Weston.
	A mythical soccer ball		2011-10-27
		From Joel: We've been working on this problem diligently and can't seem to come up with the answer book's answer. We think it may be wrong, yet want to check it with an expert. Here goes. The school's new soccer balls are covered with 64 regular hexagonal panels. Each hexagon measures 2 inches between opposite corners and 1.5 inches between opposite sides. What is the total surface area of the soccer ball? Answered by Robert Dawson and Lorraine Dame.
	A spherical ball in a conical wine glass		2011-10-26
		From Jules: A heavy spherical ball is lowered carefully into a full conical wine glass whose depth is h and whose generating angle (between the axis and a generator) is w. Show that the greatest overflow occurs when the radius of the ball is (h*sin(w))/(sin(w)+cos(2w)). Answered by Claude Tardif.
	Implicit differentiation		2011-10-20
		From Monica: Find dy/dx in terms of x and y, if sin(xy)=(x^2)-y. Answered by Penny Nom.
	A hemispherical bowl with a lead ball inside		2011-09-27
		From Jean: "(a) Water is being poured into a hemispherical bowl of radius 3 inch at the rate of 1 inch^3/s. How fast is the water level rising when the water is 1 inch deep ? (b) In (a), suppose that the bowl contains a lead ball 2 inch in diameter, and find how fast the water level is rising when the ball is half submerged." Answered by Penny Nom.
	The derivative of f(x) = (x+1)^1/2		2011-09-05
		From Carla: Find the derivative using the limit process of f(x) = (x+1)^1/2 Answered by Harley Weston.
	4 x 2		2011-08-30
		From Lucjan: how to sketch a diagram that shows 4x2 expression? Answered by Penny Nom.
	Romeo throws a pebble at Juliet's wondow		2011-08-22
		From Natalie: There is a picture of Romeo trying to attract Juliet's attention without her nurse who is in a downstairs room, noticing. he stands 10m from the house and lobs a small pebble at her bedroom window (3.5m high). Romeo throws the pebble from a height of 1m with a speed of 11.5m/s at an angle of 60degrees to the horizontal. I have already found that it take 1.74seconds to reach the window and that it does in fact hit Juliet's window however i cannot work out the speed of the pebble when it hits the window! The answer is 9.12m/s but I cannot reach this answer. Hope you can help me :) Answered by Robert Dawson.
	3.8 x 2.2		2011-08-18
		From Isaac: Question from isaac, a student: I am struggling in math & I need help on multiplying 3.8 x 2.2. Can you helpme Answered by Melanie Tyrer and Harley Weston.
	The height of a fluid in a horizontal tank		2011-07-24
		From jason: Same set up as many others, cylindrical tank on its side, but I am interested in defining the change in volume and/or fluid level as a function of time at a constant volumetric outflow. I plan on hooking a pump to the tank so "gpms' will be constant. I have a couple different sized tanks and pumps so I want a general equation. Thanks for your help. Answered by Harley Weston.
	A regular hexagon inscribed in a circle		2011-07-18
		From Courtney: If ABCDEF is a regular hexagon inscribed in a circle of radius r, prove that the length of each side of the hexagon equals r. Answered by Penny Nom.
	Golf for 14		2011-07-11
		From Doug: We have 14 players playing over 4 days. can we play with different players every day and keep the 3 x foursomes and 1 x pair format Answered by Victoria West.
	Golf for 12		2011-07-07
		From Jim: I have a golf trip scheduled with a total of 12 guys. We are playing three rounds of golf. For round 1 Players A B C D must play together. Is there a formula that would allow me to set up the other 8 foursomes with no repeats or minimal repeats? Thanks. Answered by Victoria West.
	A line tangent to f(x)=1/x		2011-06-05
		From Michael: A line tangent to f(x)=1/x in the first quadrant creates a right triangle with legs the x-axis and the y-axis. Prove that this triangle is always 2 square units regardless of where the point of tangency is. Answered by Penny Nom.
	16 golfers and 8 rounds		2011-05-26
		From Gerry: 16 golfers and 8 rounds. To have each player play with as many others as possible. Answered by Victoria West.
	The length of a belt around three pulleys		2011-05-18
		From Grant: I need to calculate the belt length around these pulleys, please can you help or refer me? Known variables D - Large Pulley Diameter d - Small Pulley Diameter c - Center Distance between D and d T - Tension Pulley Diameter x - Horizontal Distance between T and d' Centers y - Vertical Distance between T and d's Centers I need to calculate the belt length around these pulleys. Kind Regards, Grant Answered by Harley Weston.
	The volume of a triangular shaped aquarium		2011-05-07
		From Jeff: HI, I searched the site but really couldn't find my answer, at least that I could understand! I have a triangular shaped aquarium ( think of a cube, except its an equal triangle shape). all 3 sides are 48 inches, and it is 34" tall. Can you please tell me what the volume is in gallons? Thanks! Answered by Penny Nom.
	Solve x(x-3) = 5 (x+4)		2011-04-19
		From Ashley: I have to solve using the quadratic formula. And my answer should be in simplest exact form. And I can't approximate. I really need help to prepare for a test .... x(x-3) = 5 (x+4) Answered by Penny Nom.
	An antiderivative of the square root of (8t + 3)		2011-04-19
		From Caitlyn: I know how to take an antiderivative. But this one's stumping me. I need it to finish a problem. What's the antiderivative of the square root of (8t + 3) ~Caitlyn= Answered by Penny Nom.
	The volume of a triangular pyramid		2011-04-15
		From Chelsea: There is a triangular pyramid which is an equilateral on the base with all sides 16.5 and the height is 25. I have to find the volume. Please help! Answered by Penny Nom.
	2 cubic foot bags of mulch		2011-04-11
		From Ron: if I buy 2 cubic foot bags of mulch, how bags would I need to equal 1 yard? (13 bags?) Answered by Penny Nom.
	Eliminate y		2011-04-07
		From Lynn: 2x + y = 8 y + 3z =5 z + 2w =1 5w + 3x = 9 Form three equations with y eliminated Answered by Penny Nom.
	Tennis schedule		2011-04-04
		From Toni: I need to create a doubles tennis schedule for 6 players playing over a 32 week schedule where no player repeats with a partner. Answered by Victoria West.
	Designing a tin can		2011-03-31
		From Tina: A tin can is to have a given capacity. Find the ratio of the height to diameter if the amount of tin ( total surface area) is a minimum. Answered by Penny Nom.
	[(90+36-4) ÷ 2] x 15 =		2011-03-30
		From ken: [(90+36-4) ÷ 2] x 15 = Answered by Penny Nom.
	A stone is dropped into a lake		2011-03-24
		From AnneMarie: A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 25 cm/s. Find the rate at which the area within the circle is increasing after 4s. Answered by Penny Nom.
	If 25 items are evenly spread over 7 days		2011-03-23
		From michael: What is the formula to calculate: If 25 items are evenly spread over 7 days, but one day has 3 items less than the other days, what is the number if items for each of the remaining 6 days? Answered by Penny Nom.
	What is x to the power of 0?		2011-03-23
		From Jason: What is x to the power of 0? Answered by Robert Dawson.
	Regular and irregular polygons		2011-03-10
		From thaera: the difference between regular shape and irregular shapes. Answered by Penny Nom.
	Vertices and sides of a polygon		2011-03-04
		From RINA: My questions is : would a vertices and sides of a polygon be the same number.  For example, a octagon it has 8 points and 8 sides. Am i correct? Answered by Robert Dawson.
	At what rate is the grain pouring from the chute?		2011-02-26
		From MJ: Suppose that grain pouring from a chute forms a conical heap in such a way that the height is always 2/3 the radius of the base. At the moment when the conical heap is 3 m high, its height is rising at the rate of 1/2 m/min. At what rate (in m^3/min) is the grain pouring from the chute? Answered by Penny Nom.
	Slicing a rectangular parallelepiped		2011-02-23
		From tom: a) Pass a plane containing a vertex of a rectangular parallelepiped and a diagonal of a face not containing that vertex to cut a pyramid from the parallelepiped. What fraction of the volume of the parallelepiped is the volume of the pyramid thus cut off? b)Pass a plane through a cube of edge 8 in so that the section formed will be a regular hexagon. Through each side of the hexagon pass two planes, one plane containing one of the two vertices of the cube which are farthest away from the plane of the hexagon, the other plane containing the diagonally opposite vertex of the cube. Find the volume of the solid bounded by these planes. c)three of the edges of a rectangular parallelepiped that meet in a point are also the lateral edges of a pyramid. What fraction of the parallelepiped is this pyramid...? you know the my only problem is how to illustrate this one...if only i could ...can you help me....all I need is the drawing and I can do the rest ..it's fine if you'll only answer any of these but I'll be thankful if you will do the three :).... Answered by Penny Nom.
	Prove sin x = sin (pi - x)		2011-02-15
		From Janet: Prove sin x = sin (pi - x) Answered by Penny Nom.
	An irregular hexagon		2011-02-09
		From Emma: Hello, I have math question about how to find the area of an irregular hexagon. It is shaped like a backwards L and the side lengths are as follows 11cm 8cm 5cm 5cm 6 cm 3cm Can you please help me find the area of this? Emma Answered by Penny Nom.
	Multiplication and order		2011-01-21
		From Janet: IN A MULTIPLICATION SENTENCE BASED ON A DRAWING..IS THERE ANY ORDER FOR THE MULTIPLICAND ANG MULTIPLIER FOR THE ANSWER TO RIGHT? Answered by Robert Dawson.
	Integrating ln^3x/x		2011-01-14
		From ken: y=ln^3x/x from x=1 to x=11 Answered by Penny Nom.
	Angular speed		2010-12-12
		From Jason: 7 in. pulley traveling @ 175ft/sec. What is the rpm? Answered by Stephen La Rocque and Penny Nom.
	The length is twice its breadth		2010-12-09
		From jenu: The length of the rectangular field is twice its breadth. A man jogged around it 5 times and covered a distance of 3 km. what is the length of the field? Answered by Penny Nom.
	A rectangular solid		2010-12-08
		From ryan: Good day! Have a question on rectangular solids. We were asked to find the dimensions of a rectangular solid, we were only given the volume of the rectangular solid, the total area, and the altitude. I tried using the volume of the rectangular solid and was able to get the area of the base, but I don't know how to get its length and its width. Hope you could help me again. Thanks! Answered by Penny Nom.
	Simultaneous equations		2010-12-05
		From ryan: Question from ryan, a student: 3         4 --   -    --      =     1      (1) x         y 7       2             11 --   -  --        =   --       (2) x       y              12 Answered by Chris Fisher and Stephen La Rocque.
	Angular speed		2010-12-03
		From Julie: If the angular speed of a circle is 360 degrees divided by the time it took to rotate, how do I calculate ones that have greater rotations than the amount of time? I mean, you calculate the angular speed of a merry-go-around that spins once every 5 seconds by doing 360degrees/5 sec, but how do you calculate a merry-go-around that has 16 rotations every 4 seconds? Answered by Penny Nom.
	Can determine if it is scalene, isosceles, or equilateral		2010-12-01
		From Jessie: find the measures of the sides of triangle KPL and classify each triangle by its sides. my first problem would be K(-3,2) P(2,1) L(-2,-3) ...The three points they give you are the vertices of the triangle and you need to match them up. Draw the triangle and write in the vertices and the related point with the vertex. You will then do the distance formula three times to find the distance of all three sides. Once you have the three sides you can determine if it is scalene, isosceles, or equilateral...using the distance formula how do i solve this? Answered by Penny Nom.
	A man made circular lake		2010-11-25
		From ailish: A man made circular lake has a diameter of 338 m. A bridge is to be constructed across the lake in such a way that it is 119 m away from the center of the lake. How long is the bridge? Answered by Penny Nom.
	Two girls agree to mow a lawn		2010-11-23
		From Milorad: Two girls agree to mow a lawn 60m by 80m so that the first girl cuts one half by cutting a uniform strip around the lawn. How wide a strip should the first girl cut? I've been struggling with the question above, mainly with the equation and I have set it up as 2400=(60-2x)(80-2x), if this is incorrect I would like to know where I've gone wrong and also would like a full answer to see it properly done. I need an algebraic answer and not one with a diagram. Answered by Penny Nom.
	i^i		2010-11-21
		From trale: Can we use e^ix=cosx+isinx for finding i^i like that: x= pi/2 => e^(ipi/2)=0+i then [e^(ipi/2)]^i=i^i.then we find i^i= 0,207879576.... is it true? can we give value for x for free?thank you. Answered by Harley Weston.
	Convert to multiplication		2010-10-23
		From angelina: how to covert 5+5+5=15 to multiplication Answered by Penny Nom.
	An exponential equation		2010-10-19
		From Sandi: Question from sandi, a student: I have several questions similar to this one and was wondering if you could walk me through this one. I'm totally lost on how to do it. Paramecia reproduce by splitting in two. In a laboratory flask, a colony of paramecia had an initial population of 500. Each day, the population of the paramecia was counted. The results are as listed. Time (in days)------Population 0-----------------------500 1-----------------------600 2-----------------------720 3-----------------------864 4----------------------1037 5---------------------1244 6---------------------1493 7----------------------1792 8---------------------2150 1.)Using graphing calculator make a scatter plot of the data in table. I think I did this part right I set my window at Xmin=0 Xmax=10 Xscl=1 Ymin=0 Ymax=2500 Yscl=100 Xres=1 2.) Determine an exponential equation to represent the population as a function of time without using a graphing calculator.I have no clue how to do this. 3.)Suppose the flask and food supply is large enough to support the trend of the population growth. Estimate the population of the colony when the time is 10 days. Answered by Penny Nom.
	Geocaching		2010-10-15
		From Clint: I am stuck on a puzzle for Geocaching which is a GPS game. I know it is a number matrix but don't know how to start. [1 -7 16 -3 -9; 1 -3 18 -20 -33] x [1 8 -9 3 5; 0 1 0 4 2; 0 0 1 2 1; 0 0 0 1 -1; 0 0 0 0 1] = ? Answered by Stephen La Rocque.
	What is the maximum weekly profit?		2010-10-10
		From Joe: A local artist sells her portraits at the Eaton Mall. Each portrait sells for $20 and she sells an average of 30 per week. In order to increase her revenue, she wants to raise her price. But she will lose one sale for every dollar increase in price. If expenses are $10 per portrait, what price should be set to maximize the weekly profits? What is the maximum weekly profit? Answered by Stephen La Rocque and Penny Nom.
	x/200+x/400+x/600+x/800		2010-10-08
		From Ashishthombre: step by step LCM of x/200+x/400+x/600+x/800 Answered by Penny Nom.
	Rectangular arrays		2010-09-29
		From Kim: My 4th grader has started working on rectangular array that shows 2 factors of a number. The problem reads on centimeter grid paper draw as many arrays as you can for each of the #'s 2,3,4, 5,6,7,,11,12,15 and 16. That would be great except I have no idea what they are talking about and I cannot offer any help to my daughter. Answered by Penny Nom.
	A Taylor polynomial for (lnx)/x		2010-09-29
		From Dave: I have a series problem that I cannot solve. The problem asks for you to compute a Taylor polynomial Tn(x) for f(x) = (lnx)/x. I calculated this poly out to T5(x) and attempted to use this to identify a pattern and create a series in order to calculate Tn(x). However, the coefficients on the numerator out to F5prime(x) are as follows: 1, -3, 11, -50, 274... Ok, so the negative is an easy fix -> (-1)^n-1. But the other coefficients are stumping me. I can't see any sort of pattern there and I've tried every trick I know. Is there another way to go about this? Thanks! Answered by Chris Fisher.
	limit as x approaches a of ((x^(1/2))-(a^(1/2)))/(x-a)?		2010-09-29
		From emily: limit as x approaches a of ((x^(1/2))-(a^(1/2)))/(x-a)? Answered by Penny Nom.
	May Lee's cake		2010-09-18
		From Wafa: May Lee bought a cake which is circular in shape. Her sister ate a quarter of the cake. Given that the area of the top surface of the remaining portion is 520 square cm, find the diameter of the cake. Answered by Penny Nom.
	Continuity		2010-09-18
		From Carina: Hi. My name's Carina and I'm currently a sophomore in high school. I'm having a lot of difficulties in AP Calculus with continuity, one-sided limits, and removable discontinuities. Basically, I have no idea how to do them or even what they are. I read the lesson but I still don't get it. Can someone put it in simpler terms so I can understand how to complete my questions? Thank you! Answered by Robert Dawson.
	Two perpendicular chords		2010-09-11
		From edwin: two perpendicular chords AB and CD intersect at P. if X,Y are their midpoints and M the centre of the circle, prove that MP=XY. I do not a have clue on how to do it so can you please help me with it Answered by Robert Dawson.
	Maximizing the volume of a cylinder		2010-08-31
		From Haris: question: the cylinder below is to be made with 3000cm^2 of sheet metal. the aim of this assignment is to determine the dimensions (r and h) that would give the maximum volume. how do i do this? i have no idea. can you please send me a step-to-step guide on how t do this? thank you very much. Answered by Penny Nom.
	Three cars		2010-08-30
		From Anil: 3 cars are moving at speed of 4 kmph,5.5 kmph and 8 kmph in a circular track.The circular track has a distance of 11 km. What is the time taken for all the 3 cars to meet at the starting point ? Answered by Stephen La Rocque.
	A max min problem		2010-08-19
		From Mark: a rectangular field is to be enclosed and divided into four equal lots by fences parallel to one of the side. A total of 10000 meters of fence are available .Find the area of the largest field that can be enclosed. Answered by Penny Nom.
	Two cars on a circular track		2010-08-12
		From david: If two cars starts to drive at point 1 and go in a circle when will they meet? (one cars speed is faster the other ) all I need is a formula Answered by Tyler Wood.
	70 cubic meters of mulch		2010-07-30
		From zsuzsi: i have 70 cubic meters of mulch to move and an 8 tonne truck to use how much tonnage is to 1 square meter so that i can work out how many trips i need to make Answered by Penny Nom.
	The area of a hexagon		2010-07-28
		From Katie: Hi i have to find the area of a hexagon with only the side length 2cm given would you be able t help? Answered by Walter Whiteley.
	An 18ft round pool		2010-07-19
		From christine: will an 18ft round pool fit on a 12x16 ft rectangular cement slab? Answered by Tyler Wood.
	777777 times 111111		2010-07-07
		From Chew: What is 777777 times 111111 without using a calculator? Answered by Chris Fisher.
	Maximize the floor area		2010-07-07
		From shirlyn: A rectangular building will be constructed on a lot in the form of a right triangle with legs of 60 ft. and 80 ft. If the building has one side along the hypotenuse, find its dimensions for maximum floor area. Answered by Penny Nom.
	(x^3 + 11x) is divisible by 6		2010-06-24
		From PT: Given that x is a non-zero integer, how do you show that for all values of x, (x3 + 11x) is divisible by 6? I know it works but how do I answer the "all values of x" part? Thanks in advance! Answered by Robert Dawson.
	A max/min problem		2010-06-12
		From valentin: What is the maximum area of an isosceles triangle with two side lengths equal to 5 and one side length equal to 2x, where 0 ≤ x ≤ 5? Answered by Harley Weston.
	Compound interest		2010-06-01
		From Kenneth: Hello: I have a question regarding the following compound interest and future value calculation. Year 1 P + rP equals balance after the first year. Year 2 (P + rP) + r(P + rP) equals balance after the second year. Year 3 ? equals balance after the third year. This question is in two parts. 1. What would follow for year three? 2. I know that a pattern will develop. What will it be so that I can determine the extended pattern for following years ? Answered by Penny Nom.
	Integration of sin^3 (2x)		2010-05-29
		From ascher: how do you integrate this equation ∫ sin^3 (2x) dx Answered by Robert Dawson and Penny Nom.
	Weighing a 1000 lb cylinder on a 500 lb scale		2010-05-28
		From Jerry: I am trying to weigh a large possibly 1000 lb cylinder on a 500 lb scale, is this possible? If so what is the actual formula to figure out the correct weight? I am told it is possible with the fulcrum method but have not been able to find a formula. Thanks Jerry Answered by Robert Dawson.
	Two problems		2010-05-27
		From debbie: Question from debbie, a parent: hi, i have a daughter and she asked me a maths question I cannot solve. I was just wondering if you can give me the answers plus the working out so I could explain to my daughter, 1. The leftmost digit of a six-digit number N is 1. If this digit is removed and then written as a rightmost digit, the number thus obtained is three times N .Find N. 2. Four friends are racing together down a flight of stairs. A goes 2 steps at a time, B 3 steps at a time. C 4 steps at a time and D 5 steps at a time. The only steps which all four tread on are the top one and the bottom one. How many stairs in the flight were stepped on exactly once? Answered by Penny Nom.
	An optimization problem		2010-05-23
		From Marina: Hello, I have an optimization homework assignment and this question has me stumped..I don't even know A hiker finds herself in a forest 2 km from a long straight road. She wants to walk to her cabin 10 km away and also 2 km from the road. She can walk 8km/hr on the road but only 3km/hr in the forest. She decides to walk thru the forest to the road, along the road, and again thru the forest to her cabin. What angle theta would minimize the total time required for her to reach her cabin? I'll do my best to copy the diagram here:                              10km Hiker_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _Cabin       \                           |                              /        \                          |                             /      f  \                      2km                          /          \                        |                           / theta   \___________________________ /                             Road Answered by Penny Nom.
	The rejection region		2010-05-01
		From Mong: In Tests of Hypothesis, what is the decision when the test statistic we compute from the sample information is exactly equal to the critical value? that is, we reject null hypothesis or do not reject it? Thanks! Answered by Chris Fisher.
	The rate of change of y with respect to x		2010-04-29
		From Tom: I just had a quick calc question about wording that wasn't ever addressed in class. When the book says "the rate of change of y with respect to x", should it be considered how fast y is changing in comparison to x? I ask because the textbook says that "y is changing 3 times faster than x, so the rate of change of y with respect to x is 3." I'm use to rate being like velocity, as in units of distance per units of time. All we're told in class is that it's the slope of the tangent line, I was hoping you could clarify for me what exactly is meant by the wording of a "rate of change of something with respect to something else". More specifically, what "rate" and "with respect to" mean within this context? Thanks for your time Answered by Harley Weston.
	A trig equation		2010-04-28
		From Steve: 2cos^2(X)-2sin^2(x)+1=0 Answered by Harley Weston.
	cos(x) = sin(x - 1)		2010-04-28
		From alex: In the equation cos x = sin x-1 for -pi/2 A: solve for x graphically B: solve algebraically and prove the solution is correct. Alex Answered by Penny Nom.
	y = - log(x)		2010-04-28
		From Alex: y= - log(x), where y = 4.3 solve for x. Answered by Harley Weston.
	A rectangular prism		2010-04-27
		From Savannah: A rectangular prism is made of exactly 8 cubes. Find the length, width, and height. Answered by Penny Nom.
	A rectangular garden		2010-04-25
		From Billy: Tanisha wants to make a rectangular garden with a perimeter of 38 feet. What is the greatest area possible that tanisha can make the garden? Answered by Penny Nom.
	If (x, 4) is equidistant from (5, -2) and (3, 4), find x.		2010-04-21
		From abeth: If (x, 4) is equidistant from (5, -2) and (3, 4), find x. Find the point on the y - axis that is equidistant from (-4, -2) and (3, 1). Answered by Penny Nom.
	What are the dimensions of the box?		2010-04-13
		From Steven: The longest rod that will just fit inside a rectangular box, if placed diagonally top to bottom, is 17 inches. The box is 1 inch shorter and 3 inches longer than it is wide. How much must you cut off the rod so that it will lie flat in the bottom of the container? What are the dimensions of the box? Answered by Robert Dawson.
	Integrate the ((4th root of x^3)+1) dx		2010-04-12
		From Bridget: integrate the ((4th root of x^3)+1) dx Answered by Tyler Wood.
	The derivative of y=x^x		2010-04-09
		From David: So, its David, and I was wondering about the derivative of y=x^x. I have often seen it be shown as x^x(ln(x)+1), but when I did it through limits it turned out differently. Here's what I did: It is commonly know that df(x)/dx of a function is also the limit as h->0 of f(x+h)-f(x)/h. To do this for x^x you have to start with lim h->0 ((x+h)^(x+h)-x^x)/h. The binomial theorem then shows us that this is equal to lim h->0 (x^(x+h)+(x+h)x^(x+h-1)h+...-x^x)/h This is also equal to lim a->0 lim h->0 (x^(x+a)+(x+h)x^(x+h-1)h...-x^x)/h. Evaluating for a=0 you get lim h->0 (x^x+(x+h)x^(x+h-1)h...x^x)/h Seeing as the last 2 terms on the numerator cancel out you can simplify to a numerator with h's is each of the terms, which you can then divide by h to get: lim h->0 (x+h)x^(x+h-1)... which when evaluated for h=0 gives us: x(x^(x-1)). This statement is also equal to x^x. This contradicts the definition of the derivative of x^x that is commonly shown. So, my question is: can you find any flaws in the logic of that procedure? I do not want to be shown how to differentiate x^x implicitly because I already know how to do that. Answered by Robert Dawson.
	A model for the population of a Canadian city		2010-04-07
		From jess: Let t^2 represent t-squared. The population of a Canadian City is modelled by: f(t) = 12t^2 + 800t + 40,000, where t is the time in years. When t= 0, the year is 2007. a) According to the model, what will the population be in 2010? B) In what year is the population predicted to be 300,000? Answered by Penny Nom.
	A max min problem		2010-04-06
		From Terry: The vertex of a right circular cone and the circular edge of its base lie on the surface of a sphere with a radius of 2m. Find the dimensions of the cone of maximum volume that can be inscribed in the sphere. Answered by Harley Weston.
	The derivative of cos^3x		2010-04-06
		From Erson: Find y' of the given function: y = cos^3x. Answered by Harley Weston.
	Sand falling off a conveyer		2010-04-02
		From Katherine: sand is falling off a conveyer onto a pile at the rate of 1.5 cubic feet per minute. The diameter of the base is approximately twice the altitude. At what rate is the height of the pile changing when it is 10 feet high? Answered by Penny Nom.
	Pyramids and parallelograms		2010-04-01
		From Vivi: Hi, my name is Vivi, and math teacher is giving a geometry test. I tend to forget how to find the surface area and volume of triangular pyramids and parallelograms. Do you have a way of remembering how to find the surface area? Answered by Harley Weston.
	A champagne pyramid		2010-03-22
		From Kathy: I have 680 champagne glasses and my pyramid can only be 15 levels high. How many glasses need to be on each level? Is there a formula I can use? Answered by Robert Dawson.
	Water in a culvert		2010-03-18
		From Chip: Hello, I have a problem to which I know there must be an analytical solution - but as it has been 50 years since I studied math I can't remember quite how to do it!! I have a 12" round culvert in my yard that runs water all year. I would like to be able to calculate the flow through the culvert by measuring the depth of water flowing through and measuring the speed of the current. I can measure the depth and the speed, but I forget how to calculate the cross section of the flow. If you could help I would greatly appreciate it. Thank you Answered by Penny Nom.
	Angular velocity		2010-03-17
		From Lindsay: Determine the angular velocity, in radians per second, of a 14-inch car wheel, if the car is traveling at 60 miles per hour Answered by Harley Weston.
	An irregular octagon		2010-03-09
		From Gayle: Question from Gayle: I am building an irregular shaped octagon wooden box. The measurements are 291/2 inches by 211/2 inches. Sides are 12 inches. It will be 36 inches high. What would the cutting angles degrees be? Answered by Harley Weston.
	0.999 ^ (500)		2010-03-07
		From debra: I just need to know how to solve the following problem without using a calculator: .999 ^ (500). I know the answer is .606, I just want to do it by hand since I can't use a calculator on my test. Answered by Penny Nom and Claude Tardif.
	The integral of X^3/the square root of 1-x^2 dx		2010-03-07
		From William: The integral of X^3/the square root of 1-x^2 dx. Answered by Harley Weston.
	The base area of rectangular prism		2010-03-05
		From Desiree: How do you find the base area of rectangular prism that has 4 cm by 4cm by 6cm ? Answered by Penny Nom.
	1/6 x 5 x 12 = what		2010-02-19
		From dana: 1/6 x 5 x 12 = what Answered by Lorraine Dame.
	The center of a rectangular room		2010-02-16
		From Diana: Consider a rectangular room, 15 feet wide, 30 feet long and 12 feet high. What is the exact distance from any of the 8 corners of the room and its geometric center? Can you write a generic formula for such a distance? And if we keep the same proportions on all dimensions, can you write an expression for the same distance as a function of the floor perimeter? Answered by Penny Nom.
	Two bus routes		2010-02-03
		From kiyah: from 4:30 pm to 6:30 pm the route 1 bus stops every 12 min at the gym's bus stop. the route 2 bus stops there every 15 min. if both buses are now at the stop and schedule is kept, how long will it be before both buses will be at the stop again? Answered by Penny Nom.
	Everything in a cube 2 miles long?		2010-01-31
		From Naresh: in a book, i got to read this : Is it possible to pack the entire population of earth and everything that was created by humankind in a cube whose edges are 2 miles long ? Is it possible? Thanks. Answered by Stephen La Rocque.
	The inradius of an icosahedron		2010-01-21
		From fnavroth: Suppose you have an equilateral triangle. The area of the triangle is exactly 1200 square centimetres. Now suppose you have twenty of those triangles. It's possible to assemble those twenty triangles into a closed three-dimensional shape, a regular polyhedron. What would be the volume, in cubic centimetres, of the largest sphere that could fit inside the shape? Answered by Chris Fisher.
	Loading a headboard in a uhaul		2010-01-20
		From gina: I have a uhaul 9'10" long 4"9"wide 4'7"height I have a headboard 74 inches in height would it fit the box diagonally Answered by Penny Nom.
	A cone circumscribed about a given hemisphere		2010-01-19
		From Neven: The cone of smallest possible volume is circumscribed about a given hemisphere. What is the ratio of its height to the diameter of its base? (G.F.Simmons, Calculus with Analytic Geometry, CH4 Applications of Derivatives) Answered by Chris Fisher.
	A schedule for a pool tournament		2010-01-14
		From john: I need to know how to set up a pool tournament 12-14 players playing once a week, either 10-12 weeks whichever works out the best, what players would play what players week one through week ten or twelve? I hope you can help, I cant figure out the formula. thanks John Answered by Victoria West.
	A triangular prism		2010-01-13
		From Breon: what is the formula for a triangular prism? Answered by Robert Dawson.
	Trigonometry and picture hanging		2010-01-13
		From george: The top of a picture 1m high 0.8m from the ceiling. At a point on the ceiling directly in front of the picture, we wish to install a light so that the angle subtended by the picture equals to the angle of depression of the top of the picture. How far out from the wall should the light be installed? Answered by Penny Nom.
	Related Rates Problem		2010-01-12
		From Neven: A woman raises a bucket of cement to a platform 40 ft above her head by means of a rope 80 ft long that passes over a pulley on the platform. If she holds her end of the rope firmly at head level and walks away at 5ft/s, how fast is the bucket rising when she is 30 ft away from the spot directly below the pulley? (G. F. Simmons, Calculus with Analytic Geometry, pg.142) Answered by Penny Nom.
	A pair of simultaneous equations		2010-01-09
		From Yumiko: Solve the following pair of simultaneous equations. x^2 -4x = y^2-4 3y=2x - 3 Answered by Penny Nom.
	A sports schedule for the ymca		2010-01-08
		From Erich: i have to make a sports schedule for the ymca. i have 7 teams. they need to play each other 2 times. we have 3 time slots per night. i would like them to have an even number of time slots thru the season. one team must have abye each week. can you chow mw the schedul. example time 1 team 1 vs. team 2. time 2 team 3 vs. team 4 time 3 team 5 vs. team 6. team 7 bye week 1. Answered by Victoria West.
	A networking event		2010-01-07
		From Tricia: I have 70 people to go around to 10 tables with 7 at each table. only 6 from each table will rotate each time. There is 1 table monitor that always stays at same table. How do I make the rotation so everyone moves and gets to see all 70 people at the networking event? Answered by Robert Dawson.
	Dividing seashells among girls		2010-01-06
		From Eileen: A group of girls collected some seashells from the beach. They tried to divided these seashells equally among them. If each girl received 8 seashells, they would need 5 more seashells. If each girl received 7 seashells, they would have 3 seashells extra. How many seashells did they collect from the beach altogether? Answered by Robert Dawson and Penny Nom.
	A triangular pyramid		2010-01-05
		From ally: how many vertices, edges, faces in a triangular pyramid? Answered by Robert Dawson.
	Figure out the square root of something		2009-12-20
		From eric: is there an ez equation to figure out the square root of something? Answered by Harley Weston.
	A pile of sand		2009-12-16
		From Malik: Sand is leaking out of a hole at the bottom of a container at a rate of 90cm3/min. As it leaks out, it forms a pile in the shape of a right circular cone whose base is 30cm below the bottom of the container. The base radius is increasing at a rate of 6mm/min. If, at the instant that 600cm3 have leaked out, the radius is 12cm, find the amount of leakage when the pile touches the bottom of the container. Answered by Harley Weston.
	Energy in calories		2009-12-15
		From Josephine: A soft drink manufacturer claims that a new diet soft drink is now "low Joule". The label indicates that the available energy per serving is 6300 J. What is the equivalent of this energy in calories? (1 Calorie=1000 cal) Answered by Robert Dawson.
	f(x)=x+2sinx		2009-12-12
		From amroziz: for which values of x does the graph of f(x)=x+2sinx have horizontal tangent Answered by Harley Weston.
	How fast is the distance between the two cars decreasing?		2009-12-08
		From Jenny: Two cares are on a collision course toward point P. The paths of the two cars make a 30 degree angle with each other. The first car is 40 km from P, and traveling toward P at 16 km/hour. The second car is 50 km from P, traveling at 20 km/hour. How fast is the (straight line) distance between the two cars decreasing. (Hint: Law of Cosines) Answered by Harley Weston.
	Solving two equations, one with a square root		2009-11-23
		From kacie: y = square root of x+3 x-4y = -7 im having trouble with this problem...i have to find where they intersect. Answered by Harley Weston.
	The triangle formed by the tangent and the coordinates axes		2009-11-23
		From Nirmala: Given that y=1/x, x is not equal to zero. Prove that the area of the triangle formed by the tangent and the coordinates axes is 2. Answered by Harley Weston.
	Angular speed		2009-11-19
		From Atalie: The engine of a sports car rotates at 5000 revolution per minute. Calculate the angular speed of the engine in radians per second, given that 2pi radians = 1 revolution Answered by Robert Dawson.
	A triangular shaped ditch		2009-11-12
		From Tim: I am planning on constructing a triangular shaped ditch the measures 550 meters in length, 6 meters wide at the surface, .3048 meters at the invert of the ditch and 2 meters deep. How many cubic meters of material will have to be excavated to construct this ditch Answered by Robert Dawson.
	f(x)= (e^x) / [(e^x)+(ex^2)]		2009-11-10
		From natalie: I'm trying to graph the function, f(x)= (e^x) / (e^x)+(ex^2) [e to the x divided by e to the x plus e times x squared] I know that there aren't any vertical asymptotes, but is there a horizontal asymptote? and also, I'm stuck on finding the concavity for this graph. I tried to find f "(x), but it came out to be really long and I am not sure how to find the x values for f "(x) without using a graphic calculator. thanks, natalie Answered by Chris Fisher and Harley Weston.
	At what rate are the people moving apart?		2009-11-01
		From saira: A man starts walking north at 4 ft/s from a point P. 5 minutes later a woman starts walking south at 5 ft/s from a point 500 ft due east of P. At what rate are the people moving apart 15 minute after the woman starts walking ? Answered by Harley Weston.
	A path around a pond		2009-10-31
		From adeniji: find the area of a concrete path 2m wide surrounding a circular pond 12m in diameter Answered by Penny Nom.
	Painting a dome		2009-10-30
		From Jessica: A hemispherical dome with a radius of 50 ft will be given a coat of paint .01 inch thick. The Contractor for the job wants to estimate the number of gallons of paint needed. Use a differential to obtain an estimate (231 cubic inches/gallon) HINT: Approximate the change in volume of hemisphere corresponding to increase of .01 inch in the radius. Answered by Robert Dawson.
	Acreage calculation		2009-10-29
		From Angela: I am appraising a small portion of property for a right of way for a new sewer line. I have appraised many similar projects in the past; however the engineer always calculated the exact acreage and/or dimensions of the parcel being taken. My survey states the following: "141 linear ft. of 25' permanent R/W. I divided the linear feet x 12 and mult. by 25 to get the square footage, but it just doesn't seem right. Any suggestions? Am I missing something? Answered by Robert Dawson.
	An irregular quadrilateral		2009-10-29
		From riya: what is irregular quadrilateral? Answered by Penny Nom.
	Is it a rectangle?		2009-10-29
		From sefora: The coordinates of the vertices of quadrilaterals are given. Draw each quadrilateral on a grid. Determine whether it is a rectangle (show your work) P(5,1), Q(-4,4), R(-6,-2), S(3,-5) Answered by Penny Nom.
	Graphing y=(4-x^2)^5		2009-10-25
		From natalie: I want to graph the curve of y=(4-x^2)^5 without using a graphing calculator. To do this, I'm suppose to find: domain, y and x intercepts, asymptotes, intervals of increase/decrease, local max/min, concavity and points of inflection. I got all the way to the step where I'm solving the concavity and I'm stuck. I found the f"(x) and it came out to be really large polynomial. I want to know how I can solve for the x of f"(x) without the use of a graphing calculator, when the polynomial has x^6 and x^8. Thank you so much, natalie Answered by Harley Weston.
	A max/min problem		2009-10-12
		From avien: a rectangle has a line of fixed length Lreaching from the vertex to the midpoint of one of the far sides. what is the maximum possible area of such a rectangle? SHOW SOLUTION USING CALCULUS Answered by Penny Nom.
	Golf for 8		2009-10-10
		From Chris: I have a group of 8 golfers who will be playing three rounds, What is the best formula so we can all try to play with different people during the 3 rounds . Answered by Victoria West.
	24 golfers, 6 days		2009-10-03
		From patrick: i need a pairing schedule for 24 golfers for six days playing in foursomes. Please Answered by Victoria West.
	A line tangent to a parabola		2009-10-01
		From kanchan: for what value of c a line y=mx+c touches a parabola y^2=4a(x-a) Answered by Penny Nom.
	24 golfers		2009-10-01
		From Peter: I am working on a 19 week golf schedule with 24 golfers, and I would like to know how to make up six foursomes each week without having a player paired with the same golfers. Answered by Victoria West.
	5 x 8 + 6 divided 6 - 12 x 2		2009-09-24
		From Susan: 5 x 8 + 6 divided 6 - 12 x 2. I am not sure of the rules of operation for this type of question Answered by Penny Nom.
	24 golfers: 4 days		2009-09-21
		From Steven: We have 24 golfers (6 A's, 6 B's, 6 C's & 6 D's) playing 4 days. Each day a foursome consist of an A, a B, a C & a D player. Can you give me a pairing list so that no two golfers will play on the same foursome for the 4 days? Answered by Chris Fisher and Victoria West.
	Dart teams		2009-09-18
		From Sally: I have 14 dart teams. Each team has a home bar.Usually it is one week home, the next week away. I have 3 locations that have one board only, yet have 2 teams at each location. I have one location that has 2 dart boards, and 3 teams. The last location have 3 dart boards and 4 teams.Can you make me a schedule that will be home and away, and every teams plays each other twice. In case you are wondering, the bars sponsor the teams.Thank you. Sally Answered by Robert Dawson.
	solve integral of ( x^2+x+1)^5		2009-09-18
		From jaka: solve integral of ( x^2+x+1)^5 Answered by Robert Dawson.
	Common multiples of 36 and 48		2009-09-15
		From Kamaldeep: Find the first 2 common multiples of 36 and 48. Answered by Penny Nom.
	Jogging and swimming		2009-09-11
		From Brandon: Trevor swims jogs 3 days and swims every 4 days. How often does he jog and swim on the same day Answered by Leeanne Boehm.
	A circular border around a pool		2009-09-08
		From Calvin: A pool in the shape of a circle measures 10 feet across. One cubic yard of concrete is to be used to create a circular border of uniform width around the pool. If the border is to have a depth of 3 inches, how wide will the border be? ( 1 cubic yard=27 cubic feet ) Answered by Stephen La Rocque.
	4 couples seating themselves at a round table		2009-09-04
		From Hui: Q: 4 couples seating themselves at a round table. Men must seat together and women seat together. How many ways are there? Answer in the printed text is 576. I got 144. Pls advice. Answered by Claude Tardif.
	An area problem		2009-08-30
		From Amber: Area of hexagon ABCDEF with the vertices (3,0) (7,0) (9,2) (7,4) (3,4) (1,0) Answered by Harley Weston.
	Simultaneous equations		2009-08-28
		From onias: solve 3/a - 2/b = 1/2 , 5/a + 3/b = 29/12 Answered by Robert Dawson.
	A football schedule		2009-08-14
		From Bill: I am having trouble with a football schedule that has two divisions of five teams each, 1-5 and 6-10. 1-5 will play against each other in the first 4 weeks and also the the last 4 weeks with teams 6-10 completing the middle of the schedule. The schedule is 13 weeks. Thank you for your time Answered by Chris Fisher and Victoria West.
	An antiderivative problem		2009-08-13
		From Indrajit: ∫4e^x + 6e^-x/(9e^x + 4e^-x)dx = Ax + Bloge(9e2x - 4) + C then A=?......B=?.....C=? plz solve it...."^" stands for "to the power of".... Answered by Harley Weston.
	A rectangular pen		2009-08-13
		From Kari: A rectangular pen is to be built using a total of 800 ft of fencing. Part of this fencing will be used to build a fence across the middle of the rectangle (the rectangle is 2 squares fused together so if you can please picture it). Find the length and width that will give a rectangle with maximum total area. Answered by Stephen La Rocque.
	Angular speed		2009-08-04
		From Mary: The engine of a sports car rotates at 5000 revolutions per minute (rpm). Calculate the angular speed of the engine in radians per second. Use 2 radians = 1 revolution. Answered by Penny Nom.
	Torricelli's trumpet		2009-07-29
		From Gary: I was reading about torricelli's trumpet which is described by the equation1/x which is then rotated around the x axis which results in a figure which looks like a trumpet. Now in order to find the volume the integral 1/x^2 dx is used which diverges when integrated so the volume is finite.However if you integrate 1/x dx which is the formula on the plane the answer diverges. Now if you took an infinite area then rotated it around the x axis shouldn't you get an infinite volume? Notice the area I am talking about is under the line 1/x not the surface area of the trumpet which is what the painters paradox is about What am I missing? Thanks Answered by Robert Dawson.
	Golfing with an unpopular golfer		2009-07-23
		From Ian: "We are a group of 8 golfers, one of whom is unpopular. How can we construct a schedule, of two foursomes, so that each person is scheduled to play with him the same number of times. What does the week by week schedule look like?" Answered by Robert Dawson and Victoria West.
	Annular sector		2009-07-20
		From Ed: What is the name for the section of a flat ring (annulus)? Similar to a section on a radar screen, a quadrilateral but the top and bottom are curved. Answered by Robert Dawson.
	A golf league with 12 players		2009-07-17
		From Jane: My weekly golf league has 12 players in 4 threesomes. How many weeks would it take to play everyone once and not have too many duplications? What would be the schedule each week? Thanks Answered by Victoria West.
	Finding the Line Joining Perpendicular Feet		2009-07-16
		From mukulu: Please help I've been tryng to search in your data but i failed to get the solution Find the equation of a straight line joining the feet of the perpendiculars drawn from the point A(1,1) to the line 3x-3y-4= 0 and 3x+y-6=0. Answered by Janice Cotcher.
	The surface area of a rectangular pyramid		2009-07-13
		From Shivani: What is the surface area of a rectangular pyramid with a length of 6 inches, a width of 7 inches and a SLANT height of 4 inches. Answered by Penny Nom.
	Multiplying Large Numbers		2009-07-09
		From Jessica: What is 12 billion X 6 trillion? Answered by Janice Cotcher.
	Multiplying Large Numbers		2009-07-09
		From Jessica: What is 12 billion X 6 trillion? Answered by Janice Cotcher.
	Simultaneous Equations		2009-07-06
		From Mukulu: Solve the equation simultaneously X/5=(Y+2)/2= (Z-1)/4 ……………….eqt 1 3X+4Y+2Z-25=0 ………………eqt 2 Answered by Janice Cotcher.
	Investing in multiple accounts		2009-06-26
		From Kenneth: Hello: If an investor has $1000.00 to invest in multiple accounts, and he wants a total return of 4%, is there one calculation that can be used to determine what these amounts could be even though there may be numerous amounts used as answers for most of the following examples? For example, Invest $1000.00 @ 2% and 5% for total return of 4%. Invest $1000.00 @ 2%, 3% and 5% for total return of 4%. Invest $1000.00 @ 2%, 3%, and 5% for total return of 4%. Invest $1000.00 @ 2%, 3%, 4% and 5% for total return of 4%. etc. Answered by Robert Dawson.
	The surface area of a tank		2009-06-25
		From Charles: I need to calculate the external wall and top sqft surface area of a tank 54ft od x 15ft high with a dome top 54ft od x 8ft high. Answered by Penny Nom.
	(570 divided by 15) multiplied by (5 plus 26)		2009-06-24
		From Sherrie: What is the answer to this math question: (570 divided by 15) multiplied by (5 plus 26).......... Thank you, Sherrie:-) Answered by Penny Nom.
	The Pythagorean theorem		2009-06-24
		From supreet: What are some real-world applications of the Pythagorean theorem? and How are the Pythagorean theorem and the distance formula related? Answered by Harley Weston.
	Two questions from math class		2009-06-18
		From Con: Hello, My name is Con and my son is required to answer the following questions for his maths class. He has attempted Q1 through trial and error and has found the answer to 72453. Is this correct? He has attempted to draw the triangles described in Q2 in a number of ways and has found that BE can not equal ED and is dependent of angle BAC. Therefore, he claims that the triangle can not be drawn/practical. Is this correct or is there a slolution? Q1. Digits 2, 3, 4, 5 and 7 are each used once to compose a 5-digit number abcde such that 4 divides a 3-digit number abc, 5 divides a 3-digit number bcd and 3 divides a 3-digit number cde. Find the 5-digit number abcde. Q2. Let ABC be a triangle with AB=AC. D is a point on AC such that BC=BD. E is a point on AB such that BE = ED = AD. Find the size of the angle EAD. Con Answered by Chris Fisher.
	The integral of x^x		2009-06-18
		From ANGIKAR: what would be the integration of (X^Xdx)? give answer in details. Answered by Robert Dawson and Harley Weston.
	Triangular Numbers		2009-06-16
		From Chinonyerem: Question from Chinonyerem, a student: Each of the numbers 1 = 1, 3 = 1+2, 6 = 1+2+3, 10 = 1+2+3+4 ,... represents the number of dots that can be arranged evenly in an equilateral triangle:                             .                   .        . .         .         .       . . .             ... .      . .      . . .    . . . . This led the ancient Greeks to call a number TRIANGULAR if it is the sum of consecutive integers, beginning with 1. Prove the following facts concerning triangular numbers: (a) A number is triangular if and only if it is of the form n(n+1)/2 for some n >= 1 (b) The integer n is a triangular number if and only if 8n+1 is a perfect square (c) The sum of any two consecutive triangular numbers is a perfect square (d) If n is a triangular number, then so are 9n+1, 25n+3, and 49n+6 Answered by Penny Nom.
	11 golfers playing 4 rounds		2009-06-14
		From Brian: I have 11 golfers playing 4 rounds of golf. It would be great if we could play at least once with everybody. I realize we will have 2 foursomes and 1 threesome each round...can you help? Answered by Victoria West.
	The product of gradients between 2 perpendiculars lines		2009-06-11
		From Alister: how do i prove that the product of gradients between 2 perpendiculars lines equal to -1.... Answered by Penny Nom.
	A rotating schedule		2009-06-10
		From Doreen: We have seven people - we want to create a rotating schedule for two people at a time to attend one day a week with each person working the same amount of days in the year. Answered by Victoria West.
	Cubic yards in an Irregular Shape		2009-06-08
		From ron: hi i have a berm 100'w x200'L at the base and 9'tall the top is 85'L x 20'w i would to find out how many cubic yards are in the pile and the formula Answered by Janice Cotcher.
	An aeroplane flying in a wind		2009-06-02
		From Maria: The aeroplane flies in a wind of speed 50 kph from the direction S80◦W. However, the direction in which it is pointed, and its speed in still air, are such that its resultant speed and direction are 800 kph, and direction N71.6◦E I need to find the size of the angle between v and vw, in degrees to one decimal place, and find the speed at which the aeroplane would fly if the air were still, to the nearest kph. It would help me greatly if I could see a diagram illustrating the velocity va that the aeroplane would have if the air were still, the velocity vw of the wind, and the resultant velocity v of the aeroplane (diagram should be in the form of a triangle illustrating how one velocity vector is the sum of the other two) Thanks Answered by Harley Weston.
	The position of the fulcrum		2009-05-23
		From jim: I think I need a formula. I need to know how far an object will be lifted. A beam is 246 inches long on one side of the fulcrum, and 41 inches on the other side, if I push down 36 inches on the long side of the beam, how much will the short side move up? Answered by Stephen La Rocque.
	28 teams 14 lanes , 9 weeks no repeats		2009-05-19
		From paul: 28 teams 14 lanes , 9 weeks no repeats Answered by Karen Meagher.
	Fraction Word Problem		2009-05-13
		From Sonya: Debbie wants to eat 1/6 of her 12 pieces of candy. How many pieces did she eat ? Answered by Janice Cotcher.
	16 teams, 15 weeks, would like to pair up with no repeats.		2009-05-12
		From Kimberly: 16 teams, 15 weeks, would like to pair up with no repeats. Thank you so very much. Answered by Robert Dawson.
	differentiate y sin[x^2]=x sin[y^2]		2009-05-11
		From mamiriri: derivate y sin[x^2]=x sin[y^2] Answered by Harley Weston.
	Six teams, two sites, and four days		2009-05-08
		From John: I have six teams, two sites, and four days. We have decided that we want to have tri-meets, where there would be three teams competing against each other at the same site each day. Here is the problem, I need to make sure that each team sees each other team at least once and each team goes to each site at least once. Answered by Victoria West.
	The dimensions of a toy chest		2009-05-07
		From charlotta: My son needs to find the 3 dimensions of a toy chest that has to have a volume of 24 cubic feet can you show how to get the answer Answered by Penny Nom.
	Perpendicular lines		2009-05-07
		From shabnam: the line presented by y= 3x-2 and a line perpendicular to it intersect at R(1,1). Determine the equation of the perpendicular line Answered by Stephen La Rocque.
	A 6 team social softball league		2009-05-02
		From Don: Hi We have a 6 team social softball league with only two fields. Each team plays two games each Saturday. We have three time slots 10:00, 12:00 and 2:00 We play for 11 Saturdays and than have a 2 weekend playoff. All teams prefer double headers vs the split at 10:00and 2:00. How do we schedule as balanced a schedule as possible and minmize the splits ? Thanks Don Answered by Laura Morrison and Victoria West.
	Rectangular prisms		2009-05-01
		From deborah: Could you please tell me some examples of different objects in the real world of rectangular prisms? Answered by Harley Weston.
	The integral of a to power x squared		2009-04-28
		From JIM: WHEN I ATTENDED U.OF T. (TORONTO ) MANY YEARS AGO WE WERE TOLD THE FOLLOWING INTEGRAL COULD NOT BE SOLVED : a to power x squared . is this still true ? CURIOUS , JIM Answered by Robert Dawson.
	Completing the square		2009-04-27
		From Daniel: I tried following an example of yours but I still couldn't figure it out. Here is my question, 2x^2 - 6x + 1 = 0. Any help would be greatly appreciated. Answered by Stephen La Rocque.
	Common multiples of 2 and 5		2009-04-23
		From pat: what are the common multiples of 2 and 5, through 30, because i been working on it for hours Answered by Robert Dawson and Stephen La Rocque.
	Two regular hexagons		2009-04-21
		From niko: Two regular hexagons are ____________ similar. Answered by Stephen La Rocque.
	Volume of a prism		2009-04-21
		From David: The base of a rectangular prism has an area of 15.3 square inches and a volume of 185.13 cubic inches. Write an equation that can be used to find the height "h" of the prism Answered by Robert Dawson and Stephen La Rocque.
	A perpendicular line in standard form		2009-04-21
		From Kristy: Can you help me with this equation? Find the equation, in standard form of the line perpendicular to 2x-3y=-5 and passing through (3,-2) With the equation in standard form with all integer coefficient. Answered by Stephen La Rocque.
	A max-min problem		2009-04-20
		From Charlene: A fixed circle lies in the plane. A triangle is drawn inside the circle with all three vertices on the circle and two of the vertices at the ends of a diameter. Where should the third vertex lie to maximize the perimeter of the triangle? Answered by Penny Nom.
	28 golfers		2009-04-18
		From DON: HI, I HAVE 28 GOLFERS AND I NEED A SCHEDULE FOR 24 DIFFERENT DAYS THERE WILL BE 7 GROUPS OF 4 PLAYERS EACH DAY. ALL PLAYERS WOULD LIKE TO PLAY WITH ONE ANOTHER AS EVEN AS POSSIBLE (SAY 2 TO 4 TIMES EACH OVER THE 24 DAYS)...THANKS DON Answered by Victoria West.
	Exponential form		2009-04-16
		From Pete: Hi, How do you express ³√h^-4 in exponential form. I am having a lot of trouble with this one. thanks Pete Answered by Stephen La Rocque.
	10 yards of rubber mulch		2009-04-15
		From Donna: If I want to buy 10 yards of rubber mulch (bulk), but it only comes in 20 pound bags, how many bags do I need to buy? Answered by Harley Weston.
	Infinity and Aleph-Null		2009-04-14
		From Justin: Yes, I am reading the Paul Halmos book on Set theory, thanks for telling me how to get it! I was just wondering from your last answer though if the positive real infinity of calculus then corresponds to Aleph-null? I am sorry if this is a similar question to the one I asked before but I was just wondering about this! All the Best, Justin Answered by Robert Dawson.
	Choices at a restaurant		2009-04-13
		From Rob: There is a restaurant you get: Rice/Noodles (1) Main Ingredient (any) Sauce (1) 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7     8     9     10     11     12   So the question is how many different combinations are there. You can only have 1 rice/noodles in a selection and only 1 sauce in a selection but you can have between 1 and all twelve mains in a selection. there are 7 rice/noodles , 12 mains and 6 sauces. How many possibilies. I did it mentally in the restuarant, no pen, paper or calculater and i got 3276..i think thats wrong. please help Rob Answered by Robert Dawson, Stephen La Rocque and Claude Tardif.
	2sinB=3tanA		2009-04-10
		From Xanathax: ABC is a right-angled triangle. 2sinB=3tanA. Calculate the measure of angle A. Answered by Penny Nom.
	Winding paper after a break		2009-04-10
		From Olen: Question from Olen: I work in a paper mill and have been handed the task to search for a formula to determine how much paper needs to be added to a parent roll to make up the difference at the winder. (Ex. The spool diameter at the reel is 18.25" we measure roughly 33.5" to make two 58" rolls in the winder. If the is a paper break and the roll diameter in the winder is 30" how much do I add to a single parent roll (22" roughly) to make one 58 " and the 28" needed at the winder. I would appreciate any help to complete this task. I would like to be able to build a chart that operators can refer to based on what is needed. Thank you. Answered by Harley Weston.
	Positive real infinity and Aleph-null		2009-04-09
		From Justin: Hello, I was just wondering why does the positive real infinity correspond to Aleph-null? Thanks a lot for answering my question! Justin Answered by Ami and Robert Dawson.
	Parallel and perpendicular lines		2009-04-08
		From Blake: I need to know what the formula for working a problem. I need to know how to find if i line is parallel or perpendicular by only looking at the equation. i know you must know the slope but how do i find slope? Answered by Stephen La Rocque.
	Multiplication of polynomials		2009-04-07
		From Carla: I am struggling to understand Multiplication of Polynomials. No matter how hard I try to understand Multiplication of Polynomials, I just can't get it! The problem that I am trying to solve is this : -3x^3y(-y + 2 -x^2 + x) Answered by Robert Dawson.
	Sand falls from a conveyor belt		2009-04-01
		From Tracy: Sand falls from a conveyor belt at the rate of 10 cubic feet per minute onto a conical pile. The radius of the base is always equal to half the pile's height. How fast is the height growing when the pile is 5ft high? Answered by Stephen La Rocque.
	A spherical Tootsie Roll Pop		2009-04-01
		From Tracy: A spherical Tootsie Roll Pop you are sucking on is giving up volume at a steady rate of .8 ml/min. How fast will the radius be decreasing when the Tootsie Roll Pop is 20 mm across? Answered by Harley Weston.
	An isosceles triangle		2009-03-26
		From sela: An isosceles triangle has two equal sides of length 10 cm. Theta is the angle between two equal sides. a) Express area of a triangle as a function of theta b) If theta is increasing at a rate of 10 degrees/minute, how fast is area changing at the instant theta=pi/3? c) at what value of theta will the triangle have the maximum area? Answered by Penny Nom.
	A max-min problem		2009-03-24
		From Jay: Determine the area of the largest rectangle that can be inscribed between the x-axis and the curve defined by y = 26 - x^2. Answered by Harley Weston.
	The diameter of a roll of plastic		2009-03-24
		From truong: hi. i have trouble to calculate the diameter of the plastic roll. the sheet is 765 m long and 0.8 mm to wrap around the core 400 mm in dia. please help me with the formula to calculate the dia of plastic roll, thanks in advance Answered by Harley Weston.
	A rectangular open box		2009-03-21
		From tina: An open box is to be made from a rectangular piece of tin by cutting two inches squares out of the corners and folding up the sides. The volume of the box will be 100 cubic inches. Find the dimensions of the rectangular piece of tin. Answered by Stephen La Rocque.
	A dead fly is stuck to a belt that passes over two pulleys		2009-03-21
		From Jules: A dead fly is stuck to a belt that passes over two pulleys 6 inches and 8 inches in radius. Assuming no slippage,how fast is the fly moving when the large pulley (8 inches) makes 21 revolutions per second ? How many revolutions per second does the small pulley make ? How long will it take the dead fly to travel 1 mile ? Answered by Penny Nom.
	16 golfers		2009-03-18
		From Bill: We have 16 golfers. We golf for 5 days, in foursomes. It should work out that each player plays with each other player 1 time exactly. I just can't figure it out. Thank you in advance! Bill Answered by Claude Tardif and Victoria West.
	A 14 team league that is divided into 2 divisions		2009-03-07
		From Ronnie: I have a 14 team league that is divided into 2 divisions. We have a total of 18 weeks to play. I would like for each team to play the team in their division twice. The remaining 6 weeks would be played with the other division. Any help would be appreciated. Answered by Chris Fisher and Victoria West.
	A common tangent to two curves		2009-03-02
		From Jay: For what values of a and b will the parabola y = x^2 + ax + b be tangent to the curve y = x^3 at (1,1)? Answered by Penny Nom.
	Implicit differentiation		2009-03-01
		From Emily: determine the derivative y' at the point (1,0) y= ln(x^2+y^2) y'(1)= ?? Answered by Stephen La Rocque.
	36cm to the second power divide 10cm		2009-02-26
		From val: 36cm to the second power divide 10cn Answered by Penny Nom.
	A triangular pyramid		2009-02-26
		From Craig: Can you help with this question: Write the names of the faces and the number of each kind of face on a triangular pyramid? Answered by Penny Nom.
	Multiplying in different bases		2009-02-25
		From Susan: 11 base 2 X 22 base 3 + 33 base 4 = _________ base 5 Answered by Robert Dawson.
	A rectangular prism		2009-02-25
		From Christina: I am trying to find the area of the base of a rectangular prism where one cube=_1 cu in. The Answer is given in square inches. I also need the volume of the prism in cu in. For example length=3, w=2, h=5 Answered by Penny Nom.
	mutiplying decimals		2009-02-24
		From telly: how to do this sum0.24*0.398 Answered by Robert Dawson and Penny Nom.
	Time in a Swing		2009-02-22
		From Barb: I looked at the questions concerning a pendulum as I know I need to use this formula but I am stiil not able to figure this problem out. Can you help? If a child is on a swing with a 10 foot chain, then how long des it take to complete one cycle of the swing? I know I am suppose to use the formula 8T^2 = pi^2 L but I do not understand how to do this. Thanks Answered by Janice Cotcher.
	16 golfers playing one round of golf on each of four days		2009-02-22
		From Jim: I have seen solutions for other combinations of setting up a golf trip but I haven't seen one for my group. We have 16 golfers playing one round of golf on each of four days. Is there a way for all of them to play in foursomes so that everyone gets to play with everyone else? Thanks for your consideration. Answered by Chris Fisher.
	6 golfers playing 8 rounds		2009-02-21
		From evan: I have a group of 6 golfers playing 8 rounds. we would like to rotate the 3 somes so each person golfs with different people as many times as possible Answered by Chris Fisher.
	A ten player schedule		2009-02-19
		From john: I HAVE 10 PLAYERS ONE GAME PER NITE FOR 10 WEEKS WHO PLAYS WHO FOR WEEK 1 THRU 10 THANK YOU Answered by Victoria West.
	Implicit differentiation		2009-02-18
		From Sunny: Find slope of the tangent line to the curve 2(x^2+y^2)2=25(x^2–y^2) at (3,-1) Answered by Robert Dawson and Harley Weston.
	The area between the x-axis and a curve		2009-02-18
		From Lauren: This is from a homework question I can't figure out. Let R be the region in the fourth quadrant enclosed by the x-axis and the curve y= x^2 - 2kx, where k > 0. If the area of the region R is 36 then what is the value of k? Answered by Robert Dawson.
	The second derivative of h(x)=f(g(x))		2009-02-16
		From Kristina: If h(x)=f(g(x)), and is differentiable, then find h"(x). Answered by Robert Dawson.
	The surface area of a cube and rectangular prism		2009-02-16
		From Mhiko: how to derived the total surface area of a cube and rectangular prism using geoboard?? Answered by Robert Dawson.
	Nullity		2009-02-16
		From Justin: What exactly does the term nullity mean in the context of transreal numbers invented by Dr. James Anderson? Thanks for your help in answering this question! All the Best, Justin Answered by Robert Dawson.
	0/0		2009-02-15
		From Justin: Hello, I was just wondering, what is the difference between 0/0 being represented as nullity or as an indeterminate form? Justin Answered by Harley Weston.
	The height of a triangle		2009-02-14
		From GARIMA: IF THE SIDES OF TRIANGLE ARE GIVEN . HOW WE WILL CALCULATE THE HEIGHT OF TRIANGLE. Answered by Penny Nom.
	8 golfers, 5 rounds		2009-02-12
		From John: 8 of us are going on a golf trip next month. We are golfing 5 rounds. Is there any way that everyone can play with each other at least twice? I have been trying to figure it out but it always seems that someone plays with another golfer only once. Answered by Chris Fisher.
	9 golfers		2009-02-12
		From Beth: I am organizing a golf trip for 9 women. We are playing in threesomes and are playing four days. I would love to mix it up so that everyone gets to play with each other at least once. Any mathematical suggestions as to how I can make this happen?? Answered by Robert Dawson.
	A semi circular room		2009-02-11
		From Taylor: being 450pi (the area of a semi circle) how much money would it cost to lay carpet at $2.57 per foot??? if the area of a semi circular room is 450 pi ft then what is the volume being that the diameter is 60 feet and the ceiling is 16 feet tall Answered by Robert Dawson and Penny Nom.
	Solid figures		2009-02-10
		From Rebecca: I need to know the names of solid figures. I have several pictures that I need to answer what type they are. Thanks, Rebecca 3rd grade Answered by Penny Nom.
	A definite integral		2009-02-09
		From Mathata: Evaluate: integral from 0 to 1, x^2 e^x^3dx Answered by Harley Weston.
	Seating around a circular table		2009-02-09
		From Jenny: A committee of 15 -- 9 women and 6 men -- is to be seated at a circular table (with 15 seats). In how many ways can the seats be assigned so that no two men are seated next to each other? Answered by Victoria West.
	A triangular pyramid		2009-02-06
		From kamran: what would be an example of a triangular pyramid Answered by Stephen La Rocque.
	A trig limit		2009-02-05
		From Samantha: lim x-> 0 ( ( r*cos(wt +h) + r*cos(wt) )/ h ) Where r & w are constants. Answered by Harley Weston.
	Faces, edges and vertices		2009-02-04
		From sheila: what is the relationship between the number of faces and the number of edges of a triangular pyramid ? Answered by Penny Nom.
	A point on -8x^2+5xy+y^3=-149		2009-02-04
		From Vivian: Consider the curve defined by -8x2+5xy+y3=-149 a) find dy/dx b) Write an equation for the line tangent to the curve at the point (4,-1) c) There is a number k so that the point (4.2,k) is on the curve. Using the tangent line found in part b), approximate the value of k. d) write an equation that can be solved to find the actual value of k so that the point (4.2,k) is on the curve e) Solve the equation found in part d) for the value of k Answered by Harley Weston.
	12 golfers		2009-02-04
		From david: 12 golfers playing in 3 four balls over five rounds. can everyone play with everyone else at least once. Answered by Victoria West.
	Simultaneous equations with an xy term		2009-02-01
		From angelee: xy+5x-2y-10=0 2x+y=1 Answered by Penny Nom.
	7 golfers playing 4 days of golf		2009-01-30
		From Trish: I have 7 golfers and we are playing 4 days of golf. I would like to do pairings so that everyone gets to play with each other at least one time. Can you help with this? Not a math whiz here and looking for help. Thank you. Answered by Victoria West.
	limit sinx/x		2009-01-30
		From Jackie: how to evaluate limit sinx/x as x tends to zero if x is in degrees Answered by Stephen La Rocque and Harley Weston.
	A tennis schedule		2009-01-26
		From Lorraine: I need to create a tennis schedule. We have 8 players, but only 4 play at one time. I need to create a schedule for 34 matches, but of the 34 each player plays 17 times. Each player must also play with each of the other 7 the same number of times. For instance player 1 will play 17 times, and will play with the other players the same number of times as player 2 does. Is this even possible? Answered by Robert Dawson.
	An integral from 1 to infinity		2009-01-24
		From Ray: Determine the area bounded by the x-axis and the curve y=1/(x^2) from x=1 to x=infinity. A. 1.00 B. infinity C. indeterminate D. 2.00 Answered by Harley Weston.
	20 of us golf together in groups of 4		2009-01-24
		From D.: Every Sunday, 20 of us golf together in groups of 4. I am looking for a way that each of us play with 3 other people each week and ultimately get to play in groups that are unique. For instance if week 1, I play with 2, 3, 4 and then the next week I play with 5, 6, 7, and the 3rd week I play with 8, 9, 10 and so forth until I have played with everyone. Everbody else should be doing the same thing. Can you give me a schedule for this and how many weeks would it take for all of us to accomplish this where we all play with different combinations of people. (We should not play with the same person very often or even the same pairs of people but everyone should play with everybody else) I hope this makes sense........whew and thanks! Answered by Victoria West.
	Archimedes' formula for parabolic arches		2009-01-23
		From La: Use calculus to verify Archimedes' formula for y=9-x^2. Prove Archimedes' formula for a general parabolic arch. Answered by Harley Weston.
	In the shadow of a flagpole		2009-01-22
		From La: How fast is the length of the shadow of an 18 foot flagpole growing when the angle of elevation of the sun is 45 degrees and is decreasing at a rate of 10 degrees per hour? Answered by Harley Weston.
	The volume of a prism		2009-01-19
		From Mady: What is the general equation used to find the volume of a triangular prism? Answered by Robert Dawson and Harley Weston.
	Partial derivatives		2009-01-17
		From Meghan: I have a question I've been working at for a while with maxima/minima of partial derivatives. "Postal rules require that the length + girth of a package (dimensions x, y, l) cannot exceed 84 inches in order to be mailed. Find the dimensions of the rectangular package of greatest volume that can be mailed. (84 = length + girth = l + 2x + 2y)" Answered by Harley Weston.
	A 28 week golf schedule		2009-01-17
		From Don: You have a 12 man golf schedule playing 8 weeks. Can you go further and make it a 28 week schedule. 3 foursomes. any help would be greatly appreciated. Answered by Victoria West.
	A golf trip with 12 golfers		2009-01-16
		From Brad: I am organizing a golf trip with 12 golfers. We will play 5 rounds (3 foursomes each round) total and play two 9 holes matches per round (18holes). So two matches are created within each foursome. What are the possible combinations of foursomes so that everyone plays each other at least once with the least number of repeat matches? For example: Here are the foursomes for round 1:(1,2,3,4) (5,6,7,8) (9,10,11,12) match 1 round 1: 1vs2, 3vs4, 5vs6, 7vs8, 9vs10,11vs12 we can not split foursomes up for the second match (9 hole matches): So match 2 round 1: 1vs3, 2vs4,5vs7,6vs8,9vs11,10vs12 Answered by Victoria West.
	A line is perpendicular to another line		2009-01-16
		From Greg: A line is perpendicular to the line y=2x+3 and has the same x-intercept as x+3y+10. Find the equation of this line. Express your answer in the form of y=mx+b. Justify your answer. Answered by Robert Dawson.
	Multiplying negative numbers		2009-01-15
		From stephanie: hi, I'm currently working in a grade 8 class where the students are learning about integers. the students were asked to find examples of how integers are applied in real life. they were able to find aplications for: adding and subtracting both positive and negative integers. however, we could not find an example of where two negative integers would be either divided or multiplied together in real life. For example: (-2)(-4)= +8. please help. Answered by Harley Weston.
	A rectangular prism		2009-01-13
		From nika: How many bases does a rectangular prism have? What are they? Answered by Harley Weston.
	Negative rate of change		2009-01-12
		From hemanshu: when i have to find rate of change of decrease in any value my ans comes in negative why?????????? Answered by Penny Nom.
	16 golfers		2009-01-11
		From Bill: I have read many of your answers to similar questions but still need your assistance. We have 16 golfers that will be playing in 4 groups of 4 each day on an upcoming golf vacation. Can you suggest the best way to scheudle the individuals assigned to each daily foursome so that we have the most diversity in foursomes throughout the vacation. I am trying to have evryone play with as many members of the group over the week with the least amount of repetition. If you would please provide it for both 6 and 7 days, since we are not sure yet how many days we will be playing. 16 golfers-playing in groups of 4 each day-6 days 16 golfers-playing in groups of 4 each day-7 days Answered by Victoria West.
	Triangular prisms and pyramids		2009-01-10
		From KJ: What are some items found in a home or school that could be considered a triangular prism or triangular pyramid? Answered by Robert Dawson and Penny Nom.
	18 golfers and 5 rounds		2009-01-10
		From steve: We have 18 golfers 5 rounds . Would like 3 foursomes and 2threesomes each day Different groups each day. Answered by Victoria West.
	What is the maximum revenue?		2009-01-09
		From Kristy: A skating rink manager finds that revenue R based on an hourly fee x for skating is represented by the function R(x) = -200x^2 + 1500x What is the maximum revenue and what hourly fee will produce maximum revenues? Answered by Harley Weston.
	A max/min problem		2009-01-09
		From Angelica: have 400 feet of fence. Want to make a rectangular play area. What dimensions should I use to enclose the maximum possible area? Answered by Robert Dawson.
	The area of a region bounded by two curves		2009-01-07
		From Rogerson: Find the area, S, enclosed by the given curve(s) and the given line. y = x^2 - x - 1, y = x+2 Answered by Harley Weston.
	A kennel with 3 individual pens		2009-01-06
		From Jean: An animal clinic wants to construct a kennel with 3 individual pens, each with a gate 4 feet wide and an area of 90 square feet. The fencing does not include the gates. Write a function to express the fencing as a function of x. Find the dimensions for each pen, to the nearest tenth of a foot that would produce the required area of 90 square feet but would use the least fencing. What is the minimum fencing to the nearest tenth? Answered by Harley Weston.
	The area enclosed by a curve and the x-axis		2009-01-04
		From Rogerson: Find the area, S, enclosed by the curve y = -x^2 + 6x - 5 and the x-axis in the interval 0≤x≤4. Answered by Harley Weston.
	Determine y'' by implicitly differentiating twice		2009-01-04
		From Walter: Given x^3 - 3xy + y^3 = 1 , determine y'' by implicitly differentiating twice. I cannot solve this. Would you be kind enough to perform the mathematics and show the steps involved in obtaining the solution? Answered by Harley Weston.
	The area of a region in the plane		2009-01-03
		From Rogerson: Find the area, S, of the shaded region enclosed by the given cureve, the given line and the x-axis. y = -x^2 + 1 line x = 2 Answered by Harley Weston.
	24 golfers playing golf for 9 rounds		2008-12-23
		From Duane: Got 24 golfers playing golf for 9 rounds. Any formula where everyone can play with everyone else at least once. We are playing 4somes only. Thanks, Duane Answered by Victoria West.
	Pouring angles for a crucible		2008-12-20
		From Richard: I am trying to work at pouring angles and volume left in during pouring a crucible, The crucible is cylindrical and flat bottomed. I know the diameter, radius and volume of the crucibles. and the volume of liquid going into it. So lets say the crucible is only half full firstly I need to work out the angle just before its going to pour. ( I can work this out as long as there is a certain volume of liquid if its not enough I cant do it) Now the problem I also need to work out how much I should tilt the crucible to allow a certain amount out and be able to do this untill the volume reaches 0 at 90' turn. This is where I am stuck. The reason for needing to be able to work this out is so i can develop a constant flow for example 10Kg of metal per second. Thank you very much for you time Answered by Harley Weston.
	Three circular rings		2008-12-18
		From seema: three circular rings of equal radii of 1cm each are touching each other. a string runs all around the set of rings very tightly. what is the minimum length of string required to bind all the three rings ? Answered by Robert Dawson.
	Integral of cos^2 X between pi/2 and 0		2008-12-18
		From Wanda: Integral or Area of cos^2 X between pi/2 and 0. The answer that I got is -pi/4. Is this correct? If not, how did you come up with your answer? Answered by Robert Dawson.
	The 2 rightmost digits		2008-12-18
		From Peter: Is there a pattern for the 2 rightmost digits of a power? For example, one problem for a math competition was what are the 2 rightmost digits of 3^1993? Answered by Robert Dawson and Victoria West.
	Surface area of an irregular shape		2008-12-15
		From Patrick: An irregular shaped object (lets say a gold nugget, not smooth with pockets) can have its volume determined by comparing its mass in water. Is there any method or means or anything that could be used to determine the surface area of this shape? Whether that be theoretical mathematical formula to using a special infrared technique,etc... The problem I foresee is that the component parts cannot be divided into smaller geometric shapes. I would propose an answer although I don't know if it is a good one: A liquid material that dries super-thin, but has a very specific and easily determined volume/mass is coated over the object. Measure the mass difference between the beginning sample of fluid and the mass after the object has been coated. Then determine the surface area of the same mass of fluid in a geometric shape. Is this feasible? Answered by Robert Dawson.
	A sphere in a can of water		2008-12-12
		From Meghan: A cylindrical can open at the top has (inside) base radius equal to 1. The height of the can is greater than 2. Imagine placing a steel sphere of radius less than 1 into the can, then pouring water into the can until the top of the sphere is just covered. What should be the radius of the sphere so the volume of water used is as large as possible? Answered by Harley Weston.
	Golf - 24 guys 4-somes 6 rounds		2008-12-07
		From Duane: Thank you. What about 24 guys 4-somes 6 rounds everyone playing with each other at least once. Thanks again. Duane Answered by Victoria West.
	Gravity's Effect at a Distance		2008-12-06
		From ROHAN: AT WHAT HEIGHT FROM THE SURFACE OF EARTH,THE WEIGHT OF THE BODY BECOMES HALF? (RADIUS OF THE EARTH = 6400) Answered by Stephen La Rocque.
	6 golfers play threeball		2008-12-04
		From Ian: I have a group of 6 golfers wanting to play 3 rounds as 2x threeballs, but with different players each day. Is this possible? Can you provide some threeball combinations for this please? Answered by Victoria West.
	Six golfers		2008-11-25
		From Joe: I have a group of 6 golfers wanting to play 3 or 4 rounds but with different players each day if possible. We know we cannot make it happen without some playing with the same person. Can you provide some pairings for this? Answered by Victoria West.
	Jogging around a circular track		2008-11-19
		From kim: Joan wants to jog 10 miles on a circular track 1/4 miles in diameter. How many times must she circle the track? Answered by Penny Nom.
	Insulation in an attic		2008-11-18
		From Scott: A homeowner wishes to insulate her attic with fiberglass insulation to conserve energy. The insulation comes in 40-cm-wide rolls that are cut to fit between the rafters in the attic. If the roof is 6 m from peak to eave and the attic space is 2 m high at the peak, how long does each of the pieces of insulation need to be? Round to the nearest tenth. Answered by Harley Weston.
	A word problem about a regular pentagon		2008-11-16
		From Sandra: If the area of a regular pentagon is A=1.720a^2, in which a is one of the sides. Find the area of a regular pentagon with a side that measures 50cm. Answered by Chris Fisher and Penny Nom.
	Multiplication		2008-11-14
		From natalie: what is 8 times 30 Answered by Penny Nom.
	Confusion in a multiple choice question		2008-11-14
		From BJ: My son got this math problem which he could mostly solve. Here it is: The highest location in a certain country is 4525 m above sea level. The lowest point in the same country is 192 m below sea level. a) Find the difference of the two elevations. His answer: a-(-b)= a+b or 4525-(-192)= 4525+192=4717 m. No problem. b) A city is 2221 m above sea level. Is this elevation closer to the highest point or the lowest point? His answer: highest point because: 4525-2221= 2304 m (closest to the highest point) and 2221-(-192)=2221+192= 2413 m. (farthest to the lowest point). OK so far. But then he was given 4 choices for this question with no other information: a) 4717 m; lowest b) 4333 m; lowest c) 4333 m; highest d) 4717 m; highest What does it mean? What's the connection with the rest of the problem? Answered by Harley Weston.
	How fast is the distance between the airplanes decreasing?		2008-11-10
		From Crystal: At a certain instant, airplane A is flying a level course at 500 mph. At the same time, airplane B is straight above airplane A and flying at the rate of 700 mph. On a course that intercepts A's course at a point C that is 4 miles from B and 2 miles from A. At the instant in question, how fast is the distance between the airplanes decreasing? Answered by Harley Weston.
	The height of an equilateral triangle		2008-11-06
		From touqeer: My question is that how can we find the height of an equilateral triangle without using pythagoras theorem? Answered by Penny Nom.
	A trig limit		2008-11-04
		From Teri: Although I have this problem completely worked out in front of me I still cannot understand how it was done. The problem is: Find the limit. lim x->0 sin2x/tan7x. Answered by Harley Weston.
	Separating variables		2008-11-04
		From Terry: by separating variables solve the initial value problem (x+1)y' + y = 0 y(0) = 1 Answered by Harley Weston.
	A belt drives a pulley		2008-11-03
		From Rebecca: A point on a belt is moving at the rate of 30 ft/sec and the belt drives a pulley at the rate of 200 rpm. What is the radius of the pulley? Answered by Penny Nom.
	An irregular, truncated pyramid		2008-10-24
		From phillip: Hi, I have a rectangular base to square top, pyramid shape to fabricate out of steel plate (4 sections). The base is 3000mm by 800mm, the height is 1100mm and the top is 350mm square. What I need to know is the lengths of the sides of the plate(were they meet vertically). Hope ive made it clear enough. Thanks Phil. Answered by Stephen La Rocque.
	Taxes in Taxylvania		2008-10-22
		From April: Taxylvania has a tax code that rewards charitable giving. If a person gives p% of his income to charity, that person pays (35-1.8p)% tax on the remaining money. For example, if a person gives 10% of his income to charity, he pays 17 % tax on the remaining money. If a person gives 19.44% of his income to charity, he pays no tax on the remaining money. A person does not receive a tax refund if he gives more than 19.44% of his income to charity. Count Taxula earns $27,000. What percentage of his income should he give to charity to maximize the money he has after taxes and charitable giving? Answered by Harley Weston.
	Antiderivative of 1/(x(1 - x))		2008-10-22
		From Matt: derivative of dx/(x(1-x)) From what I've seen I should break apart the equation as such derivative of dx/x - dx/(1-x) and then get the 2 corresponding log functions. If that is correct why does this factoring work, if that is incorrect what is the proper way to find the derivative. Answered by Harley Weston.
	I have 6 vertices and 10 edges		2008-10-20
		From Jacquelin: I have 6 vertices and 10 edges. One of my faces is a regular polygon. Answered by Chris Fisher.
	The slope of a tangent line		2008-10-18
		From Amanda: If f(x)=square root of (x+4), and the slope of the tangent line at x=21 was 1/n for some integer n, then what would you expect n to be? Answered by Stephen La Rocque.
	Two equations in two unknowns		2008-10-17
		From Dushayne: Please help me in solving this problem: a. 3x-4y=32 5x+2y=10 b. 2x+3y=11 4x+3y=10 Answered by Penny Nom.
	Perpendicular lines		2008-10-16
		From Hailey: In the xy-plane, the line with equation 2x + y = 3 is perpendicular to the line with equation y = mx + b, where m and b are constants. What is the value of m? Answered by Penny Nom.
	Concavity and the second derivative		2008-10-15
		From Christina: I'm having trouble solving for a second derivative for the following graphing question. f(x) = (X^2+2x+4)/2x using the quotient rule, I found: f'(x) = (x^2-4)/(2x^2) however, using the quotient rule again I can't seem to solve it (concavity): f'''(x)=[(2x)(2x^2)-(x^2-4)(4x)]/[(2x^2)^2] f''(x)=[(4x^3-(4x^3 -16x)]/4x^4 f''(x)=16x/4x^4 f''(x)=4/x^3 and making the equation equal to zero result in 0=4 which doesn't seem to make sense... Answered by Penny Nom.
	The volume of fluid in a semi circular trough		2008-10-10
		From Kerry: How do I find the volume of fluid in a semi circular trough? Answered by Penny Nom.
	Linear and Angular Velocity		2008-10-10
		From Matthew: The pedal and gear relationship of a bicycle is shown. The radii of the gears are r(sub1) = 5 cm and r(sub2)= 12 cm. The radius of the wheel is r(sub3) = 30 cm. How many rotations per minute of the pedal gear will produce a racing cyclist's speed of 60 km per hr. For a diagram: http://bikepedalsgears.weebly.com/ Answered by Stephen La Rocque.
	Two modular equations		2008-10-08
		From Mhiko: please solve this Chinese remainder problem..and give me a solution or rule in order to solve this problem/ x=2mod15 x=1mod25 Answered by Stephen La Rocque.
	3,6,10,15,and 21		2008-09-28
		From jarred: i am currently stumped on a math project that requires me to find out the recursive formula for a sequence of numbers. the numbers in the sequence are 3,6,10,15,and 21. Thank you for your time. Answered by Walter Whiteley.
	The region between two circles		2008-09-24
		From Carol: Good day! Here is a picture of the problem that we need to solve. (I send the picture through e-mail.) A small circle is inside a larger circle, the only given in the problem is the chord of the larger circle tangent to the smaller circle which measures 16cm. The question is, what is the area of the shaded region? Can you answer this question? Thanks! :) Answered by Harley Weston.
	An Euler diagram and a logic argument		2008-09-18
		From Regina: Use a Euler diagram to determine whether the following argument is valid or invalid. No wizard can yodel All lizards can yodel No wizard is a lizard Answered by Penny Nom.
	A multiple choice exam		2008-09-13
		From Phalange: A multiple choice exam consists of 12 questions, each having 5 possible answers. To pass, you must answer at least 9 out of 12 questions correctly. What is the probability of passing if: a. You go into the exam without knowing a thing, and have to resort to pure guessing? b. You have studied enough so that on each question, 3 choices can be eliminated. But then you have to make a pure guess between the remaining 2 choices. c. You have studied enough so that you know for sure the correct answer on 2 questions. For the remaining 10 questions you have to resort to pure guessing. Answered by Harley Weston.
	Perpendicular		2008-09-08
		From amanda: hi my name is amanda medjuck i am in grade 7. we are learning basic geometry terms and have to define words BUT I DONT KNOW WHAT A PERPENDICULAR LINE IS PLEASE HELP ME!!! Answered by Penny Nom.
	The biggest right circular cone that can be inscribed in a sphere		2008-09-08
		From astrogirl: find the volume of the biggest right circular cone that can be inscribed in a sphere of radius a=3 Answered by Harley Weston.
	An array of tulip bulbs		2008-09-06
		From Mary: My daughter had this problem on one of her tests. She forgot to ask her teacher what she did wrong. I understand she did not answer the question in full, but what she did answer I feel is right. Please explain to me the correct answer. Thank you. Mary Answered by Harley Weston.
	Parallel and perpendicular lines		2008-09-06
		From C: Can you help me determine whether these lines are parallel, perpendicular or neither and why? Problem 1: y=3x+2 y=1/3x - 4 Problem 2: y=1/3x + 1/2 y=1/3 x -2 Answered by Penny Nom.
	How accurate is the following calculation?		2008-09-03
		From Craig: Given that these numbers are only accurate to 2 decimal places, how accurate is the following calculation? 1.73 - 2.16 + 0.08 + 1.00 - 2.23 - 0.97 + 3.02 = 0.47 How do I work out the accuracy? Answered by Penny Nom.
	Irregular polygon and Circle that Intersects All Sides		2008-08-20
		From Xetro: Hi, Suppose you have an irregular polygon(convex or concave) with n > 3 sides. The question is - Find some circle that will cut(in limiting case - touch) all the sides of that polygon. It doesnt matter how many times it cuts the side(1 or 2), it just have to cut or touch it. How to find such a circle? or how to decide if such circle even exists? What if those segments do not form a polygon but are some arbitrary segments ? Really want to know how to do it................ Thanks a lot.. Regards, Xetro Answered by Janice Cotcher.
	Angular & Linear Speed from a Sine Graph		2008-08-19
		From Kim: Kim, a student: I am given a graph with a wave. The amplitude is 5cm and the period is 4cm. I am suppose to find the angular speed. What I need to know is the formula for angular speed and how do I use these numbers to get the correct answer. Answered by Janice Cotcher.
	A triangular field		2008-08-15
		From joneka: Barb walked five times aroun a triangle field all together she walked 435 feet the first side of the triangle fiel is 23 feet the length of the other two sides are of the same measure. What are the dimensions of the triangle field? Answered by Penny Nom.
	[f(x)-f(1)]/(x-1)		2008-08-14
		From katie: Evaluate (if possible) the function of the given value of the independent variable: f(x)=(x^3)-x: [f(x)-f(1)]/(x-1) Answered by Penny Nom.
	Angles in a regular tetrahedron		2008-08-07
		From Carla: Hi guys, A regular tetrahedron has all its edges 8cm in length. Find the angles which an edge makes with the base. Thanks. Carla Answered by Penny Nom.
	Find the product of 2^35 and 5^38 in sci. notation.		2008-08-03
		From Peter: I am preparing for a competition and a lot of the non-calculator problems are like find the product of 2^35 and 5^38 in sci. notation. How would you do that? Answered by Penny Nom.
	Right Sided Limit of an Exponential Function		2008-07-29
		From joseph: I am trying to find the limit as X approaches 0 from the positive side of x to the sin of x which look like this lim x^sinx x->0+ Answered by Harley Weston.
	Integral of X^2		2008-07-28
		From Hemanshu: Integral of X^2 Answered by Janice Cotcher.
	Simultaneous equations		2008-07-23
		From Franco: Solve 3 D + E - F = -10 -2 D - F = -4 -3 D - 4 E - F = -25 Franco Answered by Penny Nom.
	The maximum range of a projectile		2008-07-22
		From kwame: the range R of projectile fired with an initial velocity Vo ,at an angle of elevation (@ )theta from the horizontal is given by the equation R = (Vo(squared) sin2theta)/g. where g is the accelation due to gravity . Find the angle theta such that the projectile has maximum range . Answered by Harley Weston.
	A square and a circle		2008-07-20
		From kobina: 4 ft of a wire is to be used to form a square and a circle. how much of the wire is to be used for the square and how much should be used for the square in order to enclose the maximum total area Answered by Harley Weston.
	multiply = 3a - 3b by a+b		2008-07-15
		From chaleen: multiply = 3a - 3b by a+b Answered by Penny Nom.
	A Falling Rock		2008-07-11
		From Rita: This question has 3 parts. If a rock falls from a height of 20 meters on the planet Jupiter, its height H (in meters) after x seconds is about H(x) = 20 - 13x^2 (a) What is the height of the rock when x = 1.2 seconds? (b) When is the height of the rock 15 meters? (c) When does the rock strike the ground? Thank you Answered by Janice Cotcher.
	A difference quotient		2008-07-10
		From Rita: Find the difference quotient of f, that is, find [f (x + h) - f (x)]/h, where h does not = 0 for the given function. Be sure to simplify. f(x) = 1/(x + 3) Answered by Janice Cotcher.
	A dog tied to a round building		2008-07-08
		From maitham: i have this question which i don't know how to solve it : One dog was linked to the outer wall of a building round of 20 meters in diameter. If the length of chain linking the dog sufficient turnover of half the distance around the building, What area can guard dog? they said that we can solve it by integral .. can you solve it for me? Answered by Harley Weston.
	A rectangular room		2008-06-30
		From Peter: A rectangular room has a perimeter of 42 feet and an area of 108 square feet. What is the length, in feet, of the shorter side? Answered by Penny Nom.
	Remainders		2008-06-30
		From vivek: what is the remainder when 2050*2071*2095 is divided by 23 ? this question needs to be done in as less time as possible. Answered by Penny Nom.
	A golf tournament		2008-06-24
		From Roland: We have a golf tournament, 12 players, three rounds. We want to pair so that we have pairings with as few duplications as possible. Answered by Janice Cotcher.
	Two forces acting on a body		2008-06-21
		From Rita: Before answering the question below, what exactly is, in basic words, resultant force? QUESTION: Two forces of 50 and 68 pounds act on a body to produce a resultant force of 70 pounds. Find, to the nearest 10 minutes or nearest tenth of a degree, the angle formed between the resultant force and the smaller force. Answered by Harley Weston.
	sin(2x)/sin(3x)		2008-06-19
		From matt: how does sin2x break down (not with identities) and how would sin3x be created. My prob. is sin 2x/ sin 3x and I want to know how the double(or triple angle) would break down. I want to be able to cancel out sins. Thanks! Answered by Harley Weston.
	A line which is perpendicular to another line		2008-06-18
		From Emily: How do you solve perpendicular bisectors with a slope and a point? Answered by Penny Nom.
	Escort cards on a rectangular table		2008-06-13
		From Susan: What size rectangular table will we need to put 230- 2" X 3.5" escort cards on for my daughter's wedding reception with a spacing of .5 inch between them on all sides? Thanks so much for your help Answered by Penny Nom.
	The current in a river		2008-06-12
		From Joi: To approximate the speed of the current of a river, a circular paddle wheel with radius 4 feet is lowered into the water. If the current causes the wheel to rotate at a speed of 10 revolutions per minute, what is the speed of the current? Express your answer in miles per hour. Answered by Harley Weston.
	The rate of change in the depth of the water		2008-06-12
		From Liz: A rectangular pool 50ft long and 30ft. wide has a depth of 8 ft. for the first 20 ft. for its length and a depth of 3 ft. on the last 20ft. of its length and tapers linearly for the 10 ft in the middle of its length. the pool is being filled with water at the rate of 3ftcubed/ min at what rate is the depth of the water in the pool increasing after 15 hours? Answered by Harley Weston.
	Two circles		2008-06-10
		From cey: the diameter of the larger circle is 20cm, and the smaller 10cm. what is the shaded area?? Answered by Janice Cotcher.
	How do i find the area of an irregular figure?		2008-06-10
		From DAVE: How do i find the area of an irregular figure? Answered by Penny Nom.
	A recursive formula for 9, -18, 36, -27, ...		2008-06-05
		From Rita: I am having trouble understanding how to write formulas (I should say create formulas) from a given sequence. It does not matter what sort of sequence it is. The confusion remains. I have not found a textbook or easy math book that explains this process for the average Joe to grasp. Here are the two questions: (1) Write a recursive formula for the sequence 9, -18, 36, -72, ... (2) Write a recursive formula for the sequence 3, 3(sqrt{3}), 9, 9(sqrt{3}) Answered by Penny Nom.
	The area of a regular pentagon		2008-06-02
		From Jenna: I would like to know if there is a formula to find the area of a regular Pentagon that is not inscribed in a circle only apothem and side length are given. Answered by Penny Nom.
	The length of a shadow		2008-05-27
		From Simon: A figure skater is directly beneath a spotlight 10 m above the ice. IF she skates away from the light at a rate of 6m/s and the spot follows her, how fast is her shadow's head moving when she is 8m from her starting point? The skater is (almost) 1.6m tall with her skates on. Answered by Stephen La Rocque and Harley Weston.
	A season schedule for 9 teams		2008-05-22
		From James: would like to put together a season schedule for 9 teams with each team playing three or 4 games leading to a 1 to 9 ranking. Answered by Victoria West.
	The angles of an irregular pentagon		2008-05-20
		From victoria: The sum of the measure of two angles is 240. If the remaining angles are congruent, what is the measure of each angle? Answered by Penny Nom.
	The weight of a concrete column		2008-05-11
		From russell: a cylindrical form is filled with a slow curing concrete. The base of the form is 10 ft in radius, and height is 25 ft. while the concrete hardens, gravity causes the density to vary from a density of 90 lbs/ft^3 at the bottom to a density of 50 lb/ft^3 at the top. Assume that the density varies linearly from the top to the bottom, and compute the total weight of the resulting concrete column Answered by Harley Weston.
	A linear model		2008-05-09
		From Shelby: How would you write a linear model to represent the population of a city that has a population of 547,725 and a growth rate of -25,195 per year with t represents the number of years since 1994? Answered by Penny Nom.
	How do you reduce an equation with multiple variables?		2008-04-30
		From Jonathon: How do you reduce an equation with multiple variables? For example, if 3x + y = k(x-3), what would x be equal to? Answered by Penny Nom.
	A bowl is the shape of a hemisphere		2008-04-28
		From josh: a bowl is the shape of a hemisphere with diameter 30 cm and water is poured into the bowl to a height h cm. how do i find the volume of the water in the bowl Answered by Harley Weston.
	A lidless box with square ends		2008-04-28
		From Chris: A lidless box with square ends is to be made from a thin sheet of metal. Determine the least area of the metal for which the volume of the box is 3.5m^3. I did this question and my answer is 11.08m^2 is this correct? If no can you show how you got the correct answer. Answered by Stephen La Rocque and Harley Weston.
	An octagonal prism		2008-04-27
		From Melanie: My son is identifying geometric shapes in the real world? We are stuck on octagonal prism, rectangular prism and square prism. Can you help me out with some examples. Thanks Answered by Penny Nom.
	At what value of t is the maximum acceleration?		2008-04-25
		From Mary: Velocity of a function (which is the first derivative of its position) is defined over the interval 0 to 12 using the following piecewise function: v(t)=-1 from 0 to 4, v(t)=x-5 from (4 to 8 and v(t)=-x+11 from (8 to 12. At what value of t is the maximum acceleration? Answered by Stephen La Rocque.
	An irregular tetrahedron		2008-04-24
		From RAUL: I am looking an expression for an edge length as function of the other five edge lengths of irregular tetrahedron. Answered by Walter Whiteley.
	A volume of revolution		2008-04-24
		From Sabahat: Hi, i have a region enclosed by both axes, the line x=2 and the curve y=1/8 x2 + 2 is rotated about the y-axis to form a solid . How can i find the volume of this solid?. (Please note that y equation is read as y =1 over 8 times x square plus 2.) I will be really grateful if you answer this question. :) Answered by Harley Weston.
	An open box		2008-04-23
		From Le: Metal Fabrication; If an open box is made from a tin sheet 8 in square by cutting out identical squares from each corner and bending up the resulting flaps, determine the dimensions of the largest box that can be made. Answered by Harley Weston.
	What is the integral of 13sin^3(x)*cos^7(x)dx?		2008-04-22
		From Cathrine: I am having trouble integrating this problem. It says to evaluate the integral but I don't know what to do or how to do it. It is the integral of 13sin^3(x)*cos^7(x)d Answered by Harley Weston.
	f(x)=sin^3(3x^2) find f ' (x)		2008-04-21
		From Michael: f(x)=sin^3(3x^2) find f ' (x) Answered by Harley Weston.
	A solid figure with 3 rectangular faces and 2 triangular faces		2008-04-17
		From Emily: I am in the 3rd grade and my teacher gave us a question. What is a solid figure with 3 rectangular faces and 2 triangular faces? Answered by Penny Nom.
	The area bounded by 3 curves		2008-04-13
		From Sabahat: Hi, I have enclosed a diagram. The diagram shows the curve y=(2x-5)4. The point P has co-ordinates (4,81) and the tangent to the curve at P meets the x-axis at Q. Find the area of the region (shaded in the diagram) enclosed between the curve, PQ and the x-axis . (Please note that the equation y is read as y=2x -5 whole raise to power 4.) Answered by Stephen La Rocque.
	f(x) =ax^blnx		2008-04-13
		From charles: supposef(x) =ax^blnx is a real- valued function. Determine exact values(not decimal approximations) fro nonzero constants a and b so that the function f has a critical point at x=e^3 and a maximum value of 1/2e Answered by Harley Weston.
	The chain rule		2008-04-10
		From joey: pls help me to Differentiate y=(3x^2-4x)^8 Answered by Harley Weston.
	A regular polygon		2008-04-09
		From chase: name the regular polygon if the sum of the measures of the polygon is 1,440 and the measure of one angle is 144 Answered by Stephen La Rocque.
	Side lengths and angles in a regular octagon		2008-04-09
		From Lori: I am a builder and need to find the length of the sides of an octagon. I know the length between the parallel sides (26 feet). What is the length of each side? What is the angle measurement? Answered by Harley Weston.
	Matrix multiplication		2008-04-08
		From manashi: i. why matrix division is not possible? ii.when we add or subtract two matrix , getting the result by addind or subtracting correspondind elements....but in case of multiplication it is not but why? Answered by Harley Weston.
	How many bags of mulch?		2008-04-07
		From MJ: I have an area that is 35' X 50' and I want to cover it with 2" of mulch. Do I take length X Width X depth? Bags of mulch are sold in 2 or 3 cubic feet per bag.....I just want to know how to do the math. can you please send me the equation? Answered by Penny Nom.
	What fraction of 45 is 10?		2008-04-06
		From Scott: 45 x fraction? = 10 Answered by Penny Nom.
	1-(1-P)^75=0.05		2008-04-05
		From Amy: 1-(1-P)^75=0.05 Answered by Stephen La Rocque and Penny Nom.
	A volume of revolution		2008-04-04
		From ted: Consider the region bounded by y=x^2 + 1, y=5-3x and y=5. Sketch and shade the given region; then set up but dont evaluate teh integrals to find the following: a) The volume of the solid generated by rotating the region about the line y=5 b) the volume of the solid generated by rotating the region about the y-axis Answered by Penny Nom.
	lim as x approaches infinite of 5x + 2/x-1		2008-04-04
		From Jordan: how to solve this. lim as x approaches infinite of 5x + 2/x-1 Answered by Stephen La Rocque and Harley Weston.
	A shape		2008-04-03
		From Joshua: what shape has 4 faces, 4 corners and 9 edges. Answered by Penny Nom.
	The integral of dx / (4x^2 - 25)^3/2		2008-04-01
		From Meghan: I have a question from the trigonometric substitution of my calculus course. integral of dx / (4x^2 - 25)^3/2 Answered by Harley Weston.
	A rectangular prism		2008-03-31
		From Chanlie: i need need to find a rectangular prism with a total surface area of 210 units. Answered by Penny Nom.
	2 times 0 times 0 times 4		2008-03-30
		From ben: what is 2 times 0 times 0 times 4? Answered by Penny Nom.
	A fish tank in the shape of an irregular pentagon		2008-03-29
		From richie: i am building a fish tank. it is going to be an irregular pentagon. the sides are going to be 24" 24" 8" 8" 32"(approximately) there will 3 right angles A, B, E my question is how to figure out the degree of the angles that are not right angles (C,D)? Answered by Chris Fisher.
	A max-min problem		2008-03-27
		From LSL: show that of all rectangle with a given area, the square has the smallest perimeter. Answered by Penny Nom.
	A hydraulic cylinder		2008-03-24
		From james: I am trying to adjust the placement of a hydraulic cylinder that raises a dump bed up from the frame of a truck. How long would the cylinder (height of a triangle) have to be to raise the bed to a 70 degree angle? The base from pivot to cylinder is 132.5 inches. Answered by Stephen La Rocque.
	A train and a boat		2008-03-15
		From Sabrina: A railroad bridge is 20m above, and at right angles to, a river. A person in a train travelling at 60 km/h passes over the centre of the bridge at the same instant that a person in a motorboat travelling at 20km/h passes under the centre of the bridge. How fast are the two people separating 10s later? Answered by Harley Weston.
	Repeating decimals		2008-03-10
		From Blaine: Is it possible to put a repeating decimal number into a calculator to solve a problem? EX: Write 39.3939... as a fraction. Answered by Penny Nom.
	The volume of a countertop		2008-03-08
		From Matthew: I need to calculate volume down to cubic feet. I pour concrete countertops and cant figure out the formula to convert inches and feet. If I have a 2.5 inch by 2 foot by 16 foot concrete countertop how do I convert it to cubic feet and hence know how many bags of concrete at .6 cubic feet per bag I will need. I am trying to input the formula into a spreadsheet. thank you so much Matt Answered by Penny Nom.
	Two perpendicular lines		2008-03-07
		From Daphne: Does anyone know how to find a line perpendicular to -3x=4y=20 and passes through the point (-12,0)? Answered by Stephen La Rocque and Penny Nom.
	A 6 pointed star		2008-03-04
		From Siddharth: When 2 congruent equilateral triangles share a common center, their union can be a star If their overlap is a regular hexagon with an area of 60, what is the area of one of the original equilateral triangles? a) 60 b) 70 c) 80 d)90 e)100 Answered by Stephen La Rocque.
	Triangular prisms and pyramids		2008-03-03
		From LORENA: hi i am in yr 6 and i need to know how many faces,vertices and edges these shapes have.. . TRIANGULAR PYRAMID . TRIANGULAR PRISM Answered by Penny Nom.
	What point on the graph y = e^x is closest to the origin?		2008-03-03
		From elvina: What point on the graph y = e^x is closest to the origin? Justify your answer. Answered by Stephen La Rocque.
	Simultaneous equations		2008-02-29
		From CONOR: I was wondering if you could help me with this problem 7x - 5y = -1 3y = 4x Answered by Penny Nom.
	A Norman window		2008-02-25
		From Jason: If the perimeter of a Norman window is 20 feet, what is the maximum area of the window? Answered by Stephen La Rocque.
	A ball bearing is placed on an inclined plane		2008-02-15
		From Leah: A ball bearing is placed on an inclined plane and begins to roll. The angle of elevation of the plane is x. The distance (in meters) that the ball bearing rolls in t seconds is s(t) = 4.9(sin x)t^2. What is the speed of the ball bearing, and what value of x will produce the maximum speed at a particular time? Answered by Penny Nom.
	Two regions with equal area		2008-02-13
		From James: There is a line through the origin that divides the region bounded by the parabola y=3x-5x^2 and the x-axis into two regions with equal area. What is the slope of that line? Answered by Harley Weston.
	A square and an equilateral triangle		2008-02-10
		From Emily: A square pen and a pen shaped like an equilateral triangle have equal perimeters. Find the length of the sides of each pen if the sides of the triangular pen are fifteen less than twice a side of the square pen. Answered by Stephen La Rocque.
	Radians		2008-02-08
		From Brian: I'm teaching Precalculus right now and will be covering the formula to convert angular speed into linear speed. My question is about the units involved. Using v=rw, if r is mearsured in feet and w is measured in radians/second then v is measured in ft/sec. What happened to the units of radians? I can't find a good way to explain why they are not part of units for velocity. Do you have a good explanation? Thanks, Answered by Stephen La Rocque.
	Multiplying decimal numbers		2008-02-05
		From alwyn: Why should when you Multiplying Decimal numbers is value becoming less and less? don't you think even decimal number is a quantity and in no chance when it multiplies its should become less or nil !!! In fact all Multiplying and or adding the value will go up and only when you subtract and divide it should become less !! Answered by Stephen La Rocque and Penny Nom.
	The radius of a circular arc		2008-02-04
		From Bill: Hi,the Central Angle of a sector of a circle is 40 degrees. The circular arc of the curve has a chord length of 3000 ft. Find the radius(r) of the circular arc. Answered by Penny Nom.
	Numbers and Operations		2008-02-02
		From Charlotte: On the TABE (Test for Adult Basic Education) test, one of the categories is number operation. I would like to know what consist of number operation. Answered by Penny Nom.
	Integration by parts		2008-01-30
		From seth: hi i really dont understand integr ation by parts. for example, the integral(t^2sintdt. i have u=t^2 and v'=sint also u'=t^/3 v=-cost for the formula i have uv-integralvu' dx this is all well and good but i cant get it right. Answered by Harley Weston.
	Angle of Elevation		2008-01-29
		From Rita: Uluru or Ayers Rock is a sacred place for Aborigines of the western desert of Australia. Chun-Wei uses a surveying device to measure the angle of elevation to the top of the rock to be 11.5 degrees. He walks half a mile closer and measures the angle of elevation to be 23.9 degrees. How high is Ayers Rock in feet? Answered by Stephen La Rocque.
	Inflection points		2008-01-25
		From Armando: Hi, Im trying to write a program that takes an equation ( f(x) = 0 ) and returns a list of the inflexion points in a given interval. there must be (I think) a mathematical method or algorithm to do this, probably involving the (second) derivate of the function. However I have not found such a method yet. Any help on this will be much appreciated. Answered by Stephen La Rocque and Harley Weston.
	Maximize income		2008-01-18
		From Chris: Lemon Motors have been selling an average of 60 new cars per month at $800 over the factory price. They are considering an increase in this markup. A marketing survey indicates that for every $20 increase, they will sell 1 less car per month. What should their new markup be in order to maximize income? Answered by Stephen La Rocque and Harley Weston.
	A large concrete shape		2008-01-16
		From Keith: what is the cubic yards of an area that is not a perfect 1/4 circle? The dimensions are 100ft. x 60ft. x 125ft. curcumferal arch x 3ft. depth? Answered by Stephen La Rocque.
	Fact families with multiplication and division		2008-01-16
		From Donna: I am trying to help my granddaughter with some math homework. I looked at what you have on fact families. Am I correct to assume that the same process applies to multiplication and division as well? Her question asks for fact families for 2, 8, & 16. Answered by Penny Nom.
	Balancing on a fulcrum (net torque and equilbrium)		2008-01-15
		From Eric: If I have a 4" bar that has no weight value with a 275lb. weight on one side and a 125lb. weight on the other side what would be the folcrum point? Please keep the answer very simple. Also is there a fixed equation to figure folcrum points? Is there an equation for if the 4" bar had a weight value? Answered by Stephen La Rocque.
	Multiplying numbers in bases other than 10		2008-01-08
		From Imaiya: In class we've been learning about numbers with a base other than ten. For example, base 7, base 5, and base 6. What's really stumping me is how to multiply these numbers, when they aren't a base of 10. I've had it explained to me once, but don't seem to understand it. Here are the equations, and I've listed the first few numbers for that particular base. Base 5: 0,1,2,3,4,10,11,12,13,14,20 etc... The Equation: 34 x 42 Base 9: 1,2,3,4,5,6,7,8,10,11,12,13,14, etc... The Equation: 56 x 78 If you could explain to me how to multiply numbers with any type of base, I'd really appreaciate it. Also if you could show me how to do one of the questions that I listed, that would really help me =) Thanks so much, and once again, thank you for your great site! Answered by Stephen La Rocque.
	The area of a piece of property		2008-01-05
		From Greg: I need to know the area of a six sided piece of property. I sent a map by regular mail. Answered by Harley Weston.
	The surface area of the rectangular solid		2007-12-30
		From Sara: For my math homework i found the volume of a rectangular solid whose deminsions were in feet and the numbers were 10 by 20 by 30 10 = hight 20 = short side base 30 = long side base and now i have to find the surface area of the rectangular solid.... i know how to do this but i can't get the right answer it should be 2,200 ft squared but i keep getting 13,00 feet squared Answered by Penny Nom.
	The integral of 1/ (x(x+1)^0.5)		2007-12-29
		From Nooruddin: Integral of dx / x(x+1)^0.5 (boundaries are 5 and 3) Answered by Harley Weston.
	The standard normal distribution		2007-12-29
		From GEORGE: Statistics texts state that in a normal distribution, 1 standard deviation covers 68%, 2SD 95% 3SD 99.7%. However, on looking at the tables for normal curve areas, the percentage for a z value of 1 is 84.13. 68 % of values are covered at a z value of 0.47. The discrepancies exist even for other values but are smaller. So why is the rule of thumb so different from the Table for Normal Curve areas? Answered by Harley Weston.
	The centroid of a polygon		2007-12-29
		From David: I am playing around with an idea. I've read previous answers to questions (using surveyor calculation methods) related to finding the area of an irregular shape parcel of land (or irregular polygon). Is there a formula or method for calculating the centroid (mid-point) for this type of polygon. I've seen plenty of methods for calculating the mid-point for a triangle or regular shape poloygon but few for an irregular shape polygon such as a parcel of land. Thanks... Answered by Harley Weston.
	Differentiate		2007-12-28
		From taiwo: i am finding it difficult to use first principle to differentiate this question: y=xcos2x. can u help me. Answered by Penny Nom.
	An irregular octagon		2007-12-23
		From Sheldon: I am attempting to construct an irregular octagon picture frame out of bamboo. The bamboo is 1" in diameter and the opening should be 20" H X 16"W. What measurements should be used? Answered by Penny Nom.
	lim sinx/(x +tanx)		2007-12-16
		From shimelis: i have problem how do you solve this equation lim sinx/(x +tanx) Answered by Harley Weston.
	Shooting an arrow over a wall		2007-12-11
		From Amy: The path of a large arrow fired from a non torsion catapult can be modeled by y=-0.0044x^2 + 1.68x, where x is the distance the arrow travelled (in yards) and y is the height of the arrow (in yards). Given the height of a castle wall, find the safest distance from the wall to launch an arrow over a 120 yard-high wall. Answered by Victoria West and Stephen La Rocque.
	Polygons		2007-12-09
		From Nicholle: a polygon with all sides the same length and all angles the same measure is called a ---- polygon. What word goes in the blank. Answered by Penny Nom.
	LCM over 100		2007-12-09
		From Aris: A teacher has more than 100 sweets. She thinks that if she give 6, 8 or 9 sweets to her students she will have no remaining in the case. What is the smallest number of sweets in the bag? Answered by Stephen La Rocque.
	System of equations		2007-12-06
		From Jenn: change the equation,x-y=4 to form y=mx+b the solution to the system of equations y=2x and y=-x+3 is Answered by Stephen La Rocque.
	Chicken and goat feet		2007-12-05
		From Kim: Old McDonald raises goats and chickens. The animals have a total of 100 heads adn 360 feet. How many goats and how many chickens does Mr. McDonald have? Answered by Stephen La Rocque and Penny Nom.
	Proving a quadrilateral is a rhombus		2007-12-03
		From Jeanie: How do you prove that a quadrilateral is a rhombus because the diagonals of the quadrilateral are perpendicular and bisect each other using the 2-column proof method? Answered by Stephen La Rocque.
	An arched entry		2007-11-28
		From amber: i am working with an arched entry. i know that the radius is 25' and the height is 20'-11". i need to know the length of the arch and degree of bend of the arch. how do i find these? Answered by Stephen La Rocque.
	Maximize the product		2007-11-25
		From David: Hi i have this site call calcchat.com, but i dont understand how they explained this can you take a look? The question is: Direction: Find two positive numbers that satisfy the given requirements. The sum is S and the product is a maximum this is what they did 1) Let x and y be two positive numbers such that x + y = S 2)P = xy 3) = x (S - x) 4) =Sx - x^2 5)...etc. the thing i dont get is how did they go from step 2 to step 3 and also i know this sound dumb but how did they get step 2? =) Answered by Harley Weston.
	A rectangular plot of farmland		2007-11-25
		From Christy: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a single-strand electric fence. With 800m of wire at your disposal, what is the largest area you can enclose, and what are its dimensions? Answered by Harley Weston.
	A curve sketch		2007-11-22
		From Ahson: Find critical points, determine the monotonicity and concavity and sketch a graph of f(x) with any local maximum, local minimum and inflection points labeled: 1. f(x) = x^4 - x^3 - 3x^2 + 1 Answered by Harley Weston.
	Area of a 17-sided lot		2007-11-21
		From Lynda: My uncle is wanting to buy this piece of land [a 17-sided polygon] but we are questioning the acerage total. the measurements are [on the attached diagram]. Answered by Stephen La Rocque.
	The derivative		2007-11-19
		From ralf: Find the derivative of the function 1-. y=1+2x8 2-. y=(1+2x )8 Answered by Harley Weston.
	A rectangle in an ellipse		2007-11-18
		From David: I need to find the max area of a rectangle inscribed in an ellipse with the equation x^2+4y^2=4.. What I have so far is f(x,y)=4xy g(x,y)=x^2+4y^2-4=0, y=sqrtx^2-4/4 f'(x)=2x^2/sqrt-4x^2+2(sqrt-4+x^2). What I need to know is how to finish the problem and find the actual mas area of the rectangle. David Answered by Penny Nom.
	lim [x + squareroot(x^2 + 3)] as x->-inf		2007-11-16
		From David: Find the limit. (Hint: treat the expression as a fraction whose denominator is 1, and rationalize the numerator.) lim [x + squareroot(x^2 + 3)] as x->-inf i got to lim -3/(x - squareroot(x^2 + 3)) as x->-inf but i'm having trouble understanding why the answer is 0 plz explain thx Answered by Harley Weston.
	A rectangular prism		2007-11-16
		From nicholas: What is the height the surface area to a rectangular prism with a volume of 350 milliliters? Answered by Stephen La Rocque.
	A limit of the form 0 times infinity		2007-11-13
		From Russell: find the following limit lim x((e^1/x) -1) as x --> infinity Answered by Penny Nom.
	Radial motion		2007-11-13
		From abdulai: a circular saw with diameter 18.4cm rotates at 2400rpm. What is the angular speed of a point on the edge of the saw blade in radians per second? Answered by Penny Nom.
	Local maxima, minima and inflection points		2007-11-13
		From Russell: let f(x) = x^3 - 3a^2^ x +2a^4 with a parameter a > 1. Find the coordinates of local minimum and local maximum Find the coordinates of the inflection points Answered by Harley Weston.
	Maximize his profit		2007-11-12
		From apoorva: During the summer months Terry makes and sells necklaces on the beach. Last summer he sold the necklaces for $10 each and his sales averaged 20 per day. When he increased the price by $1, he found that he lost two sales per day. a. Find the demand function, assuming it is linear. b. If the material for each necklace costs Terry $6, what should the selling price be to maximize his profit? Answered by Penny Nom.
	Family of functions		2007-11-12
		From Russell: Consider the family of functions f(t)= Asin3t + Acos3t +Bsin8t + Bcos8t find exact values of parameters A and B so that f(0) = 2 and f ' (0) = 1 Answered by Stephen La Rocque.
	6 consecutive multiples of 6		2007-11-11
		From jeff: find 6 consecutive multiples of 6 whose sum is the least common multiple of 13 and 18 Answered by Penny Nom.
	Two integrals		2007-11-09
		From Akilan: how to integrate these (tan x)^6(sec x)^4 and sinh(x)(cosh(x))^2. Please send me how to do this question. Having exams on Monday. Please help. Answered by Harley Weston.
	Increasing and decreasing for functions		2007-11-09
		From David: Direction: Identify the open intervals on which the function is increasing or decreasing. f(x)=1/(x^2) f'(x)= -2/(x^3) i understand how to get up until there, and the undf. is x=0, but now i'm having problem setting up the number table chart. i cant remember how, and where to place the increase and decrease + - the chart, for example <---------0----------> where would the increase and the decrease be place? Answered by Harley Weston.
	The height of a triangle		2007-11-03
		From William: I need to find the height of a triangle if the base is 15, one side is 14 and the other side is 13. Answered by Stephen La Rocque and Penny Nom.
	f(x+y) = f(x) + f(y) + 2xy		2007-11-01
		From Marcia: For all real numbers x and y, let f be a function such that f(x+y) = f(x) + f(y) + 2xy and such that the limit as h -> 0 of f(h) / h = 7, find: f(0), use the definition of the derivative to find f'(x), and find f(x). Answered by Penny Nom.
	A circular table is pushed into the corner		2007-10-31
		From Will: A circular table is pushed into the corner of a square room so that one point is 8 inches from one wall and 9 inches from the other. What is the radius of the table? Answered by Penny Nom.
	How to solve related rates problems		2007-10-27
		From David: Can you plz explain how and where you come up with an equation to solve this? Find the rate of change of the distance between the origin and a moving point on the graph of y = sin x if dx/dt = 2 centimeters per second. Answered by Stephen La Rocque.
	Area of a triangle formed by three points on a graph		2007-10-26
		From Betty: My question is 'find the are of a triangle whose vertices have coordinates (3,5),(6,-5), and (-4,10) Answered by Stephen La Rocque.
	The volume of a regular octagonal prism		2007-10-20
		From Chris: I am trying to figure out the volume of a regular octagonal prism, with side lengths of 4 inches. How do I do this? Answered by Penny Nom.
	A triangular lot		2007-10-17
		From Brian: Seeking the square footage of a triangular property lot, dimensions are: 620 X 620X 720. Answered by Penny Nom and Melanie Tyrer.
	5x + 9 = 3x + 7		2007-10-16
		From kristina: hi im kristina and i cannot figure out how 2 do these multi-step equations 5x + 9 = 3x + 7 i can on getting the wrong answer according 2 the book Answered by Penny Nom.
	lim x->1 (root x - x^2)/{1 - root x)		2007-10-16
		From Meghan: Hi! I have a question from my Calculus textbook that I've been picking at for a while and I'm stuck. lim x->1 (root x - x^2)/{1 - root x). Answered by Stephen La Rocque and Penny Nom.
	Four triangles in a square		2007-10-15
		From Kristina: A square with side lengths of 6 cm is divided into 3 right triangles and a larger isosceles triangle. If the three right triangles have equal area, find the exact area of the isosceles triangle. Answered by Stephen La Rocque.
	lim (1- 2 cosx) / (sin(x- pi/3))		2007-10-15
		From hanan: lim (1- 2 cosx) / (sin(x- л/3)) Answered by Harley Weston.
	Working with x		2007-10-12
		From Robert: The question: The measure of an exterior angle of a regular polygon is given. Find the measure of an interior angle, and find the sides. 41. 36 42. 18 44. 'X' The attachment has what she has done for 41 and 42. Need help with 44 (lots of help) Thank you in advance for your site and your help. Robert Answered by Penny Nom.
	13 year and 17 year locusts		2007-10-12
		From stefan: how many years pass between the years when both 13 year and 17 year locusts are out at the same time? Answered by Penny Nom.
	A dinner club schedule		2007-10-12
		From irv: The problem is that I have 12 couples, 1 through 12, in a dinner club, and each couple is host once with 3 of the other couples. he dinners will take place over 4 months. I am trying to not repeat any of the couples. We had the formula for 16 and 20 couples but not for 12. Are you able to help with the groupings for 12. Thanks very much. Irv Answered by Victoria West.
	A 9 team league		2007-10-11
		From Dary: I have a 9 team pool league. Each team must play each other once only. But 2 teams cannot play at the same place location each week. I can't seem to match this up and I get stuck. Answered by Victoria West.
	The average rate of change of a function		2007-10-11
		From vern: Find the average rate of change of the function over the given interval. Compare this average rate of change with the instantaneous rates of change at the endpoints of the interval. f(X)=sinX for the inverval [0,pi/6]? Answered by Harley Weston.
	Substitution method		2007-10-11
		From Kevin: 3xx+2y=-36-y=11 Answered by Stephen La Rocque.
	Coin jar		2007-10-07
		From a student: Sally empties his jar of coins. It contains $3.75 in nickels, dimes, and quarters. The number of dimes is twice the number of nickels and the number of quarters is three less than the number of nickels. Determine how many nickels, dimes, and quarters were in the in the jar. Answered by Stephen La Rocque.
	Solving four simultaneous equations (system of four linear equations)		2007-10-07
		From Johan: I need some help in solving this question x + 2y - 3z + 4w = 12 2x + 2y - 2z + 3w = 10 0 + y + z + 0 = -1 x - y + z - 2w = -4 Answered by Stephen La Rocque.
	Triangle perimeter and area		2007-10-05
		From divakar: The sides of the triangle are integers. The perimeter is 8. What is the area? Answered by Stephen La Rocque.
	Golf pairings		2007-10-02
		From Mike: Regarding arranging golf players so no person plays with anyone more than once. You have given examples for 16 and 24 players. If it can be done, i need a solution for 20 players, 4 players per team one round per day for 5 days Answered by Victoria West.
	Equation of a circle circumscribing a triangle with given vertices		2007-10-01
		From Randy: How do I determine the equation of a circle when it is circumscribed by a triangle whose vertices are (-1, 6), (3, -2), and (2, 5)? Answered by Stephen La Rocque.
	y squared over 3 times 8 over y		2007-09-30
		From John: y squared over 3 times 8 over y Answered by Stephen La Rocque.
	Sample variance and population variance		2007-09-22
		From Willy: I have a question in sample variance and population my name is Willy the question in the attached file... Answered by Harley Weston.
	Finding equations, intersection point of two lines at right angles		2007-09-22
		From Yaz: Find the equation of the line joining A(-1,-9) to B(6,120). Another line passes through C(7,-5) and meets AB at rigth angle of D. Find the euation of CD and calculate the co-ordinates of D. Answered by Stephen La Rocque.
	Least Common Multiples		2007-09-20
		From Aiyanna: What is The Lcm Of 3,7,and 8 Because my Teacher gave me That and he didnt even know the answer.... I Worked and worked but I Couldnt Find It..... Answered by Penny Nom and Victoria West.
	The perimeter of a regular polygon		2007-09-18
		From Ashwynn: why does the area of regular polygons with a perimeter of 1000m increase as the number of sides increase? Answered by Stephen La Rocque.
	An irregular lot		2007-09-12
		From Jay: How do I calculate the area of the following Lot? N 15 degrees 1 minute 22 seconds E for 182.2 feet S 89 degrees 46 minutes 26 seconds E for 218.4 feet N 51 degrees 16 minutes 21 seconds E for for 307.1 feet L= 31.63 feet with a radius of 50 feet There is a discrepancy between county records and what the landowner is telling me Answered by Stephen la rocque and Harley Weston.
	Perpendicular lines		2007-09-06
		From dinesh: we know that for two perpendicular lines m1*m2=-1perpendicular but this is not true for x-axis and y-axis? Answered by Harley Weston.
	The area of a circle knowing only the length of a chord		2007-09-05
		From James: I need some help in the right directions with a problem. I was presented with a problem where I need to find the area of a circle knowing only the length of a chord. the is a circle in the center of a larger circle (which the size of either could change) the only thing that matter is that the chord is 100 ft long and rests on top of the smaller circle. Answered by Stephen la Rocque and Brennan Yaremko.
	The tangent to y = x^3 at x = 0		2007-09-04
		From Amit: consider the equation = x^3. The equation of tangent to this curve (which is smmetrical in Ist and IVth quadrant) at (0,0) is y=0, which is x-axis. but graphically one can visulize that x-axis intersects the curve, so how can it be the tangent to the curve. Please help. Answered by Harley Weston.
	Is there a way I can calculate correct square footage for odd shapes?		2007-08-31
		From Tom: I manage a golf course, and we are about to over seed the course for the upcoming winter months. We will be over seeding all greens, fairways, and tee boxes. Noone of the area that we will be placing seed on is a regular shape. The closest shapes they would be is a circle, rectangle or square, but most of them are all odd CURVED shapes. I know what the equation is for Square ft., and I know how many Square ft. are in an acre, but I need to be precise with the amount of seed I order. Is there a way I can calculate correct square footage for odd shapes. Answered by Harley Weston.
	Can you solve this by factoring? 10r^2 - 35r = 10		2007-08-12
		From Aranxa: how do u solve this equation by factoring: 10r^2 - 35r = 10 Answered by Stephen La Rocque.
	Angular speed		2007-08-05
		From Virginia: the engine of a sports car rotates at 5,000 revolutions per minute (rpm). calculate the angular speed of the engine in radians per second. use 2n radians = 1 revolution Answered by Stephen La Rocque.
	All five angles of a pentagon ABCDE are equal		2007-08-04
		From Jerry: All five angles of a pentagon ABCDE are equal. The diagonals AC, AD and BD have the same length. Prove that all five sides of the pentagon are equal in length. Answered by Penny Nom.
	Using the chain rule to solve a derivative		2007-07-29
		From Charles: I need to find the derivative fo the following function.   _______________________ \/ ______________   \/ (x - 1) / (x + 2) + 1 Answered by Stephen La Rocque.
	Equation of a perpendicular line		2007-07-28
		From Marina: Find the equation, is standard form, with all integers coefficients, of the line perpendicular to x+3y=6 and passing through (-3,5) Answered by Stephen La Rocque.
	Multiplcation of two negative numbers		2007-07-26
		From Brett: Someone asked a question about multiplication and division of two negative numbers yielding a positive result here: http://mathcentral.uregina.ca/qq/database/QQ.09.99/butler1.html I was not fully happy with the explanation b/c I want to give me daughter a real-world example and I can't seem to find one. The following illustrates why multiplying negative numbers has become difficult to explain: 2 X 2 = 4 ----(-4)---(-2)---0---2---4 In this example we start with 2 and then want 2 more of them. When we move across the number line from 2 to our answer, which is four, we have moved only 2 units to the right. -2 X -2 = 4 ----(-4)---(-2)---0---2---4 In this example we start with -2 and then want -2 more of them. When we move across the number line from -2 to our answer, which is four, we have moved 6 units to the right. How can the phenomenon of multiplying two negative numbers being more powerful than multiplying two positive numbers be explained? -Brett Answered by Stephen La Rocque and Harley Weston.
	Guessing multiple choice answers		2007-07-24
		From carla: You are taking a multiple choice quiz that consist in 3 questions, each question has 3 possible answers only one is correct. To complete the quiz you randomly guess the answer to each question . Find the probability of guessing exactly 2 answer correctly. b) at least to answer correctly . c)less than two answer correctly Answered by Stephen La Rocque.
	A complex number in polar form		2007-07-23
		From roland: write the given complex number z in polar form lzl(p+qi) where lp + qil=1 for 3 - 4i. Answered by Harley Weston.
	f(x) = (x^4) - 4x^3		2007-07-22
		From Michael: I'm a student who needs your help. I hope you'll be able to answer my question. Here it is: Given the function f(x)=(x^4)-4x^3, determine the intervals over which the function is increasing, decreasing or constant. Find all zeros of f(x) and indicate any relative minimum and maximum values of the function. Any help would be appreciated. Thank you for your time. Answered by Harley Weston.
	A triangular trough		2007-07-19
		From janine: A trough is formed by nailing together, edge to edge, two boards 11 ft. in length, so that the right section is a right triangle. If a 15 gallon of water are poured into the trough and if the trough is held level so that a right section of water is an isosceles right triangle, how deep is the water? (231cu.in=1 gal.) Answered by Penny Nom.
	Fractions of fractions		2007-07-18
		From Bridget: Sam and Mary each owned one-half stock in a printing company. Sam sold 2/3 of his stock to Mary. What fractional part of the printing business does Mary now own? Answered by Penny Nom.
	Calculating the area (acreage) of a four sided lot		2007-07-18
		From A property owner: I have a real estate property and the lot size is something I need to find out. I know the lengths of the four sides, but it isn't a rectangle, it is an odd shape. How do I find the acreage? Answered by Stephen La Rocque.
	The area of a triangular pyramid		2007-07-18
		From Jhezelle: What is the formula of finding the surface area of a triangular pyramid? Answered by Penny Nom.
	A normal to a curve		2007-07-16
		From Samantha: The function f is defined by f:x --> -0.5x^2 + 2x + 2.5 Let N be the normal to the curve at the point where the graph intercepts the y-axis. Show that the equation of N may be written as y = -0.5x + 2.5. Let g:x--> -0.5x + 2.5 (i) find the solutions of f(x) = g(x) (ii) hence find the coordinates of the other point of intersection of the normal and the curve Answered by Penny Nom.
	The isosceles triangle of largest area with perimeter 12cm		2007-07-16
		From sharul: find the dimension of isosceles triangle of largest area with perimeter 12cm Answered by Harley Weston.
	Implicit Derivatives		2007-07-13
		From Charles: I need help computing y' by implicit differentiation the question is: y^2 + x/y + 4x^2 - 3 Answered by Stephen La Rocque.
	Derivative of a Function		2007-07-09
		From Bob: What is the derivative of the function a sub n = [n/(n+1)]^n ? Answered by Stephen La Rocque.
	Finding the radius of an inscribed circle		2007-07-05
		From Maria: I need to find the radius of a circle which is inscribed inside an obtuse triangle ABC. I know all the angles and all the lengths of the triangle. Answered by Stephen La Rocque and Chris Fisher.
	Using calculus to prove the formula for the area of a triangle		2007-07-04
		From Apratim: Using calculus how can one show that the area of any triangle is 1/2 times its base times its height? Answered by Stephen La Rocque.
	An irregular hexagon		2007-07-03
		From Rebecca: I need to find the shape of an irregular hexagon, but only have the lengths four of the sides. It actually looks like a rectangle with a trapezoid on top of it. The bottom of the rectangle is 150'. The sides are 75'. The length of the top is 130'. I do not have the lengths of the two smaller sides. Is there any way to find the area of this shape? Answered by Penny Nom.
	A cylindrical slab of concrete		2007-06-30
		From Kenn: I have a tank that needs a base of cement put in it. I dont know how to do this. The tank is 8 feet across and I want the cement to be 5 or 6 inches deep. Can you please tell me how much cement I need to do this. Answered by Harley Weston.
	The number of blocks on the face of a pyramid		2007-06-27
		From Heather: I was wondering if there was an equation in order to calculate the number of blocks on the face of a pyramid. For example: X X X X X X Is there a specific formula in order to calculate that there are 6 blocks here? Thank You, Heather Answered by Harley Weston.
	Log base 2 of log base 2 of x		2007-06-27
		From alex: y = log base 2 of lag base 2 of x The slope of the tangent to the given curve at its x-intercept is..? Answered by Harley Weston.
	Using Heron's Formula to help maximize the area of a triangle		2007-06-27
		From Claire: Given one side of a triangle is 4 cm and the ratio 1:3 for the other 2 sides. What is the largest area of the triangle? Answered by Stephen La Rocque and Harley Weston.
	The area of an irregular polygon		2007-06-27
		From chris: finding square footage of a polygon with unequal measurements Answered by Stephen La Rocque and Harley Weston.
	sin|x| and cos|x|		2007-06-25
		From Mac: Can anyone tell me whether sin|x| and cos|x| is differentiable at x=0 ? As far as i know, cos(x) and sin(x) is differentiable at all x. Answered by Penny Nom and Stephen La Rocque.
	Limits as x approaches a constant		2007-06-25
		From Mac: can you please tell me what is the reason they say "denominator is a negative quantity" in the solution 11 and "denominator is a positive quantity" solution 10 ?? If i guess correctly, for solution 10, its because of x^2 in the denominator. Answered by Penny Nom.
	Exponential form: x^y		2007-06-22
		From Kishor: whats the easy way to calculate X raised to Y where y is much greater than x. Answered by Stephen La Rocque.
	Simultaneous equations : the Elimination method		2007-06-21
		From Patricia: I need to find the value of X and Y using the Elimination method. 5/x + 3/y=4 25/x-2/y=3 Answered by Stephen La Rocque.
	Simultaneous inequalities		2007-06-18
		From Freddy: Watson Electric has production facilities in Valley Mills, Marlin,and Hillsboro. Each one produces radios,stereos,and TV sets. There production capacities are Valley Mills: 10 radios, 12 stereos, and 6 TV sets per hour Marlin: 7 radios, 10 stereos, and 8 TV sets per hour Hillsboro: 5 Radios, 4 Stereos, amid 13 TV sets per hour QUESTION How many hours should each plant be scheduled to fill an order of 1095 radios, 1230 stereos, and 1490 TV sets? Answered by Stephen La Rocque.
	What is the name of the shape that is 3D and irregular?		2007-06-14
		From alan: What is the name of the shape that is 3D and irregular? Answered by Stephen La Rocque and Penny Nom.
	Circumscribing a golden cuboid with a sphere: surface areas		2007-06-14
		From Ainslie: A golden cuboid is defined as a rectangular prism whose length, width and height are in the ratio of phi : 1 : 1/phi. Prove that the ratio of the Surface Areas of the golden cuboid to that of the sphere that circumscribes it is Phi : Pi. Answered by Stephen La Rocque.
	Angles of depression		2007-06-13
		From Phonda: The pilot of a small private plane can look forward and see the control tower for a small airstrip. Beyond that is a large factory that is 3 milies from the airstrip. The angles of depression are 12.5 degrees and 4.8 degrees respectively. Find the airplane's altitude, to the nearest ten feet. Answered by Stephen La Rocque.
	Two tangent lines to y=x^3		2007-06-07
		From stephanie: find the equations of two tangent lines to the y=x^3 function through the point (2,8) Answered by Penny Nom.
	Solving a quadratic equation using the Quadratic Formula		2007-06-05
		From Stuart: Solve the following quadratic equation: 3xsquared-5x-4=0 Answered by Stephen La Rocque.
	Finding the area of a lot without knowing the angles		2007-06-05
		From Cristin: I have a land-locked piece of land. I need to know the square footage in order to determine the acreage. My deed only gives the lengths of its five sides. Answered by Stephen La Rocque.
	What angle does the tire turn in 60s?		2007-06-04
		From San: An automobile, travelling at 80km/h, is towing a trailer. The wheels of the trailer are 40cm in diameter. Through what angle does the tire turn in 60second? Answered by Stephen La Rocque.
	The volume of a triangular prism		2007-06-01
		From Hannah: How do I find the area of the base of a triangular prism, so that I can find the volume by using the equation on the attachment. The formula is that volume equals one half times (base times height) times triangle height. Thank you for your help. Hannah Answered by Penny Nom.
	The lcm of polynomials		2007-05-31
		From devin: x^3-8 , x^3-4, x^2+4x+4 Answered by Penny Nom.
	The number of grams of sulfuric acid		2007-05-31
		From cookie: Hi, Can you please let me know if I've done this correctly? Calculate the number of grams of sulfuric acid in 0.500L of battery acid if the solution has a density of 1.28 g/mL and is 38.1% sulfuric acid by mass. Answered by Stephen La Rocque.
	Water tank volume		2007-05-29
		From Cecelia: I HAVE A SEMI CIRCULAR TANK AGAINST A WALL MEASURING 6'10" ACROSS THE WIDEST PART AND 3' FROM THE WALL TO THE FRONT OF THE TANK. THE DEPTH IS 14". PLEASE HELP ME TO CALCULATE THE VOLUME OF WATER IN THE TANK. Answered by Stephen La Rocque.
	The limit of a rational function		2007-05-28
		From Imad:      3 _______ 3 _______ lim \/ 1 + x -    \/ 1 - x x->0 ---- ----------------------------               x Answered by Penny Nom.
	A circular blob of molasses		2007-05-28
		From Julie: A circular blob of molasses of uniform thickness has a volume of 1 m^3. The thickness of the molasses is decreasing at a rate of 0.1 cm/hour. At what rate is the radius of the molasses increasing when the radius is 8 m? Thanks, Julia Answered by Penny Nom.
	Discovering the incircle of an irregular polygon		2007-05-25
		From Joaquim: I've been searching in some books and many websites, but I couldn't find a formula or algorithm for discovering the incircle of an irregular polygon, could you please help me? Answered by Walter Whiteley.
	System of equations		2007-05-24
		From Chris: Find all real solutions (x,y,z,w) of the system of equations: 2y= x + x/17, 2z= y + y/17, 2w = z + z/17, 2x= w + w/17 Answered by Penny Nom.
	Mulch price comparison (price per cubic yard versus price per cubic foot)		2007-05-23
		From Dianna: This is a 2-fold question. I am getting some mulch that is measured in 1 cubic yard for $25.00. Walmart has a 2 cubic bag for $3.00. I need to cover a 376 sq ft area. I need to know which is the best deal and how much I need to buy to cover the 376 sq ft. Answered by Stephen La Rocque.
	Set up two simultaneous equations		2007-05-21
		From Admire: The cost of producing windscreen wipers blades at a factory ais partly fixed (due to operating overheads) and partly dependent on the number of blades produced. It costs $300 to produce 1000, and $600 to produce 5000 blades. How much would it cost to produce 24000 blades? Answered by Penny Nom.
	Weight per area conversions		2007-05-13
		From Dermot: A lawn weedkiller to be spread at the rate of 35g per Sq meter. My new spreader is calibrated in lbs per 1000 sq ft !!!! Answered by Penny Nom and Stephen La Rocque.
	Null hypothesis		2007-05-13
		From Dani: A poll of 1068 American voters indicated that 48% supported te Democratic candidate for presidency. At the 0.05 level of significance, test the claim that less than 50% of American voters preferred the Democratic candidate. Answered by Penny Nom.
	Pattern for a truncated cone		2007-05-11
		From Mike: I have been trying to get this cone flat so I can build this column. Can you please help me so I can figure this out? Thanks for your help. Answered by Stephen La Rocque.
	Probability		2007-05-07
		From Danielle: A box contains 3 defective lights and 5 non-defective lights. The lights are tested one at a time without replacement. What is the probability that the 3 defective bulbs will be found in the first 3 tests? is it 1/56 by chance? Answered by Stephen La Rocque.
	Optimization - carrying a pipe		2007-05-05
		From A student: A steel pipe is taken to a 9ft wide corridor. At the end of the corridor there is a 90° turn, to a 6ft wide corridor. How long is the longest pipe than can be turned in this corner? Answered by Stephen La Rocque.
	Edging surrounding a round pool		2007-05-03
		From Carol: Hello, I am new at this and very rusty on my math. I am getting a 24 Ft. round pool and would like to put 2ft width stone (small) edging around it. How much would I need to buy. I have to buy it by the yard (cubic yard) I am not looking for an exact, just an approx. even would be great. Thanks Carol Answered by Stephen La Rocque.
	Two concentric circles form an annulus		2007-05-02
		From A student: In the diagram below, two concentric circles form an annulus. The vertical line is tangent to the inner circle, and forms the diameter of a third circle. Explain why the areas of the annulus and third circle are the same. Answered by Penny Nom.
	Angular velocity		2007-05-01
		From Bruce: a tachometer of a Ford Explorer reads 2,100 rpm at 60 mph. Find the equivalent angular velocity in degrees per minute and radians per minute Answered by Stephen La Rocque.
	A tugboat's speed		2007-04-30
		From Amanda: a tugboat must travel 24 miles against a 4 mile per hour current on the Potomac River and return. At what constant speed must the tugboat travel to make the trip in 12 hours. Round answer to the nearest tenth mph. Answered by Stephen La Rocque.
	Finding out if two line equations are parallel or perpendicular		2007-04-28
		From Vincent: Can you determine if the two lines are parallel, perpendicular, or neither 1/2x+4y=3/5 y/1 + 10/5= 8x I think there perpendicular but how would you solve the equations Answered by Stephen La Rocque.
	Maximize the volume of a cone		2007-04-27
		From ashley: hello, I've been stumped for hours on this problem and can't quite figure it out. The question is: A tepee is a cone-shaped shelter with no bottom. Suppose you have 200 square feet of canvas (shaped however you like) to make a tepee. Use calculus to find the height and radius of such a tepee that encloses the biggest volume. Can you help?? Answered by Stephen La Rocque and Penny Nom.
	A cylinder inside a sphere		2007-04-25
		From Louise: i need to find the maximum volume of a cylinder that can fit inside a sphere of diamter 16cm Answered by Penny Nom.
	Constructing an octagonal deck around a circular pool		2007-04-20
		From Cliff: [I am building an] octagonal desk encompassing 17 foot diameter circle for pool. I have seen other octagonal calculations but none of these tell me how much allowance for a circle to fit within the octagon without losing the circle edge can anyone help thanks cliff Answered by Stephen La Rocque.
	Liquid is being poured into the top of a funnel		2007-04-19
		From neroshan: Liquid is being poured into the top of a funnel at a steady rate of 200cm^3/s. The funnel is in the shape of an inverted right circular cone with a radius equal to its height. It has a small hole at the bottom where the liquid is flowing out at a rate of 20 cm^3/s. How fast is the height of the liquid changing when the liquid in the funnel is 15 cm deep? At the instant when the height of the liquid is 25cm, the funnel becomes clogged at the bottom and no more liquid flows out. How fast does the height of the liquid change just after this occurs? Answered by Penny Nom.
	Minimum cost for a fixed volume		2007-04-18
		From James: My question goes: A silo is to be constructed and surmounted by a hemisphere. The material of the hemisphere cost twice as much as the walls of the silo. Determine the dimensions to be used of cost is to be kept to a minimum and the volume is fixed. Answered by Penny Nom.
	The area of a regular octagon		2007-04-17
		From Adam: I need to find the area of a regular octagon with side length of 12.5m Answered by Penny Nom.
	Simultaneous equations		2007-04-16
		From kyrie: simultaneous equation 4x + 3y = 21 2x * y = 8 Answered by Penny Nom.
	The second derivative		2007-04-14
		From Gerry: In mathematical context,what do you understand by the term "Second Derivative" Answered by Penny Nom.
	The area of a regular hexagon		2007-04-14
		From Chantel: Could you please explain to me why the formula for a regular hexagon is 3√3/2 multiplied by side²? Thank you very much. Answered by Stephen La Rocque.
	The area of an irregular pentagon		2007-04-14
		From Steven: I have been given a coursework in which i have to investigate various shapes to find the one that would give the largest area with 1000m perimeter. I'm stuck in a part where i have to calculate the area of a irregular pentagon. i don't know where to start from. I can make up the length of all the sides (5 sides), so long they add up to 1000, but i'm not quite sure what to do after that. Answered by Penny Nom.
	What is the limit of 3.x^(3/x) as x approaches +infinity?		2007-04-11
		From Teodora: What is the limit of 3.x^3/x as x approaches +infinity ? Answered by Haley Ess.
	I am filling a hole in the shape of a cube		2007-04-11
		From Bethany: If I am filling a hole in the shape of a cube with 64 cubic yards of dirt, how many feet deep will my hole be. Answered by Stephen La Rocque.
	Find the volume of the solid		2007-04-07
		From tricia: a solid is constructed so that it has a circular base of radius r centimeters and every plane section perpendicular to a certain diameter of the base is a square, with a side of the square being a chord of the circle. find the volume of the solid at first i thought the length of a side of the square would be r, but that isn't awlays be true- only when the chord is in the center. so how can i solve this without any values? i dont understand the relationship between the chord and radius, except that the radius intercepts the chord at the midpoint. i know i hav to take the integral to get the volume, but how do i even find the area of one of the squares? please help, thanks, tricia Answered by Penny Nom.
	3 divided by 3 to it's fifth root		2007-04-06
		From Annie: How do I transform the equation 3 divided by 3 to it's fifth root to simple radical form (getting the radical out of the denominator)? Answered by Penny Nom.
	The area of a parcel of land		2007-04-03
		From Ricky: I need the attached land parcel (#0436) converted to acreage. This would be of great help to me. Thanks, Ricky Answered by Penny Nom.
	Interior and exterior angles		2007-04-02
		From Anuj: If in a regular polygon, each exterior angle is twice the interior angle,find the number of sides? Answered by Leeanne Boehm.
	Golf schedule		2007-03-30
		From Jim: I am organising a golf break for 12 golfers playing in 3 fourballs over 5 days. I would like to maximise the number of different golfers each player can play with. Any help would br greatly appreciated. Answered by Penny Nom.
	6- team schedule for softball		2007-03-29
		From Angie: I have 6-teams that can only play 3 days a week. Each team must get 18 games in for the season. I have to split them being the home team and the away team sometimes. Answered by Penny Nom.
	A beam on a lighthouse		2007-03-28
		From Lisa: A beam on a lighthouse 2000 metres away from the nearest point P on a straight shoreline revolves at the rate of 10 pi radians per minute. How fast is the beam of the light moving along the shoreline when it is 500 metres from P? Answered by Stephen La Rocque.
	Slopes of perpendicular lines		2007-03-27
		From Mykolyn: How do you find the slope of a line that is perpendicular to the graph of: y= -1/2x+4? Answered by Leeanne Boehm and Sara Ulmer.
	Schedule for a 10 team league		2007-03-27
		From Pete: I don't know if this question involves a math solution, but I am running out of ideas. I have a 10 team league. Each team must play each other once only. I can't seem to match this up and get stuck at the end. Please help. Thanks, Pete Answered by Penny Nom.
	A triangular prism		2007-03-26
		From Tom: Hi, I need to find a container in the shape of a triangular prism that will fit four table tennis balls (this is for a math project!). These balls have a diameter of 4cm, so a radius of 2. I know that the formula for finding an incircle from a triangle is: radius of incircle = 2area of triangle / perimeter of triangle But I need to know the length of one side of the triangle from the incircle (the triangle needs to be equalateral). Can you help me find a formula for this? Thanks so much! Tom Answered by Penny Nom.
	The area of an irregular pentagon		2007-03-26
		From grace: hi I am doing graphics and need to find the area of the section given to us (it is just drawn). the sides measure 15m, 35.4m, 5m, 17.8m, 35.7m. the angle between the 15m side and the 35.4m side is 17degrees, the angle between the 35.4m side and the 5m side is 73degrees. the angle between the 5m side and the 17.8m side is 151degrees, the angle between the 17.8m side and the 35.7m side is 90degrees and the angle between the 35.7m side and the 15m side is 95degrees. if you could tell me the area i would be extremely grateful. thanks very much. Answered by Penny Nom.
	y = sin(2x)		2007-03-22
		From bader: sin(2x) find dx/dy Answered by Penny Nom.
	Which solid figure has 4 more edges than vertices?		2007-03-22
		From dawn: which solid figure has 4 more edges than vertices? Answered by Penny Nom.
	The Reuleaux Triangle		2007-03-22
		From Dani: Hi! My question is: Determine how the area of the Reuleaux Triangle of width h compares to the area of a circle of width h? Thanks! Dani Answered by Penny Nom.
	28 golfers playing golf over 7 days		2007-03-20
		From ian: I have 28 golfers playing golf over 7 days I would like everybody to play with each other at least once Is there a schedule? Thank you Ian Answered by Penny Nom.
	A one pass calculation of standard deviation		2007-03-19
		From Murtaza: Hi I searched the listings but couldn't find what i am looking for. I have a dataset and i am allowed only 1 pass through it. At the end of this pass i must have the mean and standard deviation. Calculating the mean is easy as also demonstrated in your listings. I think the same can be done for standard deviation as well. But the doubt that i have is this :- Will the calculated standard deviation be sequence dependent ? i.e. if i change the order in which the data items enter the system, will the std deviation also change ?? Thanks in advance Murtaza Answered by Penny Nom.
	A line that is perpendicular to another line		2007-03-16
		From Jesse: How do you write an equation of a line that is perpendicular to y+2x+3 and passes through (3,4); I don't understand the steps of how to do this???? Answered by Stephen La Rocque and Penny Nom.
	Triple angle tangent formula		2007-03-15
		From sam: Hi I am trying to derive a triple angle formulae for tan. I know i need to use compound and double angle formulae but am finding it difficult to "clean" up my fraction to get the triple angle formulae can you show me a worked derivation?! thanks Answered by Penny Nom.
	The area of a property		2007-03-14
		From Greg: Hi my name is Greg. I have a piece of property I am trying to buy, but need to find out the square feet of it first. The four sides are unequal lengths and none at a right angle or parallel. Here are the measurement in feet. The base of the square is 29.12 feet in width. The right side of the square is 44.33 feet high. The top of the square is 28.80 feet in width. The left side of the square is 46.20 feet high. I have not done this math in ages and really need your help. Answered by Harley Weston.
	A regular quadrilateral		2007-03-13
		From Jackie: How can the measure of each angle of a regular quadrilateral be determined? Answered by Haley Ess.
	The period of a simple pendulum		2007-03-10
		From Melissa: The period of a simple pendulum of length L feet is given by: T=2pi(sqrt(L/g))seconds. It is assumed that g, the acceleration due to gravity on the surface of the earth, is 32 feet per second per second. If the pendulum is a clock that keeps good time when L=4 feet, how much time will the clock gain in 24 hours if the length of the pendulum is decreased to 3.97 feet? (Use differentials and evaluate the necessary derivative at L=4 feet.) Answer is in seconds. Melissa Answered by Penny Nom.
	An irregular pentagon		2007-03-08
		From kelly: If I have a pentagon with 2 sides of length 5 and one with a length of 2, what are the lengths of other 2 sides? Answered by Stephen La Rocque.
	Find the length of the belt		2007-03-08
		From Helen: Find the length of the belt Answered by Penny Nom.
	An irregular polygon		2007-03-06
		From Dike: How do i construct an irregular polygon Answered by Penny Nom.
	Finding the x-intercept		2007-03-02
		From Ash: Y = -1/100X^2 =27/10X +0 = 0 THE Y INTERCEPT IS 50 HOW DO I FIND THE X INTERCEPT Answered by Gabriel Potter.
	Simultaneous equations with fractions		2007-02-28
		From Alyca: Hello Math Central, I am a grade 10 student taking Academic math. Our unit right now is method of substitution and elimination. I'm stuck on this one question that I've been doing forever. Please help =) *For this equation I have to do method of elimination, but it's so much harder with fractions...could some one please explain to me how to do it step by step?* x y 2 -- - -- = - -- 3 6 3 x y 1 -- - -- = 1--- 12 4 2 Answered by Steve La Rocque and Ashley Mang.
	sin(3a), cos(3a) and tan(3a)		2007-02-28
		From mailene: hi, i...indeed,to..need..your..help how..cn..i..prove..this,formula??? sin3a=3sina-4sin^3a cos3a=4cos^3-3cosa tan3a=3tan-tan^3a /1-3tan^2a the..symbol...^is..the..expOnent Answered by Haley Ess and Penny Nom.
	The grade 6 math curriculum		2007-02-24
		From Ajay: Do you have a list of topics a 6th grade students should learn in the 6th grade? I am "rusty" in math and would like to assist my son... Example: if an icetray has X cc of water and is split into 8 parts...what is the volume of each part...is this truly 6th grade level math? Answered by Pam Fowler and Penny Nom.
	At what rate is the area of the triangle changing?		2007-02-24
		From mac: two sticks 3.5 feet long are hinged together and are stood up to form an isosceles triangle with the floor. The sticks slide apart, and at the moment when the triangle is equilateral, the angle is increasing at the rate of 1/3 radian/sec. At what rate is the area of the triangle increasing or decreasing at that moment? Mac Answered by Penny Nom.
	Surface area of a triangular prism		2007-02-21
		From Katrina: What is the formula to finding the surface area of a triangular prism? Answered by Gabriel Potter.
	Find the area of the triangle		2007-02-20
		From Christina: Graph the function f(X)= x+1/x-1 and graph the tangent line to the function at the points A:(2,3) and B:(-1,0). The point of intersection of the two tangent lines is C. Find the area of the triangle ABC. Answered by Stephen La Rocque.
	What constitutes a face for a geometric solid?		2007-02-14
		From Erica: What constitutes a face for a geometric solid? We have been getting conflicting answers from different textbooks. Some teachers are saying that cylinders and cones do not have faces. I'm thinking that cylinders have 2 and cones have 1. Please enlighten me. Thanks! Answered by Walter Whiteley.
	a specific 3-d shape		2007-02-12
		From Robby: What three dimensional shape has 6 vertices, 5 faces, and two congruent triangular bases? I can't find the answer to this question anywhere. Your help will be appreciated. Thanks, Robby Craig Answered by Pam Fowler, Gabe Potter and Walter Whiteley.
	Exponential form of complex numbers		2007-02-12
		From Austin: When dealing with imaginary numbers in engineering, I am having trouble getting things into the exponential form. The equation is -1+i now I do know that re^(theta)i = r*cos(theta) + r*i*sin(theta). Just not quite understanding the order of operations. Thanks Answered by Penny Nom.
	Simultaneous equations with envelopes		2007-02-08
		From Mick: There were 17 envelopes bought, some were brown, some were white. The brown envelopes cost one cent more per envelope than the white ones. The total cost was 80 cents. How much of each type of envelope was bought? --Many thanks! Answered by Stephen La Rocque.
	Multiplying and dividing by zero		2007-02-05
		From colin: i would like to if u multiply 1,000,000 by 0 does it equal o or 1. if you have a number eg 15689 and you divide by o what would the answer be is it 1 Answered by Penny Nom.
	The substitution method		2007-01-31
		From Victoria: how do i solve this problem using the substitution method? 2x-5= -14 -7x+14y= -5 Answered by Stephen La Rocque.
	The elimination method		2007-01-31
		From Addrianna: x-2y=2 3x-5y=7 Answered by Stephen La Rocque.
	Water in a triangular trough		2007-01-30
		From Trina: the trough is 5 feet long and its vertical cross sections are inverted isosceles triangles with base 2 feet and height 3 feet. water is draining out of the trough at a rate of 2 cubic feet per minute. at any time t, let h be the depth and v be the volume of water in the trough. a. find the volume of water in the trough when it is full b. what is the rate of change in h at the instant when the trough is .25 full by volume? c. what is the rate of change in the area of the surface of the water at the instant when the trough is .25 full by volume? Answered by Penny Nom.
	The altitude of regular n-side pyramid		2007-01-26
		From Wendimu: The altitude of regular n-side pyramid is half of it's base side.What is the angle between the lateral face and it's base? Answered by Penny Nom.
	A regular pentagonal pyramid		2007-01-25
		From Vickifazio: a regular pentagonal pyramid has a base perimeter of 1,085 ft. How long is one side of the base? Answered by Stephen La Rocque.
	Which lets you put equal groups together?		2007-01-20
		From Kathy: Which lets you put equal groups together? division, multiplication, subtraction, estimation Answered by Stephen La Rocque.
	Irregular multi sided polygon		2007-01-20
		From Graham: I have an irregular polygon. I know the length of all the sides and know approximately all the internal angles. Is there a formula or table that can calculate the area for me? Answered by Steve La Rocque, Chris Fisher and Penny Nom.
	The area of an irregular pentagon		2007-01-18
		From Ranjit: I would like to find the area of an irregular pentagon where the total perimeter is 1000m. Is there a Heron's formula for this? Answered by Stephen La Rocque.
	Angular speed		2007-01-18
		From Cristina: A car is moving at a rate of 50 miles per hour, and the diameter of its wheels is 2.5 feet. a) Find the number of revolutions per minute the wheels are rotating. b) Find the angular speed of the wheels in radians per minute. Answered by Stephen La Rocque.
	Comparing two fractions		2007-01-18
		From Kayla: Why does eight over twelve compared to one half work when you use cross multiplication. Answered by Penny Nom.
	The volume of a frustum of a pyramid		2007-01-17
		From Sam: Find the volume of a frustum of a pyramid with square base of side b, square top of side a, and height h. Answered by Penny Nom.
	A line perpendicular to another line		2007-01-13
		From Dusty: Find an equation for the line perpendicular to: 3x - 4y + 1 = 0 passing through (4,7) Answered by Leeanne Boehm and Penny Nom.
	Products with symbols		2007-01-09
		From Jennifer: Find the product of each (8x)(-4) (3x)(5y)(7z) (8x^3y)-5X^2) (6a)(3a)(-b^2) Answered by Penny Nom.
	Integrate x^8 (x^8 + 2)^2 ((x^8 + 2)^3 + 1)^4		2007-01-09
		From James: How do you integrate x^8 (x^8 + 2)^2 ((x^8 + 2)^3 + 1)^4 Answered by Penny Nom.
	Angular speed		2007-01-06
		From Robert: A rear wheel and tire on a John Deere 8520 farm tractor has a 39-in. radius. Find the angle (in radians) through which a wheel rotates in 12 sec if the tractor is traveling at a speed of 22 mph. Answered by Penny Nom.
	What are the dimensions of the most economical container?		2007-01-04
		From Ashely: A cylindrical container costs $2.00 per square foot for the sides and $3.00 a square foot for the top and bottom. The container must hold 100 cubic feet of material. What are the dimensions of the most economical container. Answered by Stephen La Rocque.
	What size pulley would I need?		2006-12-29
		From Chris: If I have a motor that's spinning at 950 RPM's with a pulley that's 6in diameter with a belt running to a generator, What size pulley would I need on the generator to make it spin at 3600 RPM Answered by Penny Nom.
	A regular polygon inscribed in a circle		2006-12-19
		From Katy: If a regular hexagon is inscribed in a circle of radius 6.72 centimeters, find the length of one side of the pentagon. How would I got about explaining this? Answered by Penny Nom.
	1, 3, 6, 10...		2006-12-15
		From Lisa: What is the nth term for the sequence, '1, 3, 6, 10...' and could you say how you got the anwser. Answered by Stephen La Rocque and Penny Nom.
	Parallel and perpendicular lines		2006-12-07
		From Valeria: I m having trouble with parallel and perpendicular lines a problem i need help with is y=6 find the slope if al line parallel to the graph of each equation Answered by Stephen La Rocque.
	Rolle's Theorem		2006-12-07
		From Erika: If f(x) = (x^2)(square root of [3-x]) on the interval [0,3] is given, Does Rolle's Theorem apply? If yes, find any values of c such that f '(c)=0 Answered by Penny Nom.
	A 15% tip		2006-12-06
		From Danielle: When she eats at a restaurant,Viviana like to leave a 15% tip,multiplying the price of the meal by 0.15. Franklin usually leaves a 20% tip,multiplying the price by 0.20.They both round up to the nearest $0.05. How much tip would Viviana leave for a $24.85 meal? Answered by Penny Nom.
	The length of each side of a regular n-gon		2006-12-06
		From Shannen: The problem is: Find the length of each side of a regular n-gon when a=80ft, n=20ft, and A is approx. 20,000 square feet. What do "a" and "n" stand for and how do I find the side length of an n-gon? Answered by Penny Nom.
	A Norman window		2006-11-30
		From Joe: a norman window is a rectangle with a semicircle on top. If a norman window has a perimeter of 28, what must the dimensions be to find the maximum possible area the window can have? Answered by Stephen La Rocque.
	Sally plays roulette		2006-11-21
		From Sherry: Sally plans to bet 100 bets of $1.00 each on red roulette. the probability of the ball landing on red is 18/38 what is the probability that Sally will win at least half the time Answered by Penny Nom.
	Calculating volume of concrete, dirt, sand, anything.		2006-11-17
		From Debbie: [This article contains a special calculator to help you find the volume (for example, the cubic yards) of material required to fill (or empty) a space if you know the length, width and depth.] We are wanting to pour a 24'x30' slab that is 5" deep. How many cubic yards of cement do we need? Answered by Penny Nom.
	Tangent lines		2006-11-09
		From Melissa: let f be a function with f(1)=4 such that for all points (x,y) on the graph of f the slope is given by (3x^(2)+1)/(2y) a.)Find the slope of the graph of f at the point where x=1. b.)Write an equation for the line tangent to the graph of f at x=1 and use it to approximate f(1.2) c.) Find whether f is concave up or concave down when x=1. Is your answer in part b an overestimate or an underestimate? Answered by Stephen La Rocque.
	Least common multiple		2006-11-08
		From Melenie: I have a daughter in 5th grade she can't seem to grasp the concept of finding LCM's does anyone have a quick easy way for her to learn????? Answered by Stephen La Rocque.
	Simultaneous equations		2006-11-06
		From An other: e^2y-x+2=0 ln(x+3)-2y-1=0 Answered by Penny Nom.
	ESL and math-speak		2006-11-03
		From Matt: My name is Matt and I am an ESL teacher in Korea. Recently I have begun tutoring a student who will be going to Canada soon as a 9th grade student. She is a very capable student and is concerned that her mathematical abilities outstrip her ability to communicate in English. I am writing mainly to inquire what level of math-speak I should teach to this student. For instance: should I be explaining geometric terms, or simply algebra? And if algebra, should I include complex numbers and the quadratic formula? If there are things that she will be taught in Canada, I'd prefer her to learn them firsthand from a math teacher. However, knowledge that she will be presumed to have I would like to teach. Answered by Karen McIver.
	Pulleys and belts		2006-10-31
		From Lynn: A belt has a linear speed of 32 mph. It is spinning three pulleys. Pulley A has diameter 14 in. radius = 7 inches Pulley B has diameter 26 in. radius = 13 inches Pulley C has radius 3 ft. radius = 36 inches Angular speed in Radians per min for I got Pulley A= .08 rads/min Pulley B= .04 rads/min Pulley C=.01 rads/min How many cm would pulley C travel in 14 seconds? Answered by Penny Nom.
	Induction		2006-10-31
		From Ross: Suppose that A and B are square matrices with the property AB= BA. Show that AB^n = B^n A for every positive integer n. Answered by Stephen La Rocque and Penny Nom.
	The area of an irregular hexagon		2006-10-30
		From Ashish: I want to find out area of an irregular HEXAGON in square feet, whose sides are as follows, Answered by Stephen La Rocque.
	The surface area of a triangular prism?		2006-10-29
		From Amanda: What is the formula for the surface area of a triangular prism? Answered by Haley Ess.
	Water is being pumped into the pool		2006-10-24
		From Jon: A swimming pool is 12 meters long, 6 meters wide, 1 meter deep at the shallow end, and 3 meters deeps at the deep end. Water is being pumped into the pool at 1/4 cubic meters per minute, an there is 1 meter of water at the deep end. a) what percent of the pool is filled? b) at what rate is the water level rising? Answered by Stephen La Rocque.
	The area of a regular octagon		2006-10-22
		From Farhana: I have a regular octagon with sides of 0.8m and I need to find the area, Answered by Karen McIver and Penny Nom.
	An approximation		2006-10-22
		From Ellen: consider the curve -8x^2 +5xy+y^3 +149 =0 Write an equation for the line tangent to the curve at (4, -1) use this equation to approximate the value of K at the point (4.2, K) Answered by Penny Nom.
	How fast is the water level rising when the water is 1 meter deep?		2006-10-19
		From Don: The cross section of a 5-meter trough is an isosceles trapezoid with a 2-meter lower base, a 3-meter upper base and an altitude of 2 meters. Water is running into the trough at a rate of 1 cubic meter per minute. How fast is the water level rising when the water is 1 meter deep? Answered by Stephen La Rocque.
	Lattice multiplication		2006-10-16
		From Patti: I am a parent of a 5 th grader, and am a bit loss in the "new" math. I know how to multiply using the "old fashion" method. But, could you please explain lattice multiplication. Answered by Diane Hanson.
	How many feet tall is the tunnel		2006-10-14
		From Charles: A tunnel in the Smoky Mountains is semicircular. At a distance of 12 feet from the center of the tunnel, the tunnel has a height of 16 feet. How many feet tall is the tunnel at its center? Answered by Penny Nom.
	Is a circle a regular shape?		2006-10-10
		From David: Is a circle a regular shape or an irregular shape? Answered by Stephen La Rocque.
	Angular speed		2006-10-04
		From Jack: A horse on a merry-go-round is 7m from the center and travels at a speed of 10km/h. What is its angular speed? Answered by Stephen La Rocque.
	Family of lines		2006-09-29
		From Sasha: could a "Family of Lines" have both parallel and intersecting equations that aren't related directly but otherwise related by each other to create a curve Answered by Chris Fisher.
	Least common multiple		2006-09-25
		From A student: What is the LCM of 10,45 and 38? Answered by Stephen La Rocque.
	A rectangular tank		2006-09-19
		From Milton: What size rectangular tank will I need to hold 841.5 gallons of water. The water level is 3'-0" from the bottom of tank. Answered by Penny Nom.
	The volume of a triangular box		2006-09-12
		From Irene: How do I find the volume of a triangular box? Answered by Penny Nom.
	The velocity of a pendulum, part II		2006-09-07
		From Erin: We saw the question in your database about the velocity of a pendulum swinging.....It is the same exact question....but there is another question......it says.... "estimate the instantaneous rate of change of d with respect to t when t = 1.5. At this time, is the pendulum moving toward or away from the wall? Explain." Answered by Harley Weston.
	How many microliters (ul) are there in 0.5 ml?		2006-08-29
		From Monica: How many microliters (ul) are there in 0.5 ml? Answered by Stephen La Rocque.
	The area of an irregular octagon		2006-08-23
		From Billy: How do you figure the area of an irregular octagon? Measurements are 4 equal sides of =BD", and 4 equal sides of =BE". It measures 1 1/2" = from flat to flat. Answered by Penny Nom.
	Differentiate Y= sin3x + cos7x		2006-08-22
		From james: Differentiate the function of x using the basic rules. Y= sin3x + cos7x Answered by Stephen La Rocque.
	A golf schedule for three days		2006-08-18
		From Jon: I was wondering if I could trouble you to assist me with the following: I am working on a playing schedule for 28 golfers. 7 groups of 4. I have 3 golf days to schedule. Ideally, I would like to schedule all 28 golfers in 7 different groups of 4 on each day. Here is the catch.....no golfer in any group can be grouped togther more than once. Every group of 4 each day will have 4 new golfers that have never played together before. Is this possible? Answered by Penny Nom.
	How fast is the water level rising		2006-08-12
		From Erin: Water runs into a conical tank at the rate of 9ft3/min. The tank stands point down and has a height of 10 ft. and a base radius of 5 ft. How fast is the water level rising when the water is 6 ft. deep? (V=1/3 pi r2 h). Answered by Penny Nom.
	A problem with exponents		2006-08-09
		From A student: (8a to the negative 2 b cube c to the negative 4/4a squared b to the negative 3 c squared) to the negative 2 Answered by Stephen La Rocque.
	The area of a lot		2006-08-05
		From Lyn: I have no idea how to find the square feet of an uneven polygon. I am in the process of making a land agreement and need to know. Please tell me how to figure out the footage and acreage of land as follows. road-front 360' back 360' left side 220' right side 180' Answered by Penny Nom.
	Gallons of water in a well		2006-07-31
		From Martha: I have a shallow water well that is 30 feet in depth. I have 8 feet of water in the well. The water well is a 30 inch in diameter. My question : How many gallons of water is in my tank? Answered by Penny Nom.
	An Integral		2006-07-30
		From Aniket: I am Aniket studing in 12 th standard At Mumbai I have following integration problem please give me a solution integral of 1/under root of (5x2 - 2x) dx Answered by Penny Nom.
	Minimizing a cost		2006-07-25
		From Edward: The cost of running a car at an average speed of V km/h is given by c= 100 + (V2 / 75) cents per hour. Find the average speed (to the nearest km/h) at which the cost of a 1000 km trip is a minimum. Answered by Stephen La Rocque.
	A perpendicular intersection of two barrel vaults		2006-07-21
		From Neal: I'm wanting to build a series of architectural models of different roman and medieval buildings out of cardboard. Once I have perfected the models I want to print them out on card stock so that school kids (or anyone else) can make the buildings. A feature of many of these models is the cross or groin vault (a perpendicular intersection of two barrel vaults). A single barrel vault is easy to imagine as a plane (a rectangular piece of cardboard) that will be folded into a semi-circular arch. The intersection of a second barrel vault and this one is presenting me with problems. The second plane needs to have an ellipse cut into it so that when it is folded into the arch, it will mate up with the curve of the first barrel vault. Given that the two pieces of card have identical widths (and therefore identical arcs in cross section) is there a way to calculate the ellipse that needs to be cut so that it can be cut before the second arch is folded? Answered by Edward Doolittle.
	Calculating the belt length of a three pulley system		2006-07-16
		From Mark: I have a 3 pulley system with sides abc and pulleys ABC. Pulley A has radius of 10cm, pulley B has radius of 20cm, and pulley C has radius of 3cm. The side lengths are: (center to center of pulleys) between pulleys AB = 75cm, between pulleys BC = 100cm, and between pulleys AC = 50cm. I set these side lengths up as (according to law of sines and cosines) a = 100cm, b = 50cm, and c = 75cm. What is the length of the belt required for this system? I need to know how I would set this problem up and solve. Answered by Stephen La Rocque.
	How many bags will it take to cover the area?		2006-06-14
		From Ken: I have area of 160 sq ft. I want to put mulch in the area 2 inches thick. The bag of mulch comes with 2 cu ft of mulch per bag. How many bags will it take to cover the area? Answered by Penny Nom.
	How many yards will I need?		2006-06-06
		From Melba: I'm am trying going to put mulch around the tree in my front yard. I am going for 6" deep and 4069.44 sq. in. around. How many yards of dirt will I need? Answered by Penny Nom.
	Math manipulatives		2006-05-29
		From Mike: Our school is looking to order a large amount of math manipulatives. Do you have a reliable, reasonably priced source that is not producing 'kits' that are intended for specific math programs like Math Makes Sense? Answered by Diane Hanson and Walter Whiteley.
	Simultaneous Equations		2006-05-24
		From Angie: Question: solve the equations 2x-3y-z=0 3x-2y+z=-5 x+3y-2z=14 for x,y,z Answered by Stephen La Rocque.
	differentiate the volume of a cylinder with V respect to h		2006-05-24
		From A student: differentiate the volume of a cylinder with V respect to h Answered by Stephen La Rocque.
	The area of a triangle		2006-05-21
		From A student: how do you find the area of a triangle? Answered by Penny Nom.
	integral of tan^4 x		2006-05-14
		From Aqil: integral of tan4 x Answered by Penny Nom.
	Twenty golfers		2006-05-08
		From Mona: We have twenty golfers and four rounds of golf. We would like to figure out how to make foursomes so that each golfer plays with as many different golfers as possible. Answered by Penny Nom.
	A hallway in an old house		2006-05-06
		From Sabrina: I am trying to determine how many square feet is in a room that is not square or rectangular. It has basically 5 walls of different lengths, it is acutely considered a hallway in an old house, how can I figure out the footage, the Length times Width requires to much wasted materials Answered by Penny Nom.
	Rate of ladder falling		2006-04-30
		From Harsh: A ladder 4 m long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a speed of 30 cm/s, how quickly is the top of the ladder sliding down the wall when the bottom of the ladder is 2 m from the wall? Answered by Stephen La Rocque.
	The perimeter of a regular octagon		2006-04-20
		From Martin: I would like to make an octagon out of 2x4 lumber. I know that the lumber needs to be cut at 67.5 degree angles, but how do I determine the length of each piece if I want to make, say, a 2.5 ft diameter octagon? Answered by Stephen La Rocque.
	Mayan multiplication		2006-04-16
		From Marca: I'm researching the Mayans, and my advisor, Dr. McDonald, stated that you may know whether the Mayans knew how to multiply. I'm finding conflicting information on the internet, and anything you could provide would be greatly appreciated. Answered by Chris Fisher.
	Given three angles and a side		2006-04-09
		From Jon: How do you figure out the length of all sides of a scalene triangle if given the measure of all angles, and one side? Answered by Stephen La Rocque.
	How many people are in the race?		2006-04-07
		From Marty: You're in a race with 1/5 of the racers ahead of you and 5/6 of them behind you. How many people are in the race? Answered by Penny Nom.
	Mastering the multiplication tables		2006-04-04
		From Ellie: I need a detailed study plan fro helping my son master his multiplication tables. Grade: 3 elementary Answered by Paul Betts.
	2x+5y=3 And -x+3y=-7		2006-04-03
		From Lloyd: simplify 2x+5y=3 And -x+3y=-7 Answered by Penny Nom.
	Find the point of inflexion for the curve y = e^x/(x^2-1)		2006-03-31
		From Sam: Hi, i am trying to find the point of inflexion for the curve y = ex/(x2-1) and i got a really complex expression for y". I can't seem to solve x4-4x3+4x2+4x+3=0 so does that mean there is no point of inflexion? Answered by Penny Nom.
	A fence around a pen		2006-03-30
		From Daryl: I hope you can help me out with the attached problem, It has been driving me crazy. Answered by Stephen La Rocque and Penny Nom.
	cos(3X)		2006-03-29
		From Joshua: I'm having trouble proving that cos(3X)=cos3X -(cosX)(sin2 X) Answered by Penny Nom.
	Angular velocity		2006-03-28
		From Ben: How do you (a) express angular speed in terms of linear speed and (b) express linear speed in terms of angular speed? Answered by Stephen La Rocque.
	The area of a block of land		2006-03-26
		From Ronald: I have a building block of land with four unequal sides and only one right angle. I want to know the total area (in metres) and how the calculations were carried out. The four sides are: Rear of property: 9.14 metres left side: 36.9 metres Right side: 32.61 Metres front to street: 27.43 Metres The front to street and right side constitute a right angle. but there are no others. Answered by Penny Nom.
	A 3-dimensional star		2006-03-15
		From Rachel: I am trying to figure out the name of a figure that consists of 8 (I think) square pyramids. There is a net drawing of this figure somewhere and I can't find it because I don't know the name. When all 8 pyramids are connected, they form a '3-dimensional star'. We did this project when I was 14 years old and I am now a 27 year old teacher and I would love to do this project with my kids. Answered by chris Fisher.
	2x+3y=0 and 3x-y=0		2006-03-14
		From Lisa: my name is lisa I am doing math for work and i have a math problem to solve and i need help with it here is the question 2x+3y=0 and 3x-y=0 this is one question can you help me please Answered by Penny Nom.
	The quadratic formula		2006-03-03
		From Miriam: Please show work and indicate "answer", using the quadratic formula - (x+2) (2x+3) = 6 Answered by penny Nom.
	The volume & surface area of a rectangular pyramid.		2006-02-27
		From Cheryl: My daughter is working on a math project & we are having a hard time finding the volume & surface area of a rectangular pyramid. Can you help us with this? Answered by Penny Nom.
	A triangle of 50p pieces		2006-02-22
		From Stuart: Ok, so i am collecting 50p pieces and arranging them on my desk in the shape of a triangle. eg 50p 50p 50p 50p 50p 50p 50p 50p 50p 50p I want to work out how much money I'm saving just by knowing how many rows of coins there are. If i can work out how many coins there are just by knowing how many rows I have I can just divide by 2 to find out the amount in dollars. Answered by Penny Nom.
	The Least Common Multiple of two primes		2006-02-21
		From Kristine: Is the Least Common Multiple to two prime numbers always their product? Why or Why not? Answered by Stephen La Rocque.
	Golfing with 8 or 12		2006-02-13
		From Carolyn: I have a couple of questions that my dad asked me and I do not think it can be done in the manner he wants it to come out to. He is going on a golf trip in June. There are going to be either 8 or 12 players playing 4 rounds of golf. The questions that he says will not work and I do not know how to figure it out either is 4 Rounds of golf is for sure. 18 hole Rounds each 4 Players to a group Either 8 or 12 players can every player play with every player in a group at least once during those 4 rounds. If this can be done can you give me the combinations for both 8 and 12 , so I can help out my dad. Along with how you you figure this out. Answered by Penny Nom.
	Is there a solid shape with 5 faces, 8 edges, and 4 vertices?		2006-02-11
		From Annie: Is there a solid shape with 5 faces, 8 edges, and 4 vertices? Answered by Penny Nom.
	An irregular quadrilateral		2006-02-04
		From Christopher: Is there such a shape as an irregular quadrilateral with 4 equal sides? Answered by Penny Nom.
	The box of maximum volume		2006-02-01
		From Elizabeth: A box factory has a large stack of unused rectangular cardboard sheets with the dimensions of 26 cm length and 20 cm width. The question was to figure what size squares to remove from each corner to create the box with the largest volume. I began by using a piece of graph paper and taking squares out. I knew that the formula L X W X H would give me volume. After trial and error of trying different sizes I found that a 4cm X 4cm square was the largest amount you can take out to get the largest volume. My question for you is two parts First: Why does L X H X W work? And second, is their a formula that one could use, knowing the length and width of a piece of any material to find out what the largest possible volume it can hold is without just trying a bunch of different numbers until you get it. If there is, can you explain how and why it works. Answered by Penny Nom.
	The median		2006-01-27
		From Wael: " median"; what does it mean and how do we calculate it? Answered by Penny Nom.
	Subdividing a polygon into triangles		2006-01-26
		From Adam: is there an algorithm to divide a regular polygon into N equilateral triangles having the same area (no limit on N), or if not, an algorithm to divide a regular polygon into N triangles having the same shape and size? Answered by Chris Fisher.
	One boundary of a pond is parabolic in shape.		2006-01-20
		From Glenn: One boundary of a pond is parabolic in shape. The boundary passes through the points A(-20,45), B(40,40) and E(30,35). The equation of the parabola is of the form y=ax2+bx+c. Find the equation of the parabola and the coordinates of the vertex of the parabola. Any assistance you could provide would be greatly appreciated. Answered by Penny Nom.
	An irregular octagon		2006-01-20
		From Robert: I am building a poker table which is in the shape of an irregular octagon. I know the table measures 72 inches long and 48 inches wide with two parallel straight sides of equal length and six smaller sides of equal length ( three at each end of the table), what I don't know are the lengths of the any of the sides. Answered by Harley Weston.
	GCF, LCM, primes and the ladder method		2006-01-07
		From Linda: How would I teach both finding the GCF and LCM with prime factors...I recall the ladder method vaguely.??? Answered by Penny Nom.
	Differentiation, powers and logs		2006-01-06
		From Claudia: Question: how do I find the derivative of x* ln(x+(e^2))^2 x^lnx x^(e^(-x^2)) Answered by Penny Nom.
	Two related rates problems		2005-12-29
		From Shimaera: #1. A manufacturer determines that the cost of producing x of an item is C(x)=0.015x2+12x+1000 and the price function is p(x)=250+2x/10. Find the actual and marginal profits when 500 items are produced. #2. At 9 a.m a car is 10km directly east of Marytown and is traveling north at 100 km/h. At the same time, a truck leaves Marytown traveling east at 70 km/h. At 10 a.m, how is the distance between the car and the truck changing? Answered by Penny Nom.
	The Mean Value Theorem		2005-12-22
		From Candace: Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given interval. Find all numbers "c" that satisfy the Mean Value Theorem. 11. f(x)=3x2 + 2x +5 [-1, 1] Answered by Penny Nom.
	Simultaneous Equations		2005-12-21
		From Matt: I have these two equations, 336 = 60a + 10b and 432 = 84a + 6b Am I right in saying both a and b are 4.8? Answered by Penny Nom.
	A max-min problem		2005-12-16
		From Julie: A car travels west at 24 km/h. at the instant it passes a tree, a horse and buggy heading north at 7 km/h is 25 km south of the tree. Calculate the positions of the vessels when there is a minimum distance between them. Answered by Penny Nom.
	Josh and John were both exposed to the flu		2005-12-16
		From Dudley: Josh and John were both exposed to the flu. John has a 25% chance of getting it, while Josh has a 75% chance of getting it. What are the chances that at least one of them has the flu? Answered by Penny Nom.
	Mrs. Faria lives on an island		2005-12-15
		From Julie: Mrs. Faria lives on an island 1 km from the mainland. She paddles her canoe at 3 km/h and jogs at 5 km/h. the nearest drug store is 3 km along the shore from the point on the shore closest to the island. Where should she land to reach the drug store in minimum time? Answered by Penny Nom.
	A loan of $50,000		2005-12-14
		From Fre: A loan of $50,000 taken today is payable within five years. a. determine the annual payments within to be made to repay the loan if interest is charged at a rate of 10% compounded annually b. show the amortization schedule Answered by Penny Nom.
	LCM		2005-12-12
		From Alex: what is the LCM of 210 and 54 and the LCM of 42 and 126 Answered by Penny Nom.
	Area of a lot		2005-12-03
		From Ben: How do you calculate the area of the following Lot? I figured the following angles from the deed, which read: N 86 degrees, 45 minutes E, for 322 feet. S 10 degrees, 30 minutes W for 113 feet. N 84 degrees, 30 minutes W for 368 feet. N 50 degrees, 42 minutes E for 76 feet. N 40 degrees, 40 minutes E for 15 feet. There is a discrepancy between two surveyors and I'd like to figure out how to calculate the Area of such a shape. Answered by Harley Weston.
	I = PRT		2005-11-16
		From Ryan: Use the formula to find the value of the variable that is not given: I=PRT;I=$2880, R=0.08, P=$12,000 Answered by Penny Nom.
	Shapes		2005-11-12
		From Tonya and Hailey: MY THIRD GRADERS TEACHER HAS SENT HOME HOMEWORK ASKING FOR THEM TO FIND REAL-WORLD OBJECT IN MANY DIFFERENTS SHAPES A FEW HAVE US STUMPED Answered by Penny Nom.
	Notation for the second derivative		2005-11-08
		From Mussawar: my question is d/dx( dy/dx) = d2y/dx2. why it is not equal to d2y/d2x. Answered by Penny Nom.
	The number is increased by the sum of its digits		2005-11-07
		From Ernesto: The number 1 is written on a blackboard. After each second the number on the blackboard is increased by the sum of its digits. is it possible that at some moment the number 123456 will be written on the blackboard? Answered by Claude Tardif.
	Velocity and acceleration		2005-10-27
		From Candace: When taking the integral of the position function, you get the velocity function, and the same for velocity to acceleration. So when you do each of these, you get a function. But when you integrate on a graph, you get an area under a curve. The area is un units squared- where do the units go when you make it an equation? How can a function be an area? Answered by Harley Weston.
	(x/1+x)^x		2005-10-23
		From A student: LIMIT x-.->0 (x/1+x)x how to solve it. Answered by Penny Nom.
	Least common multiple		2005-10-22
		From Dayna: I'm stumped! I can't seem to come up with a least common multiple of 22 and 25. Is there one? Answered by Penny Nom.
	A triangular pyramid		2005-10-22
		From Stacee: When stacking oranges to form a triangular pyramid, each orange touching 3 oranges below it. In order to have a pyramid with 6 layers, how many oranges should be on the bottom layer? Answered by Penny Nom.
	Can we take the derivative of independent variable		2005-10-18
		From Mussawar: why we take derivative of dependent variable with respect to independent variable .can we take the derivative of independent with respect to dependent.if not why. Answered by Walter Whiteley.
	The area of an irregular semi-circle		2005-10-14
		From Bob: Is there a way to compute the area of an irregular semi-circle i.e. one in which the arc length is not determined by the diameter; and is therefore not technically any part circular - yet still possessing an arched side? Answered by Penny Nom.
	Simultaneous equations		2005-10-13
		From Daniel: 5x + 3y = 22 4x - 7y = -20 Answered by Penny Nom.
	A cone with vertex (1,1,2)		2005-09-26
		From Brandon: Find the equation of a double cone with vertex (1,1,2) and which intersects the xy plane in a circle of radius 4. Answered by Penny Nom.
	U'(X) - U(X) = 0; U(0) = 2		2005-09-23
		From David: Out of interest could you please answer the following questions? U'(X) - U(X) = 0; U(0) = 2 and U''(X) - U'(X) = 0; U'(0) = U(0) = 2 Answered by Harley Weston.
	Constructing figures		2005-09-20
		From Kim: I would like to know how to draw different shapes: Regular Octagon with sides of length, 1 unit Equilateral Triangles, with sides of length 1 unit Regular Hexagons, with sides of length 1 unit Isoseles Triangles, with hypotenuse of length 1 unit Answered by Penny Nom.
	A point is moving on the graph of x^3 + y^2 = 1 in such a way that		2005-09-17
		From Gina: A point is moving on the graph of x3 + y2 = 1 in such a way that its y coordinate is always increasing at a rate of 2 units per second. At which point(s) is the x coordinate increasing at a rate of 1 unit per second. Answered by Penny Nom.
	How do you differentiate y=(x)^(x^x)?		2005-09-14
		From Calebius: How do you differentiate y=(x)(xx)? Answered by Penny Nom.
	Seven consecutive reds in roulette		2005-09-04
		From Joe: I know that the odds are a little less than 50% for either black or red comming up on a spin of the roullette wheel. My question is what are the odds of red or black comming up 7 times in a row? Answered by Penny Nom.
	The area of a lot		2005-08-29
		From Richard: My wife and I are interested in buying property in Idaho but the owner can't give us a square footage of the lot. The dimensions are as follows: 121.0 on the left side 157.0 on the right side 135.0 on the bottom 162.0 on the top The bottom right corner of the lot is a true right angle, the rest are not. Answered by Penny Nom.
	My fantasy football league		2005-08-16
		From Jim: I have to make a schedule for my fantasy football league. There are 10 teams in the league and we play a 13 week season. The challenge is we want to play each team only once during the first 10 weeks. This way no team will play another team twice without having played each team at least once. Is this possible? Answered by Penny Nom.
	At what rate is the circumference of the circle increasing?		2005-08-08
		From John: A mathematics professor is knitting a sweater. The main part of the sweater is knit in a large spiral, ending up with a diameter of 30 inches. She knits at a constant rate of 6/7 square inches per minute. 1. At what rate is the circumference of the circle increasing when the diameter is 2 inches? 2. How long will it take her to finish this piece of the sweater? Answered by Penny Nom.
	A golf outing for 16 golfers		2005-08-05
		From Bob: I have a golf outing fast approaching and I’m having a problem matching the golfers so that everyone plays a round of golf with every other golfer in the group. My problem is this: I have 16 golfers playing 5 rounds of golf. I would like a different foursome for every round of golf, that is each round (5 total) an individual is playing with 3 other players he hasn’t played with as of yet. Can you crunch the numbers and get back to me? The way I see it, we have 20 combinations (5 rounds x 4 golfers) with numbers 1 thru 16. Answered by Chris Fisher.
	Three prime numbers p,q and r, all greater than 3, form an arithmetic progression:		2005-07-18
		From Ladis: Three prime numbers p,q and r, all greater than 3, form an arithmetic progression: p=p, q=p+d and r= p+2d. Prove that d is divisible by 6. Answered by Chris Fisher.
	The area of a lot		2005-07-17
		From John: A plot of land has the following dimensions: 391 ft. x 757 ft. x 208 ft. x 788 ft. Q: How many acres is this? Answered by Harley Weston.
	A lighthouse is located on a small island,...		2005-07-14
		From Brittnee: A lighthouse is located on a small island, 3 km away from the nearest point P on a straight shoreline, and its light makes four revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P? Answered by Penny Nom.
	The sum of the digits of 2^100		2005-06-11
		From Richard: The sum of the digits was calculated for the number 2100, then the sum of the digits was calculated for the resulting number and so on, until a single digit is left. Answered by Penny Nom.
	The volume of a hopper		2005-05-28
		From Brian: I would like to know the volume of this rectangular hopper. can you help Answered by Penny Nom.
	Logarithmic differentiation		2005-05-23
		From Richard: I need to convince myself that I understand the process of differentiating y=xx. The specific question is that if I have to take the logarithm of both sides of the equation how can differentiate the following? y= {(x+2)(x+2)}/{(x+1)(x+1)} - {(x+1)(x+1)}/(xx), I have an idea that the differential of this fairly complex function is itself ... am I right or wrong. Answered by Penny Nom.
	A triangular lot		2005-05-21
		From Linda: I am looking to purchase a piece of property, and I need some help trying to figure out the square footage of the land. I know that normally if I multiply the length and width I could get my answer. However, this piece of land is an odd shape and has 3 measurements. Can you please help me. The measurements for this piece of land is: 97.8' 201.2' 139.7' Answered by Penny Nom.
	Divisibility of a^2 + b^2		2005-05-16
		From Ampa: given natural numbers a and b such that a2+b2 is divisible by 21, prove that the same sum of squares is also divisible by 441. Answered by Penny Nom.
	L'hopital's rule		2005-05-15
		From Abraham: Find the limit of [(1/(x+4))-(1/4)]/x as x approaches zero. How do you use l"hopital's rule to find this limit. I know how to do it with multiplying everything by 4(x+4), and getting the answer, -1/16.But how do you apply derivatives with l'hopitals rule to this type of problem? Answered by Penny.
	sin x + sin 2x + sin 3x + sin 4x = 0		2005-05-10
		From Elia: I tried many times, but can't get to solve the following question: sin x + sin 2x + sin 3x + sin 4x = 0 Answered by Chris Fisher.
	Some triangle problems		2005-05-06
		From A student: 1.use the heron's formula to find area of triangle ABC to nerest tenth A.a=21 b=28 c=11 B.a=23 b=28 c=12 2.Find the nearest tenth the altitude of the longest side if a=3 b=3 c=5 3.the length of each side of a rhombus is 10 cm the length of one diagonal is 12 cm find the area to the nearest square centermeter Answered by Penny Nom.
	A Taylor series for ln(x)		2005-04-16
		From Anood: i have to represent ln(x) as a power series about 2 i`m not getting the final answer which is ln 2+ sigma (((-1)(n+1)/ (n*2n))*(x-2)n). i don`t get the ln 2 part i show you my trial f(x)= ln x. f-(x)=(1/x) . f--(x)= (-1/x2)*1/2! f---(x)= (2/x3)*1/3! f----(x)= (-6/x4)* 1/4! so the pattern shows me that f(n)= ((-1)(n+1))/xn *n) so f(2)= sigma ((-1)(n+1))/2n *n) *(x-2)n so as you see i don`t get ln 2 Answered by Penny Nom.
	A flaw in a problem		2005-04-15
		From Bryce: Question: (x2-x2) = (x2-x2) x(x-x) = (x+x)(x-x) [divide both sides by (x-x)] x = x + x x = 2x [divide both sides by x] 2 = x/x = 1 Where is the flaw in this problem? Answered by Paul Betts.
	Bayes Theorem		2005-04-03
		From wei: In the January 11,1988,issue of the Oil&Gas Journal, R.A.Baker describes how the Bayesian approach can be used to revise probabilities that a prospect field will produce oil. In one case he describes, geological assessment indicates a 25% chance the field will produce oil. Further,there is an 80% chance that a particular well will strike oil given that oil is present on the prospect field. Suppose that one well is drilled on the field and it comes up dry. What is the probability the prospect field will produce oil? If two wells come up dry, what is the probability the field will produce oil? The oil company would like to keep looking as long as the chances of finding oil are greater than 1%. How many dry wells must be drilled before the field will be abandoned If the first well produces oil,what is the chance the field will produce oil? Answered by Andrei Volodin and Penny Nom.
	A wrestling schedule		2005-03-08
		From Ed: Hello my name is Ed and I am a couch of a wrestling team in New Jersey. I was doing searches for formulas on how to make a matrix for team sports and it seems to be hard to find. I came some how to your site and thought I'll give it a try. Here is what we need or are trying. Answered by Claude Tardif.
	A nine week schedule		2005-03-08
		From Greg: I'm trying to build a nine week schedule where 10 teams play each other once throughout the season. I make it all the way to week nine, then I start having all sorts of conflicts. HELP!! Answered by Claude Tardif.
	The area of a quadrilateral		2005-02-27
		From Jonathan: I want to know how to find the area of a quadrilateral. Answered by Penny Nom.
	Understanding fractions		2005-02-11
		From C.J.: I have some questions about the lesson, "Understanding Fractions" by Diane Hanson, Regina Catholic Schools. How successful was the lesson? Are there any changes you would recommend? Answered by Diane Hanson.
	A seating arrangement		2005-02-03
		From Kay: If you have 5 married couples, how many arrangements can be made if they must sit across from each other? Answered by Penny Nom.
	Differentiating F(x,y) = 0		2005-01-23
		From Jacob: In calculus, we often mention to the students that if F(x,y) = 0, then we can differentiate both sides and still get an equality. The problem is that we can't perform the same operation on F(x) = 0, say x = 0, otherwise 1 = 0, which is absurd. What is the reason? Answered by Walyer Whileley and Harley Weston.
	Finding the missing side of a triangle		2005-01-20
		From Jason: I found a geometry problem that reads as follows:In triangle ABC, Answered by Penny Nom.
	A line from the center of the patch to the periphery		2005-01-01
		From Sandrine: I am currently researching a patch disease of grasses. These patches are roughly circular. I need a term for a line from the center of the patch to the periphery. Since the patches are not perfectly circular, my supervisors tell me I cannot use the word 'radius'. What else could I use? Answered by Denis Hanson and Harley Weston.
	The area of a triangle		2004-12-30
		From Perry: What is the area of a triangle with dimensions 3"X5"X7"? Could you provide the formula? Answered by Penny Nom.
	A Reuleaux triangle		2004-12-22
		From Bob: I am trying to remember the name given to the regular figure constructed from three arcs. The figure is like an equilateral triangle except with arcs for each side. Answered by Chri Fisher.
	Three calculus problems		2004-12-09
		From Ashley: Hi, I am having a lot of trouble with three calculus questions and was wondering if you could help Answered by Penny Nom.
	A belt around two pulleys		2004-12-07
		From Ian: a belt is stretched around two pulleys whose centers are d units apart and whose radii are R and r respectively (obviously R+r<d). the challenge is to find the length of the belt, l as a formula in terms of R, r, and d only. Answered by Penny Nom.
	The lcm of 5, 3, 4, 7 and 2		2004-11-05
		From Christine: what is the lcm of 5,3,4,7,2 Answered by Penny Nom.
	The lcm of 1 and -1		2004-11-03
		From Nayiyan: I would like to know what is the LCM of (-1) and (+1) is. Answered by Penny Nom.
	Multiplying two algebraic fractions		2004-10-31
		From A parent: Multiply: x+2 x²-4 ----- x ------- x-2 x²+x-2 Answered by Harley Weston.
	GCD and LCM		2004-10-31
		From Cartalina: how do you calculate the "positive difference between the GCF and LCM of two numbers"? Answered by Penny Nom.
	The combined force of two vectors		2004-10-30
		From Brian: Two teams are playing push ball with a large 8 foot diameter ball. One team exerts a force represented by the vector a = 2i + -5j, and the other team exerts a force represented by the vector b = -8i-3j. 1.Determine the direction of movement of the ball if the i axis is due east. 2.Determine the combined force magnitude. Answered by Harley Weston.
	The force of a 5000 tonne lorry		2004-10-27
		From Aaron: A 50 tonne lorry is parked on a slope with a gradient of 4%. Due to the self weight of the lorry, what is the force * acting down the slope * acting normal (at right angles) to the slope Answered by Penny Nom.
	20 Golfers		2004-10-26
		From Ian: I have 20 golfers playing over 6 days I would like to schedule all 20 golfers in 5 groups of 4 on each day here is the catch.... I would like each player to play with each other once during the 6 days. Answered by Chris Fisher.
	Implicit differentiation		2004-10-24
		From Emily: If x^3+3xy+2y^3=17, then in terms of x and y, dy/dx = Answered by Penny Nom.
	sin(3A)		2004-10-20
		From A student: Express sin3A in terms of sinA and cosA. Answered by Penny Nom.
	The volume of a pile of mulch		2004-09-22
		From Sam: Is there a formula to determine the cubic feet of something in a pile. IE- I need to determine the cubic feet of a pile of mulch. The pile comes to a peak, so the length and width decrease as the pile increases. Answered by Penny Nom.
	Finding the height of a triangle		2004-09-14
		From A student: I have to calculate the height of a triangle. The base is 6 (units)say ab One of the top sides is 4 (units)say ca The other side is 2 (units) say cb I don't know the angles. How to find the height? Answered by Chris Fisher and Penny Nom.
	A schedule for 6 teams		2004-09-10
		From Greg: I have a schedule I need to make of 6 teams. They must play each other once however no team can be the away team twice in a row. There must be 3 home games and 3 away games for each team. Answered by Penny Nom.
	The bar over repeating digits.		2004-09-07
		From Debbie: I would like to know the name given to the bar that is written over the repeating digits of a decimal. Answered by Penny Nom.
	The distance formula		2004-09-04
		From Joe: Why do we use square roots and squares in the distance formula Wholdnt they cancel each other out? Answered by Claude Tardif.
	The integrating factor method		2004-08-05
		From A student: Whilst using the integrating factor method, I am required to integrate a function multipled by another function. say f(t) = exp(kt) and some other function g(t); where exp = exponential and k is some constant. Integral f(t)*g(t) dt or Integral exp(kt)*g(t) dt What would the result of this integral be? I have never met an integral like this before. Would it simply be exp(kt)*g(t)/k? More specifically, the problem and my attempted answer is in PDF format: In my attempted solution, I am unsure about the last two lines I have written out, as it relates to integrating a function multipled by another function. Answered by Harley Weston.
	Integrating e^sin(x)		2004-08-04
		From A student: I need to know that how to solve the integral " e^sin x", Answered by Harley Weston.
	Differentiation		2004-08-04
		From A parent: I am a parent trying to understand higher level of maths and would be very grateful if you could help with differentiating the following functions, identifying general rules of calculus: a) f(x)=e^2^xIn(cos(8x)) b) f(x)=secx/SQRTx^4+1 Answered by Penny Nom.
	Two vector problems		2004-07-14
		From Jaye: Two force, 120lb and 200lb, act on a body and make a 52 degree angle w/ ea. other. What's the magnitude of the resultant of the forces and what is the measure, to the nearest degree, of the angle that it makes with the 200lb force? Answered by Penny Nom.
	What is the name of a 3D rectangle?		2004-06-07
		From Jack: if a cube is a 3D square, what is the name of a 3D rectangle? Answered by Penny Nom.
	The Parliament of the land of Achronia		2004-05-29
		From Christine: The Parliament of the land of Achronia consists of two houses. The parliament was elected in 2003 for a period of six years beginning on Thursday, the 1st of January 2004, when the two houses had their first sessions. According to the rules, the meetings of the first house must occur every twelve days for the duration of the term, and the meetings of the second house must occur every eighteen days. For example, the second meetings of the first and the second houses were held on the 13th and 19th of January respectively. A new law can be passed on any day when both houses meet, except on a Thursday. On how many days can the parliament members pass new laws during this six year term? Answered by Penny Nom.
	Some trig expressions		2004-05-23
		From A student: Prove: sin A + sin B = 2sin(A+B/2)cos(A-B/2) cos A - cos B = -2sin(A+B/2)sin(A-B/2) cos A + cos B = 2cos(A+B/2)cos(A-B/2) sin A - sin B = 2cos(A+B/2)sin(A+B/2) Answered by Penny Nom.
	Maximizing the angle to the goal mouth		2004-05-15
		From Yogendra: You are running down the boundary line dribbling the ball in soccer or hockey. Investigate where in your run the angle the goal mouth makes with your position is at a maximum. Answered by Penny Nom.
	Related rates and baseball		2004-04-26
		From Bethany: A baseball diamond is the shape of a square with sides 90 feet long. A player running from second to third base at a speed of 28 feet/ second is 30 feet from second base. At what rate is the player's distance from home plate changing? Answered by Penny Nom.
	A changing rectangle		2004-04-03
		From A student: The width x of a rectangle is decreasing at 3 cm/s, and its length y is increasing at 5 cm/s. At what rate is its area A changing when x=10 and y=15? Answered by Penny Nom.
	Some calculus problems		2004-04-01
		From Weisu: I have questions about three word problems and one regular problem, all dealing with derivatives. Find all points on xy=exy where the tangent line is horizontal. The width x of a rectangle is decreasing at 3 cm/s, and its length y is increasing at 5 cm/s. At what rate is its area A changing when x=10 and y=15? A car and a truck leave the same intersection, the truck heading north at 60 mph and the car heading west at 55 mph. At what rate is the distance between the car and the truck changing when the car and the truck are 30 miles and 40 miles from the intersection, respectively? The production P of a company satisfies the equation P=x2 + 0.1xy + y2, where x and y are the inputs. At a certain period x=10 units and y=8 units. Estimate the change in y that should be made to set up a decrease of 0.5 in the input x so that the production remains the same. If you could just give me some hints on these questions, I'd really appreciate it. Thanks! Answered by Penny Nom.
	A partial derivative		2004-03-19
		From Penny Nom: Is it possible to differentiate the following equation, if so could you please explain. S=SQRT(T-(5/X^2)) I would like the derivative of S with respect to X. Answered by Harley Weston.
	Johann Muller		2004-03-14
		From A student: What major contributions to spherical trigonometry did Johann Muller make? Answered by Penny Nom.
	Volume of a fuel tank		2004-03-01
		From Mike: I have a fuel ank for my big truck that has a radius of 24inches and a length of 65 inches. I am trying to compute the volume of fuel in the tank. I tried pie x the radius squared times the length but no usable results. Can you help me please? Answered by Penny Nom.
	The derivative of x to the x		2004-02-14
		From Cher: what about the derivative of x to the power x? Answered by Penny Nom.
	A pyramid-shaped tank		2004-02-13
		From Annette: The base of a pyramid-shaped tank is a square with sides of length 9 feet, and the vertex of the pyramid is 12 feet above the base. The tank is filled to a depth of 4 feet, and water is flowing into the tank at a rate of 3 cubic feet per second. Find the rate of change of the depth of water in the tank. (Hint: the volume of a pyramid is V = 1/3 B h , where B is the base area and h is the height of the pyramid.) Answered by Harley Weston.
	Angular speed		2004-02-01
		From Rachel: A 4 inch pulley on a motor makes 1500 revolutions/minute. It is connected to an 8 inch saw blade. a. Find the angular speed of the pulley in radians/minute b. Find the angular speed of the saw in radians/ minute Answered by Harley Weston.
	Sin(3x), cos(3x) and tan(3x)		2004-01-28
		From Jon: What is the identity for cos3x, sin3x, and tan3x? In class, we learned double angel identities and were asked to find out the identity to these three trig functions. If you can help, please do. Also, i know that the cos4x- sin4x is the same as cos2x. Is cos8x-sin8x = cos2x also true? Thank you.s Answered by Chris Fisher.
	A problem with sets		2004-01-20
		From Jason: Given that the universal set S is the set of all sports fans, and F={x|x is a football fan} B={x|x is a basketball fan} H={x|x is a hockey fan} a)Describe (F^B)' (f intersect b)' in words b)Draw a Venn Diagram and shade the region that represents the set of football fans or both basketball and hockey fans. Answered by Penny Nom.
	Some trig problems		2004-01-18
		From Weisu: I have some questions about pre-calculus. (1) (2(cos(x))^2)+3sin(x)-1=0 (2) sin(x)cos(x)=(1/2) (3) 3sin(x)=1+cos(2x) (4) tan(x)*csc(x)=csc(x)+1 (5) sin(arccsc(8/5)) (6) tan(arcsin(24/25)) (7) arccos(cos(11pi/6)) the last problem uses radian measure. Answered by Penny Nom.
	Volume of a tube		2004-01-14
		From Mike: where can you find how to get volume of a tube: 3 in across x 3 inch high 5 in across x 5 inch high same formula for both. ONE will get the other. Answered by Penny Nom.
	Geoboards		2004-01-09
		From Elissa: What is a geoboard? I have a young girl in grade eight math who has a math question using a geoboard. Answered by Diane Hanson.
	The area of a lot		2004-01-09
		From Lea: I have a problem. I am interested in purchasing a piece of property which has the following dimensions. It is 259.10 Feet on the north side x 61.20 Feet on the east side x 217.80 Feet on the south side x 196.70 Feet on the west side. It looks like an irregular rectangle shape. How do you figure out the square footage on this irregular sized property, and what is the correct square footage answer. I have attached a survey map. Answered by Harley Weston.
	The trapezoidal rule		2003-12-31
		From Prashanth: I have a set of XY co-ordinates(say 49 points),I want to find the area enclosed by the curve joining them and the axes.I do not have an equation for the curve and I am not able to fit a curve given the points.I use the trapezoidal rule (Y1+Y2/2)*(X2-X1), Is it right? can I do this with any other method? Answered by Penny Nom.
	The angles in a regular polygon		2003-12-21
		From Ernie: If i have a measure of one interior angle of a polygon, how can i find the number of sides it has? Answered by Penny Nom.
	The area of a plot of land		2003-12-19
		From David: I have a plot of land that I cannot find the square footage of. Actually my home sits on a large lot. Local building codes require that a home is seated on no less than 7500 square feet of land and have no less than 50ft of road frontage (the rear of the lot has 65ft of frontage on another road). I need to know if I have enough square footage to build a second home on the rear lot. The lot has five sides. Only one angle is a 90 deg. angle. The others I cannot determine. Of the 4 remaining angles, all 4 angles are obtuse, or greater than 90 deg. The dementions are 89.19' x 130' x 118.52' x 65' x 170.94'. The two legs that make the 90 deg angle are 89.19' and 170.94'. The measurements fall in order using the 90 deg angle as the point of origin and proceeding clockwise, 89.19', 130', 118.52', 65', 170.94'. I have used all the skill I can muster, however, it has been a long time since school and regretably I cannot find an answer. Answered by Penny Nom.
	Multiplier and multiplicand		2003-12-17
		From Karen: The K-5 curriculum states that at a grade 5 level students should "understand and use the terms multiplier, multiplicand" The curriculum defines 'multiplicand' as " a number being multiplied by another number. A factor." There is no definition given for 'multiplier' Question: Define these words- are they just other words for 'factors'. If so, how important is it that students use these terms? It would seem like 'factors' would be the better choice of words to use. If multiplcand refers to eg. the first factor in the equation and the 'multiplier' the seond term, (if in fact it does)- is this not confusing for students when we teach them that multiplication is commutative? Answered by Penny Nom.
	The area of a triangle		2003-12-01
		From A student: Find the Area of Triangle ABC A(-3,2) B(4,0) C(0,8) Answered by Penny Nom.
	The volume of an irregular tetrahedron		2003-11-24
		From Peter: How do I calculate the volume of an irregular shaped tetrahedron where:- side a = 1.4 m side b = 1.4 m side c = 1.2 m and height = 0.75 m at the junction of sides a and b. Answered by Penny Nom.
	A riddle		2003-11-19
		From Sarah: Ok, our teacher gave us this riddle, and I cannot for the life of me figure it out. He said that there are three problems with the following proof: Answered by Penny Nom.
	Divisibility by 7		2003-11-14
		From A student: how do you test a number to see if it is divisible by 7 or not? Answered by Penny Nom.
	A circle around an irregular polygon		2003-11-03
		From Dale: How do I find the properties of a circle that is drawn around an irregular polygon of (n) sides with the lenghts of each side given and all end points of the polygon lye on the circumferance of the circle? Answered by Chris Fisher.
	How much time?		2003-10-29
		From Lori: I am a elementary teacher 3-6 math. We have just implemented the Houghton Mifflin Math curriculum. It seems to be quite difficult for most of our students. In order to get through all the material we need to do a lesson a day. Although the students are not getting the material that fast. Should we move on without all the students understanding the material or should we wait and remediate until they get it and be behind for the year. This isn't just a few kids its most of the kids. We are also suppose to teach to all the standards so if we don't get to them the students will not do well on the standardized tests. Answered by Diane Hanson.
	Maine and Nevada		2003-10-24
		From Jimmy: From 1989 to 1990, the population of Nevada increased b y 157,000, and that of Maine increased by 30,000. In 1990, the population of Nevada was 1,206,152, and that of Maine was 1,233,223. If the populations of the two states continue to increase at the same rates, when will the populations of Nevada and Maine be the same? Write a verbal model for this problem Write an equation for the model Solve the equation and answer the question. Answered by Penny Nom.
	Standard Deviation		2003-10-07
		From Rebecca: I have a task to complete, which is to calculate the mean and standard deviation of something. I have done this but am then asked to write a short explanation of my findings. I know what the mean is about, and I thought I knew what the standard deviation meant too - shows the variation from the mean. However, on a task I completed earlier the feedback I got said 'you need to tell us that it is talking about the middle 66% of the data' - that has thrown me, I don't understand that. Can anyone help me get my head round this??? Answered by Penny Nom.
	The sketch of a graph		2003-10-07
		From A student: I was wondering how do you figure out if a graph has a horizontal tangent line. One of my homework problem was to sketch the graph of the following function; (4/3)x3-2x2+x. I set f''(x) ( the second derivative) of the function equal to zero and got the inflection point:(1/2,1/6). Also i am having trouble finding the concavity for x>1/2 and x<1/2, i am getting a different answer from the back of the book, the graph i draw looks completely different from the correct answer. Answered by Penny Nom.
	Arrangements around a circular table		2003-10-07
		From Lori: How many arrangements can 6 people be seated round a circular table? Answered by Penny Nom.
	Indeterminate forms		2003-10-06
		From A teacher: Is it possible for me to find any geometrical interpretation without using calculus to explain indeterminate forms? Answered by Chris Fisher.
	Functions, graphs and derivatives		2003-10-05
		From Jathiyah: I wanted to know how would you tell (on a graph diplaying two funtions), which funtion is the derivative of the other? Answered by Walter Whiteley.
	The slope of a tangent		2003-10-01
		From A student: find the slope of the tangent to each curve at the given point f(x)=square root 16-x, where y=5 Answered by Penny Nom.
	7,473,000,000 divided by 52000		2003-09-06
		From A student: I am having trouble with a question. 7,473,000,000 divided by 52000. Our calculater gets 147311.5385. I come up with 143711.53846, and then the number starts to repeat itself Answered by Penny Nom.
	A helicopter rises vertically		2003-09-02
		From Kate: A helicopter rises vertically and t seconds after leaving hte ground its velocity is given in feet per second by v(t) = 8t + 40 / (t+2)2 How far above the ground will the helicopter be after 3 seconds? Answered by Penny Nom.
	A 6 team schedule		2003-08-31
		From A scheduler: I saw that someone put on your web site a team schedule and you helped them figure it out.Ý I have 6 teams that want to play each other once, and believe it or not, I cannot figure it out. Answered by Penny Nom.
	The quadratic formula		2003-08-31
		From Alex: I am using Houghton Mifflin's Precalculus with Limits book, 2nd edition. However, the first chapter encompasses Algebra review, and I am stuck on a problem. All that's required is to solve the following and verify using a calculator: 3y2+6y+2=0 I have solved the problem using the quadratic formula, but from what I remember, the quadratic formula is used in the case of equations following the AX2+BX+C=0 pattern. As the problem I am attempting uses a y-variable, can I still use the quadratic formula? Since I am not sure what route to take in solving this problem, I am hoping you can assist me. Answered by Harley Weston.
	A rule with a variable		2003-08-24
		From Crystal: what is a rule with a variable Answered by Penny Nom.
	A golf tournament		2003-08-23
		From Dale: I am running a golf tournament with twelve golfers. We will be playing four rounds of golf. I don't want to schedule the same two players together more than twice (if possible). How would I make a schedule that each player would play at least once with every other player? I would appreciate any help that you can give me. Answered by Denis Hanson.
	Two precalculus problems		2003-08-04
		From Kate: Please help me verify the identity: cos2x(sec2x-1)=sin2x Also I am having trouble withdetermining whether f(x) is odd, even, or neither f(x)=x3-x Answered by Penny Nom.
	The area of an odd shaped piece of property		2003-07-24
		From Barry: What is the formula for figuring the square footage of an odd shaped piece of property? Answered by Penny Nom.
	Natural logarithms		2003-07-22
		From Amanda: I'm going into my senior year of high school. I will be taking AP calculus, and my teacher gave us some homework over the summer. However, there are two things that I do not understand how to do. The first is, she wants us to be able to generate a unit circle by hand using 30, 60 and 90 degree triangles. I have used the unit circle in trigonometry, however I was never taught how to draw it. Secondly, I need to know how to do natural logarithms without a calculator. I was not taught how to do this, and the worksheet I was given only showed me how to complete them using a calculator. Answered by Claude Tardif.
	A ruler and compass construction		2003-06-29
		From Mandy: I have been searching for instructions on how to do this using a compass. Can you please send instructions step by step on how to bisect a segment into any given number of segments. (example, a way that it will work for bisecting segment into 3, 4, or even 5 congruent parts) Answered by Penny Nom.
	Odd powers of sine and cosine		2003-06-25
		From Antonio: Can you please tell me how to integrate a trig function involving sine and cosine? I know if the powers of both the sine and cosine are even and nonnegative, then I can make repeated use of the power-reducing formulas. But for the question I have on my hand, the powers of both sine and cosine are odd: ( sin3x + cos7x ) dx. Answered by Harley Weston.
	Rules of exponents		2003-05-05
		From Carl: Hi, I am a student who would like to recall how to multiply exponents. Here is such an equation: 6.02569 X 1025 X 5.254 =? Also, adding exponents. Don't I just add subtract the exponents separately? Such as 523 +15-12 =?? Answered by Penny Nom.
	Write sin(3x) in terms of sin(x)		2003-05-05
		From A student: Write sin 2x in terms of sin x Answered by Penny Nom.
	Integrating e^x sin(x)		2003-05-03
		From Lech: I am having trouble integrating the following expression by parts: ex sin(x) I used the integrator at http://www.integrals.com/ to find the solution, ? 1/2 ex cos(x) + 1/2 ex sin(x). This is easy to confirm by differentiation, however I am confounded as how to arrive at the answer. Answered by Penny Nom and Claude Tardif.
	The volume of air flowing in windpipes		2003-05-02
		From James: The volume of air flowing in windpipes is given by V=kpR4, where k is a constant, p is the pressure difference at each end, R is the radius. The radius will decrease with increased pressure, according to the formula: Ro - R = cp, where Ro is the windpipe radius when p=0 & c is a positive constant. R is restricted such that: 0 < 0.5*Ro < R < Ro, find the factor by which the radius of the windpipe contracts to give maximum flow? Answered by Penny Nom.
	A regular polygon		2003-02-26
		From Melissa: The measure of each interior angle of a regular polygon is eight times that of an exterior angle of the polygon. How many sides does the polygon have? Answered by Penny Nom.
	Multiples of all four of the numbers 2, 3, 4, and 5		2003-02-11
		From Stephanie: How many of the first 1000 positive integers are multiples of all four of the numbers 2, 3, 4, and 5? Answered by Penny Nom.
	I have three circles...		2003-01-30
		From Tony: I HAVE THREE CIRCLE THAT IS CIRCLE TOGETHER: IN CIRCLE A, THE NUMBERS ARE: 11 I KNOW IS IN CIRCLE A, BUT I HAVE THE: 5 THAT IN A AND C, I HAVE THE 2 IN THE CIRCLE C AND B AND AND A, THE CIRCLE C I KNOW THAT 10 IS IN THE CIRCLE THE 4 IN CIRCLE A: AND B: IN CIRCLE B, I KNOW NUMBER 13 IS IN CIRCLE B; BUT I HAVE THE 3 IN CIRCLE B AND C AND I HAVE THE 2 IN CIRCLE B AND C AND A ,THE 4 IN CIRCLE B AND A. HOW DO I FIND THE SUM IN CIRCLE C AND IN B IN BOTH CIRCLE A AND B AND B AND C NOT IN CIRCLE B, AND NOT CIRCLE C. Answered by Penny Nom.
	6 digit numbers from 0,0,2,2,4,4		2003-01-23
		From Amanda: How many 6 digit numbers can you make from the numbers 0,0,2,2,4,4, giving that 0 cannot come first. The number has to contain 2 twos, 2 fours, and 2 zeros. Answered by Penny Nom and Claude Tardif.
	The area of a regular n-gon		2003-01-22
		From Sophie: We have been given a piece of maths coursework. A farmer has exactly 1000 metres of fencing and wants to fence off a plot of level land. she does not mind what the shape is but it must have a perimeter of 1000m. She wants to fence off the plot of land which contains the maximum area. Investigate the shape, or shapes that could be used to fence in the maximum area using exactly 1000 metres of fencing each time. I have investigated many shapes, and I feel that a circle will have the biggest area. However we have also been asked to investigate shapes with 20 and 30 sides. My dad said that there is a formula for finding out any area of land. Do you know of this formula, if so I would be very grateful if you were to email it to me. Answered by Penny Nom.
	The least common denominator		2003-01-21
		From Brittan: Hi there I need help! My name is Brittany and i am in the 6th grade. I need help finding the least common denominator(LCD), and the book says Find the LCM of the denominators and i've done that and then it says write equivalent fractions,using the LCM as the least commonn denominator.The directions say Use the LCD to write each pair as like fractions. and the problem is 1/8 and 5/40. Could u explain how in the word u do this? Thanks a lot Brittany Answered by Penny Nom.
	Collinear Points		2003-01-13
		From Gary: Which of the 4 points are collinear when you construct the following concurrent lines or rays of a triangle? P(1), the point where the angle bisectors intersect. P(2), the point where the altitudes (or extensions) intersect (inside or outside of the triangle). P(3), the point where the medians intersect. P(4), the point where the perpendicular bisectors (or extensions) of the three sides of a triangle intersect. This is for my 9-12 high school class in geometry. My name is Gary Thanks for your help. Gary Answered by Harley Weston and Chris Fisher.
	A rectangular prism		2003-01-09
		From Julie: How many faces on a rectangular prism and how many bases? Can the base also be a face and can a face also be a base? Answered by Diane Hanson.
	Integration of 1/(2+cos(x))		2003-01-07
		From A student: integral from pi to 0 of dx/(2+cos x) i used the substitution t=tan(x/2) and i ended up with integral from +infinity to 0 of 2dt/(t2+3) which looks like an inverse tan function , and i ended up with sqr(27)/2 pi , which is not the same as my calculator's answer , so i suspct i am doing some thing wrong. can some one tell me where i am going wrong please. Answered by Penny Nom.
	Calculations		2002-12-15
		From Mahdi: This problem is rather general, but it usually makes a lot of problems. I almost have no difficulty in math and physics questions, but unfortunately I'm not at all accurate in simple one or two digit calculation. I even sometimes make silly mistakes in simple sums like 7+4=12 or 4+5=11! Is there any effective way to reduce these mistakes? Answered by Walter Whiteley.
	Construct a pentagon		2002-12-12
		From Mary: We were wondering what the instructions/formula, step-by-step, is to make a pentagon. Answered by Chris Fisher and Penny Nom.
	Differentiating inverses		2002-11-20
		From Amy: f(x)= x3+x+1, a=1 find g'(a) (g = f -1). I am having trouble finding g(a). Answered by Penny Nom.
	Why is 5 divided by 1/7 greater than 5 divided by 2/3?		2002-11-19
		From Elizabeth: Without performing the division, explain why 5 divided by 1/7 is a number greater than 5 divided by 2/3. Is the least common multiple of two prime numbers always their product? Why or why not? Answered by Diane Hanson and Penny Nom.
	The volume of water in a hose		2002-11-13
		From David: I trying to find out how much water 500 ft of 3/4 inch hose will hold. I'd also like to know how you figured the answer. Answered by Penny Nom.
	An octagon of perimeter 1,000 meters		2002-11-05
		From Stephen: my son has to work out the area of a octagon with a outside perimeter of 1,000 metres, Answered by Penny Nom.
	A triangular prism		2002-10-30
		From Daniel: I was wondering what a triangular prism was. Answered by Diane Hanson.
	Baseball, basketball and football		2002-10-08
		From Debbie: The school newspaper is interviewing 6th grade students to see what sports they follow regularly on TV. Of the 70 students interviewed; 40 enjoyed basketball; 40 enjoyed baseball; 40 enjoyed football; 20 enjoyed basketball and football; 22 enjoyed baseball and basketball; 27 enjoyed football and baseball; and 12 enjoyed all three sports. How many students out of the 70 interviewed didn't follow any one of the three sports? Answered by Leeanne Boehm, Penny Nom and Walter Whiteley.
	A max/min problem		2002-09-21
		From Evelina: A window is the shape of a rectangle with an equilateral triangle on top. The perimeter of the window is 300 cm. Find the width that will let the maximum light to enter. Answered by Penny Nom.
	Fractional exponents		2002-09-20
		From Jill: The problem is with fractional exponants: 10 1/3 mult. by 10,000 The 1/3 is an exponant of 10. Answered by Penny Nom.
	The entire earths' population would fit in the state of Texas		2002-09-18
		From Roz: I have been told that the entire earths' population would fit in the state of Texas and each person would have 1/2 acre. Is this true. Answered by Chris Fisher.
	Formulating equtions		2002-09-14
		From Theresa: Hello. In math class we have to formulate equations for certin questions for extra credit. We are allowed to ask anyone and anyone can do it for us and explain it to us. Could you please do that? Here are the questions Jordan has 3 times as much money as Reva. Together they have $44. How much money does each have? The Tigers played 48 games. They won twice as many as they lost. How many did they win? There are 900 students in Sewickley Academy. There are 20 more girls than boys. How many girls are there? A board 400 cm long is cut into 2 pieces. One piece is 66 cm longer than the other. Find the lenght of the shorter piece. Answered by Penny Nom.
	The quadratic formula		2002-09-11
		From Kathleen: im having a problem trying to understand quadratic formulas can u please help me i have problems like 3x2 - 4x - 11 = 0 how do i work out that problem? i have the formula written down but it doesnt seem to register for me. Answered by Penny Nom.
	The area of a triangle		2002-09-07
		From Phill: How do you find the area of a equilateral and other triangles? Answered by Penny Nom.
	A schedule for a fantasy football league		2002-09-01
		From Steve: i am in a ten(10) team league, split evenly into two five team divisions. we play a thirteen(13) game schedule and would like to play each team in your own division twice, and each team in the other division once. according to my rudimentary mathematics that equals 13 games. a good schedule should look somthing like this: team 1-5 = division 1 team 6-10 = division 2 team 1 should play teams 2-5 twice and teams 6-10 once. Answered by Claude Tardif.
	Distance in 3-space		2002-08-16
		From David: The question is: how do I figure out the distance of one object in 3D space to another object in 3D space? I have an object at say x = 5.872, y = 2.876, and z = 7.290; and the other object is at x = 1.129, y = -8.213, and z = -11.127. I have been suggested to use the pythagorean theory on this, but since there are three variables, I don't understand how. Answered by Penny Nom.
	Two equations		2002-07-26
		From Derek: 1. 3x + 2y = 4 2. -7x + 2y = 24 finding x and y. Answered by Penny Nom.
	7th grade math lesson plans		2002-07-23
		From Peter: Where can I get samples of 7th grade math lesson plans and curriculum for the whole year? Answered by Leeanne Boehm.
	The base 10 multipliction table		2002-07-07
		From A student: These are two questions from Math for Elementary Teachers and they have me stumped. You have two coins that are worth 30 cents. One of the coins is not a nickel. What are the two coins? The product of the diagonals of any 2x2 matrix in the base 10 multiplication table are equal. Why? Answered by Penny Nom.
	Integrating x^x		2002-06-18
		From Jeremy: I am a student at the University of Kansas and I am wondering if there is a general anti-derivative for x x (i.e. the integral of x x dx)? I've looked in a bunch of Table of Integrals and have found nothing (can you guys find it?), so I'm sort of wondering if this may be a research type question. Answered by Claude Tardif.
	A good rule of thumb when driving		2002-06-13
		From Lisa: A good rule of thumb when driving is that you should be about one car length away from the car in front of you for every 10 miles per hour that you are travelling. Suppose you follow this rule perfectly (so you are exactly the correct distance away). You are waiting at a stop light with your front bumper just touching the car in front of you. The light turns green and the car in front accelerates at a constant rate "r". Calculate how you should accelerate in order to follow the rule. Answered by Penny Nom.
	Regular polyhedra		2002-06-07
		From Sandra: The other day a colleague and I were talking about polyhedra. Is regular a term applied to polyhedra or just polygons? If so, then what would define a regular polyhedron? Would it mean all faces are regular or would it mean that all faces are identical and regular? That is, could a pyramid with equilateral triangles for lateral faces and a square base be considered regular or must the base also be an equilateral triangle? Answered by Chris Fisher.
	Constructing the square root of 3		2002-06-07
		From Allan: I am a Math 7/8 teacher. I was wondering how you would show a student how to find the exact location of the square root of three on the number line using just a compass and a straight edge. Answered by Penny Nom.
	The area of a circle		2002-06-03
		From Jessica: I am doing a maths assigment for university, which is aimed towrds primary school students(k-6). I was wondering if you could give me some information as to how I could describe to students the rule for finding the area of circle, using a circle cut up into equal sectors (like a pizza). I know it has something to do with the fact that you can make these shapes into a parallelogram, but I am a bit uncertain as to how I can express this idea clearly and articulately to students. Answered by Penny Nom.
	A spotlight shines on a wall		2002-05-25
		From Barb: A spotlight on the ground shines on a wall 12m away. If a man 2m tall walks from the spotlight toward the bldg at a speed of 1.6 m/s, how fast is his shadow on the bldg decreasing when he is 4m from the bldg? Answered by Penny Nom.
	A schedule for 24 golfers		2002-05-25
		From John: I am working on a schedule for 24 golfers. 6 groups of 4. I have 8 golf days (twice per week for a month). Ideally, I would like to schedule all 24 golfers in 6 different groups of 4 on each day. Here is the catch.....no golfer in any group can be grouped togther more than once. Every group of 4 each day will have 4 new golfers that have never played together before. Is this possible? Answered by Chris Fisher.
	Conditional probability		2002-05-19
		From Manny: In a certain school, it is known that 80% of the students use the internet for school projects, 60% use e-mail on a regular basis, and 90% use the internet for school projects or for e-mail on a regular basis. a student from this school is selected at random Determine thge probability that the student used e-mail, given that the student used the internet for school projects. ANS: how can i solve this question by useing the vin diaagram Answered by Andrei Volodin.
	What is Calculus About?		2002-05-13
		From A student: I am a high school senior and have to write an essay answering the question "What is Calculus?" I need some ideas. Thanks Answered by Walter Whiteley.
	A rectangular marquee		2002-05-07
		From Alyaa: a marquee with rectangular sides on a square base with a flat roof is to be constructed from 250 meters square of canvas. find the maximum volume of the marquee. i find this topic so hard Answered by Harley Weston.
	How will I use calculus in my career?		2002-05-06
		From Meridith: How will I, hopefully a future secondary mathematics teacher, use calculus in my career if I'm not teaching calculus? Answered by Walter Whiteley.
	A triangular prism		2002-04-28
		From A student: Need the formula for the surface area of a triangular prisim? Answered by Penny Nom.
	Triangular numbers		2002-04-26
		From Anika: Can you please tell me what a triangular number is? Answered by Penny Nom.
	Arc length		2002-04-17
		From Vix: Find the point on the curve r(t)=(12sint)i-(12cost)j+5tk at a distance 13pi units along the curve from the point (0,-12,0) when t=0 in the direction opposite to the direction of increasing arc length. Answered by Harley Weston.
	Related rates		2002-04-17
		From Molly: A tanker spilled 30 ft cubed of chemicals into a river, causing a circular slick whose area is expanding while its thickness is decreasing. If the radius of the slick expands at the rate of 1 foot per hour, how fast is them thickness of the slick decreasing when the area is 100 feet squared? Answered by Penny Nom.
	Area of a triangle		2002-04-07
		From Puzzled: What is the surface area of a triangle 13 ft x 13 ft x 18 ft? Answered by Penny Nom.
	Pairs of equations		2002-04-04
		From A student: high school level student is asking y=4x x=-4y x+y=5 3x+2y=20 y=x-1 3x-y=4 x+y=3 2x-3y=-9 x+5y=4 3x+15y=-1 . . . Answered by Penny Nom.
	Take It!		2002-04-03
		From Bryan: You are playing Take It! for $180,00 with a total stranger. There are 180 identical balls in a big vase. Each player in his turn, reaches into the vase and pulls out 1,5,or8 balls. These balls are discarded. The player who takes the last ball from the vase wins the $180,000. A flip of the coin determines that you will go first. Are you glad? How many will you take out on the first move, and how will you proceed to win the prize? Answered by Claude Tardif.
	If you conect all the vertices of a regular n-gon...		2002-04-01
		From Murray: If you conect all the vertices of a regular n-gon with lines you will have (n-3)(n/2) lines inside the polygon. I want to find out how many sections these lines divide the polygon into and how many intersections they have with each other. Answered by Claude Tardif.
	Some 5 card hands		2002-03-28
		From A student: From a standard deck of cards how many 5 card hands are possible consisting of a. exactly 4 hearts b. two cards of one kind and three of another(like a full house). Answered by Penny Nom.
	Multiplying decimals		2002-03-10
		From Kaitlin: I just recently had a test on multiplying decimals and I did not do really well on it. Only 5 kids out of 19 got a passing grade. My teacher says that she will give us a different test and we can take it again, but I'm still not sure of it. My teacher has taught me a lot and she had done a wonderful job of it but I'm just confused with where to put the decimals and stuff like that. I have a math practice workbook that I do for fun and they have nothing on decimals in it. I have checked on websites to try to find worksheets but I really couldn't find a good one. Can you please help me either give me some tips or clues or send me a worksheet. Answered by Penny Nom.
	A circular wading pool		2002-03-04
		From Patrick: The community of melfort is planning to build a circular wading pool in the park. The pool will cover an area of 1000m2. The building committee has decided to put a 5m cement pad around it. How much additional area will the cement pad take up? Answered by Harley Weston.
	The slope of a tangent line		2002-03-04
		From Ridley: Suppose a function f(x) has the line 3x+4y=2 as its tangent line at x=5. Find f'(5). Answered by Harley Weston.
	sin 2x = cos 3x		2002-02-25
		From Allan: solve: sin 2x = cos 3x Primary question: how do you handle the cos 3x? Answered by Paul Betts and Chris Fisher.
	The substitution method		2002-02-24
		From Joe: whats the answer to this question? 3x+y=11 x+2y=-3 its substitution method i am having alot of trouble figuring it out. send the answer as soon as possible. thank you Answered by Penny Nom.
	Getting to B in the shortest time		2001-12-19
		From Nancy: A motorist in a desert 5 mi. from point A, which is the nearest point on a long, straight road, wishes to get to point B on the road. If the car can travel 15 mi/hr on the desert and 39 mi/hr on the road to get to B, in the shortest possible time if...... A.) B is 5 mi. from A B.) B is 10 mi. from A C.) B is 1 mi. from A Answered by Penny Nom.
	Simultaneous equations		2001-12-17
		From Matthew: 4x + y = 4 2x - 3y = 5 what is x and y Answered by Penny Nom.
	For 7 the multiplicand is 143		2001-12-12
		From Cory: For 7 the multiplicand is 143 I am asked to solve this, if you could help me it would be greatly appreciated! Answered by Penny Nom.
	Normal lines		2001-12-11
		From Kristie: Why are perpendicular lines called normal lines? Answered by Chris Fisher.
	Two equations in two unknowns		2001-12-04
		From Courtney: y = 3x + 2 y = 4x - 5 solve for x Answered by Penny Nom.
	A lighthouse and related rates		2001-11-29
		From Melissa: A lighthouse is located on a small island 3 km away from the nearest point P on a straight shoreline, and its light makes 4 revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P? Answered by Penny Nom.
	Multinomial theorem		2001-11-28
		From Murray: Could you please state and explain the multinomial theorem (I already know the binomial theorem etc, to give you an idea of where i am) Answered by Harley Weston.
	A health club		2001-11-25
		From Maria: A health club with a membership of 650 people operates a running track and an indoor swimming pool. A survey of the membership indicates that 68% use the running track, 44% use the swimming pool, and 8% use neither. If a member is chosen at random, what is the prbability that the member uses: a) Both the track and the pool? b) Only the track? Answered by Penny Nom.
	L'Hopital's Rule		2001-11-25
		From Mike: I'm a high school senior. I'm in ap calculus and was wondering if you know the proof of L'Hopital's Rule? Our teacher said he has never been able to find it in a math book and was unable to derive it himself. Answered by Claude Tardif.
	A tangent line		2001-11-21
		From A student: write an equation of the line tangent to the graph of ey + ln(xy) = 1 + e at (e,1) Answered by Harley Weston.
	Rewriting and evaluating formulas		2001-11-19
		From A conserned mother: Due to the wide range of temperatures experienced in Canada, engineers who construct roads must allow for expansion and contraction of the road surface. The following formula is used to calculate the amount of expansion E to allow for: E= kL(T-t), where k is the constant of expansion for the road surface. L is the length of the section of highway in metres. T is the temperature of the air in degrees Celsius. t is the temperature, in degress Celsius, at which the section of the highway was constructed. Answered by Walter Whiteley.
	12 pairs playing bridge		2001-11-09
		From Diana: I have 12 pairs playing bridge against one another for 12 games. I need to have each pair partnered with another pair -- but only once. I'm looking for a schedule for play for all 12 games. They should only be able to play against another team only once also. (ex: 1/2 v 3/4 then 4/2 v 3/1) Thank you for this opportunity to solve my dilemma. Answered by Claude Tardif.
	Asymptotes		2001-11-09
		From Frank: given the function: f(x) = (x2) / (x-1) the correct answer to the limit of f(x) as x approaches infinity is: y = x+1 all math references point to this answer and the method they all use is long division of x-1 into x2 however if one were to multiply both the numerator and denominator by 1/x and then take the limit, one gets: y=x how can the descrepency between the two answers be explained? Answered by Chris Fisher and Penny Nom.
	A 3 dimensional 5 pointed star		2001-11-08
		From Kent: I am looking for a formula that will give me a layout for a 3 dimensional 5 pointed star. I want to form it out of sheet metal, using 5 polygons and soldering them at the apex. Can you please help me with this? I would like to be able to give the formula the height of the star from the bottom two points to the top point and also how deep the star is. Thank you very much! Answered by Judi McDonald.
	Manufactures golf balls		2001-11-06
		From Kevin: A company manufactures golf balls. Golf balls are each numbered consecutively 0 to 4, and then the numbering starts over with zero again. Every 12th golf ball is yellow. Every 8th golf ball is tested for defects. The company produces 120,000 golf balls in an eight-hour shift. A. How many yellow golf balls are tested for defects during the day? Explain your reasoning. B. How many of these yellow balls that are tested are imprinted with the numeral 2? Explain your reasoning. Answered by Penny Nom.
	A lighthouse problem		2001-11-02
		From A student: A lighthouse at apoint P is 3 miles offshore from the nearest point O of a straight beach. A store is located 5 miles down the beach from O. The lighthouse keeper can row at 4 mph and walk at 3.25 mph. a)How far doen the beach from O should the lighthouse keeper land in order to minimize the time from the lighthouse to the store? b)What is the minimum rowing speed the makes it faster to row all the way? Answered by Harley Weston.
	Negative times negative is positive		2001-10-26
		From Mary: I have a question about adding and multiplying positive and negative numbers. When we add two negative numbers the answer is negative BUT when we multiply two negative numbers the answer is positive. I don't understand. Why? Answered by Penny Nom.
	Why do you flip the inequality sign?		2001-10-26
		From Sean: I have a question about an inequality problem. Here it is: Solve and graph 5 - 3x => 17. (=> is greater than or equal). Please tell me why you flip the inequality sign when divinding by a negative number. Answered by Penny Nom.
	Concavity of f(g)		2001-10-25
		From Troy: Suppose f & g are both concave upward on (-infinity,infinity). Under what condition on f will the composite function h(x)= f(g(x)) be concave upward? Answered by Walter Whiteley.
	Multiplying vectors		2001-10-22
		From Murray: Could you please explain why a vector times a vector is a scalar and how to derive the formula vector a * vector b = ab cos(a,b) Answered by Harley Weston.
	Rules of exponents		2001-10-14
		From Carissa: how do you work this out? Investigate the relationship between a,b,c and d if 2a*2b=4c/4d? Answered by Leeanne Boehm.
	Maximize the area		2001-10-13
		From Mike: I have no clue how to do this problem. Here is what the professor gave to us: A=LW C=E(2L+2W) + I(PL) Where P = # of partitions E= cost of exterior of fence I = cost of interior of fence C = total cost of fence . . . Answered by Harley Weston.
	4 sinx cosy = 1		2001-10-10
		From A student: How would i differentiate the following example in terms of t (x and y are functions of t) 4 sinx cosy = 1 Answered by Claude Tardif.
	Locusts		2001-10-08
		From A parent: JOHN CONJECTURED THAT BOTH 13-YR.&17-YR. LOCUSTS CAME OUT THE SAME YEAR. ASSUME IT IS CORRECT. HOW MANY YEARS PASS BETWEEN THE YRS. WHEN BOTH 13 YR. & 17YR. LOCUSTS ARE OUT AT THE SAME TIME? EXPLAIN. NEXT, SUPPOSE THERE WERE 12YR.,14 YR.,& 16YR. LO- CUSTS,& THEY ALL COME OUT THIS YR. HOW MANY YRS. WILL IT BE BEFORE THEY ALL COME OUT TOGETHER AGAIN? Answered by Leeanne Boehm.
	The height of the lamppost		2001-10-02
		From Werner: I am working on question 51,section 3.7 ,page 191 of Stewart's Single Variable Calculus. The question involves a lamp post which is casting a shadow around the eliipse whose formula is x2 + 4*y2 = 5. I have found the derivative of the elllipse both explicitly: x/4(((5-x2)/4)0.5) and implicitly : y' = - x/(4*y). Answered by Harley Weston.
	(x^2-5x-6)/(x-6)		2001-10-02
		From Bill: given f(x) = (x2-5x-6)/(x-6) find f'(6). Answered by Harley Weston.
	GCD and LCM		2001-09-24
		From David: Find the GCD adn LCM of the following numbers. Assume p 2 to the power p, 3 to power q, 5 to power r and 2 to power q, 3 to power r, 7 to power p Answered by Penny Nom.
	Multiplying binomials		2001-09-08
		From A student: (x+1)(x+2)=? (2x-1)(x-4)=0 please tell me this question!! Answered by Leeanne Boehm.
	Don't worry too much about your difficulties in math...		2001-09-07
		From Matt: Do you know who said,"Don't worry too much about your difficulties in math, I assure you that mine are still greater"? Thanks for your help. this for extra credit and I can't find it ANYWHERE! Answered by Penny Nom.
	Earthquake warning		2001-09-03
		From Dillon: In the city of Skangai there are 6 million people.Each person has to tell 2 more people that theres going to be an earthquake. After they do they leave the city. There will be no duplications.It takes 3 minutes to tell each person. How long will it take for the whole city to know about the earthquake? Answered by Penny Nom.
	Conformable matrices		2001-08-05
		From Wayne: Can someone explain the concept of conformable matrices in a way that is easy to understand ? One definition says to multiply matrices rows and columns must conform, ie, 5 x 3 matrix times a 3 x 5 matrix. In the next example, however a 8 x 1 matrix and a 8 x 3 matrix are said to be conformable! Answered by Steve Kirkland.
	Intersection of perpendicular cylindrical surfaces		2001-07-31
		From Charlie: Please consider two right circular cylinders, perpendicular one to the other, and of unlike radii in a 3 dimensional Cartesian space with mutually perpendicular x,y,z axes. If one cylinder is centered on the y axis with radius ra, and the other on the z axis with radius rb, then the expression for the first surface would be x2 + z2 = ra2, y = any number. Likewise, the second cylinder's surface would be x2 + y2 = rb2, z = any number. It is my intent to define the curve at the intersection of these two cylindrical surfaces. From sketching the conditions it appears that this intersection resembles an ellipse folded about its minor axis. Answered by Chris Fisher.
	The Mean Value Theorem		2001-07-23
		From Corrie: I need to find if the mean value theorem exists. and if so, find all values c guaranteed by the theorem. f(x) = |x2-25| on the interval [-10,0] Answered by Harley Weston.
	A calculation with 6 numbers		2001-06-16
		From Edwin: I'm asked to come with, and program (in Ansi -C) an algorithm that calculates all the possible results of a calculation with 6 numbers and one result. For example: I want all calculations with the numbers 3, 3, 8, 8, 2, 9, and with a result of 786. all numbers may be used once, arithmetical operations allowed are + - / *, fractions are not allowed. The problem here is what is a fast method to do this (i.e. what's algorithm that can to this). Answered by Claude Tardif.
	Area between curves		2001-06-13
		From Phil: question 1 find the area bound by the curves y = x2 + 2x + 3 and y = 2x + 4 question 2 Find the volume generated by rotating the curve x2 + y2 = 9 about the x-axis Answered by Harley Weston.
	Danging couples		2001-06-06
		From Danielle: How many boy-girl dancing couples could be formed if 85 boys and 102 girls attend a school dance? Answered by Penny Nom.
	Conservation, consumption and population growth		2001-06-04
		From Steve: I'm trying to quantify the relation between conservation/consumption and population growth. For instance let's consider California: The 2000 census states that California's population grew from 29,760* in 4-1990 to 33,871 in 4-2000. I want to find r or rate of growth per year. Based on the exponential growth formula for population growth: . . . Answered by Penny Nom.
	Common solution		2001-06-02
		From Samantha: Solve for common solution: x+y=6 2x-3y=2 Solve for y in terms of x: 3x-y=4 Answered by Penny Nom.
	Multiplication		2001-05-30
		From Lindsay: Who came up with multipling? its so easy Answered by Claude Tardif and Penny Nom.
	Your DJ Business		2001-05-30
		From Linda: Your DJ Business has 6 rap, 10 rock, 6 alternative, 8 oldies, and 5 country CD singles. How many different 10-song sets can the DJ play, if she plays 2 singles from each category? and How many different 10-song sets if she plays exactly 3 rap singles and 4 rock singles in each set? Answered by Leeanne Boehm.
	A triangular pyramid		2001-05-14
		From Kumar: In a Pyramid OABC, all the three sides of the base: a, b, c are known. Also known are the angles between the three sides from the vertex O: Angles AOB, BOC, COA. With this information, is it possible to calculate the lengths of the three sides: OA, OB & OC. Answered by Chris Fisher.
	National consumption function		2001-05-09
		From Brian: If consumption is $11 billion when disposable income is 0 and the marginal propensity to consume is dC/dy = 1/(2y+4)1/2+0.3(in billions of dollars), find the national consumption function. Answered by Harley Weston.
	Maximize profit		2001-05-09
		From Brian: The marginal cost for a certain product is given by MC = 6x+60 and the fixed costs are $100. The marginal revenue is given by MR = 180-2x. Find the level of production that will maximize profit and find the profit or loss at that level. Answered by Harley Weston.
	The average value of a continuous function		2001-05-08
		From Esther: The average value of a continuous function y = f(x) on the interval [a,b] is given by ________________? Answered by Harley Weston.
	Area of a regular polygon		2001-05-01
		From Carl: What is the formula for finding the area of a regular Hexagon and a regular Pentagon Answered by Penny Nom.
	Population growth		2001-05-01
		From Gina: Suppose the population of a country increases at a steady rate of 3% a year. If the population is 50 million at a certain time, what will it be 25 years later? Define the recurrence relation that solves this problem. Answered by Penny Nom.
	A Taylor series		2001-04-27
		From Karan: Given the following information of the function f''(x) = 2f(x) for every value of x f(0) = 1 f(0) = 0 what is the complete Taylor series for f(x) at a = 0 Answered by Harley Weston.
	Oil revenue		2001-04-21
		From Brian: Suppose that t months from now an oil well will be producing crude oil at the rate of r(t), not a constant, barrels per month and that the price of crude oil will be p(t), not a constant, dollars per barrel. Assume that the oil is sold as soon as it is extracted from the ground. Find an expression for the total revenue from the oil well, R(t). A certain oil well that currently yields 400 barrels of crude oil a month will run dry in 2 years. The price of crude oil is currently $18 per barrel and is expected to rise at a constant rate of 3 cents per barrel per month. What will be the total revenue from this well? {Hint: Model the degraded production rate with the equation: r(t) = (A-Bt)e0.04t} Answered by Harley Weston.
	Differentiation		2001-04-17
		From Esther: Could you please tell me what the first derivative is of the following: y = 2/(2x+e2x) Is it (1+xe2x)/(2x+e2x)2 or perhaps -4(1+e2x)/(2x+e2x)2 ? I am a little confused between the two! Answered by Harley Weston.
	Prisms		2001-04-10
		From A fourth grade class: A fourth grade class is curious about the names that have been given to various solid geometric figures based on their shapes: are there names for solids based on a rhombus, a trapezoid, a parallelogram, a decagon, and/or a quadralateral? Answered by Chris Fisher.
	Integration by parts		2001-04-09
		From A student: how do you integrate x tan-1x dx, i know it can be done by integration by parts maybe, but i'm not sure.... Answered by Claude Tardif and Harley Weston.
	The domain of a function		2001-04-08
		From Mina: Let f(x) = (2x2+3x-17)/(x+5) What is the domain of f? What are the values of x for which f'(x) does not = 0? Answered by Harley Weston.
	The normal to a curve		2001-04-08
		From Varenne: I am having SO much trouble tackling this question and don't know what the right answer is... can you help me out? The question is Find the equation of the normal to the curve y=(x-2)2/(1-x)2 that is parallel to the line x+4y+7=0 Answered by Harley Weston.
	Common tangents		2001-04-08
		From Anne: I have been working on this problem for a while but I'm not sure I'm getting the right answer: Find the common tangents of 2y=x2 and 2y=-x2-16 Thanks for the help. :) Answered by Harley Weston`.
	Where do the lines y=2x-4 and y=x-1 intesect?		2001-04-06
		From Bryce: solve the following problem by setting them equal to each other. Solve for x and y. Where do the lines y=2x-4 and y=x-1 intesect? Answered by Penny Nom.
	Volume and surface area of a cylinder and a triangular prism		2001-03-31
		From Kevin: I was wondering how do you find the volume and surface area of a cylinder and a triangular prism. Answered by Penny Nom.
	Airflow in windpipes		2001-03-25
		From Ena: The volume of air flowing in windpipes is given by V=kpR4, where k is a constant, p is the pressure difference at each end, R is the radius. The radius will decrease with increased pressure, according to the formula: Ro - R = cp, where Ro is the windpipe radius when p=0 & c is a positive constant. R is restricted such that: 0 < 0.5*Ro < R < Ro, find the factor by which the radius of the windpipe contracts to give maximum flow? Answered by Harley Weston.
	Cube roots on a calculator		2001-03-24
		From Will: Hi my name is Will.I have a question about the calculator TI-83 Plus or the use of a scientific calculator. It is about using them to turn a cubed root to a decimal. When using that for a rational and irrational number. Rational numbers is a number that terminates or repeates. A irrational number goes on and on and uses ... (like pie). Like when you type the cube root of 8 it gives you 2, and that is a rational number. The squre root of 2 is 1.41421356... that is irrational. So why is it when you put the cube root of 16 in the calculator it says 2.5198421 that is rational it terminates at the ninth digit and my float is set for the tenth? But why when you do it by hand you get the 2 times the cube root of 2 and that is irrational? Why is that? Answered by Judi McDonald.
	Systems of equations		2001-03-16
		From joy: How do u solve problems using systems of equations? ~ finding x and y~ ex: 26 = 3x - 2y 42 = 4x + y Answered by Penny Nom.
	A jogger		2001-03-12
		From Bill: At time t=0 a jogger is running at a velocity of 300 meters per minute. The jogger is slowing down with a negative acceleration that is directly propotional to time t. This brings the jogger to a stop in 10 minutes. a) write an expression for the velocity of the jogger at time t. b) what is the total distance traveled by the jogger in that 10-minute interval. Answered by Harley Weston.
	The substitution method		2001-03-05
		From A student: Solve each system of equations by the substitution method. Show your work. y = 8 7x = 1 - y y = x - 1 4x - y = 19 Answered by Penny Nom.
	Powers		2001-03-04
		From A student: Hey, can you show me how you do .. (2xy)to the 3rd power (x) to the 2nd power? Answered by Penny Nom.
	Spins of a roulette wheel		2001-03-02
		From Bob: Here's a problem I'm working on myself.....If you look at six consecutive spins of a roulette wheel, how many combinations of red and black are possible? I.E. BRRBRB, BBBBBR, BBRRRB......ETC..... Answered by Claude Tardif.
	The domain of the derivative		2001-02-22
		From Wayne: I know that the domain of f'(x) is a subset of the domain of f(x). Is it necessarily true that the subset will have at most one less element than the domain of the original function? Answered by Harley Wesston.
	Faces		2001-02-21
		From Sandy: How many faces are there on a sphere? What are the faces of a cone? What is the definition of a "face" of a 3D object? Answered by Walter Whiteley.
	The area of platts		2001-02-20
		From Steve: I have to calculate the areas of different "platts" of land from a map, and the only thing I have are the four side measures. There are some cases where no sides are parallel, no lengths the same, and no angles are given, and I was wondering how to calculate the area of such figures. I've attached a rough sketch of a typical platt's shape. Answered by Walter Whiteley.
	Differentiation of y = x n		2001-02-17
		From Jashan: i am studying differentation at the moment i have drawn some graphs such as y=x 2. i have found the formula for the gradient of this curve, this being 2x obtained by using differentation, but i need to know the general case for the formula where y=xn in order for me to understand this topic more throughly, i would also like to know how u derived this general formula Answered by Harley Weston.
	A four digit number		2001-02-17
		From Dean: Need to find a 4 digit number that can be divided by 2, 3, 4, 5, 6, 7, 8, 9, and will always have a remainder of 1 in the answer. Answered by Penny Nom.
	A quartic equation		2001-02-15
		From George: Let P(x) = x4 + ax3 + bx2 + cx + d. The graph of y = P(x) is symmetric with respect to the y-axis, has a relative max. at (0,1) and has an absolute min. at (q, -3) a) determine the values for a, b c, and d using these values, write an equation for P(x) b) find all possible values for q. Answered by Harley Weston.
	Multiplying one and two digit numbers		2001-02-11
		From Marty: When multiplying do you put the number you are multiplying by on the top or the bottom. Example if you are multiplying by 6's would you write the problem 6 x 2 or 2 x 6 Maybe it just doesn't matter. But when you get to double digits, the double digit always goes on the top? Answered by Penny Nom.
	What is wrong with these probelms?		2001-02-09
		From Cindy: Hi, I am a planning on becomming a teacher and i am asked to find out what is wrong with these probelms and how i would go about showing a student what is wrong with them!! Error in patterns: 13/35=1/5; 27/73=2/3; 16/64=1/4 4/5+2/3=6/8; 2/5+3/4=5/9; 7/8+1/3=8/11 2/3*3=6/9; 1/4*6=6/24; 4/5*2=8/10 Answered by Leeanne Boehm and Penny Nom.
	Kinds of lines		2001-02-09
		From Robyn: What are the different kinds/types of lines? Answered by Leeanne Boehm.
	An irregular polygon		2001-02-09
		From Jason: I have a 5 sided irregular polygon I am trying to figure out the area of. There are no right angles in the polygon as far as I can tell. I do not know any angles. Answered by Chris Fisher.
	Find an exprression for f(x)		2001-02-07
		From A 12th grade AP Calc student: Let f be the function defined for all x > -5 and having the following properties. Find an expression for f(x). i) f ''(x) = 1/ (x+5)1/3 for all x in the domain of f ii) the line tangent to the graph of f at (4,2) has an angle of inclination of 45 degress. Answered by Harley Weston.
	The "goesinta" box		2001-02-07
		From Bridget: We are looking for the "proper" name of the "box" that is drawn around the dividend on a division problem: ___ 3)12 It has always been a family joke to call it the "goesinta" box, but a search of several reference sources hasn't yielded an answer -- This is a question of curiosity rather than a question for homework. Answered by Claude Tardif.
	(-2b+3)(-b-1)		2001-02-06
		From Melissa: Alright, lets say you are multiplying (-2b+3)(-b-1) and you are using "FOIL" first you would get : 2b2+2b-3b-3 then you add like-terms. when multiplying,if the bases are the same, add the exponents...does the same thing apply when you are adding the results of the multiplication even though it's addition? would the answer be 2b3-3b-3 or would it be 2b2-b-3? Answered by Penny Nom.
	Two number theory questions		2001-01-30
		From Richie: i have two questions and they are: the product of three consecutive prime numbers is 7429. Find the product of the smallest and largest of these three integers. the least common multiple of two relatively prime positive integers, a and b, is 144. if a (a>or=2) is as small as possible, compute the value of b. Answered by Penny Nom.
	Fractions of fractions		2001-01-30
		From Katie: When you multiply two positive fractions less than 1, how does the answer compare to the size of the fraction? Why? Answered by Penny Nom.
	Building a circular silo		2001-01-24
		From Natasha: We wish to build a circular silo with internal diameter 10 feet. How much concrete will we need to pour the foundation, if we only need a 1 foot wide and 1 foot deep ring on which the silo walls will sit? Assume the 4 inch thick silo wall rests on the middle of the ring. Answered by Penny Nom.
	1 + 1 = 1		2001-01-23
		From Stephanie: My friend has this as a bonus question the other day and I want to figure it out. I don't know how 1+1 in any form could equal 1. Please let me know how you come about geting that. Answered by Claude Tardif.
	7x6 by doubling		2001-01-23
		From A student: Can you think of a way to use doubling to multiply 6x7? Answered by Allen Herman.
	A problem with distance		2001-01-16
		From A student: For what values of a is the distance between P(a, 3) and Q(5, 2a) greater than the square root of 26. Answered by Penny Nom.
	8, 4, 2, 18, 1, 9		2001-01-11
		From Neyra: Place each number below in one of the blanks to create the most meaningful and realistic story possible. Answered by Claude Tardif.
	Is n^2 - 2 a multiple of n - 4?		2001-01-10
		From John: Find all positive integers n so that n2 - 2 is a multiple of n - 4. Answered by Sukanta Pati.
	Multiplication of fractions		2001-01-08
		From Angela: Questions: 1. represent multiplication of fractions via an area model 2. describe why, not just how, to round decimals Answered by Penny Nom.
	Height of the lamp		2000-12-31
		From Joey: The figure shows a lamp located three units to the right of the y-axis and a shadow created by the elliptical region x2 + 4y2 < 5. If the point (-5,0) is on the edge of the shadow, how far above the x-axis is the lamp located? Answered by Harley Weston.
	How do you integrate secant(theta)?		2000-12-22
		From Robert Williamson: How do you integrate secant(theta)? I know the answer is ln [sec(theta) + tan(theta)] but how do you get there? Answered by Claude tardif.
	A limit using l'hopital's rule		2000-12-13
		From Wassim: I need to know how to solve the: limits of (x ( to the power lamda) -1 )/LAMDA when lamda tends to zero ( the answer is that the functional form is ln x) and I still don't know how using hopital rule leads to this answer. Answered by Harley Weston.
	Is this a right triangle?		2000-12-08
		From Alicia: How would you set-up and answer a problem like these one? Triangle ABC has vertices A(-2,2), B(1,-2), and C (1,2). Use slopes to determine if the triangle is a right triangle. Answered by Penny Nom.
	Scheduling a golf vacation		2000-12-05
		From Michael: I'm having a problem scheduling matches for a golf vacation. We have 12 people playing 7 rounds of golf in 7 days. We play 2 man teams vs. 2 man teams everyday.Is there a formula so that you play WITH a different partner everyday and AGAINST as many different people as possible? Thank You for any help you may be. Answered by Penny Nom.
	A non-integrable function		2000-12-03
		From Mark Spilker: I have a proof that I cannot do here it goes. Let F(x)= 1 if x is a rational number 0 if x is an irrational number Prove the function is not intregrable on the interval (0,1). Hint: Show that no matter how small the norm of the partition, the Riemann Sum for the SigmaNotation F(wi) DeltaiX is not unique. Answered by Harley Weston.
	An integration problem		2000-11-30
		From A student: If a>0 and the integral from b to 0 of 1/(1+x) equals 1/2 the integral from a to 0 of 1/(1+x), express "b" in terms of "a" Answered by Claude tardif.
	The astronomers' calendar		2000-11-29
		From Show_Li: The calendar that astronomers use began on Jan. 1, 4713 B.C. on that day, the julian calendar, the lunar calendar, and roman tax system calendar all coincided. This won't happen again until 3267 A.D. (a). How many years ago was the astronomer's calendar started? (b). Find the number of years between times that the three calendars coincided. Answered by Penny Nom.
	Order of operations		2000-11-26
		From Margaret Pratt: My daughter has a math question and I am afraid I am of no help. Can you help? 2x5/2+1-5= She arrives at 8 as the answer and has been told this is incorrect. Any help you can give would be appreciated. Answered by Penny Nom.
	A complex calculation		2000-11-24
		From Angie: Multiply (3-2i)2=32-2(3)(2i)+(2i)2 Answered by Penny Nom.
	Comparing an integral and a sum		2000-11-21
		From Douglas Norberg: A fellow teacher asked me about a problem she wanted to give to her students. It involved whether to take a million dollars or a penny doubled a number of times. I was able to determine the number must have been .01 * 230 which is about $10 million and a lot more than $1 million. To check that I was right I used a spreadsheet and did a Riemann sum. When I finished I reasoned that I had done the task in several steps and I could have done it in 1 step. Thus I integrated .01 * 2x from 0 through 30 but the number I got was $15,490,820.0324. Why the difference? Answered by Harley Weston.
	Euler's Formula		2000-11-11
		From Denise Roberts: I'm trying to design a unit (possibly involving a Webquest) on Polyhedra and I cannot find a formula I once used. The formula involved the number of vertices (V), edges (E), and faces (F) of the polyhedra. Answered by Walter Whiteley.
	Find the rule		2000-10-27
		From Kelsa and Linda: Find the rule: It had 13 in a circle then 2 blank circles then 31 in a circle then two more blank circles. Could you please help us. Answered by Penny Nom.
	Concavity		2000-10-22
		From Alex: the question is: on what interval is f(x)=(x2)(ex)? ive found the 2nd derivative which is ex(x2+4x+2) and i did the quadratic to get -2-20.5 and -2+20.5, but i dont know what the interval is. Answered by Harley Weston.
	Connecting to a water line		2000-10-20
		From Vanja: My question is...A house is to be connected to a new water main that runs along the line y=2/3x-1. The connection point at the house has coordinates (2,9), where the units represent metres. What lenght of plastic pipe is needed to connect to the water main at the closest point? Answered by Penny Nom.
	Dividing fractions		2000-10-18
		From Paula: Why do you have to change the division sign to a multiplication sign and invert the fraction that follows the division sign in order to get the answer to a division problem when you're working with fractions? Answered by Penny Nom.
	Multiplying decimals		2000-10-16
		From Lily: I need help with mutiplying decimals (example) 2.28*0.48( * = times). Answered by Harley Weston.
	Mode		2000-09-22
		From James Barton: I have always been told that a mode is the "one" number that appears most in the set of numbers: ex.{1,3,4,6,3,2} the mode is 3. What if you have {1,1,3,4,5,5}is there a mode. I was taught long ago that there is no mode, Not i am having to teach there is two modes. 1 and 5. If this is the case if we have {1,1,2,2,3,3,4,4,5,5} that every number is the mode. True or false. This is being ambigiuous if we say all are the mode. Because no one number is used more than the others. Answered by Claue Tardif and Harley Weston.
	Permutations and Multiplication Principle		2000-09-22
		From Candice: A forester selects 4 pink and 4 white dogwoods. The trees are to be planted in row. If a tree is distinguished by color only, in how many ways can the eight dogwoods be planted? How many of these arrangements have at least two trees of the same color side by side? Answered by Denis Hanson and Claude Tardif.
	Dividing a region in half		2000-09-21
		From Kerry: There is a line through the origin that divides the region bounded by the parabola y=x-x2 and the x-axis into two regions with equal area. What is the slope of the line? Answered by Penny Nom.
	A cycloid in Cartesian form		2000-09-20
		From Billy: The parametric equation of cycloid is given: x=r(t-sint) y=r(1-cost) How to eliminate t? Answered by Harley Weston.
	A proof that 1=2		2000-09-19
		From sporky: Why does the proof for 1=2 not work? x = 1 x2 = 1 x = x2 1 = 2x (derivitive) 1 = 2(1) 1 = 2 ??? please tell me where the false logic is. Answered by Walter Whiteley.
	Circular Permutations		2000-09-18
		From J. Stuart: I am able to understand the simple theory behind circular permutations (that is, there are (n-1)! ways to arrange n people in a circle. One question, however, is giving me some difficulty. It reads: In how many ways can four married couples be arranged around a circular table if each man must sit beside his wife? Any suggestions you have would be greatly appreaciated. Answered by Penny Nom.
	Two linear equations		2000-09-14
		From David Dean: 2a + 1b = 3.39 3a + 3b = 6.59 What formula do I use to find what a = ? Answered by Harley Weston.
	Derivatives, there must be an easier way		2000-09-06
		From Brad Goorman: The direction read: Take the derivative of each expression. y = {1+[x+(x2 +x3)4]5}6 Answered by Harley Weston.
	Velocity of a pendulum		2000-08-28
		From Mekca: A pendulum hangs from the ceiling. as the pendulum swings, its distance,d cm, form one wall of the room depends on the number of seconds,t, since it was set in motion. assume that the equation for d as a function of t is: d=80+30cos3.14/3t, t>0. estimate the instantaneous rate of change of d at t=5 by finding the average rates for t=5 to 5.1, t=5 to 5.01, and t=5 to 5.001. Answered by Harley Weston.
	Some trigonometry		2000-08-11
		From Angela: I have some PreCal questions. I am a student at the secondary level. I would be very grateful for your help. Solve the equation for theta (0 <= theta < 2pi). tan2(theta) = 3 I know sec2(theta) -1 = tan2(theta) . . . Answered by Harley Weston.
	PreCalculus		2000-08-09
		From Angela: Use absolute values to define the interval or pair of intervals on the real line. <--|--- |--- ]--- |--- |--- |--- [---| ---|--> 18 19 20 21 22 23 24 25 26 A car is moving at the rate of 50 miles per hour, and the diameter of its wheels is 2.5 feet. a) Find the number of revolutions per minute that the wheels are rotating. b) Find the angular speed of the wheels in radians per minute. Answered by Harley Weston.
	L'Hospital's Rule		2000-07-19
		From Dan Krymkowski: The limit of the following as x goes to infinity is 2*y. Y is a constant. lim 2*x*log(x/(x-y)) = 2*y Answered by Harley Weston.
	Calculator and telephones keypads phones		2000-06-27
		From Thomas Smith and Veronica Yates-Riley: On a keyboard, why is the number "7" on the top of the keypad as opposed to the number "1" at the top a telephone keypad? Answered by Penny Nom.
	Divisors of 2000		2000-06-06
		From Amanda Semi: find the product of all the divisors of 2000 dog trainer time has 100m of fencing to enclose a rectangular exercise yard. One side of the yard can include all or part of one side of his building. iff the side of his building is 30 m, determine the maximum area he can enclose Answered by Claude Tardif.
	A derivative problem		2000-06-04
		From Jeff Ellis: If F(x)=(4+x)(3+2x2)2(2+3x3)3, find F'(0) Answered by Harley Weston.
	Using the inverse sine function		2000-05-31
		From Nelson Rothermel: This has me completely baffled. I have to use the laws of sine or cosine to find the angles of a triangle when I have 3 sides, so I can't go 180-x-y when I have 2 angles. Now, I have a triangle with values of 3, 7, and 9. Here are the steps I used (A,B,C are angles; a,b,c are opposite sides): angle A (16.1951 degrees): cos-1*((b2+c2-a2)/(2*b*c)) angle B (40.6011 degrees): sin-1*(b*sin(A)/a) angle C (56.7962 degrees): sin-1*(c*sin(A)/a) If you notice, A+B+C does not equal 180. According to the book, A and B are correct, but C is supposed to be 123.2038 degrees. Why doesn't it work??? Answered by Harley Weston.
	Why does division start from the left?		2000-05-24
		From Salil Dave: Addition, subtraction and multiplications start with right most digit and proceed left, but division starts from left-most digits and goes right ... why? Answered by Harley Weston.
	Angular velocity		2000-05-24
		From Ashley Milliman: The crankshaft of a particular automobile engine has an angular velocity of 1,500 rpm at 30 mph. The crankshaft pulley has a diameter of 10 cm, and it's attached to an air conditioner compressor pulley with a 7 cm diameter and an alternator pulley with a 5 cm diamter At what angular velocities do the compressor and alternator turn? . . . Answered by Harley Weston.
	Calculus Research Questions		2000-05-22
		From William Wright: I am a Calculus Teacher, and me and my class ran into these two problems without solutions in my manual, we got answers, but are unable to check them. If anyone gets this email and can respond to this with the solutions it be greatly appreciated. . . . Answered by Harley Weston.
	Radioactive decay		2000-05-18
		From Catherine Sullivan: Please help me with the following: The radioactive isotope carbon-14 is present in small quantities in all life forms, and it is constantly replenished until the organism dies, after which it decays to carbon-12 at a rate proportional to the amount of C-14 present, with a half life of 5730 years. Suppose C(t) is the amount of C-14 at time t. Find the value of the constant k in the differential equation: C'=-kC In 1988 3 teams of scientists found that the Shroud of Turin, which was reputed to be the burial cloth of Jesus, contained 91% of the amount of C-14 contained in freshly made cloth of the same material. How old is the Shroud according to the data? Answered by Harley Weston.
	Multiplying fractions		2000-05-14
		From A student: 75/2 x 1/100 = 3/8 Please show how to came up with the answer? Answered by Penny Nom.
	A matrix equation		2000-05-14
		From A student: Right now, we are dealing with matrices and we are supposed to solve the following problem on our graphing-calculators: 2a+3b-4c+d=20 a-2b+3c-5d=-14 3a+4b-2c+3d=19 5a-b+6c+4d=-5 Answered by Penny Nom.
	Trig functions		2000-05-09
		From Melissa: Find all solutions in the interval (0,2pi) 2cos2x-3cosx-4=0 Answered by Paul Betts and Harley Weston.
	Parallel and perpendicular lines		2000-05-08
		From Jimmy Lumpkins: Need a method for solving the following problem: Find the equation of a line through point P that is parallel or perpendicular to another line. Answered by Paul Betts.
	Related Rates		2000-05-07
		From Derek: How can you show that if the volume of a balloon is decreasing at a rate proportional to its surface area, the radius of the balloon is shrinking at a constant rate. Answered by Harley Weston.
	Finding a formula		2000-05-05
		From Erica Hildebrandt: If a farmer has a field and his plots are laid out in the following grid where each # represents a plot: 4 5 12 13 20 3 6 11 14 19 2 7 10 15 18 1 8 9 16 17 Of course the plot numbers aren't meaningful as I have described above. In fact they may not be numbers at all. The only constants I have are the total number of rows and columns. Using the total number of rows and columns and my current position row and column, how can I write a formula that tells me column 3 row 3 = 10, column 4 row 2 = 14, etc. I can see the pattern but can't quite get the formula. I believe I will need 2 different formulas one for even and one for odd rows. Answered by Paul Betts and Penny Nom.
	An improper integral		2000-05-04
		From A high school senior: Hi, I am a high school senior and I need help stugying for a final. I am stuck on one of the questions on my review sheet. Does the improper integral from 5 to infinity of (38/97)x converge or diverge? If it converges I also need to know how to find the approximate value accurate to .01 of its actual value. Answered by Harley Weston.
	Thearcius Functionius		2000-05-03
		From Kevin Palmer: With the Olympics fast approaching the networks are focusing in ona new and exciting runner from Greece. Thearcius Functionius has astounded the world with his speed. He has already established new world records in the 100 meter dash and looks to improve on those times at the 2000 Summer Olympics. Thearcius Functionius stands a full 2 meters tall and the networks plan on placing a camera on the ground at some location after the finish line(in his lane) to film the history making run. The camera is set to film him from his knees(0.5 meters up from the ground) to 0.5 meters above his head at the instant he finishes the race. This is a total distance of two meters(the distance shown by the camera's lens). Answered by Harley Weston.
	An indefinite integral		2000-05-03
		From Bonnie Null: I am to find the indefinite integral of: (ex - e-x)2 dx Answered by Claude Tardif.
	Minimizing the metal in a can		2000-05-02
		From May Thin Zar Han: A can is to be made to hold 1 L of oil. Find the dimensions that will minimize the cost of the metal to manufacture the can. Answered by Harley Weston.
	Two calculus problems		2000-05-01
		From Kaushal Shah: How Do WE Integrate the following Functions, Integral xtanx dx How was natural base "e" discovered and why e=2.7....... Answered by Claude Tardif.
	An expected value		2000-04-24
		From Carl Pride: Suppose that in a statistics class of size 23, each student has a probability of passing of 73 percent. sample: What is the expected number of students who will pass?? Answered by Harley Weston.
	All the roots of x^6 - 64		2000-04-15
		From Dakota: Find ALL zeros of P(x) = x 6 - 64 Answered by Walter Whiteley.
	The area of a triangle using calculus		2000-04-15
		From Todd Bowie: Hi, I am not a student but am reviewing calculus for an upcoming interview. I would like to know how to derive the area of a triangle using calculus. Thanks! Answered by Patrick Maidorn.
	2^32 + 1		2000-04-08
		From Un Etudiant: 232 +1 can be divided by 641 , why? Answered by Claude Tradif.
	Star-multiplication		2000-04-07
		From Greg Potts: I have this question to answer and I don't know where to start. 1*9=0, 9*8=72 and 2*8=9, then 9*9 =? Answered by Penny Nom.
	y = x^x^x^x...		2000-04-05
		From Michael Hackman: Find the derivative of: y = x^x^x^x... on to infinity. Answered by Claude Tardif.
	Manipulatives		2000-04-04
		From Jodi Stuker: I am a student looking for a good lesson plan using manipulatives to teach multiplication to LD students. They are currently functioning on approximately 3rd grade level in math but are age 12-14. Answered by Penny Nom.
	Riemann sums		2000-03-30
		From Joshua D. Parham: If n is a positive integer, then lim (1/n)[1/(1+1/n) + 1/(1+(2/n) + ... + 1/(1+n/n)] n->infinity can be expressed as the integral from 1 to 2 of 1/x dx Answered by Penny Nom.
	Rule of 78		2000-03-22
		From Dan Baumgarten: Can you explain the rule of 78 and the reverse rule of 78? Thanks. Answered by Claude Tardif.
	Functions that satisfy f' = f		2000-03-16
		From Kevin Palmer: Recently my calculus teacher asked his students to try and find any functions whose derivatives where the exact same as the original function. The only function then I have determined that statement to be accurate in is all the natural exponential functions. Ex. f(x) = ex, f'(x) = ex If possible could you please email me all the functions that you can find in which the original function and its derivative is identical. Answered by Claude Tardif.
	Maximize		2000-03-12
		From Tara Doucet: My question is Maximize Q=xy^2 (y is to the exponent 2) where x and y are positive integers such that x + y^2 ( y is to the exponent 2)=4 Answered by Harley Weston.
	Simultaneous equations		2000-03-11
		From Laura Molck: My name is Laura Molck and I am in Year 11 in Australia. Please help me with the following. I know that they are all simultaneous equations which I can do but I have trouble with the formulae to work the equations. Can you please help!! 1. A tent manufacturer produces 2 models, Outback and Bushwalker. From earlier sales records it is known that 20% more of the Outback model is sold than the Bushwalker. A profit of $200 is made on each Outback sold, but $350 is made on each Bushwalker. If during the next year a profit of $177,000 is planned how many of each model must be sold? Answered by Penny Nom.
	Systems of linear equations		2000-03-10
		From Ann Marie Devereux: hi there!!, I guess I have a problem!!! 3x+4y=10 (over) 4x+y=9 2x=5y+3 (over) x=3y+1 Answered by Penny Nom.
	A mixture problem		2000-03-06
		From Rebecca Edwards: A tank in which cholocate milk is being mixed contains a mixture of 460 liters of milk and 40 liters of chocolate syrup initially. Syrup and milk are then added to the tank at the rate of 2 liters per minute of syrup and 8 liters of milk per minute. Simultaneously the mixture is withdrawn at the rate of 10 liters per minute. Find the function giving the amount of syrup in the tank at time t. Answered by Harley Weston.
	Two calculus problems		2000-03-03
		From Tara Doucet: The height of a cylinder with a radius of 4 cm is increasing at rate of 2 cm per minute. Find the rate of change of the volume of the cylinder with respect to time when the height is 10 cm. A 24 cm piece of string is cut in two pieces. One piece is used to form a circle and the other to form a square. How should the string be cut so the sum of the areas is a maximum? Answered by Harley Weston.
	Triangular numbers and square numbers		2000-03-02
		From Emily McCallum: Would someone find me some math activities using triangular numbers and square number. Especially acitivities that actually form the shapes. They need to be at the 5th grade or 6th grade level. But you can not find anything that can be tauht at these level, that fine. I just need to be able to teach this new subject or kind of math to my kids. Answered by Rick Seaman and Penny Nom.
	Factoring, primes, GCF and LCM		2000-02-27
		From Ruth Kroek: My son is in grade seven, he has to do a Factoring Booklet the areas covered are: Prime #'s Composite #'s Rainbow Factoring Finding Multiples (consecutive multiples) Finding GCF of 2-3 numbers uning Rainbow factoring Finding LCM of 2 numbers using consecutive multiples prime factor trees prime factor ladders finding GCF of 2 numbers using Prime number Method Although his text 'Math Power' gives some information, we are at a loss .. Answered by Penny Nom.
	Slant height of a cone		2000-02-24
		From Jocelyn Wozney: I need help with this problem for my high school calculus class. Any help you can give me will be greatly appreciated-I am pretty stumped. "Express the volume of a cone in terms of the slant height 'e' and the semi-vertical angle 'x' and find the value of 'x' for which the volume is a maximum if 'e' is constant. Answered by Harley Weston.
	Triple angle formula		2000-02-23
		From Sara: Can one derive a triple angle formula for sine and cosine? If so, how? Answered by Chris Fisher.
	Some integration problems		2000-02-23
		From Tim Valentine: I am having a great deal of difficulty with the following integrals, can you help? I think they need the use of trig substitution or integration by parts but I cannot figure out how to begin. Thanks! The integral of 1/(2+3x2) dx. and The integral of x * square root of (4x+5) dx. Answered by Harley Weston.
	A moving point on the graph of y=sinx		2000-02-22
		From Veronica Patterson: Find the rate of change of the distance between the origin and a moving point on the graph of y=sinx if dx/dt=2 centimeters per second. Answered by Harley Weston.
	The quotient rule		2000-02-21
		From Charlene Anderson: Question: I came across a question in our book that states: Let Q(x) = N(x) / D(x) Then re-write Q(x) in a form that can utilize the Power and Product Rules. Use this rearranged form to derive the Quotient Rule. The Quotient Rule can be derived from the Power Rule and the Product Rule. One must also use the chain rule too, right? Answered by Harley Weston.
	Cross multiplication		2000-02-16
		From J E Swinton: Why does cross multiplication work? How come canceling work? Answered by Penny Nom.
	Least Common Multiple		2000-02-16
		From Kathy Heath: The way I understand it is for 2,3,9 the least common multiple is 18. Am I right? If so, I guess the least common multiple for 3,4,7 is 105. Please let me know if I'm right so I can tell my daughter. Answered by Denis Hanson.
	Play ball		2000-02-03
		From Jessie: Here's a calc question that is probably a lot easier than I am making it. If you have a legendary "baseball problem" for the related rates section of Calc I, and you are given that the runner is running from 2nd to 3rd base at a given rate, and the umpire is standing at home plate, and you are given the distance between the bases on the field, how do you find the rate of change of the angle between the third base line (from the point of the umpire) and the runner? Here is a sample prob: Runner is moving from 2nd to 3rd base at a rate of 24 feet per second. Distance between the bases is 90 feet. What is the rate of change for the angle (theta, as described previously) when the runner is 30 feet from 3rd base? Answered by Harley Weston.
	Functions		2000-01-23
		From Tara: Hi my name is Tara, I have two math problems that I need help with in my calculus math class. If f(x)= x - 2 show that (x+3)f(x)-(x+2)f(x+1)+4=0 Graph this function and use the graph to determine the range y=2x2 - 8x - 3 Answered by Harley Weston.
	The limit of f(x)/x		2000-01-22
		From Laurent Jullien: I would appreciate help to prove that a twice continuously differentiable convex function from R+ to R has the property that f(x)/x has a limit when x tends to infinity. Answered by Claude Tardif.
	Pyramids and prisms		2000-01-18
		From Tyler: What's the definition of a Triangular Prism and a Triangular pyramid. Answered by Penny Nom.
	Three dimensional rectangle		2000-01-11
		From Dennis Murphy: I would like to find out the name of a Three dimensional rectangle. Answered by Harley Weston.
	How many coins is one calculator?		2000-01-09
		From Mandy Brockmann: Tom weighed 1 pen and his calculator with 4 coins. Then he weighed his calculator and 3 pens with 12 coins. How many coins is one calculator? Answered by Claude Tardif.
	A probability experiment		2000-01-05
		From Vanessa: Duels in the town of Discretion are rarely fatal. There, each contestant comes at a random moment between 5 a.m. and 6 a.m. on the appointed day and leaves exactly 5 minutes later, honor served, unless his opponent arrives within the time interval and then they fight. What fraction of duels lead to violence? There must be a minimum number of 100 trials and things like graphing calculator, dice, spinners, and whatever are allowed. Answered by Harley Weston.
	Why study calculus?		2000-01-05
		From Trlpal: I am a high school senior enrolled in a pre-calculus class. Could you tell me what the benefits of taking calculus are and why it would be important to take the class. Answered by Walter Whiteley and Harley Weston.
	Derive the quadratic equation		2000-01-01
		From Thuy: My teacher asked us this question in which i can't understand when she asked to derive the quadratic equation. What does this mean? Answered by Penny Nom.
	Climbing stairs		1999-12-22
		From Harman Chaudhry: Paul, Michelle and Michael all climb up 54 steps. Paul climbs the steps one at a time i.e. 1, 2, 3, etc. Michelle Climbs the stairs 2 at a time i.e. 2, 4, 6, etc. Michael climbs the stairs 3 at a time i.e. 3, 6, 9, etc. How many steps are used by exactly two people? Answered by Penny Nom.
	Rectangular hyperbola		1999-12-15
		From Aarti Chand: Why do they call a rectangular hyperbola, rectangular and where the normal hyperbola looks like a rectangle and the rectangular hyperbola looks like a sqaure? Answered by Chris Fisher.
	A decreasing ellipsoid		1999-12-15
		From A student instructor: The volume of an ellipsoid whose semiaxes are of the lengths a,b,and c is 4/3 *pi*abc. Suppose semiaxes a is changing at a rate of A cm/s , the semiaxes b is changing at B cm/s and the semiaxes c is changing at C cm/s . If the volume of the ellipsoid is decreasing when a=b=c what can you say about A,B,C? Justify. Answered by Harley Weston.
	Two calculus problems		1999-12-13
		From Alan: I have 2 questions that are very new to me, they were included on a quiz and the material was never covered. Our teacher never explained the purpose and detailed explanation of how to solve the problem. Could you help? Thanks. Question 1: A ball is falling 30 feet from a light that is 50 feet high. After 1 sec. How fast is the shadow of the ball moving towards the light post. Note that a ball moves according to the formula S=16t^2 Question 2: How many trapezoids must one use in order for the error to be less than 10^-8 if we want to find the area under the curve Y=1/X from 1 to 2. Find the exact area, Graph the function and use the trap rule for the "N" that you found. Answered by Harley Weston.
	A calculus problem		1999-12-08
		From JT Wilkins: These are the questions: Show that there exists a unique function that meets the following requirements: a) f is differentiable everywhere b) f(0)= f'(0)= 0 c) f(x+y)= f(x)+ f(y), for all real values of x,y Consider the function F: R-->R (All Reals) F(x) = 0, for x irrational & 1/q, x=p/q gcd(p,q)=1 q > 0 a)determine the values x where f is continuous, respectively discontinuous. b)determine the values x when f is differentiable and for each of these values compute f'(x). Answered by Penny Nom.
	Advanced Calculus		1999-12-07
		From Kay: Hi, my name is Kay. Please help---these problems are driving me crazzzzy!!!! Your help would be greatly appreciated! Let a,b be contained in R, a . . . Answered by Claude Tardif.
	Systems of equations		1999-12-06
		From Roger Hornbaker: I am having problem figuring out x and y solutions. 5x + y = 4 3x - y = 4 3x + 2y = 6 - 3x + y = 0 Answered by Penny Nom.
	order 4+ determinants		1999-12-06
		From Joe Kron: Why is it never shown how to calculate the value of 4x4 (or larger size) deteminants by the diagonal multiply methods that are generally shown for 2x2 and 3x3 determinants? The method I'm talking about is called Cramer's Rule??? Is this method not extensible to order 4+ and if not why not? Anyway the method always shown for order 4+ is called "reduction by minors" which is not the answer to this question. Answered by Walter Whiteley.
	Multinomial coefficients		1999-12-03
		From Suraj Das: Is there a formula for the expansion of (a+b+c) to the nth power? Does it have to do with Pascal's triangle? Answered by Penny Nom.
	The chain rule		1999-12-03
		From Jennifer Stanley: This problem is making me dizzy. I would greatly appreciate a little help! Express the derivative dy/dx in terms of x. y=u^2(u-u^4)^3 and u=1/x^2 Answered by Harley Weston.
	Two calculus problems		1999-12-01
		From O'Sullivan: Question #1 Assume that a snowball melts so that its volume decreases at a rate proportional to its surface area. If it takes three hours for the snowball to decrease to half its original volume, how much longer will it take for the snowball to melt completely? It's under the chain rule section of differentiation if that any help. I've set up a ratio and tried to find the constant but am stuck. Question #2 The figure shows a lamp located three units to the right of the y-axis and a shadow created by the elliptical region x^2 + 4y^2 < or= 5. If the point (-5,0) is on the edge of the shadow, how far above the x axis is the lamp located? The picture shows an x and y axis with only the points -5 and 3 written on the x axis. the lamp is on the upper right quadrant shining down diagonally to the left. There's an ellipse around the origin creating the shadow. It's formula is given as x^2 + 4y^2=5. Answered by Harley Weston.
	Cos x = -1/2		1999-12-01
		From Pierre Boivin: When I factor[ 2cos (square) - 5cos -3], I get (2cos + 1)(cos - 3). 2cos + 1 = 0, 2cos = -1, cos = -0.5,. Using inv cos on calculator, I get 120 degree related angle. When I graph I get two values, between 90 and 180 degree and between 180 and 270 degrees. How do I find those two values. How do use 120 degree in relation with the x axis. Answered by Penny Nom.
	Two derivatives		1999-11-16
		From Gina Renicker: The derivative of: y=e(xlnx) and y=x2arctan(x1/2) Answered by Harley Weston.
	Estimating the population mean		1999-11-13
		From John Barekman: Statitistics: Estimating the population mean when the standard deviation is known: I am not sure which n to use in the formula for the confidence interval equation: x +/- z*(standard deviation/sqrt(n)) If we have data of ten people, and if we have the data of ten sets of ten people each, what is the difference in the n that we use? What is the difference between the standard deviation and the standard error? Are we using the number of sampling means or just the number of samples? Answered by Harley Weston.
	Trolls and Gargoyles		1999-11-02
		From TexGrimm: How can you seat 6 monsters - 3 Trolls and 3 Gargoyles- at a circular table if the trolls look alike and the gargoyles look alike? Does your formula work for 9 monsters - 4 trolls and 5 gargoyles? Answered by Penny Nom.
	Area of a circle and an inequality		1999-10-30
		From Adam Anderson: I have two problems. The first: prove that the area of a cirlce is pi times radius squared without using calculus. The second: show that ln(x) < x - 1 for all x > 0. Answered by Harley Weston.
	Calculating a square root		1999-10-28
		From Jonathan: What is the formula for calculating a square root? Answered by Penny Nom.
	Clockwise or Counterclockwise?		1999-10-27
		From Tim: A particle moves around the circle x2 + y2 = 1 with an x-velocity component dx/dt = y Find dy/dt Does the particle travel clockwise or counterclockwise around the circle? Why? Answered by Harley Weston.
	Derivatives with logs		1999-10-26
		From Kate: What is the derivative of 5 to the 5x-2 at x equals 0.8? Answered by Harley Weston.
	l'Hospital's Rule		1999-10-18
		From Yannick Gigandet: How can I solve these two limits : lim when n approches 1 of n[a1/n -1] lim when x approches 0 of (eax - ebx) / x Thanks for the answer! Answered by Harley Weston.
	(-5)^2, -5^2 and -(5)^2		1999-10-13
		From Jennifer Brown: What is the difference between the following problems: (-5)2, -52 and -(5)2 Our text book (Beginning Algebra, fourth edition, published by McGraw Hill, by Streeter, Huthison and Hoetzle) says the second and third problem are exactly the same. I don't see how that can be. Is there a mathematical rule that explains this? Answered by Penny Nom.
	Length of a line		1999-10-10
		From Dagmara Sarudi: My question has to do with the length of a diagonal. This problem came up when I thought about the shortest distance between two points, for example walking from one point to another in my neighborhood. I can choose a zig zag route and assuming the blocks I walk are exactly the same length, it shouldn't matter what route I took, the distance I travel should still be the same when I reached my goal. If, on the other hand I could travel in a diagonal line, the distance would be shorter. But what if, in my zig zag motion, the sections get so small the route approaches a diagonal. Shouldn't it be that each separate section added together equals the value of the two original sides? Or would it suddenly equal the value of the diagonal (which, of course was shorter than the two sides added together)? What gives? Answered by Chris Fisher and Harley Weston.
	A trig limit		1999-10-06
		From Yannick Gigandet: What is the limit, as x approaches pi/3, of (1-2cosx) / sin(x-(pi/3)) ? Answered by Penny Nom.
	towers of cubes		1999-10-05
		From Sanker: I need help to solve this Rules for bulding towers of cubes rule 1 The number of cubes on the bottom layer is always one less than the number of squares on the grid rule 2 Each new layer is made with one cube less than the layer underneath it. Investigate how many different arrangements there are of 4 cubes on top of 5 cubes on a two by three grid investigate the number of different arrangements of six cubes on top of seven cubes on a two by four grid investigate the relation between the number of arrangements of cubes and the size of the grid when there are two layers of cubes when there are more than two layers of cubes Answered by Walter Whiteley.
	Regular and irregular shapes		1999-10-03
		From Samuel Tighe: What is the difference between a regular shape and an irregular shape? Are a rectangle and a triangle regular or irregular shapes? Answered by Walter Whiteley.
	Two limits		1999-10-02
		From Jennifer: How do I find lim (1-cosx)/(x^2) as x-> 0 and lim (tan3x)/x as x->0 Answered by Harley Weston.
	Jose and Arthur		1999-09-26
		From Joel Hammer: Jose can run around the track in 40 seconds. Arthur runs with Jose but in the opposite direction. They meet every 15 second. How long will it take Arthur to make one trip around the track? Answered by Denis Hanson.
	Distance between the windows		1999-09-19
		From Lawrence: An observer on level ground is at distance d from a building. The angles of elevation to the bottom of the windows on the second and third floors are a and b respectively. Find the distance h between the bottoms of the windows in terms of a b and d Answered by Harley Weston.
	2 to the x and x squared		1999-09-17
		From John: For what values of x is 2 to the exponent x greater than x squared? Answered by Harely Weston.
	A Multiple Choice Test		1999-08-31
		From Cintra Ramnarine: I have ten questions. There are two multiple choice answers to each question. What are the chances of answering all questions correctly. Answered by Harley Weston.
	A Trigonometry Question		1999-08-28
		From Diane Simms: My question is can the following be factored. I am a teacher who needs the factors to this right away. 2 Sin2X + 2 SinX CosX - 1= 0 Answered by Harley Weston.
	Invert and multiply		1999-08-28
		From Debbie Walter: I have another question please, WHY do we invert and multiply when dividing fractions? I know that's what we do but WHY? What is the reasoning behind it? Answered by Penny Nom.
	Parametric Equations		1999-08-06
		From Nicholas Lawton: Show that an equation of the normal to the curve with parametric equations x=ct y=c/t t not equal to 0, at the point (cp, c/p) is : y-c/p=xp^2-cp^3 Answered by Harley Weston.
	A calculus problem		1999-07-22
		From Nicholas Lawton: The curve y= e^x(px^2+qx+r) is such that the tangents at x=1 and x=3 are parallel to the x-axis. the point (0,9) is on the curve. Find the values of p,q and r. Answered by Harley Weston.
	The shortest ladder		1999-06-26
		From Nicholas: A vertical wall, 2.7m high, runs parallel to the wall of a house and is at a horizontal distance of 6.4m from the house. An extending ladder is placed to rest on the top B of the wall with one end C against the house and the other end, A, resting on horizontal ground. The points A, B, and C are in a vertical plane at right angles to the wall and the ladder makes an angle@, where 0<@ Answered by Harley Weston.
	Scheduling Meetings		1999-06-25
		From Beth Carver: We have 6 groups meeting at three different places simultaneously. The meetings take place once a month each year. Is there a way to have each group meet with each of the other groups at least twice in a year, four times in each place? Answered by Chris Fisher and Harley Weston.
	Sin 4A		1999-06-22
		From Ryan Cochrane: If sinA = 4/5, and A is a first quadrant angle, find sin4A Answered by Harley Weston.
	Even and Odd Function		1999-06-17
		From Kent: There is one function with the domain of all real numbers that is both even and odd. Please give me the answer to this question before I go insane. Answered by Penny Nom.
	A circle in a square		1999-05-26
		From Jose V Peris: A circle is inscribed in a square. The circumference of the circle is increasing at a constant rate of 6 inches per second. As the circle expands, the square expands to maintain the condition of tangency. find the rate at which the perimeter of the square is increasing. find the rate of increase in the area enclosed between the circle and the square at the instant when the area of the circle is 25(pi) square inches. Answered by Harley Weston.
	Related rates		1999-05-13
		From Tammy: The sides of a rectangle increase in such a way that dz/dt=1 and dx/dt=3*dy/dt. At the instant when x=4 and y=3, what is the value of dx/dt? (there is a picture of a rectangle with sides x and y, and they are connected by z, which cuts the rectangle in half) Answered by Harley Weston.
	A Polar Plot		1999-05-06
		From Irene: Consider the polar equation r=2-3Cos(theta/2) In the interval [o, 4Pi], how would you find the area of one of the leaves and also the length of one of the edges of a leaf? Answered by Harley Weston.
	Roman Numerals		1999-04-29
		From Michelle Jenkinson: Someone proposed this question to me and I do not know the answer, so I was wondering if you could help. How, using Roman Numeral, did people add, subtract, multiply, and divide with no zero or negative numbers? Answered by Penny Nom.
	Parallel and perpendicular lines		1999-04-23
		From Crystal Pilling: My name is Crystal Pilling and I am in 9th grade algebra. We are currently studying parallel and perpendicular lines. I am having trouble with this problem: 3/4x - 5y= 16, (5,-6) I have to find a line that is perpindicular to this line on a graph. HELP ME PLEASE!!!!! Answered by Penny Nom.
	Radius of convergence		1999-04-21
		From Nowl Stave: Why is the radius of convergence of the first 6 terms of the power series expansion of x^(1/2) centered at 4 less than 6? Answered by Harley Weston.
	The average rate of change of a function		1999-04-20
		From Tammy: Suppose that the average rate of change of a function f over the interval from x=3 to x=3+h is given by 5e^h-4cos(2h). what is f'(3)? I would appreciate any help with this question. Answered by Harley Weston.
	Area of an irregular shaped objects.		1999-04-07
		From Jesse Townsend: How do I find the surface area of an irregulary shaped object such as someone's knee from the thigh to shin? Thanks. Answered by Walter Whiteley.
	Where three sequences meet.		1999-03-06
		From Ali: My name is Ali and I am in the 5th grade. I have a math question: What is the least positive integer meeting each of the following conditions: Dividing by 7 gives a remainder of 4 Dividing by 8 gives a remainder of 5 Dividing by 9 gives a remainder of 6 Help! Answered by Denis Hanson.
	Divisibility by 9		1999-02-21
		From Razzi: I've been having a hard time trying to solve the following problem and I was wondering if you could help me. For any positive integer a let S(a) be the sum of its digits. Prove that a is divisible by 9 if and only if there exist a positive integer b such that S(a)=S(b)=S(a+b). Answered by Chris Fisher and Harley Weston.
	Finding a rule for a sequence		1999-02-17
		From Lindsey Masters: I'm doing a maths investigation and i have a sequence which goes:- 13,16,25,32,45,56,73. Our teacher told us we have to find a rule by looking at the differences of the terms until we find a constant. The first differences are:- 3,9,7,13,11,17. The differences of these are:- ...... Please could you tell me how to work it out so that I could work out the rules of similar sequences. Answered by Penny Nom.
	The Board Problem		1999-02-15
		From Avery: Mr. Avery has 3-foot boards and 4-foot boards. If he puts the 3-foot boards in a line, they have the same length as the 4-foot boards put in a line. Altogether he has between 16 and 25 boards. How many 3-foot boards does he have? Answered by Jack LeSage and Penny Nom.
	Grade 4 curriculum		1999-02-09
		From John: My daughter is in grade 4 and her math teacher has asked her to write out the number 1 to 10,000. She is currently at 4567 and is sick of it. When I complained that this was not a usefull exercise she said that the Ministry of Education curriculum requires this and gave a photocopy of the page. It states: "read and write whole number to 10,000 in standard, expanded, and written forms (eg., 9367=9000+300+60+7 = nine thousand three hundred sixty-seven). Has the teacher interpreted this the wrong way? Thanks John PS. Do you have a web address for Ontario Math and Science Teachers organization? Answered by Jack LeSage.
	Lunes		1999-02-04
		From Kai G. Gauer: A prof once told me that a certain type of lune is quadrable given that the diameter is an integer. She used the construction of a right isosceles triangle within a semicircle and later constructed another semicircle on the base of the first semicircle and used area subtraction to show equality to a smaller triangle with quadrable area. What happens when the original inscribed triangle is no longer isosceles? She mentioned something about other lunes also being quadrable; but not all. What are the dimensions of other such lunes? Note: I'm not certain if I still have my hercules account; please simply post on Q&Q. Thanks! Answered by Chris Fisher.
	Modular Arithmetic		1999-02-04
		From Leslie Kupper: I am trying to do a project on modular arithmetic. I was wondering if there were any websites that include a sample lesson plan on modular arithmetic for any grade level. Let me know where and how to find them. Thanks. Answered by Harley Weston.
	Cannonballs		1999-01-27
		From Roger King: How many cannonballs can be stacked in a triangular pyramid? Answered by Penny Nom.
	The Quadratic Formula		1999-01-22
		From Eric Morgan: Hi my name is Eric Morgan and I m in 8th Grade honors math (middle) and I'd like to know how to prove the quadratic formula -b±sqrt of b(a)(c)over 2(a) Answered by Penny Nom.
	Angles in Polygons		1999-01-21
		From Jen: How do u find the interior angles of a pentagon when you are given 4 of the angles and you need to find the fifth? If you are given the measure of each exterior angle of a regular polygon, how do you figure out how many sides the polygon has? i need all information on polygons and how to find their angles!!! Answered by Jack LeSage.
	Graphing the Derivative		1999-01-18
		From Milena Ghebre: This question has been nagging me for sometime now. Is there a way of finding out the derivative of a function, just by looking at the graph of it? Answered by Walter Whiteley.
	Calculus		1999-01-16
		From Kaylea Rankin: Differentiate the following. y = 1 /(2+3/x) Answered by Jack LeSage and Penny Nom.
	Absolute value of i		1999-01-06
		From Wayne Bagley: I would like to know what is the absolute value of i. I need an answer suitable for the secondary level. Answered by Harley Weston.
	Complex numbers and the quadratic formula		1998-12-25
		From Richard Peter: My age is 16, and my name is Richard. My question relates to the topic complex numbers & the quadratic formula. I would like to know how to solve quadratic equations in which the discriminant is less than 0 (i.e. we get two complex solutions to the quadratic) 3x2+2x+5 = 0 and how mathematicians like euler contributed to this field. If it would be possible I would also like to know how this type of quadratic equations can be graphed? Answered by Harley Weston.
	Duplation method of multiplication		1998-11-26
		From Sara Whitford: I am wondering why 16 and multiples of 16 do not work in the ancient duplation method of multiplication used by the Egyptians. I discovered the method in the Journeys math text gr 7 level. Just curious. Am I doing something wrong?? Answered by Jack LeSage and Harley Weston.
	The bricklayers formula		1998-11-24
		From Rachel Kaplan: I have to do a report on the bricklayers formula N = 7LH. Can you give me any information on this. Answered by Harley Weston.
	Golf Problem - The Sequel		1998-11-13
		From Bob: Sixteen golfers, seven rounds. What are optimum combinations for each golfer to play with as many different golfers as possible? Many thanks, Bob Payson Answered by Denis Hanson.
	Triangular Numbers		1998-10-30
		From Matt: i would like to know about triangular numbers and it history i would also like to know about the history of prime numbers thank you Answered by Chris Fisher.
	Divisibility by 11		1998-10-28
		From Pat Duggleby: I am an upgrading instructor at a drop-in program in Regina. One of my students is taking General Math 30 through correspondence, and we have run into some confusing instructions. The section is about divisibility rules, and we did just fine up until the rule for Divisibility by 11. The statement is as follows: If the difference between the sum of the odd-numbered digits and the sum of the even-numbered digits, counted from right to left, is divisible by 11, then the number is divisible by 11. . . . Answered by Penny Nom.
	A Number Trick		1998-10-26
		From Brenda Meagher: I'm a 37 year old mother and i have returned to school for personal reasons. I was faced with this question. Choose any number less than 10, multiply it by 8547, then take your answer and multiply it by 13. I chose the number 8. 8547 x 8 -------- 68376 and 68376 x 13 --------- 205128 68376 --------- 888888 Any number chosen from 1 to 9 will result in the same form of answer.If the number two is used you will end up with 222,222.etc So my question is, is there another number that will results in the answers. Answered by Harley Weston.
	A Hexagon		1998-09-22
		From Lee Curtis: Could someone calculate this for me? If a hexagon is 38 feet 8 inches across, how wide would each of the six sides be? Thank you, Lee Curtis Answered by Chris Fisher and Harley Weston.
	Human Calculator		1998-09-14
		From Pam Sloan: I recently saw a special on NBC Dateline about a man known as the human calculator. They called him Mr. Math. I want to know more about his books, seminars, and activities. Also, what is his real name? Answered by Patrick Maidorn.
	The area and the circumference of a circle.		1998-08-27
		From Jason Wright: I was looking at the relationship of the area of a circle and the circumference when I realized that 2*pi*r is the derivative of pi*r^2. I was wondering if there is any connective deep dark meaning as to why this appears to be related. Thanks for any help you can give me! Answered by Walter Whiteley.
	Concurrent Lines in a Triangle		1998-08-10
		From Chris Woolf: The question is Name four types of concurrent lines, rays, or segments that are associated with triangles. Answered by Chris Fisher.
	Area and Volume		1998-07-28
		From James Pulver: I am going into 12th grade and am practicing for the SAT II. I have come across a problem that I cannot solve. It states that the front, side , and bottom faces of a retangular solid have areas of 24 square centimeters, 8 square centimeters, and 3 square centimeters, respectively. What is the volume of the solid. I need to know how to solve similar problems so is there a formula to go from area to volume? Answered by Jack LeSage.
	Volumes of Revolution		1998-07-24
		From Lorraine Wall: I'm on the section fpr The Computation of Volumes of Solids of Revolution and the following question is giving me problems: -Consider the region in the first quadrant bounded by the x-and y-axes, the vertical line x=3, and the curve y=1/(xsquared + 3) I can determine the volume of the solid by rotating the region about the y-axis using the shell method but I can't seem to be able to get started with the volume when rotated about the x-axis. Answered by Harley Weston.
	Calculus problems		1998-07-13
		From Lorraine: I'm stuck again. Can you help? This involves integration using the method of partial fractions the integral of: 7x(to the 5th) - 2x(cubed) + 3 dx -------------------------------------- x(to the fourth) - 81 Do I have to do long division to reduce the numerator to the fourth power? the integral of: 4- 16x +21x(squared) + 6x(cubed) - 3x(fourth) dx ---------------------------------------------------- x(cubed)(x - 2)(squared) Lorraine Answered by Harley Weston.
	A Calculus Problem		1998-06-28
		From Lorraine: I'm a post-secondary student taking calculus by correspondence. I'm stuck on the following question (and similar ones) Can you help? Evaluate the following indefinite integral: d(theta) ---------- 1 + sin (theta) (It says to multiply both numerator and denominator by: 1 - sin(theta) Thanks Lorraine Answered by Harley Weston.
	A trig limit		1998-05-28
		From Ann: This problem is a calculus 1 limit problem-high school level. I'm teaching myself calc over the summer and I'm already stumped. find the limit lim sec^(2)[(sqrt2)(p)]-1 p-->0 --------------------- 1-sec^(2)[(sqrt3)(p)] I'm Ann. Answered by Harley Weston.
	Multiplying by Nine - Chismbop Style		1998-04-27
		From Noria Jones: About a year ago a grade 5 teacher at my son's school taught the children how to multiply the 9 times table on their fingers quickly. It was part of a kind of finger math kind of thing... Answered by Patrick Maidorn.
	Clock Arithmetic.		1998-03-09
		From Joann Dixon: What is clock mathematics? Answered by Patrick Maidorn.
	(50^20)(20^50)		1998-02-24
		From fion: 50 power of 20 X 20 power of 50? How many zero can be found in the answer and why? Answered by Penny Nom.
	A Tightrope Walker.		1998-02-19
		From Amy Zitron: A tightrope is stretched 30 feet above the ground between the Jay and the Tee buildings, which are 50 feet apart. A tightrope walker, walking at a constant rate of 2 feet per second from point A to point B, is illuminated by a spotlight 70 feet above point A.... Answered by Harley Weston.
	Area of a triangle.		1998-02-01
		From Jodi Blucher: Is there a formula for the area of an equilateral triangle knowing the length of the sides? Answered by Chris Fisher and Harley Weston.
	The two-digit numbers from 10-99		1998-01-21
		From Alexis Riddle: My name is Alexis. I'm a student in 8th grade and I'm taking Algebra I Honors. My question is: In a string of numbers, two adjacent digits are considered as a two-digit number. For instance, the string 11012 contains the numbers 10, 11, and 12. What is the number of digits in the smallest string that contains all of the two-digit numbers from 10-99? Please help and thank you for any assistance you can give me. Answered by Penny Nom.
	Greatest Common Factor.		1998-01-09
		From Percy Stribling: how do you figure out what the greater common factor is? Answered by Penny Nom.
	Roman Numerals		1997-10-31
		From Mark Curts: I am looking for some resources for teaching Roman Numerals. I would like to expand upon the basic concepts, by locating some addition, subtraction, multiplication or division problems written with Roman Numerals. -- Mark Curts Answered by Chris Fisher.
	Some Calculus Problems.		1997-10-30
		From Roger Hung: What real number exceeds its square by the greatest possible amount? The sum of two numbers is k. show that the sum of their squares is at least 1/2 k^2. . . . Answered by Penny Nom.
	Cos(x) Cos(2x) Cos(4x)=1/8		1997-09-24
		From Tan Wang: How many distinct acute angles x are there for which cosx cos2x cos4x=1/8? Answered by Chris Fisher Harley Weston and Haragauri Gupta.
	A Trigonometric Limit		1997-09-18
		From Brian Ray: What is the limit, as x approaches 0, or tan^23x/x^2? (read, tan squared 3x over...)? Answered by Harley Weston.
	A Limit Problem		1997-09-16
		From Robert Reny: what is the limit, as x approaches 0, of 3x/2x-[x]? [] means absolute value. Answered by Harley Weston.
	Triangular Numbers.		1997-09-08
		From Rachel: Show visually that the square number 16 is the sum of two triangular numbers. Which two? Answered by Penny Nom.
	Two Questions		1997-08-28
		From Faye Tan: I am a trainee teacher. I would appreciate it very much if you could help me solve the following two problems which I think are meant for students at middle grade. 1. If a hen and a half lays an egg and a half in a day and a half, how many hens are needed to lay a dozen eggs in one day? 2. There are fewer than 200 passengers on a train. If they get off in pairs, one passenger will be without a partner. If they get off in groups of 3 or 4, there will still be one passenger left by himself. However, if they get off in groups of 5, no one will be left by themselves. How many passengers are there on the train? Answered by Penny Nom.
	The Division Bracket.		1997-04-09
		From Judy Riley: A fellow teacher recently asked if I remembered the exact word for a division bracket (not the symbol with dots, the horizontal line in a fraction, or a solidus). I couldn't. Can you help? Answered by Walter Whiteley and Harley Weston.
	Mathematical Induction and the Derivative		1997-03-18
		From Shuling Chong: "Obtain a formula for the nth derivative of the product of two functions, and prove the formula by induction on n." Any educated tries are appreciated. Answered by Penny Nom.
	Equivalent Expressions		1997-02-26
		From Karyn Jones: Josie says that s=n/(n+1) and s/(1-s)=n are two ways to write the same formula. Describe whether or not you agree with Joise. Explain how you made your decision. Answered by Walter Whiteley and Penny Nom.
	Circular Permutations		1997-02-05
		From Ed Varjassy: I have an understanding of simple problems involving circular permutations but do not understand them when they start to have restrictions. Is there any advice you can give for these more complicated permutations. Answered by Penny Nom.
	Deriving the Quadratic Formula		1997-02-04
		From James: How do you derive the quadratic formula? I know what it is, but the textbook doesn't say how to derive it. Answered by Penny Nom.
	Mathematics of Schedules		1997-01-16
		From Byron Krull: I was asked if there was a mathematical method to work with schedules. The problem is this. There are 24 teams playing weekly on 4 sheets at 3 different times of the day as follows... Answered by Denis Hanson.
	Sides in a Regular Polygon		1996-12-06
		From Rick Moss: If you are given the measure of each interior angle (162 degrees) of a regular polygon. How many sides does the polygon have? Answered by Penny Nom.
	Priority of operations		1996-11-04
		From Wallace: What is the answer to this problem? Let x=-2 and y=3. Evaluate 12x / 2y (if the old division sign is used). Answered by Chris Fisher.
	A tangent to a circle is perpendicular to the radius at the point of contact.		1996-10-22
		From Rita Leung: I wonder if there is any proof for this theorem - A tangent to a circle is perpendicular to the radius at the point of contact. If there is any proof for that, can you tell me please? Answered by Chris Fisher and Harley Weston.
	Could you tell me the name for the bar in a division problem?		1996-10-21
		From Linda: Could you tell me the name for the bar in a division problem. Not the line with dots on either side but the line that divides the two numbers? My name is Linda. I am asking for my niece who is in 8th grade. Answered by Chris Fisher.
	How many digits are there in 2^2520?		1996-10-07
		From Rita Leung: A)The number 64 is a sq., a cube, and a sixth power because 64=8*8, 4*4*4, 2*2*2*2*2*2. Find the smallest integer greater than 1 that is a sq., a cube, a 4th, 5th, 6th, 7th, 8th, 9th and 10th power. I have found that the answer is 2 to the power 2520th. B) How many digits are in the correct answer to part A? The answer is uncertain. It is either 758 or 759. Can you give me any ideas? Answered by Penny Nom.
	Repeating decimals		1996-09-09
		From Alice: What is the line called that is placed over the decimal to show that it is infinitely repeating? Answered by The Centralizer.
	Area of an annulus		1996-04-04
		From Ryan Levering: What is the area of this annulus? Answered by Penny Nom.
	(-3)x(-2)		1995-10-25
		From Azmat: Why is (-3)x(-2) = 6? Answered by Herley Weston and Ed Giesbrecht.
	calcul de durée		2012-09-03
		From laila: un bus démarre de paris à 8h 45mn s'il fait 42h 20 mn de trajet entre paris et la ville suivante à quelle heure il arrivera à la ville suivante. est ce qu'il ya un shema pour calculer ou comment procéder. je sais qu'il faut additionner 8h 45 mn à 42h 20mn, mais comment on trouve le résultat rapidement. merci Answered by Claude Tardif.
	Les dérivées partielles		2012-05-16
		From Haddouche: Bonjour, Je vous demande de bien vouloir m'éclaircir comment on calcule les dérivées partielles généralement étudiées dans les modèles de la concurrence fiscale à titre d'exemple celui de Wildasin ""NASH EQUILIBRIA IN MODELS OF TAX COMPETITION "", dont j'ai essayé toutes les méthodes et aucune d'elle n'est arrivée à trouver le résultat des dérivées de ce dérnier papier, à cet effet, je vous serais reconnaissant de m'éclaicir la méthode afin de résoudre ce problème qui pour moi un vrai mistère à percer. Je vous remercie infiniment à l'avance. Et comptant sur votre compréhension, mes salutations les meilleures. HA Answered by Claude Tardif.
	Les calcules avec les heures		2011-09-09
		From johanna: bonjour je voudrais pouvoir expliquer a mon fils ces calcules avec les heures, mais franchement je n'y comprend rien, pouvez vous m'aider. voilà le premier calcul: 1h35min29s - 46min37s deuxiéme exercice: calculer la durée d'une emission télévisé qui débute à 20h40min et se termine à 22h17min. troisiéme exercie: je suis partie en vacances le 25 juillet. Mes vacances ont durées 2 semaines. Quel jours suis-je revenu? quatroéme exercice: je pars de st-pierre, je prend le bus. je veut arrivé à st-denis à 10h et demi. je sais que la durée du trajet st-pierre /st-denis est de 1h50min. a quel heure dois-je partir de st-pierre. Answered by Claude Tardif.
	Le volume d'une boule		2009-10-22
		From ve.lu.ch: Pour calculer le volume d'une boule, il faut utiliser la formule : 4/3 x Pi x R au cube Pourquoi 4/3 ? Merci d'avance Answered by Pierre-Louis Gagnon et Claude Tardif.
	Preuve du volume d'une boule		2009-04-06
		From Geneviève: J'aimerais avoir l'explication du volume de la boule, qui est (4pi R au cube) divisé par 3. J'aimerais savoir le pourquoi de l'équation, la preuve de celle-ci. Merci! Answered by Pierre-Louis Gagnon.
	Une multiplication		2009-04-03
		From josee: 24/6x5+40-10= le x est une multiplication et il n'y as pas de parenthèses. Merci Josée Answered by Antoine Letarte and Claude Tardif.
	Calculs de minutes en heures		2009-02-23
		From Denis: Je suis en train de suivre un cours en navigation maritime et je dois changer souvent des minutes en heures. ex: 495 minutes = ?h?? Je désire avoir le cheminement le plus simple a faire pour ce type de calcul. Je ne travail pas avec excell. Je veux une formule a faire seulement avec une calculatrice élémentaire. Merci pour votre aide, j'apprécie beaucoup votre coup de main. Denis. Answered by Claude Tardif.
	Un volume d'une capacité minimal		2009-01-05
		From Pauline: je doit faire un volume d'une capacité minimal de 2500 cm 3 en quell matiere que ce soit * un prisme a base pentagonale non réguliere * une sphere * stella octangula Answered by Pierre-Louis Gagnon.
	Un tetraèdre régulier		2008-05-05
		From delabroye: La figure ci-contre est un tetraèdre régulier : AB = AC = BC = AD = 6cm 1) Représente un patron de ce tetraèdre 2) Calcule le volume de ce tétraèdre Answered by Thierry Moisan.
	Arithmétique modulaire		2008-01-10
		From hausknecht: ma grand mère a entre 60 et 80 ans.il y a un an son âge était un multiple de 3.dans deux ans son âge sera un multiple de 2,de 3 et de 9.cette année , c'est un multiple de 5.quel est l'âge de ma grand mère? Answered by Claude Tardif.
	800 poules pondent 800 oeufs en 8 jours		2007-12-17
		From LINDA: 800 POULES EN 8 JOURS PONDENT 800 OEUFS, COMBIEN 400 POULES VONT-ELLES PONDENT D'OEUFS EN 4 JOURS? Answered by Claude Tardif.
	F=4a-3c+6b		2007-11-22
		From olive: comment calcule ton ? F=4a-3c+6b mon fils et en 4ème et je suis dépassée, je ne peut pas l'aider merci de le faire à ma place. Answered by Claude Tardif.
	pente nulle		2007-08-31
		From stephanie: si la pente dune droite est nulle alors cette droite est quoi ??? Answered by Claude Tardif.
	boulier français		2007-01-19
		From Stéphanie: Je prépare une exposition sur le centième anniversaire du vieux couvent de Château-Richer dans la province du Québec qui s'ouvrira en mai 2007. Dans ce couvent les soeurs de la Congréagation du Perpétuel Secours ont enseigné pendant de nombreuses années. Pour mettre en valeur, le site et l'exposition, nous souhaitons mettre les visiteurs à l'épreuve dans l'ambiance d'une classe d'antan (début 20ème siècle) avec, entre autres, les bouliers français que nous possédons et leur faire faire des exercices de mathématiques avec. Malheureusement, nous ne savons pas comment faire les quatre opérations de base (addition, soustraction, multiplication et division) avec. Pouvez-vous nous l'expliquer de façon détaillé, s'il vous plaît? Answered by Claude Tardif.
	Ordre des opérations		2006-05-15
		From Chantal: 2324/4-153+619= je sais pas comment calculer merci Answered by Claude Tardif.
	problème de trigonométrie		2005-11-01
		From Manon: Soit un triangle ABC, de cotes a , b et c, avec A=45° et B=60°. Apres avoir demontre que 3a²-2b²=0 (que jai fais en utilisant la regle du sinus) et a²-2c²+2ac=0 (que jai fait en utilisant la regle du cosinus), vous montrerez que laire du triangle ABC peut sexprimer: { [ 3 + racine carre 3 ] / 12 } b² unites. Je ne sais pas comment arriver a cette expression de laire. Je narrive pas a exprimer c² et ac en fonction de b².. et je pense que ca pourrait vraiment aider.. puisque je suis arrive a letape: ac[(racine carre 3) / 4] avec ac = a² + c² - b² et a² = 2/3 b² ms c²= 1/3 b² + ac Answered by Claude Tardif.
	6 poules pondent 6 oeufs en 6 jours		2005-03-01
		From Nathalie: SACHANT QUE 6 POULES PONDENT 6 OEUFS EN 6 JOURS, COMBIEN 12 POULES PONDENT D'OEUFS EN 12 JOURS? Answered by Claude Tardif.
	le système RSA		2005-02-19
		From Un eleve: Je suis actuellement en classe préparatoire MP au lycée Henri Poincaré de Nancy et je souhaiterais obtenir des informations sur l'exponentiation modulaire car je réalise un TIPE sur la cryptographie et plus particulièrement le système RSA. pourriez-vous m'indiquez en quoi consiste l'exponentiation modulaire et comment cela fonctionne. Answered by Claude Tardif.
	il y a 1/6 de voitures bleues,		2005-01-24
		From Facrice: il y a 1/6 de voitures bleues, 2/9 de voitures rouges, 5/12 de voitures blanches et 1/8 de voitures vertes. Sachant que 15 voitures sont d'une autre couleur. Combien y a t il de voitures de chaque couleur. Answered by Claude Tardif.
	Hauteur d'un tétraèdre irrégulier		2003-08-29
		From Thibault: Je cherche à connaître comment calculer la hauteur d'un tétraèdre irrégulier (aucune arêtes égales) en ne connaissant que la longueur des arêtes. Answered by Claude Tardif.
	le matricule		2003-01-12
		From Sirkka: "Dans un pays totalitaire, tous les habitants ont un matricule composé de 5 chiffres. Les policiers se reconnaissent au fait que le premier chiffre de leur matricule est strictement supérieur à la somme des quatre autres. ex: 90124 9>0+1+2+4=7 Combien y a-t-il (au plus) de policiers?" Answered by Claude Tardif.
	Boulier		2001-02-13
		From Un élève: Comment se sert-on d'un boulier (non asiatique) comportant 10 rangées de 10 boules chacune? Answered by Claude Tardif.
	isomorphisme		2000-08-10
		From Romain Kroes: Pour les beoins d'un ouvrage d'économie que je suis en train de terminer, pouvez-vous me dire qui est (sont) l'inventeur de l' "isomorphisme" en mathématiques (calcul tensoriel)? Answered by Claude Tardif.
	Derivées partielle		1999-10-19
		From Arnaud Flandin: Quel est la definition des derivées partielle Answered by Claude Tardif.
	Le sang humain		1998-10-06
		From Golden: Le sang humain contient approximativement 2,5 x globules rouges. Chaque globule a un rayon de 0,004 mm. Si on le place ces globules bout a bout, quelle est la longeur de la chaine en millimetres? En kilometres? Compare toi avec la circonference de la terre (24 000 km) (Travail avec exposants) Answered by Claude Tradif.

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