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	How to calculate percentage change		2007-08-03
		From Galland: I am working on graphs and I need to find the percentage of increase from one figure to another. How do I do that? For instance staff hours for 2006 were 28011 and for 2007 were 31230. How do I find the percentage of increase? Answered by Stephen La Rocque.
	sec(pi/12)		2022-03-23
		From Diana: Please help me find the exact value of the following trigonometric expression: sec(pi/12). Thanks! Answered by Harley Weston.
	An arithmetic and a geometric sequence		2021-08-29
		From Moti: Let {an} be an arithmetic sequence such that its 1st, 20th, and 58th terms are consecutive terms of some geometric sequence. Find the common ratio of the geometric sequence. Answered by Harley Weston.
	Fibonacci numbers		2021-08-25
		From John: Make a single column of numbers. Start with two numbers of your choice. The third number is the sum of the previous two, the fourth number is the sum of numbers two and three, and so on until you have ten numbers in the column. Add up all ten numbers. Now, take the seventh number and multiply it by eleven. This product will equal the sum of the ten numbers. The same result will occur regardless of the first two numbers chosen. The question is why does the 7th number multiplied by 11 always equal the sum of the ten numbers? Answered by Penny Nom.
	Division in different bases		2021-02-06
		From Promise: Simplify the following 302 in base6 divided by 5 in base6 Answered by Penny Nom.
	0^(a+bi)		2020-12-03
		From Douglas: I realize raising 0^a = 0 if a>0 and undefined if a<=0. If have read that 0^bi is undefined for all b. What I don't understand is why 0^(a+bi) = 0 if a and b are not equal to zero. Is this purely by definition or is there a logical reason why this is the case? (I have taken Complex Analysis, so have a fairly good understanding of complex numbers.) Answered by Penny Nom.
	A problem involving distance, time, and rate.		2020-09-15
		From Ruby: Amy drove on the highways at 70 miles/hour to pick up fruits from her grandma’s garden in the morning. She stayed there for two hours. When coming back in the afternoon, she drove on the local roads at 40 miles per hour to avoid traffic. She spent a total of 8 hours for this trip, and drove a total 300 miles. How many miles did she drive each way? Answered by Penny Nom.
	Choosing 4 balls from 9		2020-07-22
		From sandiso: What is the probability associated with each possible random sample of size 4 from the population consisting of these nine balls Answered by Penny Nom.
	Adding a service charge and the VAT		2020-04-30
		From richard: was given a figure by a client been performance bonus of staff , the figure is 806,698.35 from this 806,698.35 is my company service charge of 10% and 5% of the service charge will be Vat to government in summary from 806,698.35 is 10% of service charge and 5% of service charge is the VAT Answered by Penny Nom.
	Building a house in one year		2020-04-22
		From Fify: If it takes 8 men to build a house in 450 days. How many men would it take to build the house in 365 days? Is there a specific method to calculate this please? Answered by Penny Nom.
	An arch in the form of a semi-ellipse		2020-04-20
		From Anggelica: an arch in the form of a semi-ellipse is 8 feet wide at the base and has a height of 4ft. how wide is the arch 1foot above the base? Answered by Penny Nom.
	Three consecutive odd integers		2020-04-10
		From Roxie: What is three consecutive odd integers? Answered by Penny Nom.
	Setting up a linear equation		2020-04-10
		From Jessie: Michaela and Aleah play on the same basketball team. In one game, Michaela scored one fifth of the teams points and Aleah scored one tenth of the teams points. Together, they scored a total of 42 points. How many points did the team score? I can't figure out how to put together the equation with the given variables. I have to show the work and I also need to know how to make that kind of equation. Thanks! Answered by Penny Nom.
	An arithmetic sequence		2020-04-04
		From ally: -10 ... last term 35 common difference is 3 (a) find the number of term in the sequence. i have lost the formula. 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.
	Degrees, minutes and seconds		2020-02-21
		From Jonathan: If a cone has an angle of 22 degrees, when i place it flat on a surface, the new resulting central angle is now at 68.69123834, but how come when i saw it on my friend it say 68 degree and 40 minutes, what is this minute? 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.
	Partitions of a set		2019-12-21
		From Ghani: 1. Are set partition "sets"? 2. If they are so then, why are both {{a}{b,c}} and {{a,b}{c}} said to be valid partitions of A ={a,b,c} despite them having different elements? (I understand that set are equal if they have the exact same elements). Thank you! Answered by Harley Weston.
	Some questions about sets		2019-12-15
		From M.Azzi: Hello, (I) - In set theory can a given set contain both elements and subsets, as "elements", as in : A = {1,2,{},3,{{3}},8} If yes : 1 - then, is |A| = 6 ? 2 - if the empty set is a subset of every set, 2. 1. does {} = {{}}, {{{}}} etc? , and if the is true what are the respective cardinals of the latter three? (0,1,1?). 2 . 2. Why isn't {1} equal to {{},1}? and why should these two be equal without having the same cardinality? Sorry if my questions are not well expressed. Thank you for the great service you provide. Answered by Harley Weston.
	Combinations of cities		2019-12-03
		From Oliver: Hi! I'm looking to find out how many combinations (non repeating) there are for 6 cities. If we name the cities A to F, possible combinations would include; A. A, B. B. A, B, C. A, C. B, C. C. and so on. Thank you! Answered by Penny Nom.
	Algebra		2019-11-06
		From Krizhia: How is y= 1/2 * (x-1)² be x= √2y + 1. Please show me the steps Answered by Penny Nom.
	Increasing your average mark		2019-11-01
		From Elena: After 9 weeks Mikayla has an average ark of 5 out of 10 in the weekly spelling tests. What is the minimum number of extra weeks now required to raise her average to 7? Answered by Penny Nom.
	The perimeter of a piece of a circle		2019-10-18
		From Arwin: The radius of a circle is 17 cm. A chord XY lies 9 cm from the centre and divides the circle into two segments. Find the perimeter of the minor segment. Answered by Penny Nom.
	Four less than three times a number is 20		2019-09-29
		From Linda: four less than three times a number is 20,what is the number? Answered by Penny Nom.
	The volume of a fire hose		2019-09-18
		From Carlou: How many liters of water in a 2.5 inches diameter of fire hose with a 20 meters in length Answered by Penny Nom.
	The amount of concrete in a foundation		2019-09-11
		From Lorinda: How do you calculate ( in cubic yards) how much concrete is needed for the foundation of a rectangular building 40 ft by 85 ft if the foundation walls are 8 inches thick and 7 ft 6 inches high? Answered by Penny Nom.
	What are the next three terms?		2019-06-18
		From Shriya: -6, -2 , 2, 6,10 what are the next three terms? Answered by Penny Nom.
	Finite and infinite sets		2019-06-10
		From Pretzie: What is Finite Set & Infinite Set? Answered by Penny Nom.
	(3d) Whether line segment intersects triangle		2019-04-13
		From rj: Well hello, Lets say I have a triangle, Not any ordinary triangle, but a triangle that is represented in 3 dimensions. I also have a line segment. Lets say that this triangle has points A(0,0,0), B(1,0,0), C(0,1,1) And the line segment has points D(0,1/2,0), E(1,1/2,1) In what way can I find if the line segment and triangle intersect? Their intersection point? I don't prefer matrices, because they don't make any sense, but ... if that's the only way to solve this, then do what's necessary. Thank you in advance. Answered by Penny Nom.
	4^x=2^x+6		2019-04-05
		From Olivia: How do you find the (b,n) if the solution of the equation 4^x=2^x+6 can be expressed at logb(n) where b and n are both prime numbers? Answered by Penny Nom.
	Four consecutive positive integers		2019-03-12
		From Nabila: The product of four consecutive positive integers in 24024 What is their sum? Answered by Penny Nom.
	Converting a base six number to base three		2019-03-10
		From Nina: Change 253 in base 6 to a number in base 3 Answered by Penny Nom.
	Misuse of greater than		2019-03-07
		From Kenneth: I have an old business mathematics textbook. The authors have indicated that the following expressions indicate multiplication: ? is 2/3 greater than 90; ? is 2/3 smaller than 90. They also indicated that the following expression would indicate division: 30 is 2/3 greater than ? and 30 is 2/3 smaller than ?. How can these phrases indicate multiplication and division? How can 60 be 2/3 greater than 90 and also smaller than 90 as indicated above. What were the authors thinking? I have added the page from the book that indicates what I have explained in my message Kenneth Answered by Harley Weston.
	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.
	An arithmetic sequence		2019-02-23
		From Dalal: If x+1 and -x+17 are the second and sixth term of a sequence with a common difference of 5, what's the value of x. Answered by Penny Nom.
	Margin with commission as part of selling price		2019-02-13
		From Anni: I need to find selling price to put us at 24% margin. 15% commission is based on selling price and is included in our cost. I'm trying to do it excel and keep getting a circular reference. Total cost= cost + commission (15% of selling price) Selling price=total cost + 24% margin Answered by Penny Nom.
	An arithmetic sequence		2019-01-31
		From sara: if the 6th term of an arithmetic sequence is 8 and the 11th term is -2, what is the first term? Answered by Penny Nom.
	7 spheres on a hexagonal tray		2019-01-14
		From herm: what is the length of each side of a hexagonal tray, with the height of each side 0.75 inch, to hold seven spheres, each with a diameter of 3.00 inches? The spheres are placed such that each side of the hexagon is touched by one sphere at its midpoint (and the seventh sphere is place in the center of the "ring" of the other six spheres. Answered by Harley Weston.
	Solve for x in Y=1.5x + log (1+x)		2018-12-23
		From Asadollah: Please restate below expression in terms of y Y=1.5x + log (1+x) Thanks 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.
	A line cuts a curve		2018-11-11
		From roxanne: Hello, i need to ask a question, do you mind explaining and writing the formula of how to solve equations such as "find the set values of k for which the line y-2x-5 cuts the curve y=x^2 +kx+11" please Answered by Penny Nom.
	Why 1/2 in the area of a circular sector?		2018-10-26
		From Ariel: In the equation for area of a sector=1/2r^2theta why is it 1/2? Please explain conceptually not algebraically. Answered by Penny Nom.
	Two curves		2018-09-23
		From Megan: How do i find the interception points of xy=-2 and y=x+3? Many thanks! Answered by Penny Nom.
	A rotating wheel		2018-08-24
		From Kay: A wheel with a radius of 7 inches is rotating at 4 revolutions per second. What is the linear speed v, in feet per second? Answered by p.
	Two intersecting tubes		2018-08-15
		From Tommy: Hi, I am trying to determine a mathematical model for two metal tubes joining at various degrees for weld. For instance, if I am trying to join the end of a tube to the side of another at a 90 degree angle, it will be a simple profile cut out of the joining tube. Where it gets tricky is if you want to join the new tube at a given angle. It would be very helpful if you could give insight as to how I can solve this problem or an equation I could work off of. Thanks for the help!! Answered by Edward Doolittle.
	Form a cone from a circle sector		2018-08-12
		From Tinashe: A 216 sector of a circle of radius 5cm is bent to form a cone. Find the radius of the base of the cone and its vertical angle. Answered by Penny Nom.
	Creating a number sentence		2018-06-29
		From trish: First I have to solve the problem. Then write a number sentence for the problem. The problem: By installing a $120.00 thermostat that reduces the temperature setting at night a family hopes to cut its annual fuel bill for heating oil by 8%, and recover the cost of the thermostat in fuel savings after 2years. What was the family's annual fuel bill before installing the thermostat? Thanks can't figure this one out! Answered by Penny Nom.
	Soil in a raised bed		2018-06-24
		From Georgia: Good Afternoon, I'm planning on building a raised bed garden measuring 6 feet long x 4 feet wide x 12 inches deep. I'm not sure how to calculate the amount of soil to fill it up. I will have to purchase the soil in 2 cubic feet bags. I've read several articles about this topic on various gardening websites, and one of them stated it would take a ton of soil to fill up an 8 foot long x 4 foot wide x 12 inch deep raised bed garden. I'd greatly appreciate it if you could help me out with this quandary. Thank you for your prompt and courteous response. Kind Regards, Georgia Answered by Penny Nom.
	Three consecutive whole numbers		2018-06-22
		From whaha: the sum of three consecutive whole numbers divided by 4 is equal to 6. find the numbers. Answered by Penny Nom.
	A question about the empty set		2018-06-17
		From Andrey: Hello there! I got that an empty set is a subset of every set. There is a question. Is an empty set an element of every set? ∅ ⊆ {x}True ∅ ∈{x}? Sorry if the question is easy. A set theory is a bit confusing. Answered by Penny Nom.
	The number of terms in an arithmetic sequence		2018-06-15
		From Don: how many terms in arithmetic sequence are there if the first term and the last term are 3&59 respectively in common difference is 4? Answered by Harley Weston.
	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.
	The inverse square law		2018-06-05
		From Amy: Question about inverse square law ; Hi, I'm trying to understand some nuances about this law and have been reading about it a lot online and trying out some homework for personal interest (hobby ) - not school related. I understand that the simple formula is ; 1/d^2 I was wondering about what appears to be an oddity to me, that I came across when I was working with a test example I found at this link ; http://www.softschools.com/formulas/physics/inverse_square_law_formula/82/ The problem that caught my interest was this one on that page ; "1) If a bright flashlight has a light intensity of 15.0 candela at a distance 1.00 m from the lens, what is the intensity of the flashlight 100.0 m from the lens?" So I have a few different questions about this, but the most important one is, what does it mean if we replace the "1" in ; 1/d^2 with a different value such as a ratio in the form of a decimal value, so instead we have something like this ; 0.75/d^2 ??? Does this ratio represent a curve then? I am thinking that the "1" in the normal formula represents a straight line Some of the links I was researching ; http://wisptools.net/book.php?c=3&s=2 http://www.softschools.com/formulas/physics/inverse_square_law_formula/82/ https://www.nde-ed.org/GeneralResources/Formula/RTFormula/InverseSquare/InverseSquareLaw.htm Answered by Penny Nom.
	Two odd integers		2018-06-04
		From Pleroma: The product of two alternate odd integers exceeds three times the smaller number by 12. What is the larger number? Answered by Penny Nom.
	What is the diameter of the observable universe?		2018-05-27
		From peter: The diameter of the observable universe is calculated to be 92 billion light years. What would that distance be in miles given a light year is 6 trillion miles? Answered by Penny Nom.
	Gauss' Addition of whole numbers.		2018-04-30
		From Brad: I found this on your site. Question: what is the sum of the first 100 whole numbers?? Is there a different formula if the numbers begin at a number other than one? For example What is the series I want to add is goes from 7 - 53? Answered by Harley Weston.
	Seven tangent circles		2018-04-23
		From Domenick: How to calculate the circumscribed and inscribed circles formed by seven .019685 diameter circles arranged in a circle with all seven circles tangent to each other? Answered by Penny Nom.
	Base 6 to base 4		2018-03-25
		From Malik: Hi Sir..! I just want to know the proper example with a brief explanation of conversion of base 6 into base 4. kindly reply me as soon as possible.. Thank you Answered by Penny Nom.
	Walking a fraction of a mile		2018-03-20
		From Jamie: Who walked a fraction of a mile that is closer to neither 0 nor 1 ? Explain Avery 1/6 me.Nunez 5/6 Ms. Chang 1/3 Mr. O’Leary 4/8 Miss Lee 4/6 Answered by penny Nom.
	A geometric series		2018-03-13
		From nathi: Hi I am really struggling with this question please help !!!! a pohutukawa tree is 86 centimetres when it is planted. in the first year after it is planted , the tree grows 42 centimetres in height.Each year the tree grows in height by 95% of the growth of the previous year. assume that the growth in height of the pohutukawa tree can be modelled by a geometric sequence. A)find the height of the tree 5 years after it is planted and figure out the maximum height the pohutukawa tree is expected to reach in centimetres. The maximum height part is not answered. Answered by Penny Nom.
	The intersection of a curve and a line		2018-03-08
		From lola: find the set of values of constant C for which the line y=x+c intersects the curve y=2 square root x at, at two distinct points Answered by Penny Nom.
	nC0 + nC1 + nC2 + .... + nCn = 2^n		2018-02-19
		From bristal: (QQ) Prove, nC0 + nC1 + nC2 + .... + nCn = 2^n. Answered by Penny Nom.
	A puzzling sequence		2017-12-19
		From Alan: My son has the following sequence to work out the formula for the nth term (and fing 5th and 6th terms) and I have tried a variety of ways but can't help! 1/2, 5/6, 1, 11/10 I have converted all to 15/30, 25/30, 30/30, 33/30 and so think the next two terms are 37/30 and 45/30 but I have no idea how to prove or if I am right! Any help appreciated. Answered by Penny Nom.
	An arithmetic sequence		2017-11-30
		From yo: x; 2x+1; 11 are three consecutive terms of an arithmetic sequence.calculate x Answered by Penny Nom.
	Sampling distribution		2017-10-16
		From Esther: I need 4digits combination of 235689 and without replacement. Thanks Answered by Penny Nom.
	Three consecutive odd integers		2017-10-10
		From Johanna: Three consecutive odd integers are such that the sum of the first and second is 31 less than 3 times the third 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.
	An alphabetic sequence		2017-09-17
		From malik: find the letter of the following series....? ZOTTFFSSE- Answered by Penny Nom.
	A rope formed in a semicircle		2017-08-29
		From Janna: How do I find the total length of a piece of rope formed in a semicircle that has a diameter of 8 inches? Answered by Penny Nom.
	Two circles		2017-08-13
		From Ladines: Find the equation of the circle passing through points of intersections of circles x²+y²=4y and x²+y²=2x and the center is on line y=2 Answered by Penny Nom.
	The perimeter of a sector of a circle		2017-08-11
		From Alisa: find the perimeter of the sector with radius 7 cm in which the angle at the centre is 60 degrees leave your answer in terms of pi Answered by Penny Nom.
	A semi ellipse		2017-07-25
		From Ian: The arch of the bridge is in the shape of semi ellipse,with its major axis at the water level.suppose the arch is 20ft. High in the middle,and 120 ft. Across its major axis. How high above the water level is the arch,at a point 20 ft.from the center (horizontally). Round of 2 decimal places 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.
	An arithmetic sequence		2017-07-17
		From abbi: hi there im a student in 11 grade ive been trying to do this task but i have no idea how to do it the question is Find the common difference and the n^th term of the arithmetic sequence if the first term is 4 and the twentieth sum of the terms is 1030 Answered by Penny Nom.
	Two consecutive odd integers		2017-07-14
		From Adeeb: Find two consecutive odd positive integers, sum of whose square is 290. Answered by Penny Nom.
	Three consecutive natural numbers		2017-06-11
		From Anita: Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the square of the other two by 60. Find the numbers. Answered by Penny Nom.
	Two wires between two buildings		2017-05-11
		From Bill: I need to find the height of the intersection point of two building wires< br /> Building A is 860 feet high and building B is 480 feet high. The wires existent from the top of one building to The bottom of the other < br /> The distance between is 32 feet Answered by Penny Nom.
	Yards per second to miles per hour		2017-05-11
		From Scott: If a soccer ball travels 30 yards or roughly .017 miles in 2 seconds how fast was the ball going in mph? Answered by Penny Nom.
	Selling price and markup		2017-04-24
		From Julie: What would the cost of an item be, if the sell price was $50 and the markup 48% Answered by Penny Nom.
	Baseball Cards		2017-04-20
		From Raquel: A minor league baseball team gave away baseball cards to each person entering the stadium. One group receives 28 baseball cards. A second group received 68 baseball card. If each person entering the stadium receive the same number of cards, what was the greatest possible number of baseball cards that each person could have received? Answered by Penny Nom.
	A function which is onto but not one-to-one		2017-04-16
		From Avinash: Define a function f(x):N-->N which is onto but not one-one.Where N is set of natural numbers. Answered by Penny Nom.
	Forming a cone from a circle		2017-04-15
		From Tasha: A sector of a circle subtends an angle of 216 degrees at the centre, If this sector is used to form a cone of vertical height ,8cm, calculate the base radius of the cone Answered by Penny Nom.
	Successive Differences		2017-04-06
		From Twaha: Please find the equation of the sequence 1 2 4 7 11 16 22 Answered by Penny Nom.
	Faster than as a percentage		2017-03-18
		From Maximilian: Hi, i have a strange issue with the phrase "faster than" in percentage, ie. if i have a 10MB/s connection, and somebody has a 7MB/s connection, is it 30% faster or 50% faster.- which ( affirmation, phrase, sentence ) is the right one: a:) My 10MB/S connection is 50% faster than the 7MB/s ? or b:) My 10MB/S connection is 30% faster than the 7MB/s ? Thanks in Advance, and please if you can teach me why ! 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.
	Addition and subtraction base 5		2017-01-29
		From BABAWALE: Simplify 342five +132five-223five Answered by Penny Nom.
	Feet per second to miles per hour		2017-01-27
		From ron: if a vehicle travels 50 feet in 2.5 seconds what is the speed in mph. 3600 sec in hour /5280 feet in a mile i get .68181818. how do i figure the 2.5 seconds. all the calculators I've used show 34 mph is that correct or am i forgetting the 2.5 second. please help. 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.
	The inverse of y=x^2+x+c		2016-12-21
		From Sam: What is the inverse of y=x^2+x+c for x? Answered by Penny Nom.
	The inverse of y = x(x - 2)		2016-12-21
		From Sasha: Hello, I recently stumbled upon this question and I haven't been able to figure it out. Why is the inverse of y=x(x-2) not a function? Suggest a domain restriction which would ensure that the inverse is a function. Thank You :) Answered by Penny Nom.
	4444 base five		2016-11-11
		From John: If 4444 is a number in Base5, is 624 its value? Answered by Penny Nom.
	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.
	The derivative of the inverse of a function		2016-10-28
		From Kate: Hi, I'm in a College level Calculus course and I can't seem to figure out the answer to this question. Find the derivative of f^-1(4) if f(3)=4 and f'(3)=1/7 Answered by Penny Nom.
	Subtraction of two numbers in different bases		2016-10-07
		From Wica: Hello, So happy I found this site. I am having problems with bases. My question is : Please perform the subtraction between two number over different bases : A. (5874)base 12 - (216)base 9 B. (216)base 9 - (5874)base 12 Answered by Penny Nom.
	A kinky curve		2016-10-06
		From tammie: Koch’s kinky curve is created by starting with a straight segment and replacing it with four segments, each 1/3 as long as the original segment. So, at the second stage the curve has three bends. At the next stage, each segment is replaced by four segments, and so on. How many bends does the curve have at the third stage? Answered by Penny Nom.
	A car chase		2016-09-25
		From Ms.: Car 1 is traveling down the road at 50 mph and passes Car 2 is sitting on the side of the road. Car 2 needs to catch Car 1 one half mile down the road. How fast must Car 2 drive to catch Car 1 if Car 2 waits 10 seconds before pursuing Car 1? Yes, the assumption is that the Car 2 can accelerate from a standing position and over take Car 1 rate. What is the answer or formula for this type of question? Respectfully Befuddled Mom? Answered by Penny Nom.
	How fast and how far must Car 2 travel before catching Car 1?		2016-09-25
		From Ms.: Car 1 is traveling down the road at 50 mph and passes Car 2 is sitting on the side of the road. Car 2 needs to catch Car 1 one half mile down the road. How fast must Car 2 drive to catch Car 1 if Car 2 waits 10 seconds before pursuing Car 1? Yes, the assumption is that the Car 2 can accelerate from a standing position and over take Car 1 rate. What is the answer or formula for this type of question? Respectfully Befuddled Mom? 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.
	Two sequences		2016-08-20
		From Ting: The first four terms of a sequence are 4, 20, 56 and 120. By comparing with the nth term of sequence 1,5,14 and 30 which is 1/6n(n+1)(2n+1), find a formula for nth term. Can you precisely show out how you do this questions ( with the steps please) Answered by Penny Nom.
	A search area		2016-08-13
		From tammy: if your searching an area and you go 300 km from point A and search 380° what or how much area would you search? Answered by Penny Nom.
	Five consecutive even integers		2016-08-12
		From Marcelle: The average of 5 even consecutive numbers is 112. What is the largest numbers? Answered by Penny Nom.
	The sequence 13 17 23 27 33 37		2016-07-29
		From Shriya: The first term of a sequence is 13. The following terms are found by alternately adding 4 and 6 to the previous term. The first six terms are 13 17 23 27 33 37. Find the 80th term. Answered by Penny Nom.
	Which term of this sequence has value 8?		2016-07-20
		From Lauren: Hi there Which term in the sequence -2; -5/3; -4/3 ; -1; ... has a value of 8. Since term 2 and 3 of this sequence contain fractions which can be converted to recurring decimals. What is the best way to work out the common difference here. I do however understand that to work out the nth term of an arithmetic series, the following formula Tn = a + (n-1)d. In this series a = -2 Answered by Penny Nom.
	Subsets		2016-06-26
		From Kats: How Many sub sets are in set k={6,7,3} Answered by Penny Nom.
	The inverse function for f(x)=2x^2+5x		2016-04-23
		From Ashini: The inverse function for f(x)=2x^2+5x Answered by Penny Nom.
	A sector of a circle		2016-04-21
		From mustafa: In a sector of a circle, the arc length is equal to half the perimeter of a sector.find the area of a sector in terms of r Answered by Penny Nom.
	A road trip word problem		2016-04-10
		From Marc: While on a road trip I imagined this random word problem. Suppose I start a trip of 75 miles. My initial speed is 75 miles per hour. After every mile traveled I decrease my speed by one mile per hour. After the first mile I decrease my speed to 74 miles per hour and so on for each subsequent mile traveled. How long will it take to complete the 75 mile journey? Answered by Penny Nom.
	Setting up a pool		2016-04-09
		From BETH: i am trying to cover an area for a 15x15 foot round pool with play sand before I set up the pool. My playsand bag is 50 lbs , says it covers .5 cubic feet per bag. How many bags do I need? Answered by Penny Nom.
	A square based box and a cylinder		2016-03-26
		From rajpal: i m trying to calculate an area required to hold 4.4 mln cubic metres of volume. I used square and I get below result A box shape that has dimensions 1500 meters (1.5km) by 1500 meters (1.5km) by 2 meters depth has a volume of: = 4,500,000 cubic meters (4.5 mln cubic meters) but when I use a cylinder shape, i get below result A cylindrical shape that has a radius of 850 meters and a depth of 2 meters has a volume of: = 4,539,600 cubic meters (4.54 mln cubic meters approx) why is it that the cylinder, though of same depth holds more volume than a square? kindly clarify. Answered by Penny Nom.
	A problem in base x		2016-03-25
		From Malith: determine the value of base x of (211)x = (152)8 please mentioned the steps Thank you Answered by Penny Nom.
	The inverse of a function		2016-03-20
		From Billy: f(x) = Square root(x^2 + 2x) What is the inverse? Answered by Penny Nom.
	tan inverse 1/4		2016-03-14
		From nazz: prove; tan inverse 1/4=1/3 cot inverse 52/47 Answered by Chris Fisher.
	Can you construct a regular 21-gon?		2016-03-08
		From Peter: hi, i know that if i use a compass to draw a circle, i can use the same setting to mark 6 intervals along the circle circumference, how would i go about marking out 21 equally spaced points around the circumference? if there an online calculator i can us, or some other interesting trick? tia peter Answered by Robert Dawson.
	A geometric progression		2016-03-03
		From Pauline: A woman measures the height of her child at birth and at monthly intervals afterwards.The child's height increases by 5% per month. Find the number of measurements she has made before the child's height is twice what it was at birth Answered by Penny Nom.
	Compressed Earth blocks		2016-03-02
		From John: how many 14"x10"x4" blocks do I need for a 1300sq foot house 8 foot high Answered by Penny Nom.
	A deck that is half an ellipse		2016-02-28
		From Steve: On your website, I was reading a question and your response from a girl named Angela in which you provided a formula by which her father, a welder, could figure out points on an arc corresponding to equal 3' intervals on a 30' chord where the vertex was 1' off the chord. Is there an equivalent formula when working with an ellipse? I suspect this change will make the calculations significantly more complex. I am building a deck that is half an oval, and would like to be able to mark out the perimeter by measuring the distance from regular intervals on the primary access to a corresponding point on the perimeter. I will then connect the points on the perimeter and cut a reasonably smooth arc. The length of the primary access will be 22' and width of the deck at the vertex is 9'. I would like to be able to know the distance from the primary axis to a point on the perimeter at equal intervals of 6" along the primary axis. Can you help? Answered by Penny Nom.
	Division base 5		2016-02-01
		From Jenalee: I am having problems with a dividing bases question. I reviewed two that I could find in the database and tried the question as shown but I am still getting the wrong answer. My question is 32\24043 to the base of 5 for both. Answered by Penny Nom.
	Which term of the series 2+7+12+...is 152?		2016-02-01
		From francis: whice term of the series 2+7+12+...is 152? Answered by Penny Nom.
	Subtraction in a base larger than ten		2016-01-31
		From Jenalee: Hello, So happy I found this site. I am having problems with bases. My question is 97B9 - 6A3A base 16 for both. Please help. Answered by Penny Nom.
	Percentage reduction		2016-01-30
		From Kuuku: The daily production targets in 2000 was 60,000 units this declined to 48,000 units in 2001 but was projected that further 300units reduction would be experienced in 2002. Calculate the percentage reduction by 2002. Answered by Penny Nom.
	Consecutive angles of a parallelogram		2016-01-28
		From Hanna: The consecutive angles of a parallelogram measures Answered by Penny Nom.
	Two increases of 20%		2016-01-27
		From Z: How do I find how many books are in a library given a problem like this... The number of books increase after buying 20% more in May. The number increased again by 20% after they were given 300 books. How many books did it start with?. Answered by Penny Nom.
	Two increases of 20%		2016-01-27
		From Z: How do I find how many books are in a library given a problem like this... The number of books increase after buying 20% more in May. The number increased again by 20% after they were given 300 books. How many books did it start with?. 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.
	Countable and uncountable sets?		2016-01-15
		From wilson: what are the countable and uncountable sets? Answered by Penny Nom.
	The range of a function defined piecewise		2016-01-13
		From sarah: f(x)={x-2, x<-2        {x^2-4, -2_<x_<2        {x+2, x>2 find the range Answered by Penny Nom.
	Three consecutive integers		2016-01-07
		From ronn: Three consecutive integers whose sum is 186 Answered by Penny Nom.
	A sequence		2016-01-05
		From Mia: the next three terms in each sequence. 0.4, 0.54, 0.68, 0.82, Answered by Penny Nom.
	Four consecutive integers		2016-01-05
		From sherica: my teacher gave us an assignment and it says here that; THERE ARE FOUR CONSECUTIVE INTEGERS.IF THE SMALLEST ONE IS x ,FIND THE SUM OF THE FOUR INTEGERS. that is the question ...thanks hope that u can answer it Answered by Penny Nom.
	Book sales		2015-12-30
		From Sandra: Your finance text book sold 56,500 copies in its first year. The publishing company expects the sales to grow at a rate of 20.0 percent for the next three years, and by 8.0 percent in the fourth year. Calculate the total number of copies that the publisher expects to sell in year 3 and 4. Answered by Penny Nom.
	Proof that an erroneous algebraic statement is false		2015-12-14
		From Berteanu: I need help with this proposition: "It exists x a real number that for every y real number 5*x-2*y*y=1 This is false. Let x be from R. And I need an y real number that 5*x-2*y*y!=1 Please,could you help me? Answered by Penny Nom.
	The line of intersection of two planes		2015-12-09
		From Rabz: Determine the vector equation for the intersection between the two given planes 2x+7y equal to 14,x+z equal to 7 Answered by Penny Nom.
	Roof Square footage		2015-11-11
		From Todd: Question from Todd: Good Day. I have to figure out the square footage of a quonset style roof that's not playing by the rules The building dimensions (rectangular) are 63'x135' the height of the roof is 9.25'. It not an entire Quonset, It's that style of roof,(curved). There are concrete block walls 10' up to the metal roof. Thank you! Todd Answered by Harley Weston.
	Subtraction in base 8		2015-10-21
		From Adi: Hi! Can you help me with a nagging problem, I searched a lot over the web and couldn't find it. I saw this site I gave it a try and I found it to my liking. I am confused how to subtract bases from other bases: 567 (in base 8) - 456 (in base 8) ______________ ????????? How do you do this? I do know how to carry and subtract with different bases. Can you please help me? Thanks, Adi Answered by Penny Nom.
	The sequence 1,2,4,7,11,16...		2015-10-15
		From HEMANT: what is the next term in the sequence : 1,2,4,7,11,16,? Answered by Penny Nom.
	Seven switches with 3 stages each		2015-09-15
		From jeff: We are trying to solve a combination problem. If I have 7 things that can be in 3 states (say on/partially on/off), and all 7 have to a state. How many different combinations can there be? It doesn't seem like we should treat it as 21 independent things, but not sure how to break the problem apart. Answered by Penny Nom.
	Subtraction base 5		2015-08-29
		From nakita: can u explain the quinary subtraction ... (3000) -(2342) all the numbers are in quinary number system Answered by Penny Nom.
	The distance over a Quonset		2015-08-20
		From jane: total base of hemisphere is 30 ft apex height is 20 feet what is total length over dome Answered by Penny Nom.
	The nth term		2015-07-04
		From ujjal: What is the nth term in the order 6,8,10.... Answered by Penny Nom.
	Why is the area of square not conserved when it changes to a rhombus?		2015-06-28
		From shubham: Why is the area of square not conserved when it changes to a rhombus, both have equal sides still rhombus have less area than square.?? Answered by Penny Nom.
	The intersection of a plane and a cone		2015-05-16
		From Tom: Is there a way to derive an equation that describes the perimeter of the intersection of a plane and a cone regardless of the angle of the plane to the cone. Assume that the plane does not cut through the base of the cone, the x, y, z location of the vertex is known, the distance from the vertex to the plane through the axis is know., and that the angle of the cone is known. Answered by Chris Fisher.
	The number of possible musical notes using an n-key instrument		2015-05-04
		From Farihin: Lets say that i have keys, and each key is for notes of a musical instrument, So i wanted to find out the number of notes i can get for a certain number keys, of course in the form of an equation. Notes can use as many keys, it can use 1, or 2, or 3, or even 100. Notes in real life is not as such, but ignore reality. I tried doing this but i can't seem to find a formula for it. For example, i have 4 keys, say A, B, C, and D. so, for notes that uses one key are 4, which is A, B, C, and D themselves. for notes that uses two keys are 6, AB, AC, AD, BC, BD and CD. for notes that uses three keys are 4, ABC, ABD, ACD and BCD. lastly for notes that uses all four keys is 1, ABCD. So, the total will be 4+6+4+1=15# The nth term for the first equation is n, the second is [(n^2)-n]/2 the third and the fourth, i don't know but the final answer should be like, n + [(n^2)-n]/2 + [3rd] + [4th] Sorry for the long question though... Answered by Penny Nom.
	A piecewise function		2015-04-25
		From uday: f(x)={x^2+3x+2 / x+2, x(not equal to)=-1 {4, x=-1 how to find domain and how the graph looks like Answered by Penny Nom.
	A geometric sequence		2015-04-19
		From Delfina: In a geometric sequence the second term is 15 and the fifth term is -405. Find the sum of the first eight terms 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.
	Some non-decreasing sequences		2015-04-13
		From Sky: Hi I'm a Student and i'll try my best to state the problem perfectly. The number of non-decreasing sequences of size at least 1 and at most N, such that each element of the sequence lies between L and R, both inclusive. Eg:- N=1 L=4 R=5 ans= 2. [{4},{5}] N=3 L=4 R=6 ans= 19. [{4},{5},{6},{4,4},{4,5},{4,6},{5,5},{5,6},{6,6} {4,4,4},{4,4,5},{4,4,6},{4,5,5},{4,5,6},{4,6,6},{5,5,5},{5,5,6},{5,6,6} ,{6,6,6}] Answered by Claude Tardif.
	Excavating a basement		2015-04-12
		From Randy: The cost of excavation is $4.50/ cu yd. Find the cost of excavating a basement 87 ft long, 42 ft wide, and 8 ft deep. Answered by Penny Nom.
	A tangent to y=x^3 passes through (0,2)		2015-04-05
		From Kevin: Given that the curve y=x^3 has a tangent line that passes through point (0,2). Find the equation of the tangent line Answered by Penny Nom.
	Three consecutive integers		2015-03-28
		From Aleksey: I need help how do I find the second of three consecutive integers if the sum of the first and third is 26? Answered by Penny Nom.
	Two consecutive odd integers		2015-03-09
		From gowtham: The sum of two consecutive odd integers is 20.find the integers Answered by Penny Nom.
	Integers in different bases		2015-03-05
		From Michael: Let k be a positive integer so that 28 (subscript)k = 132 (subscript)5 Answered by Penny Nom.
	Two consecutive positive integers		2015-03-01
		From meha: Find two consecutive positive integers , sum of whose squares is 365. Answered by Penny Nom.
	Solve x=r(t-sin(t)) for t		2015-02-28
		From David: I don't know how to write the function of t(x) by x=r(t-sin(t)). Can you teach me that? Answered by Harley Weston.
	A question in set theory		2015-02-25
		From Jared: If a set A={1,2,3} and set B={ {}, 1} Can B be a subset of A? Since every Set contains an {} ? Answered by Robert Dawson and Claude Tardif.
	A stone is dropped in a lake		2015-02-14
		From Wendy: Hi, I have problems solving this problem. We didn't exactly go over these kind of problems and the book doesn't have an example either. Thank you for your help! A stone is dropped in a lake, creating a circular ripple that travels outward at a speed of 80 cm/s. (a) Find a function g that models the radius as a function of time t. g(t) = (b) Find a function f that models the area of the circle as a function of the radius r. f(r) = (c) Find f compose g. f compose g = Answered by Penny Nom.
	What is our cost?		2015-01-27
		From Johanna: I have a pieces of 3/4" sch40 (round tube) 240" long at $70. What is our cost. We also add 35% to our cost for selling price. How do I figure this out? Answered by Penny Nom.
	Math in the universe		2015-01-21
		From GA: I want to find out examples in universe for this equation: sin(x)/cos(x)=1 or tan(x)=1. I know the mathematical answer of pie/4 or 45 degree angle. What I need to know is to find examples of this. I found an example in construction, for example, which is the shape of attic in the house. I want to find examples in universe like in solar system, in quasars or jets coming out of them, in galaxies, in stars, in black holes, etc Do you know of any such examples? Answered by Robert Dawson.
	1,4,9,61,52,___		2015-01-21
		From Mubashir: 1,4,9,61,,52,___,84,___,18,1,121,___ please tell me its formula and also that rule that is being applied here like adding 3 or subtracting 5 etc. Answered by Walter Whiteley.
	A sequence		2015-01-13
		From cyaz: write a rule for each sequence then find next 3 terms for 7/8, 3 1/8, 5 3/8 Answered by Penny Nom.
	211basex=152base8		2014-12-15
		From Humaira: 211basex=152base8 Answered by Penny Nom.
	A line segment of length root 5		2014-12-15
		From angela: On the dot grid below, draw and label a line segment with length square root 5 the dot grid is 8 by 10 Answered by Penny Nom.
	A truncated, square-based pyramid		2014-11-23
		From Hannah: A designer vase has the shape of a truncated, square-based pyramid. The base of the vase is a square with a side length of 15 cm. The area of the square opening is 70.56 cm2. Each of the four sides is a trapezium with slant sides 9 cm long. Find (to the nearest square centimetre) the total surface area of the vase. Answered by Penny Nom.
	Factorise 15x + 15y		2014-11-20
		From Jordan: hi i saw a question in class today that i didn't understand and i didn't really understand what my teacher was going on about so how do you factorise 15x + 15y Answered by Robert Dawson and Penny Nom.
	The density of sea sand		2014-11-02
		From Lenny: Hi There, I need to find out the the density of sea sand to convert one metric ton to cubic meter as I am submitting for a tender which is in cubic meter but the requirement is in metric ton. I searched through the web site but no density of sea sand is given though there is specific Gravity of dry sand is available. I was given a density of 1.6 to work with. If that is true am I right to say that 1 cubic meter of sea sand is equivalent to 1.6 metric ton? Please help as I am getting confused with what I am able to find out on the web. Thanks much in advance Rgds Lenny Answered by Penny Nom.
	logbase4 (sin x) = -0.5		2014-10-26
		From Susan: Solve for x: logbase4 (sin x) = -0.5 Answered by Penny Nom.
	Find the nth term		2014-10-26
		From Kenneth: According to the pattern of the following sequence. Find it's nth term: 3,9,27,81,243,.......... Answered by Penny Nom.
	A truncated square-based pyramid		2014-10-22
		From Beth: How do you find the height of the original square-based pyramid when given the sides (12cm) of the base and height (6cm) of the truncated pyramid, as well as the sides (3cm) of the base of the chopped off top (chopped off parallel to the base)? Answered by Penny Nom.
	Three consecutive odd integers		2014-10-17
		From Maddy: 3 times the largest of three consecutive odd integers is 13 more than the sum of the other two. What are the integers? Answered by Penny Nom.
	Division in base 3		2014-09-30
		From Nnubia: 1021 in base 3 divided by 2 in base 3 Answered by Penny Nom.
	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.
	Base 6		2014-09-10
		From Amanda: using base 6, what is the next number after 25? 35? 55? and 455? I need to be able to show the base 6 material. Answered by Penny Nom.
	35 base 6		2014-09-10
		From Amanda: Sorry I am having trouble understanding base, 35 in base 6 means 3 10's and 5 ones, which is the same ____ in base 10? Answered by Penny Nom.
	211(base x)=152(base 8)		2014-09-09
		From Vaidehi: Find the base value (i.e. x): 211(base x)=152(base 8) Answered by Penny Nom.
	A second grade word problem		2014-09-09
		From Beth: How do I explain to my second grader how to find the answer to the problem: My tens digit is 8 more than my ones digit. My ones digit can not be zero. Answered by Penny Nom.
	A secret number		2014-09-08
		From jai: it is smaller than half of 100, it is more than 4 tens and less than 5 tens, the tens digit is two more than the ones digit , together the digits have a sum of 6..... What is my secret number? Answered by Penny Nom.
	Cutting a round cake so that it doesn't dry out		2014-08-26
		From James: I'm wondering if there's a simple way to calculate the area between two parallel chords of a circle equidistant from its diameter, or if I have the area, to find the distance between the two chords. Here's my "problem". You may have heard of the way of cutting a round cake so that it doesn't dry out - make two parallel cuts (chords) the length of the cake, take the middle piece, then push the two pieces together. So I know the area of a 12" cake, and I want say, exactly an eighth of the cake. How wide do I cut the centre piece? Now to get even more difficult, the next day I want another eighth from the centre. How wide do I cut the next pieces, and so on...? Thanks, James Answered by Harley Weston.
	The inverse of f(x) = x^2 - x		2014-08-22
		From Tyler: Find the Inverse function of: f(x) = x^2 - x Answered by Robert Dawson.
	A price increase and a consumption decrease		2014-08-16
		From sujan: If the price of petrol increases by 25% and Rajesh intends to spend only 15% more on petrol then by how much % should he reduce the quantity of petrol he buys? 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.
	The sum of the first 50 terms of an arithmetic progression		2014-07-26
		From Joshua: Hello ...my is Joshua...I'm a grade 11 student...I got a question Calculate the sum of the first 50 terms of an arithmetic progression: 112:98:84 Answered by Penny Nom.
	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.
	Selecting a meal at a school cafeteria		2014-07-18
		From Gil: A school cafeteria offers 2 main entrees, 3 fruits, 4 vegetables, and 3 drinks. If a plate consists of 1 entree, 2 vegetables, 1 fruit, and 1 drink, how many different plates can a cafeteria manager make? Please explain how you derived at answer. Thank you Answered by Penny Nom.
	How can eight eights be 1000?		2014-06-20
		From Aamir: The digit 8 if we add it 8 time in it the answer should be equal to 1000.it may possible.i.e., 8+8+8+8+8+8+8+8=1000 Answered by Penny Nom.
	A reversed curved on a railroad track		2014-06-19
		From cherrielyn: Assuming that earth is a sphere of radius 6380 km, what is the difference in the latitudes of two cities 270 miles apart positioned on the same meridian? Thank you in advanced po! :) Answered by Penny Nom.
	Forming a cylinder from a square		2014-06-08
		From kalyani: the curved surface of a cylinder is a square of diagonal 2*square root of 2. What is the area of the base of the cylinder? Answered by Penny Nom.
	6 inches of dirt in a baseball field		2014-06-01
		From Mary: The baseball field is 20,000 Square feet, 6 inched deep I need to know how many cubic yards of dirt this will generate. Answered by Penny Nom.
	Overlapping sets		2014-05-23
		From daniel: motors inc manufactured 325 cars with automatic transmission,216 with power steering ,and 89 with both these options. How cars were manufactured if every car has at least one option? Answered by Penny Nom.
	A piecewise graph		2014-05-10
		From Zoe: Lightning Energy charges residential users for each unit of electrical energy bought from them each quarter, according to the scale below: 0-500 units cost 17 cents per unit 500-1500 units cost $85 plus 10 cents for each unit in the excess of 500 1500 or more units cost $185 plus 9 cents for each unit in excess of 1500 Sketch a graph showing the charge C as a function of U for up to 2000 electricity units Answered by Penny Nom.
	Percentage change		2014-05-09
		From hi: the hw club had 46 members in sept. in april, the club had 24 members. what was the percent of change in the hw club's membership from sept. to apan increase or decrease in membership? ril? what is Answered by Penny Nom.
	What was the selling price?		2014-04-25
		From Con: Apple built 40 32GB wifi iPads, gave away two in a contest, and sold the rest at two times the manufacturing price. If the company's total profit was $10,782, what is the selling price of one of these iPads? Answered by Penny Nom.
	A circle is divided into three sectors		2014-04-17
		From atolagbe: the area of a circle is 154cm square. it is divided into three sectors such that two of the sectors are equal in size and the third sector is three times the size of the other two put together. calculate the perimeter of the third sector. take pi=22/7? Answered by Penny Nom.
	Converting to base 5		2014-04-10
		From Usama: Convert the numbers used in the following expressions into those of base-five and solve : 21+34-108+62 Convert the result so obtained into decimal system and thus check your answer? Answered by Penny Nom.
	The locus of a point		2014-04-04
		From srishti: A point P moves such that the difference between its distance from the origin and from the axis of x is always a constant c . what is the locus of the point? Answered by Penny Nom.
	9,-4,6,-8,3,...		2014-03-31
		From Alynna: You are given the following pattern: 9,-4,6,-8,3,... Create a formula for the nth figure. I have trouble finding the formula, I need help trying to find it. Answered by Penny Nom.
	Graphing piecewise functions		2014-03-29
		From Rayven: Hi! I'm in eighth grade, taking ninth grade algebra 1. I'm confused as to how to graph piecewise functions. I know that you have already answered a question similar to this (I did my research first) but it didn't completely help me on my homework. I have to graph piecewise functions for the specified domains, and create a table for the absolute values. I know that two bars around a number means absolute value (two bars around -2 makes it +2) , but how do I graph and chart the absolute value for the following: f(x)= |x+3 | for -5≤x≤3 And then graph and chart: (on a separate graph): f(x)= {x if x≤0 {x+1 if x <0 thank you! ~Rayven Answered by Penny Nom.
	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.
	An arithmetic sequence		2014-03-20
		From Xabiso: The 10th term of an arithmetic sequence is 28 and the 7th term is 19. Calculate the common difference and the first term of the sequence. Answered by Penny Nom.
	40 meters increased by 20%		2014-03-14
		From Kyle: I need help finding out this question: 40 meters increased by 20% Is the answer 800 or is it 8? Answered by Penny Nom.
	Three consecutive whole numbers		2014-03-13
		From Abhishek: Three consecutive whole numbers are such that if they be divided by 5,3 and 4 respectively, the sum of the quotient is 40. What are the numbers? Answered by Chris Fisher.
	Determine the selling price		2014-03-08
		From augustine: knowing an auctioneer charges a 7% fee and I know I want $74,400 what is the formula to determine selling price. Answered by Penny Nom.
	What are the possible lengths of the hypotenuse?		2014-03-07
		From audrey: The three sides of a right angles triangle measure x-2, x+5, and 2x-1 in length. What are the possible lengths of the hypotenuse? ... I'm doing the equation c2=a2+b2 and subbing in the numbers but nothing makes sense Answered by Penny Nom.
	The inverse of y = 5^x		2014-03-07
		From Melody: how do you find the inverse of y = 5^x Answered by Penny Nom.
	The diameter of the base of a cone		2014-02-23
		From elwin: i have a sector of a circle that has 120 degree and 6 cm length. What will be the diameter of the base of the cone. and what is the diameter of the angle is changed to 180. Answered by Harley Weston.
	Selecting a card		2014-02-16
		From Akarsh: Cards numbered 1 to 1000 were put in a box.Ali selects cards at random.What is the probability that Ali selects a card containing at least one'3'? Answered by Penny Nom.
	A sequence		2014-02-10
		From Joshua: hello..the question I have today is... A sequence... 1,5,14,30,55,91 find the general terms. Answered by Penny Nom.
	Conics		2014-02-01
		From Kassidy: Hey, I have searched through all the questions about conics and how people use them in the real world, but none of them were very specific on how they are applied and the process, why it's so important etc. I have a project due asking these questions and it's been very difficult finding the right answer, if you could name jobs, how they are use and specifically applied that would be greatly appreciated. Answered by Penny Nom.
	A sequence		2014-01-30
		From joshua: hi...really struggle with one question that the teacher gave us... The sequence is 1,2,1,5,8,1,11,___,___ Answered by Penny Nom.
	Counting in base five using words not digits		2014-01-25
		From Randy: We all know how to count (in the base 10/decimal system) using words not numbers. For example: one, two, three, four, five, six, seven, eight, etc. However, in base 5 (for example) how would you count (in words). For sure - in base 5 the number 1 could be "one", the number 2 could be "two". However there seems to be no words to describe base 5 numbers beyond 0,1,2,3 and 4 (and perhaps 10). In base 5 the number 10 is not ten. Rather it is "five". In base 5 what word(s) describe numbers larger than 10? What words are used for 11, 12, 13, 14, 20, 21, 22, 23, 24, 30, 44,...etc. Also, consider a man and woman were married in the Gregorian year 1964. If they had an anniversary tomorrow - how long would you say they've been married in base 5 speak? In numbers their Golden Anniversary would note 200 years of marriage in base 5. How would you articulate their years together in base 5? I don't recall seeing verbiage to represent numbers in any system other than the decimal/base 10 system. Do such things exist for other systems? Answered by Harley Weston.
	An arithmetic sequence		2014-01-06
		From paris: find the twenty-fifth term of an arithmetic sequence whose first term is 12 and whose common difference is -6 Answered by Penny Nom.
	An infinite geometric series		2013-12-24
		From Muhammad: The sum of an infinite geometric series is 15 and the sum of their squares is 45. Find the series Answered by Penny Nom.
	Find the next 3 terms of the sequence		2013-12-19
		From Lanelyn: Find the next 3 terms of the sequence 2,3,9,23,48,87,__,__,__ Answered by Robert Dawson.
	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.
	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.
	A union and interception problem		2013-10-19
		From Zakir: Sir, I have some problem in union there is a Question in a book find B set if A={2,4,6,8} , AUB={2,4,5,6,7,8} and A intersection B={6,8} plz tell me how can I find the B set Answered by Penny Nom.
	Base 5 arithmetic		2013-10-12
		From Obassy: (4 2 4 3)-(1 3 x 4)=( Y 3 4 4),find the value of x and y in the subtraction above carried in base five? Answered by Penny Nom.
	Base 5		2013-09-30
		From Zakir: Sir I wanna know something about base 5 number system Why we use it and who use this ? and what is the purpose of it Answered by Robert Dawson.
	The markup on a country maple bedroom set		2013-09-26
		From steven: Bargain Furniture sells a five-piece country maple bedroom set for $1299. The cost of this set is $700. What are the markup on the bedroom set? 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.
	The sum of all whole numbers from 1 to X		2013-09-06
		From Tim: How do I develop a rule for the sum of all whole numbers from 1 to X when I have no idea how to do this Answered by Penny Nom.
	A sequence or a series?		2013-09-05
		From Rahul: Whether the following sequence is increasing or decreasing? I even do not kow whether to call it a sequence or not. an = (1/(1+n))+(1/(2+n))+....+(1/(n+n)). I am confused. It looks like a series to me. Please help. Regards, Rahul Answered by Robert Dawson.
	8 numbers from 80		2013-09-04
		From susan: Out of 80 numbers how many combinations of 8 are there and what are they. Answered by Penny Nom.
	More than half of the people said...		2013-08-26
		From Lucy: Hi, The question is: Samoa 23% Brazil 41% Sri Lanka 52% Senegal 39% Armenia 37% Croatia 20% Why is the following statement true for the data above: More than half of the people said they were interested in Sri Lanka. The reason I don't understand the problem is that because the percentages add up to be greater than 100%, that means that the 500 people(as stated in the question) who participated in the survey got to pick more than once. Therefore, it is not 52% out of 100% anymore. Thanks for taking the time to answer my question. Answered by Robert Dawson.
	Tesseract		2013-08-22
		From Dan: I am not a mathematician. This seems to me an intuitively simple enough problem that I very much need an answer to from someone who's mathematics are better than mine. Please help. The question is: for a tesseract of side length = 1 what is the distance of the center of each cube from the center of the tesseract ? I think I have calculated the distance of each vertex from the center, and of the center of each edge from the center, but the question above baffles me. (anyone not having a clue what I am talking about can brush up here http://en.wikipedia.org/wiki/Tesseract ) Thanks in advance - Dan V Answered by Robert Dawson.
	Consecutive Numbers Question		2013-08-11
		From Lucy: Hello, I have a question about consecutive numbers. So lets say a question tells you to find what three consecutive numbers are that add up to a certain number. To calculate this, would you use 2x+1, 2x+3, 2x+5 or just x, x+2, x+4. Also, the same question for even numbers. Would you use: 2x, 2x+2, 2x+4 or just x, x+2, x+4. My math book is confusing because it uses the first strategy(the 2x+…) in some situations and the second strategy(x+…) in other situations. Thus, can you provide me an explanation of why you would use the strategy that is correct? Specifically, my book answered this question: If “n” is the first of five consecutive odd numbers, what is their average, using n,n+2….=5n+20 and average is n+4(this is the answer),. For the question: the sum of 4 consecutive odd integers must be: Divisible by 8 but not necessarily 16(this is the answer), it used the strategy 2k+1, 2k+3…=8k+16. Thank you so much for taking the time to answer my question. Answered by Harley Weston.
	Practical uses of trigonometry		2013-08-06
		From tharindu: use of trigonometry Answered by Penny Nom.
	Slicing through a cone to form an ellipse		2013-08-06
		From Pulkit: we get an ellipse on slicing through a cone. Is there a relation between central axis of the cone and this ellipse? Does it pass through the any of the foci of the ellipse? Answered by Chris Fisher.
	The area of a semicircle		2013-07-28
		From Lucy: Find the area of the the figure described: a semicircle with arc length 3 pi. Answered by Penny Nom.
	A geometric sequence		2013-07-16
		From Relebohile: Find the n^th term of 3,6,9,12,24,48... Answered by Penny Nom.
	Three consecutive odd integers		2013-07-08
		From sparsh: Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is: Answered by Robert Dawson.
	Inverse trig functions		2013-05-19
		From ky: hello, so iv'e been asked to draw a triangle with sides of 3, 4, and 5. And find the measure of all three angle using sin-1, cos-1, tan-1. I got really confuse, I'm taking the SAT pretty soon and it would be great to get this... THANX Answered by Penny Nom.
	Points of intersection		2013-05-02
		From Bianca: Find the sets of values of k for which the line y=kx-4 intersects the curve y=x^2-2x at two distinct points. 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.
	How do i write log_8(P) =7 in exponential form?		2013-04-14
		From nancy: How do i write this in exponential form log8P =7 Answered by Penny Nom.
	If 4 cooks can bake 8 pies in 6 hours?????		2013-03-18
		From Kenneth: Hello: I want to determine which quantities are directly and inversely proportional in order to determine the answer for the following:. If 4 cooks can bake 8 pies in 6 hours, 2 cooks can bake how many pies in 4 hours? Answer: 2 2/3 pies Can someone fully explain what I need to know in order to determine what is directly and inversely proportional in the example above? I thank you for your reply. Answered by Robert Dawson.
	Increasing and decreasing sales		2013-03-06
		From Meghan: Pace Design's sales increased by 30% in the first year, increased by 60% in the second year, decreased by 60% in the third year and increased by 90% in the fourth year. What was the cumulative change in sales over the 4 years? Answered by Penny Nom.
	Your profit should be 20% of your cost		2013-02-21
		From anis: if the customer says your profit should be 20% of your cost.. 1) my selling value should be cost +20% of cost = SP or 2)cost / 0.80 = SP which is correct...if the second answer is right how should i justify my customer Answered by Penny Nom.
	Write a rule for the sequence		2013-02-20
		From Angelia: Write a rule for the sequence. Then, find the unknown term. 1 3/8, 1 ¾, 2 1/8, _______, 2 7/8 Think: The pattern is increasing. Add 1/6 to find the next term. Rule: _______________ Answered by Penny Nom.
	How can I teach how to change bases?		2013-02-20
		From Tammy: How can I teach how to change bases? For example 80 base 10 changed to base 3. Thank you! Answered by Harley Weston.
	A curve in 3-space		2013-02-14
		From pardeep: we have to show that the curve r(t)=(cos t)i+(sin t)j+(1-cos t)k ,0<=t<=2pie; is an ellipse by showing it to an intersection of a right circular cylinder and a plane. i got the eqn. of the cylinder but did not get the eqn of plane. Answered by Harley Weston.
	Is a line lying in a plane an open or a closed region?		2013-02-13
		From pardeep: please help with this question on the open and closed intervals :: Is a line lying in a plane an open or a closed region? my teacher says it is a closed region reasoning out that it contains all it boundary points. please help how is it so? 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 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.
	A triangular island		2012-12-29
		From Udit: A long time ago Mr Gibson found an island shaped as a triangle with three straight shores of length 3 km,4 km and 5 km. He declared an 'exclusion zone' around his island and forbade anyone to come within 1 km of his shore. What was the area of his exclusion zone? Answered by Penny Nom.
	A raised bed in the shape of an octagon		2012-11-22
		From pat: I want to make raised-bed gardens - usually 4' square, but want to be more creative by creating octagonal boxes. The ideal size for square beds is 4'x4'. The boards are 8' long, so I want to get as much out of a board as I can. If I want an octagon with a diameter of 4', I think the sides would be (rounded off) about 1.5' each using 2 full boards with a little waste and the growing space would be less than a 4' square (16 square feet). If I want to increase the length of each side to 2' each (getting the max from a board), what will the diameter of this octagon be so I can determine the growing space of the box. (The reason a 4' square is important in gardening, besides maximizing the wood, is that a person can reach into the center to plant and pick veggies without stepping on the soil, so diameter is important). My math days are long over and I'm having trouble working with octagons! Thank you! Answered by Harley Weston.
	Difference of squares		2012-11-19
		From Qelibar: Please factorise x^2y^2 - 4 Answered by Penny Nom.
	Factor (6a^2-5a+1)(8a^2-6a+1)(12a^2-7a+1)		2012-11-16
		From bailey: Factorise f(a)=(6a^2-5a+1)(8a^2-6a+1)(12a^2-7a+1) thus find [f(a)]^1/2 Answered by Penny Nom.
	Stairs for the new community center, part 2		2012-11-13
		From Emily: Plans for a set of stairs for the front of a new community center use the ratio of rise to run of 2 units to 5 units. B. Sketch a set of stairs that meets the rise-to-run ratio of 2 units to 5 units. Answered by Penny Nom.
	A function with 3 asymptotes		2012-10-19
		From rimoshika: find a function that have 3 Asymptotic : y=x/y=sinx/x=-1 Answered by Penny Nom.
	The nth term of a sequence		2012-10-19
		From Emily: I don't understand how to do this question: Nth term for 9, 7, 5, 3, 1 Is there a fast way to do nth term for this question? Or in fact any question? 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.
	Functions		2012-09-18
		From nayeem: I tried with many functions but I am not getting the exact values please help me A give an example of a function whose domain equals the set of real numbers and whose range equals the set the set {-1,0,1}? B Give an example of a function whose domain equals (0,1)and whose range equals [0,1] C.Give n example of a function whose is the set of positive integers and whose range is the set of positive even integers D. Give an example of a function whose domain is the set of positive even integers and whose range is the set of positive odd integers E give an example of function whose domain is the set of integers and whose range is the set of positive integers. F. Give an example of function whose domain is the set of positive integers and whose range is the set of integers. please show me the work Please give me the trick of finding such functions Answered by Robert Dawson and Harley Weston.
	Functions		2012-09-18
		From nayeem: I tried with many functions but I am not getting the exact values please help me A give an example of a function whose domain equals the set of real numbers and whose range equals the set the set {-1,0,1}? B Give an example of a function whose domain equals (0,1)and whose range equals [0,1] C.Give n example of a function whose is the set of positive integers and whose range is the set of positive even integers D. Give an example of a function whose domain is the set of positive even integers and whose range is the set of positive odd integers E give an example of function whose domain is the set of integers and whose range is the set of positive integers. F. Give an example of function whose domain is the set of positive integers and whose range is the set of integers. please show me the work Please give me the trick of finding such functions Answered by Robert Dawson and Harley Weston.
	Equivalent sets		2012-09-13
		From asif: show that (-1,1)~(1,1) or give its counter example Answered by Harley Weston.
	The hypotenuse		2012-09-06
		From Jeevan: how can i find the height and base of a right angle triangle if i have the hypotenuse only ? Answered by Penny Nom.
	A security code		2012-09-01
		From Breanna: The code is made up of five two digit numbers from 01 to 20 entered in a certain order. How many different security codes are possible with this system Answered by Penny Nom.
	Minutes and seconds		2012-08-29
		From Casey: I have to write a variable equation. The questions says there are 60 seconds. but we need to write and equation to solve for minutes. Is it 1/60 or 1/s Answered by Robert Dawson.
	An arithmetic progression		2012-08-22
		From A student: the 3rd term of an A.PPP is 10 more than the first term while the 5th term is 15 more than the second.find the sum of the 8th and 15th terms if the 7th term is 7 times the first term. Answered by Penny Nom.
	John's electronic store		2012-07-25
		From Jora: Electronic Store John opened an electronic store in December. During his first month, He sold 10 LCD TVs and 20 Plasma TVs. His income during that month was $12800. In January, he sold 25 LCD TVs and 40 Plasma TVs for an income of $27600. In February he projects to sell 30 LCD TVs and 50 Plasma TVs. If John expenses are $28900 in February, how much money will he have after paying the expenses? Answered by Penny Nom.
	A cylinder is to be filled with peas.		2012-06-12
		From Silje: Hi! How can I solve the following question without the use of a calculator? "A cylinder is to be filled with peas. It is done like this: At 12:00 o'clock you put 1 pea in, at 12:01 you put 2 peas in, at 12:02 you put 4 peas in, at 12:03 you put 8 peas in, and so on. This continues until 14:00 o'clock (two hours later), when the last peas are put in and the cylinder is full. At what time is the cylinder half full?" Answered by Robert Dawson.
	Expanded exponential form?		2012-06-12
		From Ramon: express the numbers 990 614 000 005 in expanded exponential form. Answered by Harley Weston.
	A geometric sequence		2012-06-10
		From vicki: The sum of the first three terms of a geometric sequence of positive integers is equal to seven times the first term, and the sum of the first four terms is forty-five. What is the first term of the sequence? Answered by Penny Nom.
	The area of a semicircle		2012-05-28
		From Rebecca: how do you find the area of a semi circle and then how do you add the area of a semi circle and the area of a rectangle? Answered by Penny Nom.
	Division in base eleven		2012-05-27
		From Zoe: How do you divide numbers that are in base 11? For example; 9A7A6A divided by A Answered by Penny Nom.
	The nth term		2012-05-05
		From Justin: Which expression can be used tofind the nth term in this sequence? 94,75,56,37,18,..... My choices are A. -19n=113        B. -21n+115 C. -19+75        D. 21n+73 Please explain how to get the correct answer. I think it is A. but I am not sure, Answered by Penny Nom.
	How to find the base length of a isosceles triangle if only the sides are given?		2012-04-25
		From aqilah: how to find the base length of a isosceles triangle if only the sides are given? Answered by Chris Fisher.
	The inverse of y = x^2 - 2x		2012-04-20
		From Shona: How do I Find the inverse of the function y= x^2 - 2x ? Answered by Penny Nom.
	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.
	1+2+4+8....= -1		2012-04-02
		From Andy: In this minutephysics video, it's claimed that 1+2+4+8....= -1 Is this true, and if so, how? < href="http://www.youtube.com/watch?v=kIq5CZlg8Rg">http://www.youtube.com/watch?v=kIq5CZlg8Rg Answered by Robert Dawson.
	The power set of A		2012-03-24
		From rashdin: Can you find a set A, |A|=4 and define a bijective function between A and P(A)? Answered by Penny Nom.
	The length is inversely proportional to the width		2012-03-18
		From David: For a given set of rectangles, the length is inversely proportional to the width. In one of these rectangles, the length is12 and the width is 6. For this set of rectangles, calculate the width of a rectangle whose length is 9 Answered by Penny Nom.
	Forming a triangle from 3 line segments		2012-03-15
		From rustom: A point X is selected at random from a line segment AB with midpoint 0. Find the probability that the line segments AX, XB, and A0 can form a triangle. Answered by Penny Nom.
	An increase/decrease in profit		2012-03-13
		From Thanikasalam: It is understood that increase/decrease in profit for current year compared to the previous year is done by the formula (x-y)/y, with x=profit on current year and y=profit on previous year. How do we derive this formula? If we work on this formula of calculating increase/decrease in profit, we get x/y-1 * = (x-y)/y = x/y - y/y = x/y - 1 How do you justify the 1 in the equation above. How to derive the formula and how do i prove it? Answered by Penny Nom.
	Four digit combinations from 1,2, ..., 9		2012-02-26
		From Errol: show me a list with all four digit combination numbers from 0 -9 Answered by Penny Nom.
	A geometric sequence		2012-02-24
		From Camille: Find x if the sequence 5,10,x+2 is geometric. Answered by Penny Nom.
	If x ix directly proportional to y then ...		2012-02-19
		From Crystal: I understand that we say x and y are proportional, then y = kx. Generally when we say x is proportional to y, we think that when x increases y increases. Now I am questioning whether that is actually true. If k is negative, then when x increases, y DECREASES. My question is does this mean this statement is incorrect: If x is proportional to y, when x increases, y increases proportionally. Is it more correct to say: If x is proportional to y, when x increases, y either increases proportionally or decreases proportionally. Along the same line of reasoning, when x is inversely proportional to y, we think that when x increases y decreases, but that is true only if k is positive. Is that correct? Answered by Harley Weston.
	Figures with dots		2012-02-15
		From A: Okay so my daughter came home and had this question for homework from her teacher. I have no idea what it means HELP!! The question shows a figure that is a square. It has 5 dots on the top, bottom and on the sides looks similar to this: . . . . . .       . .       . .       . . . . . . they want to know 3 more ways to show the number of dots in the figure. They have already shown one with just counting them and the other one that they showed was circling the four corner dots and then taking the dots in between with a number sentence set up like this: 4+4*(5-2) = 4+4*3= 16. They also besides giving 3 ways want us to write a number sentence and an algebraic sentence to show the number of dots in the figure with "n" sides. Please help! So confusing ! I don't know if my square turned out or not but it should be 5 across the top and bottom and on the sides and no dots in teh middle it is just the outside. Answered by Penny Nom.
	Can the result of the calculation be 2?		2012-02-09
		From Thomas: You have the digits 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9 in a random order side by side and put randomly between two digits a colon, so that a division comes into existence. Can the result of the calculation be 2? Answered by Robert Dawson and Chris Fisher.
	A tree growth modelled by a geometric series		2012-02-08
		From Steph: Hi I am really struggling with this question please help !!!! a pohutukawa tree is 86 centimetres when it is planted. in the first year after it is planted , the tree grows 42 centimetres in height.Each year the tree grows in height by 95% of the growth of the previous year. assume that the growth in height of the pohutukawa tree can be modelled by a geometric sequence. A)find the height of the tree 5 years after it is planted and figure out the maximum height the pohutukawa tree is expected to reach in centimetres Answered by Penny Nom.
	Notation for the second derivative		2012-02-06
		From Shafira: In all math textbooks, it is written that d/dx ( d/dx) (y)= d2y/dx2. Why do they write it as d2y/dx2, not as d2y/d2x2? Answered by Robert Dawson.
	Two sectors of a circle		2012-02-03
		From Wayne: I am not even sure what to ask. I have to two lengths of feet and an angle of degrees, and I have to find the area? **Problem attached Thanks, Wayne Answered by Penny Nom.
	Properties of real numbers applied to subsets		2012-02-01
		From Mark: Hello - The questions that I have for you is do the properties of real numbers (such as the associative, commutative, identity, inverse, and distributive law) apply to ALL the subsets of real numbers? In other words, do all those properties work for the Natural Numbers? The Whole Numbers? And so on and so forth. I understand that they are all real numbers, but for instance: the identity is whenever you add zero to a number, you get that number back. But does that work with, say, with only the odd numbers? Zero isn't odd so can that property actually apply to JUST the odd numbers? Any consideration would be greatly appreciated! Answered by Robert Dawson.
	1 + 3 + 3^2 ...+3^(n-1) = 3^n - 1/2		2012-01-27
		From Vicki: I am trying to find out how to do show how this proof was worked. Here is the end result 1 + 3 + 3^2 ...+3^(n-1) = 3^n - 1/2 This equation was used to find the number of white triangles in the Sierpinski Triangle Answered by Walter Whiteley.
	Two shapes		2012-01-06
		From muhammad: Question from muhammad, a student: a boy has two pieces of wire each 99cm long .he bends them into the shapes shown below.calculate the radius of each figure,giving each answer to two decimal places.figures are one is semicircle and other on is half of the semicircle. Answered by Harley Weston.
	A 46% increase		2012-01-03
		From kabilan: increase a price of £8.24 by 46% and give the answer to the nearest penny Answered by Robert Dawson.
	The number of digits in a number base m		2011-12-22
		From Jash: Assume there is a number system of base m. The one property of this system is: If 2 numbers written in this system, which have 'a' and 'b' as the number of digits are multiplied, then the product of the 2 numbers will have a number of digits which is a function f(a,b). In other words, as long as the number of digits of the 2 numbers are constant, the number of digits of their product is a constant. Find m. Answered by Robert Dawson.
	Three consecutive numbers		2011-11-29
		From Michael: Find three consecutive numbers such that the second number squared is equal to the first and third added together Answered by Penny Nom.
	Converting from base 4 to base 10		2011-11-29
		From anjg: How to convert base 4 number 2^11 to base 10 number? Answered by Penny Nom.
	Four carpenters can build eight houses in 10 days.		2011-11-23
		From Kenneth: Four carpenters can build eight houses in 10 days. Two carpenters can build how many houses in 15 days? Answered by Penny Nom.
	What was the cost price of the article?		2011-11-10
		From tashana: By selling an article for $320,the profit was 20% of the cost price.what was the cost price of the article. Answered by Penny Nom.
	The sum of a series		2011-11-07
		From Rattanjeet: Find the sum of 1(1/2) + 2(1/4) + 3(1/6) + 4(1/6)(3/4) + 5(1/6)(3/4)2 + 6(1/6)(3/4)3+ ... where 1/6 + (1/6)(3/4) + (1/6)(3/4)2 + ... constitutes a geometric series. Answered by Penny Nom.
	A scale drawing		2011-10-30
		From aretha: i have a scale drawing of a house floor plan, don't understand how to find the answer. the drawing is 1in: 3ft. need to find the length / width/and the actual length/width of the living room,kitchen, 3bedrooms deck,sitting room, entry, and closet Answered by Penny Nom.
	Three consecutive terms of an arithmetic sequence		2011-10-30
		From Juliette: Find X when x, 1/2x + 7, 3x -1 are consecutive terms of an arithmetic sequence. Answered by Penny Nom.
	Expanded form		2011-10-12
		From Chris: Write this number in expanded form 4 326 180 501 Thanks!!! Answered by Penny Nom.
	Three consecutive odd integers		2011-10-07
		From Muneera: Find 3 consecutive odd integers so that 3 times their sum is 5 more than 8 times the middle one? Answered by Penny Nom.
	A reservoir has the shape of an inverted cone		2011-10-03
		From Roger: a reservoir has the shape of an inverted cone whose cross section is an equilateral triangle. if water is being pumped out of the reservoir at a rate of 2m^3/sec, at what rate is the depth of the water changing when the depth is 40 meters? Answered by Penny Nom.
	58 choose 4		2011-08-26
		From Jean: Using only the numbers 1-59, how many times would the number 23 appear in combinations of 5 numbers? ... Can a list be provided as well? Thank you very much, Jean Answered by Penny Nom.
	Two line segments in the plane		2011-08-15
		From Tim: For this problem I actually have tried to visualise the image in my head many times. This question makes my head spin. Four points lie in a plane. They are partitioned into two pairs so that the sum of the lengths of the segments joining the points of each pair has the minimal possible value. Prove that these segments have no common points. Answered by Chris Fisher.
	A sequence		2011-08-14
		From intesar: how do i figure this out 0,1/6,2/9,3/12 Answered by Penny Nom.
	The third term of a sequence		2011-08-13
		From sammantha: Find the 3rd term of the sequence, an=1.5(4)n - 1. Answered by Penny Nom.
	Infinite Logarithmic Series		2011-08-08
		From Sourik: Dear Expert, In my Amithabha Mitra and Shambhunath Ganguly's "A Text Book of Mathematics" I found the formula of log (1+x) where the base is e and x lies in between -1 and +1.As I want to learn Mathematics,I am not satisfied with the mere statement of the formula.Please help giving me the full proof. Thanking you, Sourik Answered by Robert Dawson.
	The nth term of a sequence		2011-07-01
		From Rachel: I am trying to help my son get ready for our Aims test and I am not much help. The sequence is 2,5,10,17 The question is which equation represents the rule for finding the nth term for this sequence a. an=n + 1 b. an=2n2 c. an=n2+1 d. an=2n+1 Answered by Penny Nom.
	The nth term		2011-04-30
		From Samantha: predict the general term, or the nth term, An for the sequence. 1/2,2/3,3/4,4/5,5/6 Answered by Penny Nom.
	Find the rate at which the searchlight rotates		2011-04-17
		From Meredith: A searchlight is position 10 meters from a sidewalk. A person is walking along the sidewalk at a constant speed of 2 meters per second. The searchlight rotates so that it shines on the person. Find the rate at which the searchlight rotates when the person is 25 meters from the searchlight. Answered by Penny Nom.
	sin x = -0.25		2011-03-29
		From Wayne: How do you solve for x in the equation sin x = -0.25 the answer is 3.394 and 6.030 but I don't know the steps they used to calculate this Answered by Penny Nom.
	A true or false trig question		2011-03-24
		From Abeth: True or False: Since cot (theta) = cos (theta)/sin (theta), if cot (theta) = 1/2, then cos (theta) =1 and sin (theta)=2. My answer before was true, but not my answer is false. Can you give me a solution on this matter. thanks. Answered by Penny Nom.
	A 15% increase		2011-03-22
		From Abeth: Bobby dela Cruz is the purchasing agent for school supplies of a certain university. Because of new research projects, Bobby ordered an additional 32,500 worth of supplies this month. This is a 15% increase from last month. What was the value of the school supplies that Bobby ordered last month? Answered by Robert Dawson.
	Three consecutive odd numbers		2011-03-11
		From George: Write an equation three consecutive odd numbers whose sum is 75 Answered by Penny Nom.
	A family of circles		2011-03-01
		From steffi: Find the equation of the family of the circle passing through the the point of intersection of x^2+ y^2 -4x-28=0 and x^2 +y^2 -4x-20+52=0; the member tangent to x=7. Answered by Penny Nom.
	Converting base 3 to 5		2011-02-28
		From Harry: Hey Math Central, I came across your website and im in need of help on my maths c assignment. I have to convert base 3 to 5 without converting back to ten. I heard that you can use patterns in 3 and 5 to make an equation but im not sure how to and i also heard you can use logarithms but i dont know how to use those so im kinda stumped. Answered by Robert Dawson.
	An imaginary infinite geometric tree		2011-02-18
		From Elise: An imaginary infinite geometric tree grows 1m the first day. 2nd day 2 branches and right angles to each other and each 0.5 m long. 3rd day two new branches at ends of each of previous days' 2 branches, again at right angles, and only .25m long each. And so on, infinitely. Q: Use relationships of right-angled triangles and high school level knowledge of geometric series to show the tree height is limited to (4 + sqrt2)/3 m and width to (2(sqrt2 + 1))/3 m. Answered by Robert Dawson.
	Reversing the digits		2011-02-08
		From rejie: if the digits are reverse , the number is 9 less than the original number.what is the equation? Answered by Penny Nom.
	Three consecutive numbers		2011-01-31
		From parth: name 3 consecutive numbers,each less then a 100,the smallest # is divisible by 6 the next is divisibel by 5 and the largest divisible by 4 Answered by Penny Nom.
	A player runs from second base to third base		2011-01-30
		From Marie: A baseball diamond is a square with side 90 feet in length. A player runs from second base to third base at a rate of 18 ft/sec. At what rate is the area of the trapezoidal region, formed by line segments A, B, C, and D changing when D is 22.5 Distance A is the players distance from first base when running from 2nd to third. Distance D is his distance from 3rd base. Distance C is the distance from 3rd to 3rd to Home. Distance B is the distance from Home to First. I have found dA/dt in a previous problem. Answered by Penny Nom.
	The perimeter of a semicircle		2011-01-29
		From Keith: I have the perimeter of a semi circle of 37 but how do I calculate the diameter from this. This is all the information I have. Answered by Penny Nom.
	The sequence 2,3,5,5,8,7,11		2011-01-19
		From taylor: number relationship in number sequence 2,3,5,5,8,7,11 Answered by Chris Fisher and Penny Nom.
	tanθ=1.192		2011-01-15
		From Adori: Use a calculator to approximate two values of the θ (0 ≤θ≤2π) that satisfy the equation. a) tanθ=1.192 I do not understand how to find the second value of θ. Answered by Harley Weston.
	What is next in the sequence?		2011-01-13
		From jodi: what is next in the sequence 1, 1/4, 1/9, 1/16, 1/25 Answered by Penny Nom.
	Set notation		2011-01-10
		From Ron: The question asked in a handout: 8k - 5 < 35, keI I believe the answer to k is 5. But what does the k e(E) I mean in this? Answered by Harley Weston.
	Semicircles and the Pythagorean Theorem		2011-01-09
		From Jas: Okay well, in math we are learning about the pythagorean theorem and we have to do a math journal on the question: ****Can you replace the squares (that are put on the sides of a right triangle) with semicircles and still get the same answer?? I do not understand because i tried doing an example and comparing it with a normal way of doing it and I didnt get the same answer! Answered by Penny Nom.
	A sector of a circle		2011-01-07
		From Alice: the radius of a circle is 7cm the angle of the sector is 68 how do you find the Answered by Penny Nom.
	Line segments		2011-01-04
		From Izsak: What is the formula to find the number of segments that can be named by a given number of points on a line? Answered by Penny Nom.
	[sec^2x]*[sec^2x]		2010-12-16
		From Hari: [sec^2x]*[sec^2x]=...? Answered by Penny Nom.
	A geometric progression		2010-12-15
		From Abeth: find the value of x so that 2(x-1), x+3, x will be a geometric progression. Answered by Penny Nom.
	A sector of a circle		2010-11-29
		From Mel: Find the area of a sector of a circle that has a central angle of 13pi/18 and a radius of 12cm. Round answer to nearest 10th degree Answered by Penny Nom.
	Hours minutes and seconds		2010-11-26
		From beket: I need to turn 1.486588292 into real time hours minutes and seconds. I keep getting multiple answers. Online conversions give me 1 hour 29 minutes and either 11 or 12 seconds. On the calculator I get 1 hour 29 minutes and 20 seconds. Can you explain how to turn this decimal into time? Answered by Robert Dawson and Penny Nom.
	Intersecting polygons		2010-11-17
		From Laura: How can I estimate the amount of intersection (area or better a normalized number) between two polygons if I have the cartesian coordinates of their vertices? Thank you in advance, regards, Laura Answered by Robert Dawson.
	The perimeter of a semicircle		2010-11-11
		From gayathri: the area of semicircle is 1925sq.cm find perimeter Answered by Stephen La Rocque.
	Three consecutive odd integers		2010-11-07
		From karen: find three consecutive odd integers such that twice the sum of the second and the third is 43 more that three times the first Answered by Penny Nom.
	How far must the pitcher travel to get to the ball?		2010-11-04
		From ken: A baseball player bunts a ball down the first base line. It rolls 35ft at an angle of 26 degrees with the first base path. The pitchers mound is 60.5 ft from the plate. How far must he travel to get to the ball. Answered by Penny Nom.
	The base of an isosceles triangle		2010-10-24
		From Brian: how can I find the base of an isosceles triangle from the height and the perimeter? Answered by Penny Nom.
	Four consecutive integers		2010-10-21
		From Mickey: Find four consecutive integers such that the sum of the first three integers is 20 more then the fourth integer. I know that for consecutive integers the algebraic expression is x+x+1+x+2+x+3 Answered by Penny Nom.
	A division sentence for an array		2010-10-05
		From Laura: On a math test Grace needs to look at an array and write a division sentence for the array. Grace writes 18/3=6 on her answer sheet. Describe what the array on Graces test looks like. 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.
	rat sequence		2010-09-24
		From Vishal: this is known as rat sequence. I want to know the logic pf this :- 1,2,4,8,16,77,145 Answered by Chris Fisher.
	A reverse PST calculation		2010-09-23
		From Manning: Hi, I'm a manufacturing contractor in Saskatoon. The way to calculate PST for us is using total contract amount x 70% then 5%. For example, contract amount of $100 x 70% x 5% = $3.5 (PST). The subtotal is using contract amount + PST. $100 + $3.50 = $103.50. If you only know the subtotal is $103.50 including PST, how do you reverse calculation to get the contract amount? Thank you very much for your help. Answered by Harley Weston.
	A taxi ride		2010-09-22
		From Jack: A taxi ride costs you $2 for the first km and 10 cents for each tenth of a km thereafter. Sketch a graph of the total cost $C(x) for a ride of xkm, for 0 < x < 2. Hint: The graph is not smooth. How will I start this question off? I tried the table of values method, and then graphed it, but it comes out as smooth, Answered by Stephen La Rocque.
	Find the point of contact of the circles		2010-09-20
		From Sandra: If the center of circle A = (-1,-3) and the radius of it is √20, the center of circle B = (5,9) and the radius of it is √80. Find the point of contact of the circles A and B. Answered by Janice Cotcher.
	The nth term		2010-09-14
		From Anna: The problem is 2n-2. find the nth term. I'm lost as how to even begin Answered by Penny Nom.
	Differentiable on an interval		2010-08-12
		From Dave: Hi I was wondering if a function can be differentiable at its endpoint. For example if I have Y = X^2 and it is bounded on closed interval [1,4], then is the derivative of the function differentiable on the closed interval [1,4] or open interval (1,4). They always say in many theorems that function is continuous on closed interval [a,b] and differentiable on open interval (a,b) and an example of this is Rolle's theorem. Thank you for your help. Answered by Robert Dawson.
	An 18ft round pool		2010-07-19
		From christine: will an 18ft round pool fit on a 12x16 ft rectangular cement slab? Answered by Tyler Wood.
	Remainders		2010-07-17
		From GARY: WHAT NUMBER DIVIDED BY 11 LEAVES 1, DIVIDED BY 13 LEAVES 8, AND DIVIDED BY 17 LEAVES 3. Answered by Chris Fisher.
	A pattern in a puzzling sequence		2010-07-09
		From Martha: A1 2 3 B 5 6 7 C 9 10 11 D 13 14 15 USE THIS PATTERN SUGGESTED TO HELP YOU FIND THE MISSING TERMS IN THE PROBLEM BELOW: a) H _ _ _ b) R _ _ _ c) _ _ 50 _ d) _ _ _ 63 e) _ @#$ where @ + # + $ = 258 Answered by Tyler Wood.
	The product of 2 consecutive integers		2010-06-28
		From Sharon: the product of 2 consecutive integers is -6 less than the square of the larger number. find the smaller number Answered by Penny Nom.
	The intersection of two graphs		2010-06-27
		From Austin: In depth explanation of how to find the intersection points of functions y=-4t+300 and y=-4.9(t-5)^2+300 Answered by Stephen La Rocque.
	Selling price, cost and profit		2010-06-22
		From Alex: The profit on a certain television set is 16.5% of the cost price. If the profit is $330, Find: a) the cost price b)the selling price of the television Answered by Penny Nom.
	The area of a circle		2010-06-12
		From grier: please, what is the area of a semicircle with arc length 3pi? Answered by Penny Nom.
	A cylindrical vessel with belled ends		2010-06-01
		From George: surface area of a vessel with a cylindrical length of 60 feet, a diameter of 10 feet, and with belled ends of 5-foot radius Answered by Penny Nom.
	Math in the workplace: nursing		2010-05-24
		From Taylor: How is math used in the workplace - Nurse Anesthetist? Answered by Penny Nom.
	The number of gallons of water in a basement		2010-05-23
		From George: A basement with dimensions 68 ft long by 42 ft wide by 10 ft deep is flooded to the ceiling calculate the number of gallons of water in the basement. 70 Answered by Penny Nom.
	Divisibility by 3		2010-05-23
		From Cathleen: To math central. I have to do a maths extension question that I don't understand. At first I thought I did. It is about the dividing by three. In one part of the question, it asks me to show that the rule of division by three does not work for 23142 with a little 5 down the bottom. What doe base 5 mean? We first thought that the little 5 down the bottom meant multiplying y the power of five. Can you please tell me what it means so I can finish this question? Answered by Penny Nom.
	The hypotenuse of a triangle		2010-05-22
		From linda: find the length of the hypotenuse of a triangle with legs of 12in. and 17in. round to the nearest hundredth Answered by Tyler Wood.
	Percentage increase		2010-05-20
		From Rebecca: Question from Rebecca: In 2008 my land was valued at $84,000. In 2009 my land was re-valued at $235,000.00. What is the percent increase between the two values? I want to be able to express "the value was increased by x%." Answered by Harley Weston.
	The product of two consecutive even integers		2010-05-11
		From Terry: The product of two consecutive even integers is 14 more than their sum. Find the integers. Answered by Penny Nom.
	The nth term		2010-05-09
		From Jessica: what is the nth term of 3, 9, 19, 33, 51 please help Answered by Walter Whiteley.
	A geometric progression		2010-04-30
		From Kalyani: sum of infinite geometric progression is 9 and common ratio is 1/10 then sum up to 8 terms is? Answered by Chris Fisher.
	Sales taxes in Quebec		2010-04-28
		From carole: I work at a company where we use transport companies and we often get credits on their invoices. I need to know how to subtract the sales taxes from these credit amounts. (5% TPS and 7.5% TVQ). Is the equation: Amount / 1.05 = then this amount / by 1.075=? Answered by Penny Nom.
	4 + 10 + · · · + (6n − 2)		2010-04-21
		From Lan: Find the sum 4 + 10 + · · · + (6n − 2). The answer is 3(n^2) + n. How? Answered by Penny Nom.
	The area of semi circle		2010-04-16
		From sagir: how to find the area of semi circle? Answered by Penny Nom.
	A sequence		2010-04-13
		From Essence: hello, I am having trouble doing my math homework. It asks me to write the first five terms of each sequence .I can not figure it out because it is a fraction. The Problem Is: {2n+1/2n} Answered by Penny Nom.
	A geometric sequence		2010-04-13
		From glen: A geometric sequence has a first term of 0.1024, a second term of 0.256, and a middle term of 156.25. how many terms are there in the whole sequence? i know that r=2.5 but i dont know how to find how many terms there are. Answered by Penny Nom.
	Counting by sevens		2010-04-13
		From Larry: Lee counted by 7's beginning with one of the whole numbers from 1 through 7, until Lee passed 1000. If Lee counted three of the following numbers, which number did Lee NOT count? a. 107 b. 184 c. 534 d. 641 Answered by Robert Dawson and Penny Nom.
	The area of a field of view		2010-04-07
		From Frank: I know we have a field of view of 90 degrees and the distance we can cover is 6 miles. What is the area we can cover/view? A formula would be nice to have since the diameter or distance of the wedge area can change and the degree of the field of view can also change. Thank you and I look forward to hearing from you. Frank Answered by Penny Nom.
	Body measurements		2010-04-06
		From Amirul: Recently I'm proposing my research question to my teacher for my extended essay. I'm an IB student. My research question is regarding the estimation of human in buying trousers through reference of neck. What does the relation between the diameter of the neck and the diameter of the waist? I want to see how far does the estimation theory is true for different type of people with different BMI(body mass index).. But teacher said that it is golden ratio...so nothing interesting... =( really??? But i search on net.... state that my idea seems do not have any relation with the golden ratio so far..... i just want ask you... am I able to perform in my extended essay if i continue with this research question?? Answered by Robert Dawson.
	1/1+1/2+1/3...		2010-03-31
		From Mohd: you explained the way of getting the summation of 100 series numbers but what is the summation of the numbers 1/1+1/2+1/3+1/4+1/5.............................+1/100 Answered by Robert Dawson.
	The angle of intersection between two lines		2010-03-25
		From Madhumitha: How to find the angle of intersection between a line x=249 and another line which is of the form y=m*x+c; Line1 has a slope of infinity so what does the angle of intersection turn out to be? Or how can i find it? Answered by Chris Fisher.
	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.
	A 14 side well house cover		2010-03-12
		From Kenneth: I am 35 yr I am wanting to build a well house cover. I'm trying to figure out how long the pieces need to be and what angle they need to be for a 4 ft dia with 14 side well house. I would love an answer but would also like to know how to figure it in the future. Thanks Kd Answered by Harley Weston.
	Prove A intersect B =X iff A = X and B = X		2010-03-06
		From Gloria: how would you prove A intersect B =X iff A = X and B = X Answered by Tyler Wood.
	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.
	2+3 =10 and 7+2=63 and ...		2010-03-01
		From brenda: if 2+3 =10 and 7+2=63 and 6+5 =66 and 8 +4 = 96 then 9+7+ ?????? its driving me crazy !! Answered by Penny Nom, Claude tardif and Melanie Tyrer.
	The hypotenuse		2010-02-27
		From Dannielle: how do you find the hypotenuse if a=8 and b=6? Answered by Penny Nom.
	The test for some disease is 99% accurate		2010-02-24
		From baaba: Assume that the test for some disease is 99% accurate. If somebody tests positive for that disease, is there a 99% chance that they have the disease? Answered by Chris Fisher.
	A geometric sequence		2010-02-22
		From Kelsey: _, 2, _, _, 250, _ i don't know how to fill in the missing terms Answered by Penny Nom.
	The first five terms of a sequence		2010-02-14
		From Joanne: Find the first five terms of the sequences with the nth term given as follows. n^2+3n Answered by Penny Nom.
	Can a line segment curve over two planes?		2010-02-14
		From Graham: I am working on a math fair project. Can a line segment curve over two planes? Such as, if I had a three dimensional L bracket and I drew a line segment on it with a marker starting on the bottom of the L and had it curve around the corner and up the top, would it still be considered one line segment? Or is that two line segments? Is there a rule that a line segment can only occupy one plane? Thank you. Graham Answered by Chris Fisher.
	A square corner		2010-02-11
		From Trevor: I am building a new house and wish to set it out on site with the use of profile boards and string. I want to be certain it is correct in terms of squareness. I have a vague idea that the square on the hypotenuse should be equal to the sum of the squares of the other two sides. I get a little lost here and need some help. The building is a rectangle measuring 40x30 feet to exterior brickwork. I guess that the length of the hypotenuse should be exactly the square root of the combined squares of the two sides. Using the above measurements could you give me calculations from nuts to soup as to the correct length of the diagonal. And what adjustments are needed if everthing is not in accord. Trevor. Answered by Robert Dawson.
	A sequence		2010-02-07
		From Shalev: hi, i had a job interview yesterday. it had mathematical questions. couldn't solve 1. i m obsessed with it. please find out what the answer is.. it goes like this: 2,4,5,5,8,6,_,_,14,8 thank u very much Answered by Claude Tardif.
	The perimeter of a semicircle		2010-02-04
		From Sarah: The perimeter of a semicircle is doubled when the radius is increased by 7. Find the radius of the semicircle. Answered by Tyler Wood.
	A sector of a circle		2010-02-04
		From trisha: Given a circle with a radius of 6 inches. Find the area of the sector that is formed by an arc of 36 degrees. Round your answer to the nearest tenth of an inch. Answered by Penny Nom.
	Consecutive even integers		2010-02-03
		From cassandra: find 2 consecutive even integers whose sum is 34 find 3 consecutive even integers such that 3 time the middle interger is 10 more than the greatest. Answered by Tyler Wood.
	A sequence		2010-01-27
		From Haku: if there are 8 dots in the first shape, 13 in the second, 19 in the third, and 26 in the fourth, then what is the formula? Answered by Penny Nom.
	A sequence		2010-01-22
		From brahmaji: 0 7 26 63 _ 215 342 fill the blank? find the missing number Answered by Robert Dawson.
	Angle of incline		2010-01-20
		From Alan: how do I fnd the angle of an incline with a measurement of 0.042 with an adjacent of 1.2mtrs?. Thank You Answered by Penny Nom.
	Percentage increase from a negative to a positive		2010-01-12
		From Greg: If a company had a net lost in 2005 of $11,234 and net income of $3231 in 2006, what is the percentage annual growth in income between the two years? Answered by Robert Dawson.
	Improper fractions		2010-01-12
		From Blanca: Between which two consecutive natural numbers does the improper fraction 57/56 lie? Answered by Robert Dawson.
	The domain, range and inverse of a relation		2010-01-08
		From Nazrul: Given that A={-2,-1,0,1,2}, S={(x,y): x belongs to A, y belongs to A and y^2=x}. How can I find the domain and range of the relation S. What is the inverse relation of S. Please show me the process in details. Thank you. Answered by Penny Nom.
	The area of a sector		2010-01-07
		From angelkem: how do you get the area of the circle, the sector, the shaded sector, non shaded sector and its total area if the diameter is 20 cm and each area of the circle is 45 degrees? Answered by Penny Nom.
	Consecutive odd intergers		2010-01-06
		From keyanna: list five consecutive odd integers, starting with -3 Answered by Robert Dawson.
	Holiday for 7 golfers		2010-01-05
		From Andy: I am having difficulty scheduling pairings for a forthcoming Golf holiday. There are 7 players and we will be playing 7 rounds - each round will be a 3 ball and a 4 ball. I am trying to work out a schedule that means everyone plays with each other roughly the same number of times (with a minimum of, say, 3 times if possible). Also, we are looking to ensure everyone plays in roughly the same number of 3 and 4 balls. Any suggestions would be much appreciated (we leave in 10 days time). Thank you. Answered by Victoria West.
	Profit increase from 10% to 15%		2010-01-03
		From taha: A shopkeeper sold a pen for $13.20 to a make a profit 10 percent.In order to earn a profit of 15 percent,he should have sold it for? Answered by Penny Nom.
	Triangles on a base of 2.4 meters		2009-12-26
		From Allan: Please,How do I calculate the height of a triangle when I only know the width of the base line,It is 2.4 mtrs. Thankyou very much. Answered by Penny Nom.
	The acute angle formed by intersecting lines		2009-12-17
		From Katie: To the nearest tenth of a degree, find the size of the acute angle formed by the intersecting lines 3x + 2y = 12 and x - 2y = -2. Was is necessary to find the intersection point? Answered by Robert Dawson.
	The second derivative of y = x³ (x² + 5)		2009-12-14
		From Kyrie: Find d²y/dx² for this function: y = x³ (x² + 5) Answered by Penny Nom.
	A circle problem		2009-12-14
		From Fawad: AP is a tangent at P to a circle centre O, where AP=6cm. The straight line AQC is such that QC= 9cm. Find the length, in cm of AQ. Answered by Chris Fisher.
	Bases larger than ten		2009-12-14
		From Nick: For numbers in bases larger than ten, what are the digits by mathematicians' conventions? I assume the first 10 are always 0-9. I know two computer science conventions (for hexadecimal (A-F case-insensitively) and for base 85 (case-sensitivity plus 23 other characters)) and as a school student I learned that base 12 uses either T and E (which confused me when I thought they stood for Eleven and Twelve) or A and B, the latter as capitals only. Clearly, these conventions are in conflict. I saw your reply in http://mathcentral.uregina.ca/QQ/database/QQ.09.99/magin1.html as accessed a few minutes ago but hope that in the 10 years since then mathematicians have arrived at a convention. Have they? Thank you. -- Nick Answered by Claude Tardif.
	A number base that's not a positive integer		2009-12-11
		From Nick: Is it possible for a number to have a base that's not a positive integer? Base 1 gives a result that's meaningless but possible. I have no concept of a base 0, a negative base, or a fractional base, never mind any other base. I think there isn't any base that's not a positive integer, but, knowing that math keeps jumping ahead and sometimes has inventions before anyone knows how to exploit them, I think I'd better ask. Thank you. Nick Answered by Robert Dawson and Claude Tardif.
	7 36 14 18 28 9 56 x y		2009-12-06
		From lisa: what is the sequence of x and y 7 36 14 18 28 9 56 x y Answered by Penny Nom.
	What number comes next?		2009-11-25
		From Mark: Can someone help and give me the break down of how to solve. 5,3,1,-1 Answered by Penny Nom.
	The point of intersection of the pair of straight lines		2009-11-19
		From Stephanie: Find the point of intersection of the pair of straight lines: y=-3x-9 -y=4x+2 x = _______ and y = ________ I am totally confused. Please help Answered by Robert Dawson.
	A baseball diamond		2009-11-18
		From maelee: the official distance between home plate and second base in baseball diamond is 120ft. Find the area of the official ball diamond & the distance between the bases. Answered by Robert Dawson, Chris Fisher and Penny Nom.
	6 numbers from 53 numbers		2009-11-17
		From MIGUEL: IM A STUDENT IN HIGH SCHOOL AND IM HELPING THE SOCCER COACH WITH PLAYS SO I NEED ALL THE POSSIBLE NUMBER COMBINATIONS OF NUMBERS 1- 53 IN SETS OF SIX THE NUMBER CAN ONLY BE USED ONCE IN EACH SET. Answered by Penny Nom.
	A sequence of letters and numbers		2009-11-10
		From Maria: What is the last ten letters and numbers in the following series and how do I work it out so I can explain it to an eleven year old. J1F8M1A0M1J0J1 Answered by Robert Dawson, Claude Tardif and Harley Weston.
	A drawing of a baseball diamond		2009-11-09
		From Beth: My husband has a drawn diagram on a piece of paper of a baseball diamond. He knows that on the paper 1 1/16" (1.6875") = 90 actual feet. How do we calculate how many feet 5 7/8" on the paper would be? Answered by Penny Nom.
	Consecutive odd integers		2009-11-09
		From Erin: I'm having trouble with consecutive integers. i know it goes n + n + 1 + n + 2 and so on, but if its odd then do the numbers change to odd ones? i don't know the question is: the sum of four consecutive odd integers is -72. write an equation to model this situation and find the values of the four integers Answered by Robert Dawson and Penny Nom.
	What's the next term?		2009-11-03
		From bharat: if 1=5 2=25 3=325 4=4325 5=? Answered by Robert Dawson and Penny Nom.
	The extended real numbers		2009-11-02
		From Justin: Hello there, I was wondering is the set of extended real numbers a closed set or an open set? Justin Answered by Robert Dawson.
	Consecutive positive integers		2009-11-01
		From Madi: I'm doing my homework, and there are questions on Consecutive Positive Integers. I was just wondering, what is a consecutive integer? Or to be more specific, what is a consecutive POSITIVE integer? Answered by Penny Nom.
	The intersection of two graphs		2009-10-30
		From asma: by using the suitable scales,draw both the graph of x/2 + y/4 =3 and y=2 on the same graph paper.Find the points of intersection of the two graph. 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.
	Four consecutive odd integers		2009-10-24
		From Tonya: the sum of four consecutive odd intergers 2008 what are the intergers Answered by Penny Nom.
	What jobs use conics?		2009-10-22
		From denise: i have to type a paper on what jobs use conics and i can not find anything can you help thanks Denise Answered by Penny Nom.
	The inverse of f(x)=-1/x^2		2009-10-22
		From Jasmine: how to solve f(x)=-1/x^2 --> find f-1[x], than state if its a function Answered by Harley Weston.
	A sequence		2009-10-20
		From Alyce: The rule of this sequence is k=1/8n. Find the 8th term of the sequence. 1/8, 1/4, 3/8, 1/2, ... Thanks! Answered by Penny Nom.
	The hypotenuse of a right triangle		2009-10-18
		From steven: the perimeter of a right triangle is 20 cm. its area is 15 sq cm. find its hypotenuse. Answered by Penny Nom.
	The next three terms		2009-10-16
		From Shawn: I'm a parent and don't know how to help my 6th grader solve for this problem. Name the next tree terms in this sequence and tell the rule used to find each: -1,0,1,0,1,2,3,8,25,..... Answered by Chris Fisher.
	What is the next term?		2009-10-04
		From julia: patterns 18 46 94 63 52 61 what is the next one? Answered by Penny Nom.
	How many terms are there in this sequence?		2009-09-28
		From tabby: How many terms are there in this sequence? 5,1,-3,...,-111 Answered by Penny Nom.
	Seven circles		2009-09-20
		From Bobbi: try to put number 1 to 7 in seven circles (one in the middle, 3 on top, 3 below) so the numbers in each row of three circles--vertical, horizontal, and diagonal -- add up to 12. Each number can be used only once. Answered by Stephen La Rocque.
	Segments of a ring gasket		2009-09-20
		From Robert: I am in the process of making an Excel spreadsheet in which our sales team just needs to enter the outside diameter, inside diameter, and number of segments to price ring gaskets that are too big to fit on a sheet of material and need to be cut into segments. With your help I was able to create a spread sheet that can calculate the Chord lengths, and Segment height on a single gasket segment. I am now stuck trying to come up with a formula to figure out the height of the second segment when it is stacked on the first segment, then use it to add more depending on the quantity of segments needed. I have an illustration below showing 2 segments (of a gasket that was segmented into 4 pieces) stacked together. I need to find a formula to get the dimension from "A" to "B". Answered by Harley Weston.
	A sequence		2009-09-19
		From Oliver: I am struggling to work out the missing terms in the following sequence: 1, 3, _, 7, 11, 18, _ Answered by Chris Fisher.
	Cubes and squares		2009-09-16
		From Stanley: What is a three consecutive digit number like 5,6,7 , which is two less than a cube and two more than a square? Answered by Robert Dawson.
	A sequence		2009-09-15
		From Derek: what are the next four numbers in this sequence 1/8, 1/4, 3/8, 1/2... Answered by Penny Nom.
	The nth term of a sequence		2009-09-11
		From Michael: My son has this question as part of his key stage 3 maths homework- The nth term of a different sequence is n - 2/n^2. We've got to find the first three terms of the sequence. Answered by Claude Tardif.
	Bisecting rays		2009-09-09
		From frank: Ray OC bisects angle AOB, ray OD bisects angle AOC, ray OE bisects angle AOD, ray OF bisects angel AOE, and ray OG bisects angle FOC: if angle BOF=120 degrees, then find angle DOE? Confused! Answered by Penny Nom.
	The intersection of two graphs		2009-09-02
		From Jaqueline: Find the points of intersection of the graphs of the equations x^(2 )+ y^2=25 and 2x + y = 10 Answered by Penny Nom.
	Price increases and decreases		2009-09-02
		From craig: I work for an industry that bases it price increases and decreases on commodity pricing - Customer get confused on how/why we calculated new prices due to movement in the market - Price go up x% for every $10 of movement in the market - For this example- Movement went down by $30 and it is 2% for every $10 - so price decrease was 6%. Customer's price is currently $100. We say - $100/1.06= new price of $94.3 Customer says - $100*.94= new price of $94. They don't understand that if board went back up $30 which would be 6% increase, they wouldn't be back at $100 if they multiplied on the price decrease. $94*1.06=$99.64 vs. $94.3*1.06=$100 (Back to the original price) What is the best way to explain to customer besides using this example? Any help or info is appreciated. Craig Answered by Victoria West.
	Arithmetic Sum & Sequence		2009-09-01
		From Alice: Find the 24th term of this sequence 6.8,8.0,9.2... Find the sum of the first 21 terms Answered by Janice Cotcher.
	Cardinality of infinite sets		2009-09-01
		From Brian: I was reading an answer to a question on your site regarding infinite sets (http://mathcentral.uregina.ca/QQ/database/QQ.09.01/carlos1.html), and I think they may have got the answer wrong. I his example, he claims that the set of real numbers BETWEEN 0 AND 1 is larger than the set of positive integers. Please correct me if I am wrong, but I believe those two sets are -- pardon the expression -- equally infinite. For any integer, there is a corresponding real number between 0 and 1, and vice versa. For instance, using the decimal as a "mirror", you can create a mirror image of any real number between 0 and 1 as an integer (i.e. 0.1234 gets mirrored as the integer 4321 -- I could write it out algebraically, if you want, but you get my point) Am I wrong? Thanks, Brian Answered by Victoria West.
	Sequence problem		2009-08-18
		From James: I have the equation: tn = (n)(n+1)/2 Which gives the sequence: 1, 3, 6, 10, 15 etc. However, I'd like to be able to solve for n. So that a t of 6 would give me the answer of 3, and t of 10 would give me the answer 4 etc. Answered by Stephen La Rocque and Victoria West.
	Subtraction base 5		2009-08-09
		From Nikki: can you help me how to do subtraction in base 5 notation. example is 3434 - 51? how do you do this in base 5? can you please explain how you do this & the answer as i have no idea. Thank you kindly Nikki Answered by Harley Weston.
	An infinite set		2009-08-07
		From Islam: How can I prove that the set of all odd natural numbers is an infinite set. Thank you. Answered by Robert Dawson.
	Percentage decrease		2009-08-04
		From Bill: How to calculate the Percentage Increase or Decrease of a $ value. Example - Site Spend for 01-01-2008 thru 07-31-08 was $ 3,465,660 Site Spend, 2009 YTD as of 07-31-09, was $ 1,673,405 Site Spend down what % between these two amounts ? Answered by Penny Nom.
	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.
	Intersection of Two Curves		2009-07-27
		From Amarah: Find the coordinates of the point A( this point is where the two lines intersect). Justify answer question : here is a curve x^y =y^x (for x,y>o) Answered by Janice Cotcher.
	How can I trisect an angle?		2009-07-27
		From Nazrul: How can I trisect an angle? Answered by Robert Dawson.
	The inverse of F(x)=x^2-6x+13, for x>3		2009-07-26
		From Juan: The function F is given by F(x)=x^2-6x+13, for x>3. A. Write F(x) in the form (x-a)^2+b B.Find the inverse function F^-1 C.State the domain of F^-1 Answered by Penny Nom.
	Finding the Common Difference and Number of Terms of an Arithmetic Sequence		2009-07-24
		From Juan: In an arithmetic sequence, the first term is -2, the fourth term is 16 and the nth term is 11,998 A. What is the common difference? B. What is the value of n. Answered by Janice Cotcher.
	A sundial on an elliptical cylinder		2009-07-22
		From Leo: I want to build a sundial where the shadow falls on an elliptical cylinder. I can calculate the coordinates of the points on the cylinder that I want to mark. My problem is that I will have to make the surface as a flat sheet and bend it into an elliptical shape. However, I cannot work out a scheme to transfer the coordinates I know into a distance that will work when I bend the shape. Help! Answered by Robert Dawson.
	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.
	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.
	A sequence		2009-07-11
		From jamie: what is the next number in the sequence and what is the relationship of the numbers? 36,16,20,10,12, _ Answered by Penny Nom.
	A base 7 number and a base 9 number		2009-07-09
		From koteawarao: Find a base 7 three-digit number which has its digits reversed when expressed in base 9. ans: (281) base 7 and (182) base 9 Answered by Harley Weston.
	A binary equation		2009-07-07
		From Chinonyerem: Find a bitwise solution (i.e find xi so that each xi E {0,1}) to 32 = x1 + 2x2 + 4x3 + 9x3 + 20x5 Answered by Harley Weston.
	The retail price for an ice cream scoop		2009-07-05
		From Patricia: Hi - I am trying to figure out the fairest retail price for an ice cream scoop. We have an ice cream parlor and the cost of the ice cream we buy by the bulk container has recently been increased so now we must charge more for our scoops. We pay a wholesale price of $25.40 for 242 ounces of ice cream. The cost per ounce is $0.105. What is the formula for figuring out how much to charge retail per scoop? This is probably so simple but confusing to me. Please help. Thank you! Answered by Harley Weston.
	Prove that the set of all positive odd integers is an infinite set		2009-06-20
		From Nazrul: How can I prove that the set of all positive odd integers is an infinite set. Thank you in advance. Answered by Victoria West.
	Successive differences		2009-06-18
		From Jonathan: I'm trying to find the next number sequence for this equation: 1 11 35 79 149 251, my problem is that I worked it out and ended up with a single number 17. What am I doing wrong. Thank you for any help. Answered by Robert Dawson and Penny Nom.
	Subsets		2009-06-16
		From Tracy: Suppose C is the subset of D and D is the subset of C. If n(c)=5, find n(D) What other relationship exists between sets C and D? Answered by Penny Nom.
	Two ships and a lighthouse		2009-05-27
		From Chelsey: I have a question in regards to how do I know when to use tangent or cosine when determining angles. The question is: Looking north from the observation deck of a lighthouse 60 m above the sea, a lighthouse keeper sees two ships. The angles of depression to the ships is 5 degrees and 10 degrees. How far apart are the ships? I don't understand which one to use when solving the equation. Answered by Harley Weston.
	A sequence		2009-05-26
		From Jay: what is the equation that would give me the next 3 numbers in this progession: 0,1,5,14,20 Answered by Stephen La Rocque.
	What type of conic section is this?		2009-05-22
		From Donna: What type of conic section is 3x² + 3y² - 4y - 8 = 0 Answered by Penny Nom.
	An infinite geometric series		2009-05-18
		From terri: find the sum of the infinite geometric series 14 -7 +7/2 -7/4 +..... A. 7007/13 B. 2002 C. 28/3 D.5005/7 Answered by Stephen La Rocque.
	A sequence		2009-05-18
		From Richard: This is my question about sequences. Write down the nth term of the following sequences. 1/2, -3/4, 9/8, -27/16 Plz help me solve the question! Answered by Penny Nom.
	A number sequence		2009-05-08
		From alicia: what is the next number 1,2,6,42,1806------? is it 1954? Answered by Robert Dawson, Chris Fisher, Penny Nom and Claude Tardif.
	How do you convert 1248 to base 6?		2009-05-02
		From Tamara: How do you convert 1248 to base 6? Answered by Penny Nom.
	Stairway construction		2009-05-02
		From Olivia: Hi, I'm Olivia and I'm in 8th grade studying algebra 1. I'm having some trouble with my math project. It has to do with rules of stairway construction. It says that there are two generally accepted rules to building stairs. Rule 1: x+y=43 and x+y=46 (cm) Rule 2: 2y+x=61 and 2y+x=64 (y is the riser and x is the tread length) I cant figure out how to graph them...it says they're supposed to intersect to make a square which is like the safety zone for building stairs (the stairs' rise and tread lengths are plotted as points) any points outside of that square are considered unsafe. Did i explain it ok? Thanks for your help. --olivia Answered by Penny Nom.
	2+6+12+20+30+42		2009-04-24
		From fredy: what is the sigma notation for the series 2+6+12+20+30+42? Answered by Stephen La Rocque.
	Miles per hour and feet per second		2009-04-22
		From mary: A car traveling at 60 miles per hour, how many feet per second has it traveled? Answered by Robert Dawson.
	Percent increase from a negative number to a positive number		2009-04-21
		From Brian: I have no problem calculating year over year net profits but am having trouble when it comes to a negative. 2007 Net Profit = -110,333.00 2008 Net Profit = 66,054.00 Brian Answered by Harley Weston.
	The center of an ellipse		2009-04-21
		From Nae: what is the ellipse center of 5x^2+3y^2=15 Answered by Stephen La Rocque.
	$65.09 is 70% greater than the average price		2009-04-11
		From Kelly: Hello! I know you might be thinking that I didn't look through your previous answers, but I really did. Here's my dilemma- I have a percent increase equation that is missing the 'old" value. I know that $65.09 is 70% greater than the average price, but I do not know the average price. How do I go about finding that? I tried to set up an equation, but its throwing me off because the unknown variable is in there twice, and it's been a long time since I've taken math Thank you for your help...greatly! Answered by Penny Nom.
	The axiom of choice and constructibe sets		2009-04-10
		From sydney: The axiom of choice asserts the existence of certain sets, but does not construct the set. What does "construct" mean here? For example, does it require showing the existence and uniqueness of some function yielding the set? In general, what does it mean to require the existence of a mathematical object be tied to a construction of it? Answered by Claude Tardif.
	Direct and inverse relationships		2009-04-06
		From allison: A piece of string is cut into n pieces of equal lengths L (1) does n vary directly or inversely with L Answered by Penny Nom.
	Three consecutive odd integers		2009-04-02
		From Brian: Find the greatest of three consecutive odd integers if the product of the second and third is 8 more than 13 times the first. Answered by Robert Dawson.
	A 25 team league		2009-03-31
		From brad: 25 teams are in a league in which each team plays everybody once how many games must be scheduled ? Answered by Penny Nom.
	Adding in base six		2009-03-29
		From Lucy: If you are working in base 6, what do you have to add to 4(base 6) to get 10(base 6)???? Answered by Penny Nom.
	Uses of Pythagorean theory		2009-03-27
		From Britta: Please, give me some complex real life situation examples where the pythagorean theory is used. It must be a grade 8 or grade 9 level of thinking as that is what is my teacher's demands. Answered by Robert Dawson.
	The base of a triangle		2009-03-25
		From yinna: how do I find the base of a triangle who's height is 2 times the base and the area is 9? Answered by Penny Nom.
	The base and height of an isosceles triangle		2009-03-23
		From Chris: How do you find the base and height of an isosceles triangle that has 2cm legs? Answered by Harley Weston.
	An equation for a line with a changing slope		2009-03-21
		From Ben: Is there anyway to write an equation for a line with a changing slope. e.g. A cell [hone company has a initial fee of 50$ paying for the first 100 minutes, the rate then increases to 10 cents per minute, then at 500 minutes the rate is 5 cents per minute. If so please tell how. Thanks Answered by Penny Nom.
	A plane cuts a line segment		2009-03-17
		From Manis: Find the ratio in which the line joining (2,4,16) and (3,5,-4) is divided by the plane 2x-3y+z+6=0. Answered by Robert Dawson.
	License plates and poker hands		2009-03-14
		From CC: You have a license plate it can have 6 numbers/letters you can use the numerals 0-9 and the letters A-Z how many combos are possible and how did you figure it out? Question 2, Your dealt an Omaha hand You have KKKQQ, how many different hands can consist of the same cards. Answered by Harley Weston.
	A sequence		2009-03-13
		From Shelly: Which sequence satisfies the rule n/4? Answered by Stephen La Rocque.
	Three consecutive odd integers		2009-03-11
		From Susan: Find three consecutive odd integers such that the sum of the first, twice the second, and three times the third is 70 Answered by Penny Nom.
	A sequence		2009-03-11
		From Vly: 2; 6; 26;126;626 find the nth term Answered by Harley Weston.
	The angles of a triangle		2009-03-11
		From Marissa: The angles in a triangle measure 7x-1, 18x+2, and 5x+10. Determine whether the triangle is acute, obtuse, or right. State your reasons clearly. Answered by Robert Dawson.
	Trifecta		2009-03-09
		From Annie: I want to know how many combinations are there for the first 3 horses in a race of 20 horses. For example, the horses can come in 1, 5, 7 or 7, 5, 1 which are totally different combos. I've only found formulas where the 1, 2, 3 and 3, 2, 1 are counted as the same combo. In horse racing every combo is different. Thank you. Answered by Penny Nom.
	A property that decreases in value every year by 10 percent		2009-03-07
		From PEter: there is a competition problem where a cottage is worth 25000 years, but it decreases in value every year by 10 percent. Without a calculator, is there a way to find after how many years, the cottage will be worth 2500? (besides multiplying it out and besides logs) Answered by Stephen La Rocque.
	The ratio test		2009-03-06
		From Haley: Use the ratio test to determine whether the series in convergent or divergent. (2/5)+(4/10)+(8/15)+... Answered by Harley Weston.
	Infinite sets and infinite limits		2009-03-06
		From Justin: Hello, I know I have asked a similar question before but I was just wondering if set theory applies to the lim x->0, y=1/x=infinity and if so, what type of infinity would it be? Thanks a lot for your help with this question! Regards, Justin Answered by Robert Dawson and Harley Weston.
	Direct, inverse and indirect proportionality		2009-03-04
		From Brian: My 14 year old is confused about indirectly proportional and inversely proportional. On searching on the internet we were directed to: http://mathcentral.uregina.ca/QQ/database/QQ.09.00/ellis1.html Here leanne starts explaining indirectly proportional and ends up describing inversely proportional. Has Leanne got it wrong ? What is indirectly proportional. Thanks Brian Answered by Chris Fisher.
	Convergent or divergent?		2009-03-03
		From Betsy: Use the ratio test to determine if the series is convergent or divergent. 1+1/2^2+1/3^3+1/4^4 I know the general terms are a(n)=1/n^n and a(n+1)=1/(n+1)^(n+1) but I can't simplify r=lim(n->inf.)=n^n/(n+1)^(n+1) Answered by Robert Dawson.
	An array with 2 more rows than columns		2009-02-28
		From Mario: Write a division sentence modeled by an array that has 2 more rows than the number in each row. Answered by Penny Nom.
	Where do X, Y and Z go?		2009-02-27
		From Aj: A E F H I K L M N T V W B C D G J O P Q R S U where do X, Y and Z go? Answered by Robert Dawson.
	1 3 6 10 15....		2009-02-26
		From Allie: 1 3 6 10 15.... i know the pattern is +2 +3 +4 +5 and so on...but i dont know how to write an equation to find the nth term. help! Answered by Robert Dawson and Claude Tardif.
	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.
	wo consecutive numbers with a product of 9506		2009-02-25
		From sofie: find two consecutive numbers with a product of 9506 Answered by Penny Nom.
	Pressure at Given Depth		2009-02-22
		From Tamara: A sea is 3km deep. The average density of sea water there is 1020 kg/m^3. What is the water pressure at the bottom? Answered by Janice Cotcher.
	One vertex angle of a regular octagon is trisected		2009-02-19
		From Chelsy: Suppose one vertex angle of a regular octagon is trisected as shown in the figure. Each side of the octagon measures 4 units. Find the area of the shaded area. Answered by Robert Dawson.
	The volume of a cylinder		2009-02-18
		From jim: given the volume of a cylinder at 565m^3 and the height of 20m how do i calculate the cross section area in order to determine the compression strength of the cylinder Answered by Harley Weston.
	More on infinity and Set Theory		2009-02-17
		From Justin: I greatly appreciate your help I was just wondering from your previous answer, why doesn't Cantor's cardinal numbers in set theory apply to the limit x->0, y=infinity? Justin Answered by Robert Dawson.
	Miles per hour to kilometers per second		2009-02-17
		From Tamara: If a car goes 60 miles in an hour how many kilometres will it go in a second? Answered by Penny Nom.
	Infinity and Set Theory		2009-02-17
		From Justin: I was just wondering is the limit x->0, y=1/x=infinity, the biggest uncountable infinity according to Cantor's cardinal numbers in set theory? Justin 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.
	In what base is 3x3= 10?		2009-02-14
		From David: In what base is 3x3= 10, 3x3=11, 3x3 = 12? is there a fast way to see this or do I have to create multiplication tables until I find the right one? Answered by Penny Nom.
	y = p q^t		2009-02-12
		From Conor: y= p x (q (to the power t) ) ; y= 100 when t = 2 and y= 4 when t= 0 a) find p and q b) hence find y when t=4 Answered by Stephen La Rocque.
	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.
	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.
	Congruent line segments		2009-02-05
		From casie: marica drew one-line segment on a graph with endpoint of (0,9) and (0,4). she drew another line segment with endpoints (1,1) and (6,1). are the line segment congruent?explain Answered by Penny Nom.
	The sequence 5, 12, 19, 26, ...		2009-02-04
		From Vickie: Hello, Here's the question. Ryan wanted to play basketball on a team, He started practicing shooting everyday to improve his skills. The first day he make 5 shots, the second day he made 12 shots, the third day he made 19 shots, and the fourth day he makde 26 shots. If the first day was March 1 and the pattern continues, how many shots will Ryan make on the last day of April and the last day of July? My daughter's answers were 425 for April and 1069 for July. Are these correct and what would be the formula for this question? ? +N=? I don't know please help. Thank you, Vickie Answered by Robert Dawson and Penny Nom.
	A piecewise function for monthly salary		2009-02-03
		From Josh: A sales rep for a drug company is paid on the following scale. His base salary is $1600 per month. He is also paid a commission of 2% of sales over $20,000. When his gross sales reach $30,000 he is then paid 4% on the amount above that until his sales reach $50,000 after which point his commission becomes 6%. His commission reaches 8% when his sales total goes over $100,000 for the month. Set up a piecewise function for the information above. Answered by Harley Weston.
	Calculating markup		2009-02-03
		From Tonya: I'm trying to figure out the formula for the following, I have a product that I want to receive a certain profit, but with this product I also have to pay a percentage of commission to someone. I need to know how to calculate my new selling price taking into account the markup percentage, but I don't want my cut to be lowered. I have calculated the markup percentage to get my new selling price with the commission, but it lowers my cut once I pay the commission and I don't want it to do that. Thanks Answered by Penny Nom.
	What do I need to pass the course?		2009-02-02
		From Lynnette: If I received 100% on my assignment which is worth 20% of my total mark and 87% on my midterm which is worth 40% of my total mark what would I need to get on the final exam which is worth 40% of my mark. To pass the course I must have 80% or above. Thanks. Answered by Penny Nom.
	The sequence 2n! - 1		2009-02-01
		From Penny: I am trying to help my son with this problem. Find the first five terms of the sequence that can be written from the formula A= 2n !-1. Answered by Penny Nom.
	The intersection of two lines		2009-01-30
		From kaylee: how do you find and graph the intersect of these two equations: y=2x-4 (and) 2y=x thanks, kaylee Answered by Stephen La Rocque.
	Ambitious 7th Grader		2009-01-28
		From John: I have been asked to tutor a 7th grader who is very good in math. He is taking the most advanced course that his school offers to 7th graders. This course will cover Algebra 1 over a period of two years, using McDougal Littell's Algebra, Structure and Method, Book 1, a book I like a lot. I have been hired not to help him with his schoolwork, which is too easy for him, but to guide him through something in math beyond his schoolwork. This was his idea, an idea which surprised his parents, but one which they support. Do you have a suggestion for me? If so, I would be very grateful to hear from you. I think this could be a lot of fun for me and my new student, if I pick the right path. Thanks and best regards, John John Answered by Robert Dawson, Victoria West and Walter Whiteley.
	Percentage increase		2009-01-19
		From Destiny: In 1990 there were 25 springs in the park. This year there are 35 springs in the park. What is the percent increase? Answered by Penny.
	The point of intersection of the straight lines		2009-01-18
		From Kieran: Find the point of intersection of the straight lines y=2x+4, and y+2x-16=0 Answered by Robert Dawson and Penny Nom.
	Segments of a sphere		2009-01-16
		From Herman: How do I solve for a segment of a sphere so that the orange peel or pie shaped section is converted to a flat surface with dimensions. I form large diameter domes, elliptical and sphere heads on a press. I enter the diameter say 30 feet with two segments above and below the equator and the total number of segment around the circumference at say 18 so the widest part of the pie shaped section will fit my press. How do I take the upper or lower course above or below the equator and figure the height of the orange peel shape, the chord length at top and bottom, and solve for the right angle at 2 degree increments down the arc length of the pieces so I can layout the flat plates prior to pressing. Thanks for your help. Answered by Robert Dawson.
	A seven card poker hand		2009-01-12
		From Sean: from a standard card deck, seven cards are chosen at random. find the probability that the set chosen contains exactly three of each of two different face values. the second part of the problem asks the probability that the card hand contains exactly three 2's and exactly three 5's. Answered by Robert Dawson.
	(a x b) intersect (b x a)		2009-01-08
		From sean: is it possible to have two sets such that n((a X b) intersect (b X a) =3 Answered by Harley Weston.
	A union B and A intersect B		2009-01-07
		From Jim: Suppose A and B are sets and (A union B) = (A intersect B). Is it true that A=B. Answered by Penny Nom.
	y varies jointly as x and the square of z and...		2009-01-05
		From peter: I don't really get the terms in this problem. Could you explain it: If y varies jointly as x and the square of z and inversely as the cube of w, by what factor is y increased when z is doubled and w is divided by 3 and x remains the same? 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.
	What is f^-1(3) when f(x)=2x-1?		2009-01-03
		From Peter: how do you do functions like f^-1(3) when f(x)=2x-1? Answered by Penny Nom.
	Jon's bank account		2009-01-03
		From Abigail: Hi, i have an exam soon (monday =[ ) in my revison book, it shows two peoples bank accounts- and then it says "write a formula to show the balence of Jon's bank account after n weeks of 2003" this is the table show Jon's Bank account Weeks Week 1 Week 2 Week 3 Week 4 Week 5 Balance(£) 970 1035 1100 1165 1230 Answered by Penny Nom.
	A spill of oil on a flat surface		2008-12-19
		From Phillip: Hello, my question is: If I spilled 25 gallons of diesel fuel on a flat surface how much area would the spill cover? How would I mathematically figure it out? Thanks! Answered by Robert Dawson and Harley Weston.
	The inverse function for F(x)=x^3+x		2008-12-18
		From alireza: I want inverse function for F(x)=x^3+x Answered by Robert Dawson.
	The middle term of an arithmetic sequence		2008-12-15
		From Leigh: Find the sum of the first fifteen terms of an arithmetic series if the middle term is 92 Answered by Penny Nom.
	Annual percent growth		2008-12-13
		From Joe: If Wall-Mart had sales of $58,200,000,000 in the year 2002 and $90,800,000,000 in the year 2006. 1. Find what percent that increase is of the 2002 sales? I came up with (9.08*10^10 - 5.82*10^10) / 5.82*10^10 * 100 = 56.01% increase. Is this correct? 2. What was the percent GROWTH in Wal-Mart's sales from 2002-2006? I am having trouble figuring out how to do the Growth problem. I would appreciate any help. Answered by Harley Weston.
	The third vertex of a right triangle		2008-12-10
		From prashant: how to calculate coordinates of third vertex in a right angle triangle given the coordinates of hypotenuse as (1,3) and (-4,1) Answered by Robert Dawson.
	Division in different bases		2008-12-02
		From MICHELLE: DIVIDE 538 BY 14 IN BASE 2, 3, 4 & 5 Answered by Penny.
	A log base 2 problem		2008-11-26
		From dave: solve for x (log base 2 of x) - (log base 2 of (x-2)) = 3 Answered by Penny Nom.
	Sec(2x)		2008-11-23
		From Evan: Prove that this is an identity... sec2x = sec^2x / 2 - sec^2x Answered by Harley Weston.
	The nth term of a sequence		2008-11-20
		From kim: Find the next 2 terms of the sequence. 11n+2.5 Answered by Harley Weston.
	The height, base and perimeter of a triangle		2008-11-17
		From Zack: How would i calculate the height of a triangle if the base is 10cm and the area is 50cm²? If possible how would i calculate the length around the the triangle. Answered by Penny Nom.
	License plates		2008-11-17
		From Clayton: Okay, so in this situation a license plate must have four letters (A-Z) and four numbers (0-9), ex. ABCD-1234, where repeating a letter or number is allowed ex. AAAA-1234, or ABCD-1111, or AAAA-1111. The order of letters first numbers second, or number first, letters second is allowable, and each state has its own plates, so ABCD-1234 from New York, and ABCD-1234 from Minnesota are considered different combinations, how many different license plates could there be? Answered by Penny Nom.
	The nth term of a sequence		2008-11-16
		From Robin: How do I solve for the next term in the following sequence, I just don't want the answer...I want how to do it to. x,x -1, x -2 Also, how do I solve for the nth term? I can't understand the explanations I've found. He has numbers subscripted in his equations. Answered by Victoria West.
	The midpoint o a line segment		2008-11-15
		From Jane: The vertices of a triangle are at (1,7), (6,-1) and (0,3). Find the coordinates of the midpoints of the sides. Answered by Penny Nom.
	A cross-sectional area		2008-11-13
		From David: I am doing a science project examining the tensile strength of seaweed fronds. I need to calculate the cross-sectional area from the major and minor diameters of the elliptical central axis of the seaweed frond. What formula would I use to get this. The strength of the segments is expressed in terms of cross-sectional area of the frond at the test site. Answered by Penny Nom.
	1/8, 2/7, 1/2, 4/5, ..., ...		2008-11-06
		From katie: Inductive reasoning, what 1/8, 2/7, 1/2, 4/5, what would be the next two in th sequence. Answered by Penny Nom.
	An arch is in the form of a semi ellipse		2008-11-03
		From jessica: An arch in the form of a semi ellipse has a span of 10 meters and a central height of 4 m. Find the heights of the arch at a point of 3 meters from the semi minor axis. Answered by Penny Nom.
	A sequence		2008-10-26
		From Nicole: what is the rule to this sequence 3,6,12,24,48..... Answered by Penny Nom.
	The sequence 49,48,46,43,39...		2008-10-26
		From Kyle: What number comes next in the series 49,48,46,43,39...? Answered by Stephen La Rocque.
	The sequence 6,1,6,2,6,4,6,8,6,		2008-10-26
		From Kyle: What number comes next in the series 6,1,6,2,6,4,6,8,6,? Answered by Stephen La Rocque.
	The amount of diesel fuel in a tank		2008-10-26
		From Mike: I have an cylinder shaped oil tank that holds approx. 283 gals of diesel fuel. The tank is laying on on its side, (like taking a garbage can and laying it down on its side). What is the formula to calculate how much oil is in the tank at any given time. If the tank was sitting on end it would be easy to figure out, but it is not. Answered by Stephen La Rocque.
	nth term		2008-10-22
		From jen: what is a nth term and how do i find the nth term of any sequence Answered by Penny Nom.
	A canal with cross section a semicircle		2008-10-19
		From Connor: a canal with cross section a semicircle is 10m deep at the centre. Find an equation for the semicircle and use it to find the depth 4m from the edge Answered by Penny Nom.
	An arithmetic series		2008-10-17
		From Laura: In an arithmetic series 5+9+13+...+tn has a sum of 945. How many terms does the series have? What formula do I use? Answered by Penny Nom.
	Bags of wheat seed		2008-10-16
		From Gayle: If you want to plant 26 seed per square foot (wheat) on one acre of land and the seed comes in 50 lb bags and there are 13,500 seed per pound (675,000) per 50 pounds, how many bags do you need to plant per acre? Answered by Penny Nom.
	Bags of pennies		2008-10-11
		From paul: jenny divided 15 pennies among 4 money bags.she could then pay any amount from 1p to 15p just by giving bags.how many pennies did jenny put in each bag? Answered by Penny Nom and Victoria West.
	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.
	A 10% increase in supply		2008-10-10
		From Irena: How do you find begining inventory if after 10% increase in supply you got 27.5 units Answered by Penny Nom.
	Three consecutive integers		2008-10-07
		From pam: Find three consecutive integers such that the greatest increased by twice the least is 293. Answered by Penny Nom & Chris Fisher.
	The rise over the run		2008-10-07
		From Mak: what is the ratio of the rise to run? Answered by Penny Nom.
	Area of a semicircle		2008-10-06
		From Benjamin: How do you find the area of a semi-circle if the diameter is a variable. Answered by Penny Nom.
	Does an oval have sides?		2008-10-02
		From reid: My 6 yo neice came home with her math homework and she was supposed to identify which objects had sides.One of the objects was an oval.I don't believe it has sides because it is curved and I don't think that would make it an object with sides.What would be the correct answer?Thanks,Reid Answered by Janice Cotcher.
	The empty set		2008-09-29
		From wahab: Why a null set is called a set? the definition of set includes that a set is a collection of well defined objects But a null set is having no value. Answered by Harley Weston.
	The nth term		2008-09-29
		From shauna: The first five numbers in a sequence are 40, 37 34, 31, 28 Find an expression for the nth number in the sequence. Answered by Penny Nom.
	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 area of an arched transom		2008-09-28
		From Ivan: What is the formula for figuring out the square footage of arched transom windows & doors? Answered by Harley Weston.
	Increase pricing by 5%		2008-09-28
		From Adrian: I am working to increase pricing by 5%. If the price is 100, I would typically use the formulas 100 * 1.05 = 105, which is a $5 increase. An associate suggests I divide to get the desired increase. For example, using $100 with a 5 percent increase. I would use the forumula 100/.95 = 105.26. Thas is a 5.26 increase. Can you explain this method to me an why the different increases? Which one is correct. Answered by Penny Nom.
	Two consecutive numbers		2008-09-21
		From tomas: what is the two consecutive numbers with a product of 4160? Answered by Penny Nom.
	The area of a garden		2008-09-20
		From Hannah: How do you find the area of a semi circle when no measurement is given? The question is find the area of the garden which is semi circular. The measurements are 24m and 26m and the semi circle's height is 10m! Answered by Penny Nom.
	Finding the Pattern in a Sequence		2008-09-16
		From sjp: please could you help me find the nth term for 8 4 0 -4 -8 and -4 -1 4 11 20 Thank you Answered by Janice Cotcher.
	The nth term of a sequence		2008-09-13
		From lavett: what is the Nth term in the sequence when the sequence is 2,4,8,16... and the term numbers are 1,2,3,4... Answered by Stephen La Rocque.
	The height and base of a triangle		2008-09-12
		From Bailey: The length of the base of a triangle is 1cm less than 5 times the height of the triangle. The area of the triangle is 21 square cm. What is the the height of the triangle and the length of the base of the triangle? Answered by Stephen La Rocque.
	0.151515...=15/99		2008-09-08
		From Emma: This week, my Algebra teacher told us about the pattern between infinitely repeating decimals and their corresponding fractions. (ex. .2222222...= 2/9, .151515...=15/99, 456456456...=456/999, etc.) I was just wondering the reason why this pattern occurs. Is there a certain element that causes this pattern to occur? Thanks -Emma Answered by Penny Nom.
	An exclusion zone around a triangle		2008-09-07
		From Awrongo: A long time ago Mr Gibson found an island shaped as a triangle with three straight shores of length 3 km,4 km and 5 km. He declared an 'exclusion zone' around his island and forbade anyone to come within 1 km of his shore. What was the area of his exclusion zone? Answered by Stephen La Rocque and Penny Nom.
	A security camera		2008-09-07
		From Rita: A security camera in a neighborhhod carnival is mounted on a wall 9 feet above the floor inside a video gallery. What angle of depression should be used if the camera is to be directed to a spot 6 feet above the floor and 12 feet from the wall? Answered by Stephen La Rocque and Harley Weston.
	The selling price		2008-09-04
		From Robert: Client wants to sell his property providing he is left with 100000.00$ net. How do I calculate selling price if commission is 6% and taxes on the commission 6% Fed and 7.5%prov. I'm taking the real estate class and this one really got me. Answered by Penny Nom.
	Half a circle		2008-09-04
		From brandon: what are the area and perimeter and area of half a circle?? Answered by Penny Nom.
	Aboriginal number groupings		2008-09-04
		From Barbara: Our current place value system is based on the notion of 10s. Did Aborginal people use a similar system or did they group numbers differently? Answered by Harley Weston.
	Four weights		2008-08-25
		From Darla: A balance had known weights of 1/2 lb, 1/4 lb, 1/8 lb, and 1 oz. Edna's object weighted 2 oz. more than Paul's. Each used 3 known weights to weight his or her object. which know weights did each use? Answered by Penny Nom.
	Eccentricity of an Elliptical Orbit		2008-08-20
		From Gina: A satellite has an elliptical orbit around the earth with one focus at the earth’s center, E. The earth’s radius is 4,000 miles. The highest point that the satellite is from the surface of the earth is 800 miles, and the lowest is 200 miles. What is the eccentricity of the satellite’s orbit? Answered by Janice Cotcher.
	The intersection of the medians		2008-08-18
		From Katie: Q: A Triangle is positioned with one side on the x-axis, the coordinates for the triangle are (-a,0), (a,0), (b,c) a) Find the coordinates of the point of intersection of the perpendicular bisectors of the sides b) Find the coordinates of the point of intersection of the medians c) Find the coordinates of the point of intersection of the altitudes Answered by Penny Nom.
	A 3% increase		2008-08-18
		From RENEE: I need to know how to do a 3 percent increase for $118,200......x's it by 3% will not work please answer fast Answered by Penny Nom.
	Graphing a piecewise function		2008-08-12
		From Shanti: how do you graph a step function or piecewise function such as u^2 if u is greater than or equal to -2 and less than 1 2- u if u is greater than or equal to 1 and less than 4 Answered by Penny Nom.
	The base of a triangle		2008-08-10
		From Mark: What is the formula I need to use to find the base of a triangle sail that is 16 feet high and has an area of 64 square feet. Answered by Stephen La Rocque and 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.
	Arc-length and sector-angle		2008-08-06
		From Benson: If chord length, radius are given, How to find the sector angle and arc-length Answered by Janice Cotcher.
	Cost of pencil is rising every year since 7 years ago		2008-08-06
		From Mari: Cost of pencil is rising every year since 7 years ago. If the cost of pencil last year was 60 cents which is the sum of the cost from the last two previous years, what is the cost of the pencil now, the cost seven years ago. Answered by Penny Nom.
	Demographics		2008-07-25
		From shahrukh: Each year for 10 years ,the population of a city increased by 5% of its value in the previous year. If the initial population was 200 000 ,what was the population after 10 years ?? Answered by Penny Nom.
	The midpoints of the sides of a quadrilateral		2008-07-22
		From JOEL: A QUADRILATERAL A,B,C,D HAS THE CO -ORDINATE [2,5],[8,7],[10,3]&[0,1] RESPECTIVLY [B,E,G,H] ARE THE MID POINTS OF THE SIDES AB,BC,CD&DA RESPECTIVLY FIND THE MID POINTS OF [FG]&[FH] Answered by Penny Nom.
	Taking two math classes		2008-07-21
		From Bailey: i am going into the 7th grade, but i am going to be taking 9 th grade math. i was wondering if anyone could help survive doing two different math classes at the same time. Answered by Harley Weston.
	Three consecutive positive integers		2008-07-20
		From AC: find three consecutive positive integers such that the product of the first and third, minus the second, is 1 more than 4 times the third Answered by Penny Nom.
	Choosing 5 numbers out of 39 numbers		2008-07-18
		From robert: Please list the way I can choose 5 numbers out of 39 numbers, without repeating them, starting at number 1. Please send me a list of all 120 combination. Answered by Harley Weston.
	Does the sequence 1 2 4 8 16 32 etc have a name?		2008-07-17
		From Richard: Just an idle thought really. Does the simple sequence 1 2 4 8 16 32 etc have a name? Answered by Victoria West.
	1, 2, 4, 8, 16, 32 ...		2008-07-15
		From eve: I have to find out the fomula for: 1, 2, 4, 8, 16, 32 ... Answered by Penny Nom.
	A reflected line segment		2008-07-14
		From Peter: Segment AB has endpoints A(-1,2) and (3,1). Segment AB is reflected over the y-axis such that A becomes A' and B becomes B'. What is the positive difference between the lengths of segment AA' and segment BB'? Answered by Janice Cotcher.
	Choosing a number from 1 - 400		2008-07-04
		From Peter: The numbers 1-400, inclusive, are put into a hat. What is the probability that the first number chosen at random is a multiple of 4 or 17? Express your answer as a common fraction. How do you do this the question without a calculator? Answered by Leeanne Boehm.
	A series solution of y' = xy		2008-07-03
		From sasha: I've to find the power series solution of the differential equation: y' = xy. I don't know how to find the recursive equation. Can you please help me. Thanks Answered by Harley Weston.
	Percentage increase		2008-06-29
		From Paul: Could you please help me with this question. I was paying $98.00 a month for my health insurance premium, now it is up to $125.83 How much of an increase is that as a percentage increase, and how can I do this on a calculator. I'd like to know how much my increase is as a percentage. Answered by Penny Nom.
	A 7-digit odd number		2008-06-26
		From Godryk: I am the smallest 7-digit odd number. my ones digit is the sum of my thousands, and ten thousands digits. What number am I? Answered by Penny Nom.
	Product of Two Integers		2008-06-25
		From devin: two consecutive integer have a product of 240. what are they Answered by Penny Nom.
	How do you change bases?		2008-06-17
		From Peter: How do you change bases eg. 121 from base 3 to base 5? Answered by Penny Nom.
	A piecewise equation		2008-06-16
		From John: AT&T charges $39.99 for 450 minutes per month. It charges 45 cents per minute over the 450 minutes. How can I make a piecewise equation of this problem? Answered by Penny Nom.
	An ellipse and circle with the same area		2008-06-09
		From Michael: The area of the ellipse if equal to the area of a circle with radius=40 ft. Find the values of a and b using appropriate algebraic techniques, not basic math computations. A=pi ab and satisfy the constraint a+b=100???? Answered by Penny Nom.
	Geometric sequences		2008-06-08
		From Rita: A geometric sequence is given. Find the common ratio and write out the first four terms. (1) {(-5)^n} (2) {(2^n)/(3^(n - 1)} Answered by Penny Nom.
	90% of gross leaseable footage		2008-06-07
		From Rosalind: 90% of gross leaseable footage in the shopping center, being 394,577, excluding that square footage leased by major anchor tenants, being 284,747. Would you deduct the 284,747 from the 394,577, then multiply by the 90%. Or would you multiply the 394,577 by the 90%, then deduct the 284,747? 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 path of a baseball		2008-06-04
		From Tom: How high would a batter have to hit a ball to clear the stadium roof in right field if the distance to the right field fence is 320 feet from home plate? Is this solvable? Answered by Janice Cotcher.
	Calculating a price based on markup		2008-06-03
		From Sheldon: I know the most common form for retail businesses of calculating a price based on markup is: Cost/(1 - Markup), but how is this supposed to work for a business that desires a markup of over 100%. Answered by Harley Weston.
	Two consecutive negative even numbers		2008-06-03
		From Chelsea: The sum of the squares of two consecutive negative even numbers is 100. Find the integers, Answered by Penny Nom.
	Inverse variation		2008-05-22
		From leria: In Boyle's law, the pressure of gas varies inversely with the volume of the gas. A volume of 11.2 liters of air exerts a pressure of 2.0 atmospheres. determine the constant of variation and write an equation the models the relationship between the pressure of the gas P and its volume, V. Use the equation to predict the volume of air necessary to exert a presure of 0.25 atmospheres. Answered by Janice Cotcher.
	How much seed do I need per plot?		2008-05-13
		From Jaye: The plot size is 5 m X 2 m. The seeding rate is 12Kg/ha. How much seed do I need per plot? I have failed to get a proper answer. Thank you. Answered by Penny Nom.
	Selling price		2008-05-10
		From Roxane: I'm trying to figure out the formula for the following, I have a product that I want to receive a certain profit margin, but with this product I also have to pay a percentage of commission to someone. I need to know how to calculate my new selling price taking into account the markup percentage, but I don't want my gross margin to be lowered. I have calculated the markup percentage to get my new selling price with the commission, but it lowers my profit margin once I pay the commission and I don't want it to do that. Answered by Penny Nom.
	The area of a sector of a circle		2008-05-10
		From lupio: a problem asks for the area of a sector in a circle,no central angle,in circle is given only 5cm radius, three answers 180-90-35 can't find a way to start.Help Answered by Harley Weston.
	The inverse of a function		2008-05-03
		From keith: please help me find the inverse of this function: h(t) = 2 + 4 ln(1-5t) Answered by Stephen La Rocque.
	The standard form of an ellipse		2008-04-30
		From Rebecca: I have to write the following equation into standard form of an ellipse: 9(X-1)^2 + (Y+1)^2 = 1 Answered by Stephen La Rocque and Harley Weston.
	3-3+3-3+3.........up to infinite terms = ?		2008-04-25
		From Jatin: 3-3+3-3+3.........up to infinite terms = ? Answered by Stephen La Rocque.
	Two intersecting circles		2008-04-17
		From Muhammad: Hi, how can we find the perimeter and area of the region common to two intersecting circles of radii 6 cm and 4 cm with centers 7 cm apart. Answered by Harley Weston.
	Conic sections		2008-04-14
		From Christine: In my analysis class we are learning about conic sections. Our project is to create a genral statement of the definition of conic sections. Truthfully, I have absolutely no clue on how I should write that. Could you help me? Answered by Walter Whiteley.
	The maximum area of a pizza slice		2008-04-12
		From charles: A slice of pizza in the form of a sector of a circle has a perimeter of 24 inches. what value for the radius of the pizza makes the slice largest[when o is the central angle in radians, the area of the sector is given by A= r^20/2and the length on the circle is given by s=r0 Answered by Harley Weston.
	Two function problems		2008-04-10
		From keith: find the domain: F(x)= 1/ {ln (x+5) - ln (7-x)} find the inverse: g(t)= sqrt {2-3 ln (1-t)} Answered by Penny Nom.
	cosec [arccos (1/y)]		2008-04-09
		From Tom: I am having trouble with this question. For y > 1, the value of cosec [arccos (1/y)] is? 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.
	Two consecutive odd integers		2008-03-24
		From Jarrod: the sum of two consecutive odd integers is 24. Find the two integers Answered by Stephen La Rocque.
	Circles and semicircles		2008-03-23
		From sally: Hi i am sally , i need to know what is the formula of : Find perimeter and area of a semicircle ? Find the area of a circle whose circumference ? Answered by Penny Nom.
	5 9 1 6 10 12 2, where does 3 fit in and why?		2008-03-22
		From Cassidy: number sequence 5 9 1 6 10 12 2, where does 3 fit in and why? Answered by Claude Tardif.
	4,12,24,40,60,84		2008-03-18
		From kirsty: Here are the first six terms of a sequence. 4,12,24,40,60,84 Find in terms of n, an expression for the nth term of teh sequence. Answered by Stephen La Rocque.
	Distance seen		2008-03-18
		From Nev: formule: Distance Seen S = 1.225 x square root of H S = Distance seen in Miles H = Height in Feet What dose 1.225 Relate To ? Answered by Stephen La Rocque.
	The nth term		2008-03-16
		From ryan: need help figuring nth term for 1, 2, 5, 14, 41...... could you please help Answered by Penny Nom.
	1, 1, 2, 3, 5, 8, 13, ___ ___ ___		2008-03-13
		From Karen: What is the rule for the following pattern, and what would come next? 1, 1, 2, 3, 5, 8, 13, ___ ___ ___ Answered by Penny Nom.
	Inverses of functions		2008-03-13
		From jess: if g(x)=2x+3 find g^-1(g(4)) how do I sovle I cant's figure out what to do with the 4 Answered by Stephen La Rocque.
	Two consecutive odd positive integers		2008-03-12
		From Sarah: The sum of the squares of two consecutive odd positive integers is 74. What are th integers? Answered by Penny Nom.
	Estimate the cube root of 270		2008-03-11
		From Tom: (a) By plotting suitable graphs, estimate to one decimal place the cube root of 270. (b) With reference to your answer to part (a), use 8 iterations of a Bisection Search to refine your estimate. Use the nearest whole numbers either side of your estimate from part (a) as starting values. (c) Using either of your starting values from part (b) as first guess, use the Newton-Raphson method to find the true value of the root (to 6 decimal places). Repeat using the other starting value from part (b) and compare the two results. Answered by Harley Weston.
	Base 5 arithmetic		2008-03-06
		From Jana: Hello, my name is Jana, i have asked a question here previously about how to count in base-5. I am happy now because i can convert any number now and it is very easy for me. The only thing i am having trouble with is understanding how to do a maths sum or times base-5 numbers. it is just a bit hard for me. So do you think you could explain how to do a sum in base-5 and how to do a multiplication sum. Please help...Thankyou Jana!! Answered by Harley Weston.
	What was the ostrich's speed in miles per hour?		2008-03-03
		From jacob: If it took an ostrich 2.5 seconds to travel 110 feet and the average speed is 44 feet/ seconds, what was the ostrich's speed in miles per hour? Answered by Penny Nom.
	Convert from base 6 to base 12		2008-03-02
		From Jade: I am trying to convert 13405 base 6 to a base 12 number. I am not allowed to go into a base 10 number. How will can I base 12 without doing anything with base 10? Thank you kindly. Answered by Stephen La Rocque and Penny Nom.
	The perimeter of a sector of a circle		2008-02-28
		From erica: What is the perimeter of a sector if the radius is 18 and the middle arc is 150? Answered by Penny Nom.
	3 consecutive odd integers		2008-02-28
		From Pat: For 3 consecutive odd integers, twice the first integer, plus 5 more than the second integer, plus three less than four times the third integer equals -85. Find the 3 consecutive odd integers. Answered by Penny Nom.
	The surface area of an ellipse		2008-02-25
		From paritosh: how is the surface area of a elliptical dome be calculated when the two diameters are 55 metres and 35 metres and the height of the structure is 13.4 mts? Answered by Harley Weston.
	Counting in base 5		2008-02-24
		From Jana: my name is Jana, i really need help with a maths question at school. Im confused about how to count up from1-20 in a base-5 format! I'm in year 5 and i really don't get all the complicated stuff. Answered by Stephen La Rocque.
	Actural cost, selling price and commission		2008-02-21
		From LiSa: I have a question about a few things if anyone can answer... ex. actual cost (AC) = $1000 selling price (SP) = $ amount earned for company (C) = 15% of... selling price? commission 1 (C1) = 2.5% commission 2 (C2) = 2.5% How would you calculate how much the company's commission amount would be as well as the amounts for the other 2 that get 2.5%? And what would the selling price be? (the 15% $ + 2.5% $ + 2.5% $ ?) Is the 2.5% taken from the original amount? I am soooo confused! If anyone could help, that would be great! Answered by Harley Weston.
	Find the next terms		2008-02-20
		From Darrin: I was given a number sequence and can't figure out the next terms to this 2,9,20,35,66,91...... Answered by Penny Nom.
	Classifying a triangle		2008-02-07
		From kevin: scalene triangle 8 ft base right side 9.5 left side 12 ft what is the angles Answered by Penny Nom.
	The perimeter of a semicircle		2008-02-02
		From Lisa: How do you find the perimeter of a semi circle when you are only given the diameter, say 24 units? Answered by Penny Nom.
	Cross-sectional area of a fire hose		2008-01-27
		From Tom: My question is this I know the equations for the final answer but the book skips how to get to one section of the equation. Q=(a)(v) A= The cross-sectional area of the conduit in square feet (ft2). So if you have a 5 inch hose how do they get A=0.136 ft2 ? And I know the velocity already v= velocity in ft per second. Answered by Stephen La Rocque.
	How do I convert mcg to ml?		2008-01-27
		From David: How do I convert mcg to ml? Answered by Stephen La Rocque.
	O.T.T.F.F.S.S		2008-01-25
		From Omar: What is the next letter in the following sequence: O.T.T.F.F.S.S Answered by Penny Nom.
	Three consecutive odd integers		2008-01-24
		From daniel: find three consecutive odd integers such that three times the second minus the third is 11 more than the first. help! i have x+1, x+3, x+5 as my 3 odd integers is this correct its been a while. Answered by Penny Nom.
	1/2, 1/2, 3/8, 1/4, 5/32, 3/32, 7/128		2008-01-22
		From Neil: Find the next two terms in the following number sequence 1/2, 1/2, 3/8, 1/4, 5/32, 3/32, 7/128 Find a general rule for the nth term of the sequence Answered by Penny Nom.
	Choosing 6 numbers from 42		2008-01-19
		From Marcus: If i have 42 numbers to choose from and i could only choose 6 numbers at a time without choosing the same number twice in the same row, how many possibilities are there? Answered by Penny Nom.
	A sector of a circle		2008-01-17
		From Amandsa: What is the formula for finding the sector of a circle? Answered by Penny Nom.
	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.
	The area of a sector of a circle		2008-01-11
		From Serenity: A denotes the area of a sector of a circle of radius r formed by the central angle theta. Find the area A if r=10 meters and theta = 1/2 radians. Answered by Penny Nom.
	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.
	Practical applications of sequences		2008-01-01
		From carl: can you give me examples of different kinds of practical applications of sequences? Answered by Penny Nom.
	Find the lengths, and explain in a 'let statement'		2007-12-20
		From Cordilla: the length of the sides of a triangle are 3 consecutive whole numbers. The perimeter of the triangle is 102 meters. Find the lengths, and explain in a' let statement'. Answered by Stephen La Rocque and Harley Weston.
	A 45-45-90 triangle		2007-12-13
		From Aaditya: explain to me please how to do the 45-45-90 theorem when one of the legs(not the hypotenuse) is 3. How do you find the remaining two sides? please help me out. Answered by Leeanne Boehm.
	How many houses must they paint?		2007-12-12
		From Natalie: The question is: Four boys work together,painting houses for the summer.For each house they paint they get 256 pounds. If they work for four months of the summer and their expenses are 152 pounds per a month, how many houses must they paint for each of them to have one thousand pounds at the end of the summer? Answered by Penny Nom.
	Imprecise measurements		2007-12-09
		From Sara: Hi! A water tank, in the shape of a cuboid (length 1.6 m, height 1.2 m, breadth 0.8 m), is full of water. Water is drained from the tank at a rate of 8 litres per minute. The dimensions of the tank are given to the nearest 10 cm. The rate at which the water is drained from the tank is given to the nearest 0.5 litres per minute. (a) Calculate the smallest possible time to drain the tank. (b) Calculate the greatest possible time to drain the tank. Many thanks!!! Answered by Stephen La Rocque.
	Three consecutive numbers		2007-12-08
		From Aris: The product of 3 consecutive numbers is 1716. Find their sum. Answered by Stephen La Rocque.
	A portion of a circle		2007-12-07
		From Richard: please could you tell me the formula and answer to the following. I have a circle portion with a radius of 150mm and an angle of 120 deg. If an arc is drawn from one point to the other as the radii touch the circle circumference, i need to know the area of the segment and the formula to carry out the answer. Many Thanks Answered by Penny Nom.
	A right triangle		2007-12-06
		From Shubhomoy: The co-ordinates of a hypotenuse are (1,3) and (-4,1). Find the equations of the perpendicular sides. Answered by Harley Weston.
	Representing different bases		2007-12-05
		From Sudhir: What does a number subscripted to another one denote? (I know that a number superscripted to another denotes the power, but the subscript number is something I have never seen before.) Answered by Stephen La Rocque.
	Percentage increase in profit		2007-12-04
		From Dee: If I had a certain % increase in profits for the entire year, why can't I add the profits I made for the first 1/2 of the year to the profit I made in the second 1/2 of the year to get the total year end profit percentage? Or how can I compare the increase/decrease for each 1/2 of the year to the total % increase/decrease? Answered by 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.
	O,T,T,F,F,S,S,?,?,?		2007-11-28
		From Kim: What are the next 3 letters in this sequence? O,T,T,F,F,S,S,?,?,? Answered by Stephen La Rocque.
	Direct and inverse variations		2007-11-27
		From Julie: Please Help I do not understand this question. X varies directly as the square of S and inversely as T. How does X change when S is doubled ? When both S and T are doubled ? I appreciate your help with this problem. Answered by Stephen La Rocque.
	Elimination of mayan prisoners		2007-11-19
		From Jim: An evil Mayan emperor decides to make an example of 1,000 prisoners. He stands them in a circle with numbers one to a thousand marked on their shirts. He then starts counting: "one in, two, in three out" The third man is immediately executed. This continues round and round and round the circle. While the number in the circle shrinks, every third prisoner is pushed out and executed. And it continues even when there are only two prisoners left alive. What number is on the last prisoner's shirt? Answered by Victoria West.
	Sides and vertices		2007-11-17
		From derek: What is the correct name for a 2D geometric shape that would look like one slice from a round pizza and how may sides and vertices would it have? I believe you would say it has one vertex and two sides with the curved boundary not resulting in vertices or a side. Your help is much appreciated. Answered by Chris Fisher and Walter Whitelty.
	A matrix equation		2007-11-16
		From stephanie: Im supposed to solve ( 1 tan =E8/2) ( 1 tan =E8/2)^(-1) (-tan =E8/2 1 ) (-tan =E8/2 1 ) Matrix AA<(-1)=I Answered by Penny Nom.
	Two sequences		2007-11-14
		From Kim: Pattern........what comes next? 1,4,9,16,25,_____,____ 1,4,9,16,27,40,__________,_______ Answered by Penny Nom and Gabe Potter.
	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.
	What number best completes the series?		2007-11-12
		From Grace: What number best completes the series? 2 3 7 13 27 ____ Answered by Stephen La Rocque, Penny Nom and Harley Weston.
	The sequence 3,12,26,45....		2007-11-12
		From Tra: I can seem to find the realtionship in these sequence of numbers, I am looking for the next three. How can I determine that, I have tried everything??!!! 3,12,26,45.... Answered by Penny Nom.
	Meters per second to miles per hour		2007-11-08
		From Niecey: If Greg was timed at 0.91 seconds for 10 meters running the 100 meter dash, at that speed, could he pass a car traveling 15 miles per hour in a school zone? Answered by Penny Nom.
	The base and height of a triangle triangle		2007-10-31
		From mike: How do you find the length of the base or the height of a triangle if the area is 30 square feet? Answered by Penny Nom.
	Subsets of a set		2007-10-30
		From Snehal: 1. Let an denote the number of subsets of f{1,2, 3.... n}including the empty set and the set itself.) a) Show an = 2an-1 b) Guess a formula for the value of an and use induction to prove you are right Answered by Stephen La Rocque.
	Dividing a segment into 3 congruent parts		2007-10-30
		From Carolyn: I am doing construction. I have a line segment drawn. I need to divide a segment into 3 congruent part. How do I do that? Answered by Penny Nom.
	Variation		2007-10-29
		From deeqa: 1. A car traveled 175mi at a certain speed. If the speed had been 20mph faster, the trip could have been made in 1hr less time. Find the speed 2. The average weekly allowance A of children varies directly as their grade level, G. If the average allowance of an 8th-grade student is $8.56 per week, what is the average weekly allowance of a 5th-grade The time T required to do a job varies inversely as the number of people P working. It takes 2hr for 4 working. It takes 2 hrs for 4 volunteers to distribute flyers to a neighborhood. How long would it take 12 volunteers to complete the job? Answered by Penny Nom.
	Combinations and horse races		2007-10-28
		From Ian: How do I calculate the number of combinations for: Horse races,1 horse in each race.I want all combinations covered. e.g.5 races, 1 horse in each race. R 1&2, R 1&3,R 1&4, R 2,3,4,5, R 1,2,3,4,5 etc etc.I have worked it out manually to 27 combinations but if I want to cover more than 5 it will be a big excercise to work out the cost manually. Many Thanks Answered by Victoria West.
	Is there a practical use for radian measure?		2007-10-26
		From Paula: Is there a practical use for radian measure in any profession? Which professions might us radian as opposed to degree measure? Answered by Harley Weston.
	The perimeter of a circle sector		2007-10-25
		From sara: Hi! The area of a sector of a circle is 25 sqcm. The radius of the sector is 6 cm. Calculate the perimeter of the sector. Many thanks!!! Answered by Penny Nom.
	A sixfold increase		2007-10-24
		From Fred: If I have $500 and it grew to $3,000, what is the correct description of the increase? Is it a sixfold increase (sextupled), or a fivefold increase (quintupled)? When I divide $3,000 by $500, the result is six, therefore, a sixfold increase? Answered by Stephen La Rocque.
	Converting bases		2007-10-24
		From Johanna: Is there an easy way to convert from base to base. For example, base 5 to base 9 or base 2 to base 4 etc Answered by Stephen La Rocque and Penny Nom.
	The nth term		2007-10-18
		From shannon: Ok , what i am having problems with is the nth term. I get how the numbers come together, but i am having trouble with finding the nth term. Answered by Penny Nom.
	Paying with silver - Part 2		2007-10-17
		From Shanna: The paying with silver problem. I understand how to do the problem, but could you please explain how you would use base 2 arithmetic to solve it. Answered by Penny Nom.
	the sum of two consecutive integers is 51		2007-10-17
		From Keira: the sum of two consecutive integers is 51 Answered by Penny Nom.
	0,1,2,3,6,11,20,37,68...		2007-10-16
		From Pat: Describe the rule for this pattern: 0,1,2,3,6,11,20,37,68... Thanks Answered by Penny Nom.
	How much water is in a hose?		2007-10-12
		From Bryan: I need to know how much water (gal) is in a hose thats 100' long by 5" in dia. Thanks Answered by Stephen La Rocque.
	77,49,36,18,...		2007-10-11
		From Kim: Find a pattern and predict what comes next in this sequence 77,49,36,18,________________. Answered by Penny Nom.
	Inverses of Quadratic Functions		2007-10-11
		From Elliot: I'm a special education tchr trying to demonstrate how to find the inverse (using algebra) of quadratic functions. Any help would be greatly appreciated. Answered by Steve La Rocque and Harley Weston.
	Base 10 to base 5		2007-10-09
		From Angela: I've been searching online for the past week and I cannot find an Algorithm to convert from base 10 to base 5. Can anyone give me a step-by-step instruction on how to do this? Answered by Stephen La Rocque.
	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.
	A sequence of numbers		2007-09-30
		From eleanor: can you find the nth term of the sequence ( n starts at three) 1=? 2=? 3= 4 4= 10 5=20 6 = 35 7= 56 i only hand the 3rd 4th 5th 6th and 7th numbers in the sequence can you please tell me how to find the nth term and what is it :) Answered by Stephen La Rocque and Victoria West.
	The nth term		2007-09-29
		From zoe: what is the nth term for the following sequence... 5, 2, -1, -4 Answered by Leeanne Boehm.
	Describe the pattern		2007-09-29
		From Baffled: Given a rule, extend a pattern and describe it in informal mathematical language: a) 1, 6, 16, 36, _ b) 2, 6, 14, 30, _ c) 1, 8, 22, 50, _ d) 3, 9, 27, _ e) 2, 7, 17, 37, _ Answered by Stephen La Rocque and Penny Nom.
	Four consecutive integers		2007-09-28
		From Joshua: We were given a question that involved consecutive integers. I can not seem to solve this question and I am the top student in my class.The question states: Find four consecutive integers such that twice the sum of the two greater integers exceeds three times the first by 91. How do you solve this question? Thank you very much for your support. Answered by Penny Nom, Stephen la Rocque and Claude Tardif.
	A sector of a circle		2007-09-26
		From A student: hi im stuck on this question. i have tried to do some, could you please che= ck it and help me.the answers i have worked out are in red. the question is= attached. thank you. Answered by Penny Nom.
	The nth term		2007-09-25
		From Bobby: whats the nth term of 2,12,22,32 ? Answered by Penny Nom.
	A geodesic dome		2007-09-25
		From Roger: In my Science-Fiction series, I have a Dyson's Sphere tiled with regular hexagons. The number of hexagons is over 300,000 and the radius of the Sphere is roughly 80,000,000 miles. The actual size of the Sphere and hexagons have been left flexible until I can come up with a definite number of hexagons that would fit. My problem is the pattern of hexagons which would fit within the sphere without leaving gaps or overlapping. My best guess has been to use four equilateral triangles composed of 78606 hexagons, (396 per edge) arranged around the sphere with six 'zippers' to connect them and four 'caps' at the points, for a total of 316804 hexagons. Given the fact that each Hex is the same size, does this seem plausible? Is there some pattern formula I can use to play with these figures? Simple divsion of areas will not work if the number derived will not fit into the pattern to leave a perfectly tiled surface. Thank you. Answered by Chris Fisher.
	The sequence 2,4,7,11,16,22		2007-09-22
		From Simon: I thought i understood how to explain how to work out the nth term on a sequence of numbers until my son had this sequence to work out - 2,4,7,11,16,22 We have worked out the 2nd differance is +1 but nothing else seems to fit. Im sure the answer is staring us in the face but cant see the wood for the trees! Answered by Denis Hanson and Steve La Rocque.
	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.
	A fraction sequence		2007-09-21
		From marissa: i have read the examples you have on fraction sequences, but i am still having a hard time understanding how to figure this out. for example: __ 1 2/5 __ 3 __ __ __ __7 Answered by Stephen La Rocque.
	Letter number sequence		2007-09-21
		From Hope: The challenge problem of the week in 6th grade math is a letter number sequence. J 1 F 8 M 1 A 0 M 1 J 0 J 1 _ _ _ _ _ _ _ _ _ _ They are to find the next 10 letters and numbers in the line. They were given a hint : look at the letter sequence by themselves and you should recognize it. Does it just repeat starting with the F 8 M 1 etc.? Thank you for your help. Answered by Claude Tardif.
	The hypotenuse		2007-09-20
		From Kasey: What is the hypotenuse of 96 squared and 108 squared? Answered by Penny Nom.
	What is the inverse function of y=x^3 +x?		2007-09-19
		From saman: what is the inverse function of y=x^3 +x Answered by Harley Weston.
	Number sentences		2007-09-15
		From jen: list the addition number sentences that can be written using two sets of cards with the numbers 5 6 and 7. which number sentences have the same addends but show a different order?,,,,,,,,,,,,,,Ithis is for my son in 3rd grade and for the life of us we can't figure it out,,thanks for this elementary help Answered by Harley Weston.
	The nth term		2007-09-13
		From Rookin: Can you help me find the nth term for this ... 20,17,14,11,8 i'm really confused oh and could you also tell me how you got the answer? Answered by Steve La Rocque, Claude Tardif and Harley Weston.
	The perimeter of a semi-circle		2007-09-11
		From Confused: What is the formula for the perimeter of a semi-circle? Can you please help me out!!! I need this answer by tomorrow. Answered by Stephen la Rocque.
	What are the next two terms?		2007-09-11
		From Sassy: I can't figure out what the next two integers in this pattern are 3,9,6,12,9 are. Answered by Stephen la Rocque.
	A sequence of fractions		2007-09-10
		From mitch: find an expression for T(n), the nth term of the sequence 1/5, 3/8, 5/13, 7/20, 9/29 Answered by Stephen La Rocque.
	Segments on a line		2007-09-10
		From Cathy: This question was on my daughter's geometry assignment. Write a general rule of formula for finding the number of segments that can be named by a given number of points on a line. For example, 2 points on a line = 1 line segment; 3 points on a line = 3 segments; 5 points on a line = 10 segments. Answered by Penny Nom.
	The nth term		2007-09-09
		From Conor: Please can you help me with this question on the subject of the Nth term. 3.5, 5, 6.5, 8, 9.5 5.1, 7.2, 9.3, 11.4... Answered by Penny Nom.
	nth term in this series		2007-09-07
		From danii: im trying to solve the nth term for this pattern. 1 3 6 10 15 21 28 any help would be appretiated Answered by Stephen la Rocque.
	The next term		2007-09-07
		From Ariel: Please explain to me why -3^2 is a -9. One calculator give me an answer of positive 9. WHAT IS THE NEXT TERM IN Each sequence/ What is its term number? 1/2, 2/3, 3/4, 5/6 6/7 1, 1/4, 1/9, 1/16 Answered by Stephen la Rocque.
	A sequence		2007-09-06
		From aimee: i have the sequence 1,5,14,30,55 and i have been told to use An squared times Bn times C and my working should look like this 1 5 14 30 55       4 9 16 25          5 7 9             2 2 But how do i do this Answered by Penny Nom.
	A sequence of fractions		2007-09-05
		From Arjun: 1/2 3/5 5/8 7/11- need to find the nth term. I did search the data base & found one for fractions but what I want to know is when calculating nth term for the denominator in the example give in your database how do we get (n-1)? When we deduct the actual term with the one that is in the table give in your example it is more that one. Could you please explain solving the above example? Answered by Penny Nom.
	The first five terms		2007-09-04
		From JP: Find the first five terms of a sequence with the nth term n^2+2n+1 and 2^n. Answered by Penny Nom.
	Speed of sunrise		2007-09-04
		From Robert: Facing west in a car, you are watching the sun rise (through the rear view mirror). It peaks the horizon, you take off driving. How fast would you have to drive, to see it rise again? Answered by Stephen La Rocque.
	2,6,7,21,22,66,67		2007-08-28
		From EDWIN: this doesnt make any sense to me....... i cant find the pattern... 2,6,7,21,22,66,67 Answered by Leeanne Boehm and Stephen La Rocque.
	Applications of sequences and series		2007-08-27
		From Trish: I'm a grade 12 learner working on a math project based on sequences and series. I'd like to know the different types of sequences and series such as fibonacci, fourier, farey, etc. I've already used the Fibonacci Sequence and Harmonic Series and need two more. The simpler the sequence or series type the better. I'd also like to know in which non-mathematical areas use sequences and series and how. Areas such as engineering or science. Answered by Penny Nom.
	Where do you use trigonometry?		2007-08-21
		From jenny: where do you use trigonometry besides architecture and engineering? Answered by Stephen La Rocque.
	The tens digit		2007-08-21
		From Arul: Hi.. Please help me on this question.. Sequence 2, 7, 22,…after the first three terms, each term is three times the previous term plus 1, a(n+1)=3an + 1. What is the sum of tens digit 33rd and tens digit of the 35 term? Answered by Penny Nom.
	Common factors		2007-08-19
		From John: I have problem factorising 2p^3 - 34p. Please advise me. Answered by Leeanne Boehm, Steve La Rocque and Penny Nom.
	Percentage change		2007-08-19
		From nona: If inputs increase by 30% and outputs increase by 15%, what is the percentage change in productivity? Answered by Stephen La Rocque.
	Area and perimeter		2007-08-16
		From sheryl: a 50*70 horse pen is 240 feet and 3500 square feet a 60*60 horse pen is 240 feet and 3600 square feet why is there a 100 square feet difference? Answered by Penny Nom.
	Percentage change		2007-08-13
		From Karen: I need a formula for calculating percentages in Excel. For example, we = sold 4 units of an item one month, and 105 units the next. I need a = formula to calculate the percentage increase in sales units. Also, if = 5251 were sold one month and 651 the next, what is the formula for = calculating the percentage difference? Please help, thank you. Answered by Penny Nom.
	Twenty dining tables		2007-08-13
		From priya: Utkarsh bought 20 dining tables for Rs 120000 and sold these at a profit equal to the S.P of 4 dining tables.Find the S.P of one dining table.(give the answer in statements) Answered by Stephen La Rocque.
	A right triangle		2007-08-11
		From Peter: Ok, is it possible to find the height and base of a right triangle when all the information you are given is the length of the hypotenuse? I also know that the angle between side b and the hypotenuse is 45 degrees. please help. Answered by Walter Whiteley.
	4,18,48,100, __		2007-08-07
		From Jeremy: What is the next number in the following sequence? 4,18,48,100, __ Answered by Leeanne Boehm and Stephen La Rocque.
	Linear systems and inverses		2007-08-06
		From Marsia: explain how inverses are used to solve linear systems. Answered by Penny Nom.
	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.
	A sequence of numbers		2007-07-27
		From Shamik: Question: A sequence of numbers is defined in the following way. B(1) = 1 B(n) = B(n-1) + {Sum of the digits of B(n-1)} for n > 1. B(1) = 1 B(2) = 2 B(3) = 4 B(4) = 8 B(5) = 16 B(6) = 23 B(7) = 28 B(8) = 38 B(9) = 49 ::::::::: and so on ... Is the number 123456789 a term in the given sequence? Shamik Answered by Claude Tardif.
	Countable and uncountable sets		2007-07-24
		From Mac: Hi, i tried to read few webpages related to the countably infinite and uncountable sets. Even i read few questions from this forum. But i am not convinced with this explanation. If you have any good book that explains this in layman term, please redirect me to that. 1) Can you please explain what is the difference between these too ? 2) How could you say set of Natural number and set of even numbers are countably infinite ? N={1,2,3,...} and Even= {2,4,6,...} When an element in the even set is some 2n, we will map it to 'n'.So now we have a bigger number(2n) right ? Sorry, i didn't understand that. ... Can you please help me out to understand that ? Answered by Harley Weston.
	Equality of sets		2007-07-23
		From Mac: Hi, I learnt set theory recently. My teacher and few of the weblink actually give different definition for basic set. Can you please solve this ? My teacher says, {1,2,3} and {1,1,2,3} is also set. But in this link http://library.thinkquest.org/C0126820/setsubset.html it says, "A set has no duplicate elements. An element is either a member of a set or not. It cannot be in the set twice." and "{1, 2, 3} is the same as the set {1, 3, 2, 3, 1}" My question is, 1. Whether duplicates allowed in the set or not ? 2. Even if the duplicates are allowed, {1,2,3} and {1,1,2,2,3,3} are same or not ? Answered by Penny Nom and Harley Weston.
	Comparing flow rates of two pipes		2007-07-14
		From Kenneth: If two water pipes are 3 feet long, but one of them has a 1 foot diameter and the second has a 1 1/2 foot diameter, what simple mathematical method can be used to determine how much faster one pipe can drain water than the other pipe? Answered by Stephen La Rocque.
	Can't find circumference of an ellipse		2007-07-06
		From Michele: I need to figure the circumference of an oval and I know the height and width. Answered by Penny Nom.
	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.
	The area of part of a circle		2007-06-21
		From Sarah: Hi, I need help finding the area of a part of a circle that involves a chord. I need this answer/help very soon if at all possible. I have attached a drawing of what I am trying to solve. Thank you for your help! Sarah! Answered by Penny Nom.
	Finding the center of an ellipse		2007-06-20
		From Sima: find the center of the ellipse with the equation 3x^2 +4y^2+18x-32y-5=0 Answered by Penny Nom.
	What is the 100th term?		2007-06-15
		From George: I have the sequence 50,120,235,406,644 the 1st difference is 70,115,171,238 the 2nd difference is 45,56,67 the 3rd difference is 11,11 i used the a*n^3+b*n^2+c*n+d rule but the a turns out to be a decimal because 11/6 is 1.833333333 and so i cant find the formula for the 100th term term. Answered by Penny Nom.
	Percentage increase and decrease		2007-06-13
		From Anna: I just want to if the following formula is used for the computation of a PERCENTAGE DECREASE: Old Value - New Value/ Old Value x 100% My immediate superior is under the impression that the said formula works ONLY for the computation of a percentage INCREASE. He believes that the formula for a percentage DECREASE: Old Value - New Value/ NEW Value x 100% On this score, I want to know the correct formula for the computation of percentage decrease. Thank you so much. Answered by Penny Nom.
	Composition functions		2007-06-12
		From Gilligan: Find functions f and g so that f(g(x)) = H. (1) H(x) = (1 + x^2)^(3/2) (2) H(x) = int(x^2 + 1) I don't know where to start. Answered by Stephen La Rocque.
	A sequence of circles		2007-06-11
		From Ann: Please help with solving the following problem!!! A circle is inscribed in an equilateral triangle with a side of length 2. Three circles are drawn externally tangent to this circle and internally tangent to 2 sides of the triangle. 3 more circles are drawn externally tantgent to these circles and internally tangent to 2 sides of the triangle. if this process continued forever, what would be the sum of the areas of all the circle? the answer 1 parent came up with was Pie over 2, but we don't know how he did it. Can you please show the work or explain the answer to this problem? Thank you Ann p s my daughter is in 9th grade math. Answered by Steve La Rocque, Chris Fisher and Penny Nom.
	How many terms in this sequence?		2007-06-11
		From Jesse: How do I find how many terms are in the sequence? 51, 48, 45, ...., -75 Answered by Stephen La Rocque and Penny Nom.
	The intersection of two planes		2007-05-31
		From Sarim: How to find a intersection of two planes? Answered by Penny Nom.
	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.
	A point on a semicircle		2007-05-28
		From arun: a semi circle is drawn with ab as diameter from p a point on ab a line perpendicular to ab is drawn meeting circumference of semi circle at c, ac = 2cm, cd = 6cm find area of the semi circle? Answered by Penny Nom.
	The surface area of a fire hose		2007-05-26
		From Vanessa: Why do we need to find the surface area of a fire hose (cylinder). Answered by Stephen La Rocque.
	The circumference of an ellipse		2007-05-25
		From Graham: I have an ellipse that I need to find the circumference of. It is 40ft at its longest point and 25ft at its shortest Answered by Penny Nom.
	Normal distribution		2007-05-24
		From Paula: Consider a data set that is normally distributed. The mean of the data set is equal to 10,000. a.) Suppose that, for this data set, 10,625 has a "z-value" = 2.5. Solve for the standard deviation of the data set. b.) Solve for the "z-value" of 9,900. Answered by Penny Nom.
	Base seven		2007-05-19
		From Dan: A number X is converted to base 7 and becomes a four digit number. Its leftmost digit is removed and written again as the rightmost digit. The number thus obtained is twice X. Find the decimal representations of all such numbers X. Answered by Penny Nom.
	Parabolas in the real world		2007-05-18
		From Katherine: Hi, my name is Katherine, and my mean old math teacher just assigned us a test in which we have to write two examples of how parabolas are used in the real world, each one page single spaced, size 12!! I know you have already answered some questions like this, but I still don't understand the whole baseball thing, and any other way parabolas are used. And how I can write a whole page on it. But that's my problem, not yours, I just need help with a little explanation on how parabolas are actually used today. I know this might be kind of confusing for you, but imagine how it is for me!! Answered by Stephen La Rocque.
	Comparing the areas of various shapes		2007-05-16
		From Kathy: If the perimeters are the same, which has the greater area, a circle, a square, an ellipse, or an octagon? Answered by Stephen La Rocque.
	Maximizing the volume of a cone given the slant length		2007-05-14
		From Christina: A coffee filter for a new coffee maker is to be designed using a conical filter. The filter is to be made from a circle of radius 10cm with a sector cut from it such that the volume of coffee held in the filter is maximised. Determine the dimensions of the filter such that the volume is maximised. Answered by Stephen La Rocque and Kerstin Voigt.
	Finding the hypotenuse without Pythagorus		2007-05-11
		From Shelbie: How do i find the hypotenuse of a right traingle not using the pythagorean thereom if i have the measurements of the legs? Answered by Stephen La Rocque.
	Probability of H.I.V. tests		2007-05-07
		From Danielle: A medical test detects H.I.V. Among those who have H.I.V., the test will detect the disease with probability 0.95; among those who do NOT have H.I.V., the test will falsely claim that H.I.V. is present with probability 0.0125. Among those who take this test, 4% have H.I.V. The test is given to Lucille, and indicates that she has H.I.V. What is the probability that Lucille actually has H.I.V.? Answered by Stephen La Rocque.
	A point inside a circle		2007-05-04
		From edgemitter: There is a point inside a circle (but not in its center) where two perpendicular secants intersect, dividing the circle into four regions with different area. Calculate the area of the four regions Answered by Walter Whiteley.
	Hypotenuse		2007-05-03
		From ashley: how do you find the hypotenuse Answered by Penny Nom.
	3, 6, 12, 21, 33, 48, 66		2007-05-02
		From Siew: I need to find the nth term formula for the sequence : 3, 6, 12, 21, 33, 48, 66 Answered by Stephen La Rocque.
	Percentage change		2007-05-01
		From katie: i no many people have asked about this but im still unsure what is percentage change i have my ks3 tomoro so please reply asap thankz Answered by Penny Nom.
	The sum of two or more consecutive integers		2007-04-26
		From nana: some numbers can be written as the sum of two or more consecutive integers(we consider positive integers only) other number (eg. 4) cannot be express in this way. let us call a number which can be expressed in this way a SOALTCI( sum of at least two consecutive integers) a). list the first few SOALTCI and conjecture the general formula. b). Prove that any number of the given form(in your answer (a)) is a SOALTCI Answered by Penny Nom.
	A triangle problem		2007-04-23
		From Dimitri: In the triangle ABC, M is the midpoint of AB and N is the midpoint of AC. Prove that CM and BN cannot bisect. (I can prove it by contradiction if it is a scalene triangle, but i cant seem to prove it for isosceles) Answered by Chris Fisher.
	Two lines intersect at a right angle		2007-04-20
		From ellen: The line with the equation 3x + by = 6 intersects with the line 6y + ax = c at right angles at the point (4,6). Determine the values of a, b & c. Answered by Stephen La Rocque.
	The second derivative		2007-04-14
		From Gerry: In mathematical context,what do you understand by the term "Second Derivative" Answered by Penny Nom.
	Intersection of a line and a circle		2007-04-12
		From gaby: The sum of two numbers is 9. The sum of the squares of the two numbers is 41. Find the numbers. Answered by Steve La Rocque and Melanie Tyrer.
	Choosing 6 from a set of 12		2007-04-12
		From Darren: there are 12 numbers (1-2-3-4-5-6-7-8-9-10-11-12) how many times can i pick 6 different numbers? Answered by Stephen La Rocque.
	Where will volume 13 go?		2007-04-12
		From Shawn: A novice librarian shelved a twelve-volume set of encyclopedias in the following order from left to right. Volumes 8, 11, 5, 4, 9, 1, 7, 6, 10, 3, 12, and 2. Using her system, where will volume 13 go? Answered by Stephen La Rocque and Penny Nom.
	Pythagoras was right		2007-04-11
		From Vineet: in a right angle triangle, hypotenuse side is less than the sum of other two sides, how the square of hypotenuse is equal to the sum of squares of other two sides? Answered by Stephen La Rocque.
	What are the first 3 terms of this sequence		2007-04-10
		From kyrie: what are the first 3 terms of this sequence n-2 divided by n squared Answered by Stephen La Rocque.
	4,7,16,43,...		2007-04-04
		From claire: What is the explicit definition for the sequence 4,7,16,43,...? Answered by Stephen La Rocque and Penny Nom.
	What is the hypotenuse of a right traingle		2007-04-04
		From debbie: what is the hypotenuse of a right triangle with sides of 38 meters and 24.2 meters. Answered by Stephen La Rocque.
	A set of points in space		2007-04-04
		From Lenny: What is a set of points in space the same given distance from its center point called? Answered by Stephen La Rocque.
	Algebra		2007-04-03
		From Emily: 9,365 and 2,242 added to the difference between 255 and half of a number is 11,784. What is the number? Answered by Haley Ess.
	In what base does 25+25=51?		2007-04-03
		From Jenna: In what base does 25+25=51? Answered by Stephen La Rocque and Penny Nom.
	A geometric series		2007-04-03
		From jessica: If a geometric series includes 54-18+6-2 as its fifteenth through eighteenth terms, find the sum of the second through the fifth term, inclusive. Answered by Stephen La Rocque.
	Direct and inverse Variation		2007-04-03
		From liz: how do you tell if an equation varies Directly or Inversely? ex. x= 2y or xy+12=3 i know that if you have three numbers (x. y, z) that it varies jointly but how do you tell if it is Inverse or Direct? Thanks for the Help! -liz Answered by Stephen La Rocque.
	What does inverse graph represent?		2007-03-30
		From san: what does inverse graph represent? Answered by Penny Nom.
	Is the inverse of a function always a function?		2007-03-29
		From San: Is the inverse of a function always a function? Please justify. Thank You! 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.
	The angles in a right triangle		2007-03-28
		From Golaan: I need the to understand the formula for finding either of the acute angles of a right triangle given it's hieght length and base length. I want to find the degrees of either accute angle. So for this example I have a right triangle with a height of 410 meters and a base length of 1,700 meters. I don't understand cosine, sine, and tangent or the other ones at all. So if the solution includes those (which I believe it does) could b very verbose yet in a very elementary way? The purpose of ths is that I have to define the general incline angles (or grade) of various areas of terrain. I know the distance by map and also the the altitude at either endpoint. Answered by Penny Nom.
	The foci of an ellipse		2007-03-27
		From Brad: I am trying to figure out how to find the foci of an ellipse x^2/7 + y^2/16 = 1. Since 16 is the largest denominator I know the major axis is going to be the y axis. Do I now take 7-c^2=16. c^2=16-7, c^2=9, c=3. So is my foci (0,+-3). Answered by Penny Nom.
	An inheritance problem		2007-03-23
		From Carl: A father of 3 boys, who owns 17 horses dies. He leaves his first son 1/2 of the horses. The sons hate each other. The father leaves the second son 1/3 of the horses. They are ready to kill each other. He leaves his youngest son 1/6 of the horses. Without cutting the horses into pieces how do they split the horses? I heard this puzzle when I was 12 years old. 1968 The preacher rides up on his horse and said "If I give you my horse will you quit fighting ? They agree to stop fighting?" Why? Answered by Penny Nom.
	Two consecutive odd numbers		2007-03-19
		From Alicia: The sum of two consecutive odd numbers is divisible by 4. Can you make similar statements about the sum of three consecutive odd numbers and of four consecutive odd numbers? Generalize your findings. I tried : n= smallest odd number therefore the next = n, n+2 and the second =n+4 and the third = n+6 Now n+ n+2+n+4+n+6/4 Please help I am not sure of this I am just trying Answered by Penny Nom.
	Choosing numbers with no two consecutive		2007-03-15
		From Meghan: How many combinations are there of 3 numbers chosen from 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 but where no 2 of the 3 numbers are consecutive? Thank you! -Meghan Answered by Penny Nom.
	A truncated cone		2007-03-10
		From Russell: Hello, I have attempted to use two of your answers already given and had no real success. This young lady is making a cat food dispenser using a truncated cone. The top of the cone as a diameter of 5 inches with a height of 6 1/2 inches and diameter of 3 inches for the bottom. Could you please map out a solution for the both of us to understand? Thank you so much for your time and for this wonderful service. Russell Answered by Penny Nom.
	Seven digit account numbers		2007-03-09
		From Miranda: Account numbers for the Central Oil Company consist of seven digits. If the first digit cannot be 0, how many account numbers are possible? Thank you so much!!! Answered by Penny Nom.
	A circle is stretched horizontally by a factor of 2		2007-03-07
		From bob: I was wondering if you could double check my work? the question is as follows: The circle X^2+y^2-2x-3= 0 is stretched horizontally by a factor of 2 to obtain an ellipse what is the equation of this ellipse in general form? Answered by Penny Nom.
	Finding the vertical height of a roof		2007-03-05
		From Zainab: The question is: If the vertical height if a triangle is half the width of the base and the slant length is 6 metres, find the exact vertical height of this part of the roof. I'm actually confused about finding out the height of an equilateral triangle if you're only given the length or slant height. Please help! O.o Answered by Stephen La Rocque.
	Direct and inverse variation		2007-03-03
		From Rene: Hi I'm Rene, I'm stuck with some problems in direct and inverse variation. I know how to solve direct and inverse problems when only one variation is in a question at a time. EX: p varies inversely as the square root of q, and when p=12, q=36 find p when q=16 12*6 =p*4 72=4p 18=p But how would you solve a problem like..... If s varies directly as r and inversely as t, and s=10 when r=5 and t=3, for what value of t will s=3 when r=4 ? Answered by Penny Nom.
	The intersection of two lines		2007-02-28
		From Tamara: I was told to make a graph to help solve this question. I was given two equations. One was x-2y=3 and the other was 2x+y=-4. We have to change it to the equation of the line format. Then we graph the line and find the point where they meet. I've been trying to do that, but when i check the answer, It turns out wrong. It's meeting in the wrong spot. I need help please. Answered by Penny Nom.
	Find the nth term		2007-02-27
		From Dinky: My teacher has set us a project, but i am having trouble finding the nth term for this. the numbers are: 1, 2, 6, 24, 120 could you please help me? thank you dinky113 Answered by Stephen La Rocque and Penny Nom.
	Social security numbers		2007-02-27
		From Tish: Social Security numbers are in the form ###-##-####, where each symbol represents a number 0-9, how many are possible with this format? Will we ever run out of Social Security numbers? (This is one question with two parts, I saw some examples but I am still confused because if there are 1 million possibilities then how have we been able to issue out numbers to over 280 US citizens?) (For the second part a yes or no answer is sufficient) Answered by Penny Nom.
	Cutting the top off a circle		2007-02-25
		From Daniel: If a circle as a diameter of D I cut off a straight part at C from the top What is the formula to find the area of the left over part? Answered by Penny Nom.
	Arithmetic Series		2007-02-18
		From Krista: Question- The sum of the first 4 terms of an arithmetic series is -8 and the sum of the first 5 terms is 500. Determine the sum of the 3 terms. Answered by Stephen La Rocque.
	What is the index of the term '119' in the sequence 2, 5, 8, 11?		2007-02-16
		From joey: What is the index of the term '119' in the sequence 2, 5, 8, 11? Answered by Penny Nom.
	The nth term		2007-02-13
		From Sarah: I am having difficulty in finding the nth term for 7,49,343,2401. Could you please help me in finding the correct answer? Answered by Stephen La Rocque.
	The sum of a sequence		2007-02-11
		From joey: find the sum of the first 98 terms of the sequence 3, 5, 1, 3, 5, 1, 3, Answered by Penny Nom.
	Piecewise Functions		2007-02-09
		From Steph: h(x)={-2 if x<0 {x+1 if 0< x <10 {-1/2x+16 if x>10 PLEASE HELP Answered by Penny Nom.
	Find the next 3 terms of the sequence		2007-02-07
		From rose: find the next 3 terms of the sequence 2,3,9,23,48,87 Answered by Penny Nom.
	A triangle inscribed in a semicircle		2007-02-06
		From Benneth: Consider a triangle inscribed in a semicircle with a radius of R. What are th possible perimeters for the triagle? And the areas? Answered by Penny Nom.
	A 3-digit number in base 7 has its digits reversed when expressed in base 9.		2007-01-28
		From Ashley: A 3-digit number in base 7 has its digits reversed when expressed in base 9. Find this number. Answered by Penny Nom.
	The area of a ellipse		2007-01-25
		From Ranjit: I have a task in which i have to find the area of a ellipse. i find this difficult because i have only been provided with the perimeter, which is 1000m. Answered by Chris Fisher.
	Line segments on dot paper		2007-01-21
		From Khaori: The three line segments below are drawn on centimeter dot paper. a. Find the length of each segment to the nearest ten-thousandth of a centimeter. b. Could these line segments be arranged to form a triangle? If no, explain why or why not. If yes, answer this question: could they form a right triangle? Explain why or why not. Answered by Penny Nom.
	5,8,11,14,17		2007-01-18
		From Mairead: the sequence i was given was 5,8,11,14,17 what is the nth term and what is the 10th term ? Answered by Paul Betts.
	Points of intersection		2007-01-18
		From Mark: Find the points of intersection of the given pair of curves. 2x - 3y = -8 and 3x - 5y = -13 Answered by Steve La Rocque and Haley Ess.
	An octagonal bird house		2007-01-13
		From Soren: I'm in the process of building a birdhouse that is an octagon (based on previous questions, looks like that's a familiar tune). The essential elements are known, but I get stuck when trying to determine the angle for the cuts that would be made to the thickness of the wood so that they all fit together when assembled. Each octagonal section is 7 inches in width and the peak of the roof will be 2 inches higher than the sides. My sense is that the angle cuts that need to be made to the 'height' of each piece of wood. By height I mean the thinnest part of the wood that is neither the length nor the width to use colloquial terms. While it's clear that a slight angle is needed, it would seem that the angle would necessarily change as the distance from the top of any one side to the peak changes. Please advise if more clarification is needed. The 2 inches is random and can be changed if more convenient. Whew! Answered by Harley Weston.
	What is the percent of the decrease?		2007-01-10
		From Bill: if the value of xyz company stock drops from $25 per share to $21 per share, what is the percent of the decrease? Answered by Penny Nom.
	Three consecutive odd integers		2007-01-08
		From Emma: Find three consecutive odd integers such that the sum of the first and second is 27 less than 3 times the third. Answered by Stephen La Rocque.
	Twice the smaller of two consecutive integers is the larger increased by 5.		2007-01-08
		From Evan: Twice the smaller of two consecutive integers is the larger increased by 5. find the integers. Answered by Stephen La Rocque and Penny Nom.
	13.78g /11.3mL		2007-01-05
		From Judd: 13.78g /11.3mL Answered by Penny Nom.
	How do I determine the length of an ellipse if the width and area are known?		2007-01-04
		From Tom: How do I determine the length of an ellipse if the width and area are known? Answered by Steve La Rocque and Karen McIver.
	An octagonal birdhouse		2006-12-30
		From Verner: I am building a octagon birdhouse,what degree would I cut each side of each piece of wood to assemble the birdhouse? Answered by Penny Nom.
	Percentage increase		2006-12-21
		From Wang: The last week of a month a car dealership sold 12 cars. A new sales promotion came out the first week of the next month and the sold 19 cars that week. What was the percent increase in sales from the last week of the previous month compared to the first week of the next month? Answered by Penny Nom.
	Find the total distance the swing traveled before it stopped.		2006-12-17
		From Leah: Rebecca's little sister liked for her to push her in the swing at the park. The other day Rebecca pulled the swing back and let it go. She would have kept pushing, but she suddenly saw a friend at the other end of the park. The swing traveled a total distance of 10 feet before heading back the other way. Each swing afterwards was only 80% as long as the previous one. Find the total distance the swing traveled before it stopped. 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.
	The nth term		2006-12-15
		From Lisa: I have worked out that the nth term for 1, 4, 9, 16 is n squared and 3, 5, 7, 9 is 2n - 1, so what is the rule for the sequence 1x3, 4x5, 9x7, 16x9? Answered by Penny Nom.
	The nth term		2006-12-14
		From Hepzibah: what is the definition of nth term and n? Answered by Penny Nom.
	Base 5		2006-12-11
		From Shelley: how do you convert decimal numbers to a given base for example 2,875 to base five? Answered by Stephen La Rocque.
	Sectors of a circle		2006-11-30
		From Maithreyi : A circle of diameter 21m is divided into three sectors with central angles 60degree,120degree and 180degree. Find the area of each sector? Answered by Stephen La Rocque.
	Percentage increase		2006-11-29
		From Toya: I have some statistics from year to year based on drug seizures.(units= lbs) e.g. in 2005 123lbs seized in 2006 1518lbs seized. now i worked out the percentage increase as to be in the thousands which from looking at the figures is correct however i don't want to say 1000% increase. using another formula current- previous *100 I got 92%. what exactly does this 92% represent and how can i use this number when presenting my answers instead of using 1000 + % Answered by Stephen La Rocque and Penny Nom.
	An arithmetic series		2006-11-28
		From Jillian: Find the sum of 21 terms of an arithmetic series that has an eleventh term equal to 30. Answered by Penny Nom.
	A geometric sequence		2006-11-28
		From Jillian: Find x so that 2x, x + 5, x - 7 are consecutive terms of a geometric sequence. Answered by Stephen La Rocque.
	A problem involving logs		2006-11-26
		From Beth: any help would be appreciated on how to solve without using the change of base formula for logarithms in the solution and check of the solution!!! log256 (x) + log16 (x) + log4 (x) + log 2 (x) = 7/4 Answered by Stephen La Rocque and Penny Nom.
	Arithmetic with base -2		2006-11-26
		From Yuva: can we do arithmetic ,base -2. If yes, how and if not, why. Answered by Stephen La Rocque.
	The area of a semicircle		2006-11-25
		From Melinda: If the radius of a semi-circle is 9ft what is the area? Answered by Karen McIver and Penny Nom.
	An Easement		2006-11-21
		From Ms Porter: I need to acquire a 20 feet easement for a project and I need to know how many square feet are in a 20 feet easement? Answered by Penny Nom.
	The Fibonacci sequence		2006-11-21
		From Ross: Let f0 = 0; f1 = 1,... be the Fibonacci sequence where for all n greater than or equal to 2 fn = fn-1 + fn-2. Let Q = (1+square root of 5)/2. Show that for all positive n greater than or equal to 0, fn less than or equal to Q^(n-1). Answered by Penny Nom.
	Conic sections		2006-11-19
		From Joyce: My son has a project on conic sections. I need the following information on Parabola, Circle, ellipse,and hyperbola. He can't find the following information for each conic section: equations with explanations, four uses for each shape and Shape explanation. Answered by Penny Nom.
	On day 1 on which day will 96 students donate food?		2006-11-19
		From Veydee: during a canned food drive the number of students who donate food doubles each day. If three students donate food on day 1 on which day will 96 students donate food? we have to find the term rule for this pattern Answered by Penny Nom.
	Induction		2006-11-16
		From John: Find a formula for 1/(1x3)+1/(2x4)+1/(3x5)...+1/(n(n+2)) by examining the values of this expression for small values of n. Use mathematical induction to prove your result. Answered by Penny Nom.
	Sigma from 0 to infinity of (n^3 / 3^n)		2006-11-15
		From Cedric: I'm wondering how you would find if this series converges or diverges? Sigma from 0 to infinity of (n^3 / 3^n) Does the n^3 dominate, or does the 3^n dominate? What about higher powers like n^10 / 10 ^ n ? Which one would dominate then? Answered by Penny Nom.
	The empty set is a subset of every set		2006-11-14
		From Narayana: The empty set is a subset of every set Answered by Stephen La Rocque and Penny Nom.
	Some applications of conic sections		2006-11-13
		From Burt: how are circles, ellipses, and hyperbolas used in everyday life Answered by Penny Nom.
	Piecewise functions		2006-11-08
		From Kait: We discussed how to graph piecewise functions today and I'm very lost!! I'm sitting here staring at this problem that says: f(x){2x+1, if x <1 f(x){-x+4, if x is greater than or equal to 1. Answered by Penny Nom.
	1,4,9,16,25,36.....		2006-11-06
		From Teje: i cannot find the next number for this sequence 1,4,9,16,25,36..... could u help please Answered by Stephen La Rocque.
	The semester grade		2006-11-03
		From Caroline: Can you tell me how to calculate a grade based on a percentage formula where 15 assignments account for 40% of the grade and 3 tests account for 60% of the semester grade. Answered by Penny Nom.
	Kilowatts and Horsepower		2006-11-03
		From Michael: How many Kilowatts=1 Horsepower or Horsepower=1 Kilowatt? Answered by Stephen La Rocque.
	The sum of 2000 consecutive integers is 1000		2006-10-29
		From Matias: if the sum of 2000 consecutive integers is 1000, then the sum digits of the greatest of these 2000 integers is? Answered by Penny Nom.
	Three consecutive integers		2006-10-29
		From Jimmy: Basically i want to know how you prove that the product of any 3 consecutive integers is a multiple of 6 Answered by Stephen La Rocque.
	The real numbers with decimal representations consisting of all 1s.		2006-10-29
		From Ivessa: Determine if the following set is countable or uncountable : the real numbers with decimal representations consisting of all 1s. Answered by Steve La Rocque and Walter Whiteley.
	How many sequences are possible?		2006-10-28
		From Sam: A fair eight-faced die with faces numbered 1,2,3,4,5,6,7 and 8 is tossed six times and the sequence of numbers is recorded. How many sequences are possible? Answered by Penny Nom.
	Direct and Inverse variation		2006-10-27
		From Vishalinee: i'm not sure how to use the words direct variation and inverse variation to describe thre relationship between: a. speed and distance b.speed and time c. distance and time. and then i need to create equations using the descriptions. i am really messed up with direct and inverse variation. Answered by Karen McIver.
	Three consecutive odd numbers		2006-10-21
		From Pige: The sum of three consecutive odd numbers is 387. Find the numbers. Answered by Penny Nom.
	A trillion seconds?		2006-10-16
		From A student: How many years, days, hours, minutes, and seconds in a trillion seconds? Answered by Stephen La Rocque.
	Percentage increase		2006-10-15
		From Amanpreet: in yr 7, bill was 1.28 m tall, in yr 9 he was 1.67m tall. calculate his percentage increase in height Answered by Stephen La Rocque.
	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.
	Plotting percentage change		2006-10-11
		From Beckie: I have worked out a set of percentage differences which are all percentage decrease. Should i express them as a negative percentage as -20%? I also need to plot them on a graph and am not sure whether to just use the percentage difference as it is, in which case i get a positive gradient, or include a negative axis and plot them in this way, in which case i would get a negative gradient. I think the slope of the curve will be the same either way so it might not matter! Answered by Penny.
	One-quarter of all 3-subsets of the integers 1,2,3....,m contain the integer 5		2006-10-09
		From Hina: If one-quarter of all 3-subsets of the integers 1,2,3....,m contain the integer 5, determine the value of m. Answered by Steve La Rocque and Claude Tardif.
	The area of an oval		2006-10-08
		From Bruce: area of an oval: 60" x 120" Answered by Stephen La Rocque.
	How many line segments are necessary?		2006-10-04
		From Varun: If you place 35 points on a piece of paper so that no three are collinear, how many line segments are necessary to connect each point to all the others? Answered by Stephen La Rocque.
	A number pattern		2006-10-02
		From Tim: The patterns that went in 2s, 4s and 5s we got, but we are stuck on the pattern that doubles. We can't come up with the rule or equation that solves it. With the first number being the term number and the second being the term, this is the pattern: 1-1 2-2 3-4 4-8 5-16 6-32 7-64 100-128 What is the rule for this? Answered by Stephen La Rocque and Penny Nom.
	The hypotenuse		2006-10-02
		From Ashley: How do you find the hypotenuse of a right triangle? I don't understand how to find c. Answered by Stephen La Rocque.
	The focus of a parabola		2006-10-01
		From Lily: I have a mathematical assignment which includes applications of parabolas, hyperbolas and ellipses in the real world. I have been searching the internet and now I am ware that most of the applications of parabolas have a connection with what people call "the focus". However, I do not think I clearly understand what "the focus" of a parabola is. Would you please explain it to me? Answered by Penny Nom.
	2 5 11 17 23 31 ?		2006-09-28
		From Bernice: How do you determine the next number in the following sequence: 2 5 11 17 23 31 ? Answered by Penny Nom.
	Piecewise functions		2006-09-24
		From Claudia: hi! i was just looking at a question by someone else about piecewise functions, but i still don't get it. my problem is g(x){x+2 if x <-2} g(x){2x - 1 if x> or = -2} Answered by Penny Nom.
	Find the nth term		2006-09-13
		From Shakira: my question is - Find an expression for the nth term of each sequence. a. 6,15, 28, 45, 66 b, 1/5, 3/8, 5/13, 7/20, 6/29 - these are fractions Answered by Penny Nom.
	-5, 3, -2, 1, -1, 0, __, __		2006-09-12
		From Sherrie: next two terms in the sequence: -5, 3, -2, 1, -1, 0, __, __ Answered by Stephen La Rocque.
	Brackets and more brackets		2006-08-29
		From Michelle: Feeling stupid asking but it's been awhile ... {{{2}}} ...what is this really saying ....are the outer brackets = null? Answered by Stephen La Rocque.
	Points of intersection		2006-08-20
		From Gianella: Find the points of intersection by solving this problem analytically. y= x cubed y= x Answered by Stephen La Rocque.
	Find the points of intersection		2006-08-18
		From Ingrid: The question says find the points of intersection of the graphs of the equation, and check your results analytically. x squared + y squared=25 2x+ y=10 Answered by Stephen La Rocque.
	A concrete semicircle		2006-08-15
		From John: I have to figure out how many yards of concrete I need for a semicircle. I have a radius of 21 feet and the concrete is 4" thick. I took 3.14 x (21)^2 then divided by 40 to get how many yards of concrete but that doesn't seem right. Answered by Penny Nom.
	Marking out a circle		2006-06-28
		From Peter: given a straight line. how do i work out the off sets ( at right angles) at several intermediate points. to set out a 5.0m arc that has a 18.0m radius. Answered by Stephen La Rocque and Penny Nom.
	The area of a house		2006-06-28
		From Michael: I would like to know how to measure the area of a house? Answered by Penny Nom.
	The area of a sector and a triangle		2006-06-23
		From Howard: I thought of the following problem which is similar but much simpler than the tethered goat problem: What is the angle(it is more illustrative in degrees)of arc of a unit circle so that the area between the chord it subtends and the arc length is equal to the area of the triangle with opposite side the subtended chord. Answered by Stephen La Rocque and Penny Nom.
	As close to 841 as possible		2006-06-21
		From Alan: using these numbers by either add subtract division multiply come up with the answer as close to 841 100 25 10 7 6 3 Answered by Paul Betts.
	13 57 91 11 31 51 ??		2006-06-15
		From Chastity: im trying to determine the missing number in the sequence 13 57 91 11 31 51 ?? Answered by Claude Tardif, Steve La Rocque and Natasha Glydon.
	The perimeter of a pool		2006-06-05
		From Troy: How many Linear feet would a pool be if the pool was 18 by 38 foot oval Answered by Penny Nom.
	What is the value of csc (-2pi/3)?		2006-06-04
		From Kishor: What is the value of csc (-2pi/3)? Answered by Stephen La Rocque.
	What is the sum of the first 100 whole numbers?		2006-05-31
		From Jo: what is the sum of the first 100 whole numbers? Answered by Natasha Glydon, Paul Betts and Penny Nom.
	The area of part of a circle		2006-05-29
		From Larry: need to find area of a circle between a given line (cord) to the circumference of the circle (see attachment). I often review blue prints of homes and many times have to know the area the home. Answered by Stephen La Rocque and Penny Nom.
	The nth term of a sequence		2006-05-24
		From A student: please could you give me a formula for the following numbers for my teacher 3 8 15 24 35 Answered by Chris Fisher.
	Three purses		2006-05-22
		From Marcee: If you take $20 from the first and put it into the second of three purses, the second would then contain 4 times as much as remains in the first. If $60 of what is now in the second is put into the third, the third will contain twice what is in the first and second together. Now, if $40 be removed from the third and put into the first, there will be half as much as in the third. What did each purse originally hold? Answered by Penny Nom.
	We are 2 pairs of consecutive 2 digit numbers ...		2006-05-13
		From A perent: We are 2 pairs of consecutive 2 digit numbers that are factors of the number of feet in a mile. Who are we? Answered by Claude Tardif.
	A person is given 3 true or false questions		2006-05-11
		From Larry: A person is given 3 true or false questions. They have no idea of the answers. What is the probability of the person getting them all correct? Could you show me a tree for this. Answered by Penny Nom.
	Small pipes and large pipes		2006-05-09
		From geece: A large fresh water reservoir has two types of drainage system. Small pipes and large pipes. 6 large pipes, on their own, can drain the reservoir in 12 hours. 3 large pipes and 9 small pipes, at the same time, can drain the reservoir in 8 hours. How long will 5 small pipes, on their own, take to drain the reservoir? Answered by Penny Nom.
	Adding consecutive numbers		2006-04-26
		From Lisa: When I have a total that is the sum of consecutive numbers, how do I figure out what the numbers are? Answered by Stephen La Rocque.
	Geometric sequence and basic functions (graphs)		2006-04-20
		From Marlene: Which of the basic functions is related to the geometric sequence: Linear, Quadratic, Rational, or Exponential? Can you give me an example of how it would be used in normal life? Answered by Stephen La Rocque.
	Arithmetic and Geometric Sequences		2006-04-19
		From Skye: If the 1st, 4th, and 8th terms of an arithmetic sequence are consecutive terms in a geometric sequence, find the common ratio of the geometric sequence. Answered by Stephen La Rocque.
	Reverse percentage		2006-04-19
		From Mike: How would I calculate a reverse percentage? Let me give you an example. I have two values that calculate to a success rate of 93.32. Total=1546051 Failures=103302. (1546051-103302)/1546051=93.32% success. Now how much would I need to increase the total value to get the success up to 95%? Answered by Stephen La Rocque.
	Overlapping area of two circles		2006-04-15
		From Jade: Given two identical circles where the radius (6 units) is the distance between the centers, what is the area of the overlapping region? Answered by Stephen La Rocque.
	What is the cost price?		2006-04-14
		From Purushotham: If the selling price is 120 and the profit is 20%, what is the cost price? Answered by Stephen La Rocque.
	The product of successive terms in sequences		2006-04-13
		From Forrest: 1) Find three successive terms in an arithmetic sequence such that their sum is 24 and their product is 440 2) Find three successive terms in a geometric sequence such that their sum is 21 and their product is 216 Answered by Penny Nom.
	Finding the inverse of a function		2006-04-12
		From Sam: If g(x) = 2x+3/5 then how do I find the inverse? Answered by Walter Whiteley.
	Arithmetic Sums		2006-04-12
		From Angel: (a) In a particular arithmetic sequence, u6 = 344.5 and u20 = 88.3. Find S28. (b) In a particular arithmetic series, S10 = 495 and S15 = 1005. Express S15 in sigma notation. Answered by Stephen La Rocque.
	Sum of a Geometric Sequence		2006-04-11
		From Andre: In a particular geometric sequence, U3=-3.6 and U10=12.9. Find S16 and S17. Answered by Stephen La Rocque.
	A plant increases its height by 1/2 the first day,...		2006-03-30
		From Andy: A plant increases its height by 1/2 the first day, 1/3 the second day, 1/4 the third day and so on. How many days did it take to grow to 100 times its height? Answered by Stephen La Rocque.
	Can an equilateral triangle have an obtuse angle?		2006-03-26
		From Chris: Can an equilateral triangle have an obtuse angle? I'm thinking not, because all sides must be equal, but does that also imply that all angles are equal? Answered by Stephen La Rocque.
	The cartesian product of a countably infinite collection of countably infinite sets		2006-03-25
		From Geetha: Is the cartesian product of a countably infinite collection of countably infinite sets countable infinite? Answered by Penny Nom.
	How much fabric do I need?		2006-03-25
		From Michelle: I AM DECORATING A STAGE FOR A BOARD OF DIRECTORS MEETING AND I NEED TO BUY FABRIC AND I DON’T WANT TO WASTE $$ BY BUYING TOO MUCH FABRIC OR NOT ENOUGH FABRIC. THE AREA THAT I’M NEEDING MATERIAL FOR IS, 12ft HIGH BY 34ft WIDE. THE FABRIC COMES IN ROLLS OF 60” (inches) x 100 yards. SO HOW MUCH FABRIC SHOULD I NEED TO FOR THE AREA I’M WANTING TO COVER? Answered by Stephen La Rocque and Penny Nom.
	Piecewise functions		2006-03-21
		From Kris: First Problem: Southeast Electric charges .09 cents per kilowatt-hour for the first 200 kWh.The company charges .11 cents per kilowatt-hour for all electrical usage in excess of 200 kWh. How many kilowatt-hours were used if a monthly electric bill was $57.06? The answer I came up with is 360, is that right? and also how do I set it up in an equation form? Second Problem: A construction worker earned $17 per hour for the first 40 hr of work and $25.50 per hour for work in excess of 40 hr. One week she earned $896.75. How much overtime did she work? I came up with 8.5 hrs over-time worked. Again I don't know how to set up the equation to come up with the answer. I need some pointers on how to figure out story problems! If you have any suggestions that would help me out I would be very grateful. Answered by Penny Nom.
	How far from Earth is Neptune?		2006-03-21
		From Scott: A laser beam travelling at the speed of light bounces off the planet Neptune and returns to Earth in 29 960.72 s. The speed of light is 299 792.5 km/s. How far from Earth is Neptune? Answered by Penny.
	The square footage of an area in my backyard		2006-03-17
		From Kim: I need to find out how to calculate the square footage of an area in my backyard that is in the shape of a "slice of pie". There are two sides that are straight lines that come together at the top to form a point, and then at the bottom is a curved line that joins the two other lines together. I need to figure out how to calculate the square footage that is inside the area. Answered by Penny Nom.
	Divide the product of three consecutive positive integers by their mean		2006-03-12
		From Sandy: When I divided the product of three consecutive positive integers by their mean, I got 99. What is the smallest of the three numbers? Answered by Stephen La Rocque.
	Two consecutive even integers		2006-03-11
		From Cheryl: Find two consecutive even integers that have a sum of 450 Answered by Stephen La Rocque.
	How many of these cubes have no wax of them?		2006-03-10
		From Iban: cube cheese is 4cm wide, 4cm long, 4cm high. three faces of the cube meet in the corner covers thin layers of wax. The cheese is then cut two, then cut 64 small cubes, which is the length 1cm. How many of these cubes have no wax of them? Answered by Stephen La Rocque.
	8,_,4,9,1,_,10,3,_,0		2006-03-08
		From Rachel: I cant figure out this sequence if someone could help me 8,_,4,9,1,_,10,3,_,0 Answered by Claude Tardif.
	A nine digit number		2006-03-06
		From Ryan: What is the total number of possible combinations of a nine digit number (ie., social security number) including repeating numbers? Answered by Stephen La Rocque and Penny Nom.
	2,4,9,6,5,6,____,____,____,...		2006-03-06
		From Mike: I am having problems figuring out the following sequence: 2,4,9,6,5,6,____,____,____,... We were able to guess that the pattern simply started to reverse itself, but I was wondering if there were other possibilities. Answered by Claude Tardif.
	The nth term		2006-03-05
		From Umar: my question is what is the nth term for a house of cards 4 stories high if you use the following numbers: 2 7 15 26 Answered by Penny Nom.
	A 5900% increase		2006-03-03
		From Pat: I want to find out the % of production increase from 250 dolls a month to 15,000 dolls a month. i think it is 5900% but that seems too high. Answered by Penny Nom.
	A cone with an oval as base		2006-03-01
		From Richard: I am trying to find the volume of a cone that is not round but oval. Answered by Penn Nom.
	Luke and Slim have only one horse.		2006-02-26
		From Emily: Luke and Slim have only one horse. Luke rides for the agreed on distance and then ties up the horse for Slim, who has been walking. Meanwhile, Luke walks on ahead. They alternate walking and riding. If they walk 4 miles per hour, and ride 12 miles per hour, what part of the time is the horse resting? Answered by Penny Nom.
	The nth term of a sequence		2006-02-21
		From Mike: I'm having trouble finding the nth term in an equation, can you help me? Answered by Stephen La Rocque.
	Percent gain		2006-02-14
		From Bill: If a stock is bought at $3.50 and sold at $5.80, what percent was the gain? Answered by Penny Nom.
	Find two consecutive integers whose product is 182		2006-02-09
		From Anthony: Find two consecutive integers whose product is 182 Answered by Steve La Rocque.
	The intersection of a line and a circle		2006-02-02
		From Bernice: if i am given an equation of a circle and 2 points in a line how do i know if the line intersects the circle and how do i determine the points of intersection Answered by Chris Fisher.
	Arithmetic progressions		2006-01-31
		From A student: 1)the sum to n terms of a particular series is given by Sn=17n-3n2 a)find an expression for the n term of the series b)show that the series is an arithmetic progression 2)a particular arithmetic progression has a positive common difference and is such that for any three adjacent terms ,three times the sum of their squares exceeds the square of their sum is 375.Find the common difference Answered by Penny Nom.
	An array problem		2006-01-31
		From Cynthia: Write a number sentence for this array........ It's a rectangle box 3 down and 4 wide. Answered by Penny Nom.
	Percentage increase in sound intensity		2006-01-29
		From David: I am doing some emotion response mapping. Being a composer I know how to push the heart beat tempo by a % increase of BPM in my music. I want to know how to calculate an increase in intensity of sound. Now I have 60 decibels. I want an increase of intensity by a factor n% with out going over 156 decibels. Answered by Penny Nom.
	how can i find the height of a triangle if i have the base and the hypotenuse		2006-01-27
		From Kelsey: how can i find the height of a triangle if i have the base and the hypotenuse Answered by Penny Nom.
	Sectors and arcs		2006-01-25
		From Wael: How is the area of an arc (alpha*pi*r squared/360) derived? How is the length of an arc (alpha*pi*r/180) derived? Answered by Penny Nom.
	Finding the nth term in fractions		2006-01-23
		From Zarina: Each term in this sequence is made by increasing the numerator by 1 and the denominator by 3. here are the first five terms: 1/4, 2/7, 3/10, 4/13, 5/16, ... (a) write an expression for the nth term: Answered by Penny Nom.
	A sequence of circles and tangents		2006-01-16
		From Paul: Consider a circle whose center is (2,2) and whose radius is 1, and the straight line that goes through the origin and that is tangent to this circle so that the intersection between them is as shown in the attached picture. With this new point we make a new circle whose radius is half of the first one, and we calculate the corresponding intersection point with the same suppositions as in the first case. We repeat the process to the infinite. Find the distance between the center of the circle in the infinite and the origin (point (0,0)). Answered by Chris Fisher.
	Percentage change when you start from zero		2006-01-02
		From Joseph: I am not sure if my meaning for calculation for a percent change (C-P/P)x100) is correct. In this case, C=10, P=0, does this mean 100 percent increase from previous period? Answered by Harley Weston.
	The area of a sector of a circle		2006-01-02
		From Natashia: How do you find the area of a shaded sector of a circle? Answered by Penny Nom.
	Joey had 8 drinking glasses, all of different sizes.		2005-12-29
		From Danielle: Joey had 8 drinking glasses, all of different sizes. he has lined them up from smallest to largest and numbered them #1 (smallest) to #8 (largest). he knows that glass #4 holds 10 ounces and that glass #7 holds a pint, or 16 ounces. Now he wants to figure out how much all the others hold! He experiments by filling up different glasses with water and pouring the water back and forth into other glasses. Her are his results: Answered by Penny Nom.
	Percent change		2005-12-17
		From Marie: What is the percentage change when 1500 becomes 2000? Answered by Penny Nom.
	Percentage increase		2005-12-15
		From Luiz: I would like to know how much net income in % we have increased from 2005 to a 2006(projection). 2005 Net Income Actual: $1,599,887 2006 Net Income Budgeted: $2,067,339 Answered by Penny Nom.
	Find the nth term		2005-12-14
		From Kevin: How do i find the nth term of 1 4 9 16 25 36 Answered by Penny Nom.
	The stair problem		2005-12-06
		From Arnold: My daughter had me help her with some of her college math problems that require finding the pattern. The problem was the stair problem where you can climb either 1 step or 2 steps at a time. How many combinations are there to get to the 10th step. I found the data set that solves the answer to the question, but is there an equation that expresses the answer in terms of n? 1 2 3 4 5 6 7 8 9 10 stair number 1 2 3 5 8 13 21 34 55 89 number of possible combinations Answered by Harley Weston.
	An Arithmetic sequence		2005-12-01
		From Aana: The first term in an arihmetic series is 25 and the 3rd term is 19. Find the number of terms in the series if its is 82. Here's what I did to find d a+2d=19; 25+2d= 19 ;19-25=2d d=-6/2=-3 This is where I'm stuck. Can you please provide me with some guidance. Answered by Penny Nom.
	The sum of n consecutive integers		2005-11-27
		From Craig: If 875 is expressed as the sum of n consecutive integers (n > 1), then the number of possible values of n is? Possible Answers: A) 15 B) 8 C) 7 D) 16 E) 4 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.
	How many passengers boarded the plane in Phoenix?		2005-11-03
		From Vish: Passengers boarded a plane in Phoenix. In Dallas 1/2 of the passengers got off and 4/5 of the original number got on. In Memphis 3/4 of the passengers got off and twice the number of remaining passengers got on. In Chicago 2/3 of the passengers got off the plane leaving 39 passengers. How many passengers originally boarded the plane in Phoenix? Answered by Penny Nom.
	A tangent to a parabola		2005-11-02
		From A student: Find the point on the curve y=x2 where the tangent to the curve is parallel to the secant line connecting (-1,1) and (2,4) Answered by Penny Nom.
	2, 6, 12, 20, 30, ...		2005-11-01
		From Rebecca: I have a sequence of I have a sequence of 2, 6, 12, 20, 30, and have no idea how to figure out the nth term please help! Answered by Claude Tardif.
	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.
	Calculer la clé		2005-09-29
		From Un eleve: Chaque individu a un numéro INSEE de 13 chiffres auquels est adjointe une clé de deux chiffres. voici comment est calculée cette clé : Answered by Claude Tardif.
	Open dots and closed dots		2005-09-29
		From Cynthia: When graphing the solutions of an inequality, what is the difference between an open dot and a closed dot? Answered by Penny.
	Find the next 5 terms		2005-09-24
		From Grant: n+7, 2n-0.5, 4n. Find the next 5 terms of each one and explain the sequence in words Answered by Penny Nom.
	Converting from base ten to base five		2005-09-21
		From Julie: My sister is home schooled and we are trying to convert from base 10 to base 5. We are trying to teach and we have never had this in school. If we could have some examples of some problems and how to do them we would appreciate this. Answered by Penny Nom.
	Percentage increase		2005-09-19
		From Dory: Last year sales was 120,000 $ and this year sales is 280,000 $, there was an increase in sales. what I would like to know is the percentage increase between the years with the formula. Answered by Penny Nom.
	A 3-dimensional pie shape		2005-09-17
		From Bill: Your site appeared in my search for the name of a 3-dimensional pie shape. 2-d would be a sector of a circle. As it it curved, I don't believe it is in a the polyhedra family. Can you help me find the mathematical term for it? Answered by Chris Fisher.
	Find the first five terms of this sequence?		2005-09-17
		From Jade: my homework says can you find the first five terms of this sequence? 5n-6 i can`t figure it out. Answered by Penny Nom.
	Elliptic trigonometry		2005-09-15
		From Krystal: I'm currently searching for a science project topic and i have the idea of deriving elliptic trigonometry analogous to circular trigonometry. My questions are: Is this project "possible" to do? Answered by Chris Fisher and Harley Weston.
	A piecewise function		2005-09-15
		From Duncan: A child is assigned to your care and she has a headache. The parent has authorized the administration of Children's Tylenol. Read a box of Children's Tylenol (or any other similar drug) and find the directions for administration. Note the child's weight and the corresponding dosage. (Be sure the drug you choose has a minimum of 4 weight intervals.) Answered by Penny Nom.
	Finding the nth term		2005-09-12
		From Paul: Hi , Im having a problem helping my daughter to find the Nth Term in the following sequences. 1/3 1/2 3/5 2/3 and 1 3 6 10 Answered by Penny Nom.
	The sum of a series		2005-08-31
		From Aamod: Find the sum of the given series till n terms: (14\1*3) + (24\3*5) + (34\5*7)............... till n terms Answered by Chri Fisher.
	1,4,9,1,6,2,5,3,6,4,9,6,4,8,1		2005-08-30
		From Liz: Find the next four numbers to the sequence 1,4,9,1,6,2,5,3,6,4,9,6,4,8,1,___,___,___,___. Answered by Penny Nom.
	cos x * cos 2x * cos 4x * cos 8x		2005-08-29
		From Leandro: A = cos x * cos 2x * cos 4x * cos 8x What's the value of log A at base 2? Answered by Chris Fisher and Penny Nom.
	y = log(x) + x. Solve for x.		2005-08-26
		From Alain: I have the following equation: y = ln(x) + x How do I solve for x? Answered by Penny Nom.
	Is this percentage change or percentage increase?		2005-08-15
		From Betty: When calculating a percentage, if the formula is A(new) - B(old)/A(new) Is this percentage change or percentage increase? Answered by Penny Nom.
	The Maclaurin series generated by f(x)=x^ cosx + 1		2005-08-10
		From Latto: f(x)=x3·cosx + 1. but when I take the derivatives, I couldn't see a pattern. Can you help? Answered by Penny Nom.
	The equation of an ellipse		2005-07-17
		From Allan: I working on a problem that asks me to give the equation of an ellipse when only the location of the directrix and the length of the latus rectum are given. No other points on the ellipse are given. Again, the only "givens" are: Length of latus rectum = 12 Location of directrix is x = 16 If I could determine the eccentricity, I could proceed from there by taking the ratio of the distance from a focus to the latus rectum point to the distance of the point from the directrix, but I lack the x coordinate of c. I've searched the text, and feel I've "missed something" somewhere! I note that the latus rectum segment is unique in one respect in that it is parallel to the directrix, where any other line segment on the ellipse to the focus would not be. Please indicate where I'm going wrong. Answered by Chris Fisher.
	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.
	Percent change		2005-07-01
		From Betty: Can you tell me the difference between Percentage Change, Percentage Increase, Percentage Difference and please give an example of each, I am very visual. Answered by Penny Nom.
	A geometric sequence		2005-06-21
		From A student: The first three terms of a geometric series are 3(q+5), 3(q+3), (q+7) respectively. Calulate the value of q. Answered by Penny Nom.
	The circumference of an oval pool		2005-05-18
		From John: I have an oval pool of which I am trying to find the circumference. it is 38 feet long and 19 feet wide Answered by Penny Nom.
	Angle of incline		2005-05-15
		From Kyle: What is the degree of incline of a 12 foot plank that goes from 10.5 inches on one end to zero inches on the other? Answered by Penny Nom.
	Adding consecutive integers		2005-05-13
		From Yas: i need some help with my work which is to investigating sums of consecutive numbers for example: 15= 4+5+6 and 15=1+2+3+4+5 Answered by Penny Nom.
	A 5% increase		2005-04-27
		From Debra: How can I determine the increased percentage of a dollar amount? I.e.: One dollar amount is $202 and another is $150, how can I determine the 5% increase from last year on the $202 dollar amount? Answered by Claude Tardif.
	The least integer of a set of consecutive integers		2005-04-19
		From Lucia: The least integer of a set of consecutive integers is -25. If the sum of these integers is 26, how many integers are in the set? Answered by Penny Nom.
	Percentage increase		2005-04-19
		From Tom: What is the percentage increase from (negative -$9262.00) to (positive $3840.00)? 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.
	Two overlapping circles		2005-03-20
		From Safi: I have a problem to calculate the area of two overlapping circles because two circles are overlap then how i calculate the overlap area to subtract from the area of both circle. Answered by Penny Nom.
	Dimensions of a roof		2005-03-18
		From A roofer?: A right triangle (roof of a house) has a base of 7 feet and a 22 degree angle. What is the height of the roof and what is the hypothenus of the triangle. Answered by Penny Nom.
	Biodiesel		2005-03-08
		From William: My son is doing an demonstration for science class about how to make biodiesel. we are having problems with the conversion. for instance we think there are approx 190 liters in 50 gallons. Is this correct? Also if you needed 3.5 grams of lye per liter, would that be 662g of lye. Answered by Penny Nom.
	Spraying roses		2005-03-03
		From A student: A litre and a half of water has 0.045 grams of herbicide added for spraying roses. How many grams of herbicide per litre is this? Answered by Penny Nom.
	Reverse pecentage		2005-03-01
		From Nathan: Question for you. If I have spent $10.00, what is the mathamatical equation to figure out what the G.S.T (7%) was? Also if I were to spend $80.00 on a hotel, and I would like to know how much G.S.T (7%) and how much provincial tax (6%) I spent how would I go about this. Answered by Penny Nom.
	A countably infinite collection of countably infinite sets		2005-02-26
		From Feroz: Suppose a set can be divided into a countably infinite number of countably infinite sets.Then can the original set be considered as a countably infinite set? Answered by Penny Nom.
	Each interior angle of a particular polygon is an obtuse angle...		2005-02-22
		From Victoria: Each interior angle of a particular polygon is an obtuse angle which is a whole number of degrees. What is the greatest number of sides the polygon could have? Answered by Walter Whiteley.
	arcsech x		2005-02-10
		From Monica: Prove that arcsech x = ln[(1 + (1-x2)(1/2)) / x ] Answered by Penny Nom.
	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.
	A line segment connecting two vertices of a polygon		2005-02-02
		From James: What is a line segment (not a side) connecting two vertices of a polygon called? Answered by Penny Nom.
	Sum to n terms of the series i.(2^(n-i))		2005-01-28
		From Satya: Sum to n terms of the series i.(2n-i) Answered by Penny Nom.
	Quadratics		2005-01-05
		From Usman: Hi, in my Grade 11 Functions math class we have been assigned the task of finding jobs and careers related to quadratics, I have done many searches but have been unsuccessful, then I saw your website and e-mailed. I also have to use an example of a math problem that the job uses, then solve it, this will all compile on bristol board for a presentation. I would greatly appreciate it if you could send me some links and references of sources that refer to this subject. Answered by Harley Weston.
	An elliptical table		2005-01-03
		From Roger: Want to make an elliptical table, say the long (major) axis is 4 feet, and the short (minor) axis is 3 feet. I can construct this figure, but I'm trying to figure out what the exact dimension of a rectangle within this ellipse will be if I make the table a drop leaf type where the drop dimensions are equal for each end of both the long and short axes. Intuitively, it looks like there is one and only one solution. 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.
	An arithmetic progression		2004-12-24
		From A student: the 4th and 5th term of an arithmetic progration 47 and 52 respactively find a)d b)a1 c)a50 Answered by Penny Nom.
	Irrigation and a sector of a circle		2004-12-23
		From Chuck: A friend of mine is a farmer and uses Pivots to irrigate portions of his land. The crop rows are in straight lines that all form chords of a large circle. The intent is to determine area between any two "boundary" rows expressed in acres. Answered by Harley Weston.
	The gradiant of a hill is 9%		2004-12-18
		From Jim: The gradiant of a hill is 9%. What angle is created by the run/rise of the hill and 0 degrees? Answered by Penny Nom.
	Two intersecting lines		2004-12-18
		From James: Imagine a vertical line 1.107' tall. Leaving the top of this line, sloping down to the right at a 4:1, at what horizontal distance will the line strike a second line, which leaves the the bottom of the vertical line sloping down to the right at a rate of .02 ft/ft (or 2%)? There is a fairly easy solution to this, but I have lost my notes! Answered by Harley Weston.
	A sequence		2004-12-11
		From Amanda: Find the nth term of the following sequence 4, 10, 28, 82 Answered by Penny Nom.
	Geometric sequence		2004-12-04
		From Lesa: Find a formula for the geometric sequence: (√3 - √2), (4 - √6), (6√3 - 2√2), … Answered by Penny Nom.
	Cost before the markup		2004-11-23
		From Norman: the sum of eg $130 includes the markup of 30%. However I need to calculate the percentage to apply to the $130 to assess the cost ie $100. Answered by Penny Nom.
	Proof by induction		2004-11-20
		From Vic: Problem: Find the first 4 terms and the nth term of the infinite sequence defined recursively as follows: a(1) = 3 and a(k+1) = 2a(k) for k -> 1. Note: Quantities in brackets are subscripts -> means 'equal to or greater than'. Using the recursive formula, the first 4 terms are; a(1) = 3, a(2) = 6, a(3) = 12, a(4) = 24 The nth term a(n) = 2n-1 x 3 (equation 1) Equation 1 must be proven using mathematical induction. This is where I am having a problem. Answered by Penny Nom.
	A sequence		2004-11-19
		From Liucy: Find the Nth term: 10 40 90 160 250 Answered by Penny Nom.
	A 40% reduction		2004-11-10
		From Cathy: I'm having trouble figuring out how to figure a percentage??? it's easy to find what 40% of any given number is, but how would i accurately figure out what is the final number is when i know the number after the 40% has been removed? when i add 40% to this number it obviously is lower than it should be. the best i could figure is; x=?-40% ---------------> x-?=-40% i'm all confused???? Answered by Penny Nom.
	The points of intersection of two graphs		2004-11-05
		From Benjamin: How do I find the points of intersection of the two functions: 1) y = 2 - e-x 2) y = 1 + x2 Answered by Harley Weston.
	A 40% increase in garage space		2004-10-20
		From Dianna: A bus company recently expanded and no longer has enough room in its garage for all of its buses. Twelve of the buses have to be stored outside. If the company decides to increase their garage space by 40%, this will give them enough room for all of their current buses, plus enough room to store another twelve in the future. How many buses does the company own? Answered by Penny Nom.
	The third derivative		2004-10-15
		From Holly: Why would you ever take the third derivative? Answered by Harley Weston.
	Direct and inverse variation		2004-10-05
		From Abraham: Given that y varies inversely as x and x varies directly as z.If z is doubled then y is halved.Why is that true.Please explain.I'm having trouble understanding the different types of variation Answered by Penny Nom.
	1,3,6,11,18,29,__		2004-09-21
		From Guillermo: How do you get to the answer of this sequence 1,3,6,11,18,29,__ Answered by Claude Tardif.
	f(x) = x-4 if x<2		2004-09-21
		From Dani: Hi, my name is Dani. I'm in tenth grade Algebra 2, and I'm learning about a lot of different kinds of functions, and I can't quite seem to understand how every part of the piecewise function works. I understand most of it, I think, but I've been looking at an example in my math book, and I'm not sure how they got the answer they did. The part I don't understand reads: "Graph f(x) = x-4 if x<2" and "Identify the domain and range." The picture in the book shows an open circle at (2,-2), with an arrow going down and to the left with the slope being one. How did they get the open circle to be at (2,-2), and why does the arrow point where it does? Answered by Penny Nom.
	B={A,{A}}		2004-09-20
		From Muhammad: Let A be a set and let B = {A,{A}}. (a) Explain the elements of set B (with some example) (b) Prove that A is not a subset of B. Answered by Penny.
	The hypotenuse of a right triangle		2004-09-20
		From Shannon: I am trying to find the hypotenuse of a right triangle with only the length of the opposite side. What is the formula as I don't have the length of the adjacent side? Can I compute it without knowing what the other two angles are? Answered by Penny Nom.
	Perimeter and area of a semi_circle		2004-09-18
		From A student: I want to know how to find the perimeter and area of a semi-circle and a quarter-circle. Answered by Penny Nom.
	A challenge		2004-09-17
		From Lasse: xy xx xyx xxx xyxx "x" and "y" each represents a number. Find out the system to make the next line Answered by Penny Nom.
	The length of a cut		2004-09-17
		From Florita: My daughhter, who is a 9th grader is attempting to cut a piece of wood after determining the length of the cut for the hypotenuse. These are the measures: a=4squared, b=6squared. She determined that c should equal 52. But when she measured the actual piece to be cut, c measured 39.5 inches! Can you offer any insight as to what she is doing wrong? I have suggested that she may be working with an Acute rather than a Right angle . But she insists that it is a Right angle after using a "framing square". Answered by Claude Tardif.
	1+3+5+...+(2n+1)		2004-09-10
		From Emma: Prove that 1+3+5+...+(2n+1)= (n+1)2 Answered by Penny Nom.
	An inverse		2004-09-09
		From Hillary: I cannot figure out the inverse of this function. f(x)= 1/2x -1 Answered by Penny Nom.
	The nth term		2004-09-08
		From Alex: What is the nth term?... Like what is it?, How do I find it?, and how exactly is used?... Answered by Penny Nom.
	d varies inversely with g		2004-09-07
		From Ashlyn: d varies inversely with g when d=-8 and g=2 a. write d as a function of g using function notation. b. find d(10). Answered by Penny Nom.
	The intersection of planes		2004-09-07
		From Joshua: I was wondering about the intersection of planes. Can planes intersect? Answered by Penny Nom.
	Nine minutes		2004-09-02
		From A student: You have two hour glasses-one measures 7 minutes and one measures 4 minutes.How can you time 9 minutes? Answered by Penny Nom.
	The radius of a circle		2004-08-24
		From Peter: If you slice any circle with a line, and call the distance of the line between intersections the "y" length and the perpendicular length to the shorter side of the curve the "x" length, what is the resulting equation for the radius? Answered by Penny Nom.
	The series from i=1 to n :ai		2004-08-18
		From Ken: a.) Explain the difference between the series from i=1 to n :ai and the series j=1 to n :aj b.) Explain the difference between the series from i=1 to n:ai and the series from i=1 to n :aj Answered by Penny Nom.
	The intersection of two graphs		2004-07-28
		From JJ: Is there a way to find the intersections of these graphs algebraically? x^2 + y = 4 & 2x - y = 1 I got (1.45, 1.9) and (-3.45, -7.9) with a graphing calculator. AND THESE... y = 3.29x & y = 5.5(x^0.5)+ 10000 I got x at 3133 with a graphing calculator. Answered by Penny Nom.
	The railing around a pool		2004-07-26
		From Bob: I have a 15' circular above ground pool. Around the perimeter of the pool are eleven (11) sections of railing. Each rail has 5 slots at each end for pins. I have calculated that the length of the arc under the railing to be 51.4". what I am trying to determine is the distance between the end points of the arc so that I can figure out which slot to use in the rails without going round and round the pool moving and removing the rails until they finally fit. Been there, done that, no fun. Answered by Penny Nom.
	The inverse of a quintic function		2004-07-22
		From A student: I'm really having trouble finding out the inverse of this quintic equation. F(X)= X5+3X3+1.I know that this quintic has an inverse because it is one to one. But I can't find a method to solve this. Finding the inverse of a quadratic or a cubic equation is a lot easier, but with this quintc I am really lost. I even know how the graph of this equation and its inverse looks like, but I'm not sure if Iam getting the right equation. Please help me out. Answered by Penny Nom.
	The number of blocks in a mile		2004-07-18
		From Valerie: I don't know if you can help me but I was wondering how many blocks are in a mile in Ocean City, New Jersey? Answered by Penny Nom.
	Two puzzles		2004-07-13
		From Fred: A young man's car developed a flat tire while he was driving along a deserted street. He pulled over to the curb and did all the usual things; removed the hub cap; unscrewed the lugs and rested them carefully in the hub cap, jacked up the car. As he was putting the spare tire onto the axle he accidentally kicked the hub cap. The lugs rolled out, and all five of them rolled down a nearby grate. Peering through the bars of the grate the man thought he could see the lugs about 6 feet below in a shallow water puddle. He had a problem, how do you think he solved it? It is noon, your lunch hour, but you can not go out because there is a terrific hailstorm. Turning on your radio you hear the weathercaster predict that the hail will change to rain and that it will pour all day today. How can you determine the sun will be shining in 36 hours? Justify your answer. Answered by Penny Nom.
	An Octagonal playhouse		2004-07-13
		From Levi: I'm building an octagon playhouse for my son that is 8 feet wide. what would be the measurements of each of the eight sides. Answered by Harley Weston.
	Choosing 5 numbers from 1,...,36		2004-06-30
		From A lottery player?: how many combinations are there for the numbers 1thru 36 when only using each number once in groups of five Answered by Penny Nom.
	Jack's social security number		2004-06-08
		From A student: Jack's social security number contains each of the nonzero digits exactly once. By examining the digits from left to right, he also found that 1 divides the first digit evenly, 2 divides the sum of the first two digirs evenly, 3 divides the sum of the first three digits evenly, and so on, until 9 divides the sum of all the digits evenly. What is Jack's social security number? Answered by Penny Nom.
	The base of a triangle		2004-05-25
		From Ralph: With a 30 degree angle at the top of a triangle and a height of 15 what is the base? Answered by Penny Nom.
	Programming without trig functions		2004-05-25
		From Derek: I am a programmer trying to calculate the following. What is the formula to find the cross-sectional area of a cylinder with out using any trig functions? or better yet, how can you calculate any given volume in a cylindrical tank with spherical heads with out trig functions? I am using a PLC (programmable logic controller) to do this and trig functions are not available. Answered by Harley Weston.
	Setting up an equation		2004-04-30
		From Matt: I am trying to determine the dimensions of a 22 megapixel digital camera chip that has a 3:2 ratio. We know then, that: 3x = 2y (or 1.5x = y) and that xy = 22 Beyond this, I don't know how to hook those 2 seemingly unrelated facts together. Answered by Penny Nom.
	The sum of 4,0,-4..., -156		2004-04-28
		From Christina: find the requested sum of the arithmetic sequence 4,0,-4..., -156 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 geometric sequence		2004-04-13
		From Michael: In a geometric series, the sum of the 2nd and 3rd terms is 60, and the sum of the 3rd and 4th terms is 240. Find the sum of the first 7 terms. Answered by Penny Nom.
	What is the nth term		2004-04-07
		From Jason: 1 4 10 20 35 56 84 what is the nth term Answered by Claude Tardif.
	Trisecting an arbitrary angle		2004-04-06
		From Joe: Where can I submit my effort on trisecting an arbitrary angle with only a straightedge and a compass? I can do it but I do not have the smarts to prove it.S Answered by Chris Fisher.
	The intersection of two graphs		2004-03-31
		From Benjanim: How do I find the points of intersection of the two functions: 1) y = 2 - (e^-x) 2) y = 1 + (x^2) I know that I have to set them equal to each other, but I can't solve for x. Please help :-) Answered by Penny Nom.
	The degree sequence of a graph		2004-03-31
		From Ali: How can i find out {6,6,5,5,5,3,2}is not the sequence of the points of a simple graph,without drawing it? Answered by Penny Nom.
	Sections, area and acres		2004-03-23
		From Tony: An acre , it can be any size right . so when they refer to a section of a township which is 640 acres, also 1 square mile does this mean that 1 sections length if sqaure and there is 5,280 ft in 1 mile does it meanthat if you took 1 side of the square of of 4 sides the lenth would be 5,280 feet long and by multiplying 5,280 x 5,280 it would give you the square mile in square feet. i guess what I 'm asking is what is the perimeter of 1 acre if it was shape like a square. sorry to make this confusing but if you can help I would appreciate it. Answered by Penny Nom.
	What's the next term?		2004-03-22
		From Garrett: A friend hit me with these questions and won't tell me the answer nor how... please help? I've racked my brain and did all sorts of formulas, but I can't get it to work out... please... What's the next number in this series... 5, 12, 17, 29, 46, ? And this series... 12, 19, 28, 39, 52, 67, ? and these... ocoa, boco, oboc, dobo, odob, ? Answered by Claude Tardif.
	Baseball games		2004-03-14
		From Fabian: Let's say I have 12 different Baseball games. There is one of only 2 possible outcomes for each of the 12 games. How would I fugure out how many combinations there are for the 12 games and for 11,10, and so fourth. Answered by Penny Nom.
	Equivalent sets		2004-03-06
		From A student: If A=(1,2,3,4,...) and B=(5,10,15,20,...), is A equivalent to B. Why or Why not ? Answered by Penny Nom.
	Cosine of 35 degrees		2004-03-03
		From Jason: How do you find the exact solution to cosine 35 degrees. Answered by Chris Fisher.
	An elliptic cone		2004-02-24
		From Ben: I am building a model for my architecture class. I need to build a elliptic cone out of chipboard and i have no idea how to do this. The cone needs to be 20in tall and the ellipse has a max radius of 10in and a min radius of 8in. So my question is how do i lay this out on a piece of paper so that i can form the cone after i cut it out. Answered by Penny Nom.
	A worm crawling home		2004-02-18
		From Cindy: A worm is crawling to his home which is one meter away. The longer he crawls the weaker he gets and the less he can crawl the next day. If he crawls within 1/3000 of a meter of his home, he will find food. He must eat within twelve days. The first day he crawls 1/2 meter. The second day he crawls 1/4 meter. The third day he crawls 1/8 of meter. This pattern continues for twelve days. Make a Chart that shows the distance he has covered at the end of each day and the total he has covered at the end of each day. Does he make it to the Food in time? Answered by Penny Nom.
	Geometric sequences		2004-02-03
		From Alan: hello, I am a junior in precalculus. we started working on geometric sequences today, it makes perfect sense on how it works. but why is it called that? if you could send me an answer to why geometric sequences have that name, I would be much appreciative. Answered by Chris Fisher.
	Intersecting a line and a curve		2004-01-29
		From Senthil: between line and curve how can i find intersection point? could you write me the formula and explanation also sir. Answered by Penny Nom.
	Sets		2004-01-27
		From Susan: My child has the following problems to solve, and we are puzzled. 1. Compare the subset symbols to the inequality symbols of less than or greater than. 2. If A, B & C are sets such that A has 47 elements, B has 32 elements, and C is a proper subset of B, what can you say about the number of elements in the following sets: A U B? A intersect B? B U C? and B intersect C? Answered by Penny Nom.
	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.
	The product of any n consecutive integers		2004-01-18
		From Fazia: I have to prove that the product of any n consecutive integers is divisible by n!(eg:the product of five consecutive integers is divisible by 5!) It's easy enough to plug in numbers and prove it is true, but i'm finding it difficult to come up with a proper proof. Answered by Claude Tardif.
	Two consecutive negative integers		2004-01-17
		From Amanda: Find two consecutive negative intergers whose product is 182. Answered by Penny Nom.
	37 with four 4'2		2004-01-03
		From Myra: Using four fours and only four fours to get an answer of 37. Answered by Claude Tardif.
	Percent increase		2003-12-24
		From Frank: How does one figure the percent of increase or decrease in the cost of an item? Answered by Penny Nom.
	An elliptical race track		2003-12-16
		From Judy: the inner rail of a race track is a perfect ellipse. the track is a standard width all the way around. how can i prove that the outer rail is a ellipse? Answered by Penny Nom.
	Finding angles		2003-12-02
		From Jason: I AM TRYING TO SOLVE A TRIG PROBLEM AND HAVE FORGOT HOW TO DO IT. WHAT I HAVE IS A RIGHT TRIANGLE WITH SIDE A BEING 14 FEET AND SIDE B BEING 3 FEET, USING PYTHAGOREAMS THEOREM SIDE C SHOULD EQUAL 14.318 FEET ON A RIGHT TRIANGLE BUT I AM TRYING TO REMEMBER HOW TO FIND MY ANGLES OTHER THAN THE ONE THAT IS 90 DEGREES. Answered by Penny Nom.
	A point and a line		2003-11-19
		From Meenakshi: Given a line segment L(x1,y1) to (x2,y2) and a Point P(x3,y3). I need the formula to find a point on the line L that is closest to the point (x3,y3). Answered by Penny Nom.
	The 4th difference		2003-11-17
		From Jack: If i had a sequence which was the same at the 4th difference, aka difference to the 4th, like: 1 5 14 30 56 96 (sequence) 4 9 16 26 40 5 7 10 14 2 3 4 1 1 then what would be the set formulars to find out a, b, c, d, and e as i know the equation has to be an4+bn3+cn2+dn+e 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.
	root24 = 2 root6		2003-11-13
		From Burke: I know that all algerbra can be represented visually, for example: Y=9x+3 is a line on a two dimentional plane. Could Math Central please send me a visual representation of the proccess of simplifying square root like root24 equals 2root6 Answered by Penny Nom.
	Chisenbop		2003-11-06
		From Jaclyn: Hi there i was wondering if you would have any information on "counting on your fingers" or " Chisabop". Answered by Penny Nom.
	Knitting gauge and felting		2003-10-27
		From Sara: I wish to create a pattern to knit an item that will then be felted, thus, shrink as a result. In order to determine the proper gauge to use in creating the item, I produced a gauge swatch, noted the original properties and then the post-felting properties. They are as follow: Before Felting: 20 stitches(width) x 20 rows(height)yielded: Gauge: 3.2 stitches(width) and 4 rows(height) = 1" Dimensions: 6.25"(width) x 5.25"(height) After Felting: 20 stitches(width) x 20 rows(height) Dimensions: 4"(width) x 3"(height) How do I calculate the percentage change in size to accurately determine the number of stitches and rows needed to produce the desired dimensions for the finished (felted) item? Answered by Penny Nom.
	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.
	Arithmetic in bases other than 10		2003-10-22
		From Kim: how do you add, subtract, multiply and devide in base 3, base 5, etc? Answered by Penny Nom.
	Squares in a rectangle		2003-10-21
		From Raj: Draw a rectangle with sides of 3 and 4. Divide the sides into 3 and 4 equal parts respectively. Draw squares joining the points on the sides of the rectangle. You will have 12 small squares inside the 3 x 4 rectangle. If you draw a diagonal of the rectangle, it will intersect 6 of the the 12 smaller squares. Similarly, if you have a 4 x 10 rectangle, the diagonal would intersect 12 of the 40 squares inside the rectangle. Is there an algebric equation that determines the number of squares that will be intersected by the diagonal of a rectangle? Answered by Chris Fisher.
	1 + 1 = 10		2003-09-17
		From David: could you please explain to me how 1+1=10 thanks Answered by Penny Nom.
	The mean house price		2003-09-10
		From Carol: Question: I have to find the mean from the following example: Price Range £000 No of Houses 55 and under 60 3 60 and under 65 6 65 and under 70 13 70 and under 80 21 80 and under 100 15 100 and under 130 7 130 upwards 1 I know when calculating the mean you use the mid points of the classes, but how does this work for the 130 upwards class? Also, does this still work given the difference in the classes (ie. 1st class is 5, 5th class is 20, etc). Any help to get me started would be greatly appreciated. Answered by Penny Nom.
	Converting from base 10 to base 5		2003-09-10
		From Susy: My son, who is 9 in grade 5 has been asked to convert base 10 numerals into base 5. His first question of: 24(10) he has calculated to be 4x5 + 4x1 = 44 (5) The next question however is the tricky one.Ý We know the answer is supposed to be 100 but we find it difficult to get this in the way he understands it. 25 (10) = _________________ 100 (5) Can you help us figure out how we reach the answer. Answered by Claude Tardif and Penny Nom.
	Consecutive integers		2003-09-07
		From Amy: I was wondering if there was a proper way to write the solution to a problem requiring consecutive integers? Is it okay to write the solution as 5,4,3,2,1 or must it be written as 1,2,3,4,5? Answered by Penny Nom.
	Can 2 vertical planes intersect?		2003-09-06
		From Erin: My question is can 2 vertical planes intersect? Answered by Penny Nom.
	One million seconds		2003-09-04
		From Vince: If you can write a number each second for one million seconds, how many hours would it take? Answered by Penny Nom.
	Grooming the king's horses		2003-09-04
		From Janelle: the stable boy had 90% of the kings horses groomed.the next day the king acquired 25% more horses. Now there was 105 horses not prepared for the kings men. How many horses did the king originally have? Answered by Penny Nom.
	Converting to base 10		2003-08-28
		From Karen: My son is in 5th grade.Ý He is learning how to convert numbers from base 2 to base 10, and base 5 to base 10.Ý Can you explain it to me in the simplest terms? Answered by Penny Nom.
	Graphing a piecewise function		2003-08-24
		From Amber: How do i begin to graph a piecewise function, absolute function or step function? Answered by Penny Nom.
	39 consecutive natural numbers		2003-08-19
		From A student: Prove that among any 39 consecutive natural numbers it is always possible to find one whose sum of digits is divisible by 11. Answered by Penny Nom.
	Percentage decrease in sales		2003-07-31
		From Linda: If I had sales in January of 2002 that were $42,493.73 and sales that were $37,281.59.Ý The difference is $5374.50.Ý What is the percentage of decrease in sales? Answered by Penny Nom.
	Is 3/5 CLOSEST to 0, 1/2 or 1?		2003-07-09
		From A student: I would like to know is 3/5 CLOSEST to 0, 1/2 or 1. And can 3/10 go either way as to be closest to 0 or 1/2. Answered by Penny Nom.
	Setting up a word problem		2003-06-30
		From Christie: A rectangular corral is forty feet longer than it is wide. If the perimeter is 220 feet, determine the length and width of the corral. Answered by Penny Nom.
	Sesame Street on Stage		2003-06-25
		From Christie: Sesame Street on Stage has different ticket prices for adults and for children under 6. Beth and her two children, ages 3 and 4, paid $15 to gain entrance, while Jamie and John Jacobs and their 2-year old daughter got in for $19.50. What is the ticket price for adults? Answered by Penny Nom.
	A 40% markup		2003-06-12
		From Nick: I am attempting to determine the Retail price of an item that costs me 11.00. Our company wants to sell it at a markup of 40%. I calculated this two ways, first the way I thought it should be done. Second, the way the calculator does it (and my accountant). Cost + Cost*(percentmarkup/100)= retail price 11.00 + 11.00*.40 = retail price 11.00 + 4.40 = 15.40 retail price Using the calculators Mark Up key the answer is 18.33. Or 7.33 more than the cost or 67%. I am confused by this Mark Up key and how it calculates. I used a cost of $10.00 and marked it up 50%. I thought it should equal $15.00 but the calculator says $20.00? This seems to be 100% markup, yes? Can you explain the difference between the way I did it and the way a Business calculator does it? Answered by Penny Nom.
	A project about crosses		2003-06-10
		From Joel: I have this project to do about crosses and I can't think of what the answer is for the following questions: What is the area rule of the crosses (the table below will help you)? Cross Number Area sq cm 1 5 2 13 3 25 4 41 5 61 I also need to know what the formula is for it? Answered by Penny Nom.
	Teaching second grade		2003-06-10
		From A teacher: I am going to be teaching second grade next year. How can I differentiate instruction in mathematics to meet the needs of all of my students, from those who need intervention to those who need challenges? What are some techniques I can try for this grade level? Answered by Diane Hanson.
	$1/week for week 1 and then double each week		2003-05-28
		From A student: I AM DOING A PROJECT FOR MATH I AM TRYING TO CREATE A SEQUENCE BASED ON: MAKING A SALARY OF $1/WK FOR THE FIRST WEEK WITH IT DOUBLING EVERY WEEK FOR 52 WEEKS, SO MY SEQUENCE LOOKS LIKE THIS: 1,2,4,8,16,32,64,128,256,512,1024 ETC. THERE WOULD BE 52#'s TOTAL IN MY SEQUENCE.I BELIEVE IT IS CALLED A FINITE SEQUENCE. MY QUESTION IS HOW DO I CREATE A FORMULA/RULE FOR THIS PARTICULAR SEQUENCE? MY GOAL BEING TO FIND THE 52nd TERM IN THE SEQUENCE. Answered by Penny Nom.
	Two sequences that agree in the first 4 terms		2003-05-26
		From A student: Is it possible to have two formulas that define sequences that agree on the first four terms but not the rest? Answered by Penny Nom.
	The cross-section of a football field		2003-05-25
		From Francis: Have you ever walked on a football field covered with artificial turf? If so, you probably noticed that the field is not flat. The profile of the surface is arched and highest in the centre, permitting rainwater to drain away quickly. height from base to highest point- 45.75 centimetres distance of the field- 50 metres a) The diagram shows the profile of an actual field, viewed from the end of the field. Assuming that the cross-section is a parabola, find the algebraic model that describes this shape. b) Use your equation to determine the distance from the sidelines where the field surface is 20 cm above the base line. Answered by Harley Weston.
	A trig identity		2003-05-20
		From Patty: Please help with the following 1/ tanx + cotx = sinxcosx Answered by Penny Nom.
	R= 5.3lnx + x.		2003-05-11
		From A student: Reaction R to a dose x is given by: R= 5.3lnx + x. For a certain drug, R must not exceed 21. Show that a dose between 8 and 12 units satisfies this requirement & find, correct to 5 decimal places, the greates value of x which satisfies this condition? Answered by Harley Weston.
	positive multiples of 10 that are the sum of four consecutive integers		2003-05-01
		From Taurus: How many positive multiples of 10 that are less than 1000 are the sum of four consecutive integers? Answered by Penny Nom.
	Profit for a dance studio		2003-04-28
		From Craig: A dance studio charges $80 per student for a series of 2 hour lessons. The studio's costs are $30 per hour for the instructor, $15 per lesson for the room rental, and $3 per student for miscellaneous expenses. If x is the number of students enrolled in the class, express the studio's profit P(x) in terms of x. Find the profit if 10 students are enrolled in the class. Answered by Penny Nom.
	The product of four consecutive integers is 3024.		2003-04-25
		From pillar: The product of four consecutive integers is 3024. What are those numbers. Answered by Penny Nom.
	One one		2003-04-22
		From Brad: find the next two rows of numbers? 1 1 1 2 1 1 1 1 2 3 1 1 2 1 1 1 2 1 3 Answered by Leeanne Boehm.
	Chopping trees		2003-04-19
		From Tamara: The master needs some of the trees (twenty, to be exact) at the back of his spooky old mansion cleared to make way for a new evil laboratory, so he decides to send some his slaves to do the work for him. He initially sends out four of his men, armed with axes, to chop the trees down. Due to the fact he is very impatient, every ten minutes he sends out another man to help with the work. Assuming that it takes one man 30 minutes to chop down 1/3 of a tree, how long till all twenty trees are chopped down? Answered by Penny Nom.
	How many hits?		2003-04-06
		From Jack: My name is Jack. I'm a uncle. Student is in the 5th grade email is above. If a baseball player at sping training had a good season with the following: one seventh of his hits were doubles. 12.5% of his hits were home runs. But didn't have any triples. How many hits did he have? Can you give me an explanation of you solved the problem. Answered by Penny Nom.
	Uses of conic sections		2003-04-01
		From William: My name is William and I am doing a research paper on conic sections for my 12th grade math class. Part of the project is to find two conic sections in our world today and explain what there purpose is. I really need help in this area because I've been searching the internet for where conic sections are used in our world today and I really can't find anything. If you can tell me specific building or a pyramid that contains conic sections that would be great. Or even something in the universe would be helpful. Answered by Leeanne Boehm.
	Friends and enemies		2003-03-24
		From Becky: Consider a room that contains six people. Any two people are either friends of each other, or they are enemies. A. Argue why there are three people, all who are friends, or there are at least three people, all who are enemies B. Rephrase the situation using graph terminology, using all of these terms correctly: vertex, edge, graph, complement, clique, independent set, and bipartite. Answered by Penny Nom.
	A sequence that converges to e		2003-03-16
		From Dane: Something I noticed fooling around with a calculator about 30 years ago. Considering e = 2.718281828459045.... Using Window's Calculator you will find 1.111 = 2.8531167... 1.01101 = 2.731861... 1.0011001 = 2.71964085... 1.000110001 = 2.71841774... 1.00001100001 = 2.7182954... 1.00000110000011 = 2.178231875... 1.000000110000001 = 2.178219643... There apears to be a pattern. My conjecture is: 1.'infinite number of zeros'11'infinite number of zeros'1 = e. Answered by Penny Nom.
	A section of land		2003-02-25
		From Bev: How many acres in a section of land? How many square miles is in a secion of land? Answered by Penny Nom.
	Percentage decrease		2003-02-20
		From Hope: What number decreased by 331/3% is 30? Answered by Penny Nom.
	Numbers in base 5		2003-02-16
		From Lori: I'm trying to help my 6th grader with converting numbers like 82 to base 5 and 182 to base 12. We saw your examples on 613, but still are confused. Answered by Penny Nom.
	Finite differences		2003-02-10
		From Jenny: I need to find a formula that will work with any number. I am finding the volume of a 3d cross- shape. Here are my results so far: Term Number 0 1 2 3 4 5 nth term 1 7 25 63 129 231 1rst diff 6 18 38 66 102 2nd diff 12 20 28 36 3rd diff 8 8 8 I can't seem to find a formula that will work with any number. Any help would be much appreciated. Answered by Penny Nom.
	Three consecutive positive intergers		2003-02-09
		From Yew: Prove that when we multiply any consecutive positive intergers, the result is always divisible by 6. ex. (7)(8)(9) = 504 = 6 (84) Answered by Penny Nom.
	The sum of the first 1000 even integers		2003-02-06
		From Jill: What is the sum of the first 1000 even integers? Answered by Paul Betts.
	Arithmitic sequence		2003-02-01
		From A student: I am having problems solving this arithmetic sequence... 1, 5, 10, ___, 50, 1.00, ___, 10.00, ... I believe the answers to be 25 and 5.00 but I can't figure why. Answered by Claude Tardif.
	1+2+3+...+500		2003-01-31
		From Brian: What is the sum of the numbers from 1 to 500 inclusive? Answered by Paul Betts.
	25% more		2003-01-16
		From Charlie: If I buy something for $10 and want to sell for 25% more, do I multiply by 1.25 or divide by .75? Or another way - why do I get $13.33 when dividing by .75 ? 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.
	What is larger than infinity?		2003-01-12
		From Dana: What is larger than infinity? Answered by Claude Tardif and Harley Weston.
	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.
	Repeating decimals		2003-01-08
		From A student: If k=.9repeating, and 10k=9.9repeating then 10k-k=9k, k=1 therefore .9repeating=1 and 1/3=.3repeating 3x1/3=.3repeatingx3, 3/3=.9repeating, therefore 1=.9repeating It would seem to me that .9repeating approaches one but never quite makes it. Can you clarify? Answered by Penny Nom.
	Constructions of polygons		2003-01-03
		From Garrett: Our teacher just finished the constructions unit, and he mentioned briefly about odd sided figures such as pentagons and septagons, only that they're very hard. My question is, how do you draw, with a compass and a straight edge, a pentagon and septagon? Answered by Chris Fisher.
	The intersection of conics		2002-12-19
		From Glenda: We are studying systems of equations where two conic sections are the two equations that we are solving simultaneously. We were studying the number of solutions that are possible if you have an ellipse and a parabola. We all agree that there can be none, one, two, three or four solutions. The question that the students had for me was whether or not a portion of an ellipse and a parabola can overlap and thereby allow an infinite number of solutions. What should I tell them? Answered by Chris Fisher and Harley Weston.
	A bouncing ball		2002-12-14
		From Eman: Q : When a childís ball is dropped from a height h metres on to a hard, flat floor, it rebounds to a height of 3/5h metres. The ball is dropped initially from a height of 1.2m. Find the maximum height to which the ball rises after two bounces. Find the total distance that the ball has traveled when it hits the floor for the tenth time. Assuming that the ball continues to bounce in the same way indefinitely, find the total distance that the ball travels. Answered by Penny Nom.
	A geometric sequence		2002-12-02
		From Wanda: the fifth term of a geometric sequence is 5/16. the common ratio is 1/2. What are the first four terms of the sequence. Answered by Penny Nom.
	Combinations of 1,2,3,...,10		2002-11-27
		From Gord: If I had the numbers from 1-10 how many different combinations would i have.....would it be 100....since that is 10 squared. Answered by Penny Nom.
	Making 7		2002-11-26
		From Bill: At one time I had the answer to this math equation but I have lost it and can't seem to regain it. I may be going at it wrong but as I recall there were the numbers 1 through 4, and the std operators, +, -, /, *, and parentheses. The object was to make the four numbers with the operators equal to 7. Each number and operator may be used only once. My 9 year old loves these quizzes but I can't give it to her if I can't provide the correct answer. Answered by Claude Tardif.
	A two stage rocket		2002-11-26
		From Hoda: a two stage rocket accelerates in free space by ejecting fuel at a constant relative speed , v(ex). the full fuel load makes up 80% of the initial mass of the entire two stage rocket . the rocket accelerates from rest until at the end of the first stage when 75% of its fuel has been burnt. find an expression for the speed of the rocket at the end of the first stage in terms of v(ex). Answered by Claude Tardif.
	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.
	The horse race		2002-11-19
		From Pat: The Horse Race Three horses run a race. In how many different ways can the three horses finish the race if ties are allowed? Answered by 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.
	Chisanbop		2002-11-07
		From Paul: I'm trying to find the book/books that explain this system? I have one small book that explains the very beginning of the system, but covers only about 10 to 20%. I'v tried several book sellers and have had no luck. Answered by Diane Hanson.
	What is nth term?		2002-11-06
		From Joga: What is nth term: First sequence: 2, 4,7,11, 16, nth term Second sequence: 4,10, 28, 82, nth term Answered by Penny Nom.
	A house's selling price		2002-11-05
		From Tanisha: a CERTAIN REAL-ESTATE AGENT RECEIVES $6 FOR EVERY $100 OF A HOUSE'S SELLING PRICE. HOW MUCH WAS A HOUSE SOLD FOR IF THE AGENT $10,725._ Answered by Penny Nom.
	Compass points		2002-11-05
		From Mhairi: I was asked this in maths but I am not sure if it is geography. Name all the compass points? We have been given 8 but he told us there is more and we have to name them. Answered by Chris Fisher.
	The percentage grade of that hill		2002-11-05
		From Cathy: If there is an 80ft climb over a kilometer(about 3280ft) what is the percentage grade of that hill? Answered by Penny Nom.
	Jimmy's hits		2002-10-27
		From Patty: One seventh of Jimmy's hits were doubles 12.5% of his hits were homeruns Jimmy had 82 singles He did not have any triples How many hits did Jimmy have? (Be sure to include the equation that represents the number of hits) Answered by Penny Nom.
	x 4 + x 5 = 100		2002-10-27
		From Bill: One of my students has stumped me. He asked how to solve the equation 4 x + 5 x = 100 All I can think of are graphing methods to get an approximate solution. What am I missing? Answered by Harley Weston.
	Two problems		2002-10-14
		From Eva: a) How many different equivalence relations can be defined on the set X={a,b,c,d}? b)Show that 6 divides the product of any 3 consecutive integers. I know it is true that 6 divides the product of any 3 consecutive integers. However, i have problem showing the proof. Answered by Leeanne Boehm and Penny Nom.
	Tree diagrams		2002-10-12
		From Denean: For lunch, students can choose juice or milk; hamburger or pizza; and a banana or apple. How many lunch combinations can the students make? In an experiment, Monty can use paper towels or cloth. He can choose red, green, or yellow food coloring. How many combinations are there? Answered by Penny Nom.
	Nixon, Jefferson, and Madison		2002-10-08
		From Lisa: The longest-lived US presidents are John Adams(age90), Herbert Hoover (also90), and Harry Truman (88). Behind them are James Madison, Thomas Jefferson, and Richard Nixon. The lattter three men lived a total of 249 years, and their ages at the time of death form consecutive odd integers. For how long did Nixon, Jefferson, and Madison live? Answered by Penny Nom.
	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.
	Sums of evens		2002-09-14
		From Rosa: How do I find a geometric way to easily compute sums of consecutive even numbers 2 + 4 + 6 + .... Answered by Leeanne Boehm and Harley Weston.
	Base 5 numbers		2002-09-13
		From Vera: ? how do you change a base 10 number to base 5 Answered by Penny Nom.
	7+8+9+...+1000		2002-09-11
		From Shirley: My question is what is the formula for adding up numbers when you don't start with number 1? For example 3 + 4 + 5 + 6 = 18. But how could you arrive at the answer without adding all the numbers? Answered by Penny Nom.
	How do start from 2700 and get 35% back out?		2002-09-09
		From Dennis: 2000 x 0.35 = 700 + 2000 = 2700 How do start from 2700 and get 35% back out? If I have 2700, how do I figure out that 35% of 2000 is 700 and adding the two them together will get me 2700? Answered by Penny Nom.
	Social security numbers		2002-09-06
		From Chris: How many different number combinations are there for the social security system? We know that there are only a certain ammount of combinations available and the current US population is at 281 million. The number system should include as many nine digit combinations as possible using the numbers 0-9 in multiple different spots. Answered by Penny Nom.
	8,27,64 . . .		2002-09-05
		From Mike: We have been trying with no luck all night to complete the following math pattern (next 3 entries) 8,27,64 . . . Any ideas?? Answered by Penny Nom.
	1, 2, 4, 8, 16, 32, etc.		2002-09-04
		From Ginger: I've been working with finding the nth term for a few weeks, and i can't seem to figure this one out! 1, 2, 4, 8, 16, 32, etc. Answered by Leeanne Boehm.
	Express 5120 as a sum of consecutive numbers		2002-08-25
		From Todd: Express 5120 as a sum of more than 1 consecutive number. Answered by Leeanne Boehm.
	Sets and elements		2002-08-22
		From Dianne: I want to know why its okay to say that, for example, 6 is an element of the set of integers, but you get counted off for saying that the set of 6 is an element of the set of integers. How come? Answered by Judi McDonald.
	A paper model of a cone		2002-08-14
		From Bruce: I have made a paper model of a cone, cut a sloping section, and removed the top. I have drawn the major and minor axis on the paper surface of the section. The major axis is not symmetrical about the minor axis. To me, this is not an ellipse. To me, an ellipse is a tubular section, because this gives a symmetrical major axis. What is your opinion? Answered by Walter Whiteley and Chris Fisher.
	Percentage		2002-07-20
		From Sally: If 20% of 100 is 80, then why is the percentage difference between 80 and 100 25%. Answered by Penny Nom.
	A polygon inscribed within an ellipse - Part 2		2002-07-08
		From Steven: I recently sought your advice about a problem that I have been working on for eight years or so concerning a polygon inscribed within an ellipse. I think that I may have confused matters by the way in which I put the question and hope that the enclosed diagram will clear matters up. In the ellipse below I have drawn three chords inscribed within one quadrant ( this would pertain to a twelve sided figure within the whole ellipse). These chords are exactly the same length as each other, for example if the major axis of the ellipse was 360 and the minor axis 240 I have worked out that a twelve sided figure would have sides of 78.2487. However I worked this out empirically with a method that could only be described as gruelling I would be most grateful if you could tell me of a method that would work for any ellipse and any number of sides. Answered by Chris Fisher.
	An equalateral polygon inscribed within an ellipse		2002-06-30
		From Steven: How would you calculate the length of one of the sides of an equalateral polygon (of n sides) inscribed within an ellipse ( of any eccentricity ) where all of the vertices exactly touch the perimeter of the ellipse? I know that when the eccentricity is zero ( i.e a circle ) the formula: r * (sin(180/n) * 2) will suffice. But what about when the eccentricity is greater than zero? Answered by Chris Fisher.
	What is the next term?		2002-06-21
		From A student: What is the next term in the sequence: 1, 5, 14, 30..... Answered by Penny Nom.
	| n + 4 | + | 3 - 2n | = 16		2002-05-24
		From Randall: I don't seem to be able to solve this: | n + 4 | + | 3 - 2n | = 16 Answered by Penny Nom.
	Sequences that agree on their first four terms		2002-05-16
		From Mike: Are there two formulas that define sequences that agree on their first four terms, but differ on the fifth term and all succeeding terms? Answered by Chris Fisher.
	The law of cosines and obtuse angles		2002-05-09
		From Bryant: The question that I am pondering is that I need to derive the law of cosines for a case in which angle C is an obtuse angle. Answered by Penny Nom.
	What's the next term?		2002-04-29
		From A student: Find the nth term for the following: 1) 12, 30, 56, 90, 132 2) 6, 30, 84, 180, 330 3) 8, 15, 24, 35, 48 4) 10, 17, 26, 37, 50 5) 24, 40, 60, 84, 112 6) 24, 60, 120, 336, 504 Please show the FULL working out. Answered by Penny Nom.
	Conversion of units		2002-04-29
		From Matt: I am having trouble finding a workable equation for the following problem, particularly the conversion of two systems of measurement. The question states that there are 27 grams of salt in a kilogram of seawater. And it asks how many tonnes (1 tonne = 1000 kilograms) of salt are there in one cubic kilometer of ocean. It also says that the density of seawater is 1.1 g/cm3. What is the equation and how do I figure out how many kilograms there are in a cubic kilometre? Answered by Harley Weston.
	Ratios		2002-04-17
		From A student: Medication is givin at 1cc. per 20 pounds of body weight. A dog weighs 16 pounds how many ccs. of medication does the dog get? Dr. Lee wants you to prepare 1000 ml. of a 10% dextrose solution in lactaed ringers for diuresis or a patient you have a 1 L bag of lactated ringers and 500 ml of 50% dextrose for injection. How would you prpare the solution? Answered by Penny Nom.
	Diagonals in a polygon		2002-04-10
		From Murray: If you have a regular polygon with n sides and you draw all (n-3)n/2 diagonals how many intersection will they form with each other and how many sections will they devide the polygon into. Answered by Caude Tardif and Chris Fisher.
	Composition of functions		2002-04-06
		From Yvonne: In our new text book, the following question occurs: State the domain and range of g(f(x))given that f(x) = -x2 - 4 and g(x) = sqrt(x) The range of f(x), x<=-4, is the domain of g(x). BUT, there is no solution in the Real numbers for g(f(x))= sqrt(-x2 - 4). In the solutions it says that this is not a function and therefore does not have a domain or range. Is it a relation? Is it anything? 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.
	A cone in 3 space		2002-03-20
		From Matthew: Let C in R3 be the cone defined by x2 + y2 - z2 = 0 (A) Let P be the plane described by x + 2z = 1 (i) Find a description of P in terms of two parameters s and t . . . Answered by Walter Whiteley.
	Percentage difference		2002-03-08
		From Tedd: Can you give me the formulas for calculating percentage differences between two numbers? For example: if the first number is 10 and the second number is 15, then the second number is 50% larger than the first number. However, the formula to calculate that percentage won't work if the first number is greater than the second number as in the following example: The first number is 15 and the second number is 10, with the second number being 33.3% less than the first number. Or maybe I'm mistaken and the same formula will work in both situations. Answered by Penny Nom.
	A sequence		2002-03-07
		From Caroline: hi, here is the problem, 1 11 21 1211 111221 _ _ 2_ _ _ we can't get the sequence of the last line ,with the 3rd number being 2,thanks Answered by Walter Whiteley.
	1,4,27,____,_____46656		2002-02-21
		From Brenda: 1,4,27,____,_____46656..... please find the fourth and fifth numbers in this sequence. Answered by Penny Nom.
	Alfredos house number		2002-02-21
		From Aunt Patty: Alfredos house number is between 20 and 35. The sum of the digits is less than 5. If you subtract 1 from it you would get a multiple of 3. If you add three, you get a multiple of 5. What is Alfredos house number. Answered by Penny Nom.
	The perimeter of an ellipse		2002-02-14
		From Harry: I am planning to build a coffe table with an ellipse of 24x36 for the top. I wish to decorate the edge and need to know the lenght of the perimeter for lay out purposes. Is there an easy way to approximate this figure with out using intergal calculus? Answered by Penny Nom.
	Parabolas		2002-02-03
		From Kuang: -Who is credited for working with or studying the Parabola? -What is a conic section? -What does a parabola look like? -How is a parabola formed? -Where and how are parabolas used today in the real world? Answered by Harley Weston.
	Baseball and sit ups		2002-01-31
		From A student: A baseball team won 8 more games than it lost. If it played 56 games, how many games did it win? On the first day of practice, Paul did 3 sit ups. On the second day he did 5, and on the the third day he did 8, and on the fourth day he did 12. If this pattern continued, how many sit-ups did ihe do on the sixth day of practice? Answered by Penny Nom.
	The size of a lot		2002-01-26
		From Claudia: I own a piece of property that I need to know the square feet for assessment purposes. The figure they came up with is wrong. They measured from one point to another and halved the sums but that means I own the cul de sac and we don't. My lot is 55 feet wide and one side is 108.96 feet and the other side is 146.04 that extends all the way to a circle. The front of the lot on the cul de sac is stated on the survey like this. 78.21 feet where R=40 feet. This large arc is taken off the size of our land. How many square feet is our lot. Answered by Harley Weston.
	Successive differences		2002-01-20
		From Linsey: what is the rule for working out the formula for a sequence with three lines of difference? eg. 1, 3, 7, 15, 29 1st line differences: 2, 4, 8, 14 2nd line differences: 2, 4, 6 3rd line differences: 2, 2 Answered by Penny Nom.
	Rolling 5 sevens before rolling a six or an eight		2002-01-20
		From Tony: When rolling 2 dice, what is the probability of rolling 5 sevens before rolling a six or an eight? Answered by Andrei Volodin and Penny Nom.
	My salary is doubled everyday for 30 days		2002-01-17
		From Kanishk: I recieve 1 penny the 1st day, 2 pennies the 2nd day, and my salary is doubled everyday for 30 days. How much money will I have by the end of the 30 day time period? (Is there a way of solving this problem without a chart?) Answered by Penny Nom.
	A sequence		2002-01-16
		From Chris: I have spent two days trying to determine the pattern to the following set of numbers: 1,4,9,1,6,2,5,3,6,4,9,6,4,8,1,____. I need the next four numbers to the sequence. Answered by Claude Tardif.
	Children and probability		2002-01-16
		From Bill: If a family has four children, what is the probability that all 4 are the same sex? Answered by Vanrei Volodin.
	Papy's Computer		2002-01-11
		From Mary-Anne: My second-grade son brought home a fun math worksheet which involved calculating sums using "Papy's Computer." I had never heard of this before and found it to be quite interesting. Each digit in a decimal number is represented by a 2x2 grid. Each grid square corresponds to one of the numbers 1,2,4, or 8. Answered by Harley Weston.
	A sequence of number pairs		2002-01-10
		From Terry: Three is the first number of a pair, and 8 is the second. a. If 50 is the first number, what is the second number? b. If 200 is the first number, what is the second number? c. If 89 is the second number, what is the first number? d. If a number n is the first number, what is the second number? 3-8 4-11 5-14 6-17 ____ ____ ____ 10-29 ____ ____ ____ Answered by Peny Nom.
	450 students		2001-12-19
		From Jessie: My teacher told me that the number of ways of lining up the 450 students in our school is larger than the number of atoms in the universe. Is this right? This question came to Good Question, a regular feature on the CBC Morning Edition radio show in Saskatchewan. Answered by Denis Hanson and Harley Weston.
	A 7% increase		2001-12-12
		From Lorraine: how do you calculate an old salary if the only information you have is current salary and the percentage increase received. For example if I make $15.86 an hour and I received a 7% increase, how much did I used to make? Answered by Penny Nom.
	Can a infinite set be smaller than another infinite set?		2001-11-29
		From Carlos: Can a infinite set be smaller than another infinite set? If so why? Answered by Chris Fisher and Penny Nom.
	3, 6, 10, 15, 21		2001-11-29
		From Patrick: we are trying to find the expression to solve for the nth term in the pattern 3, 6, 10, 15, 21 Answered by Denis Hanson.
	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.
	Undetermined coefficients		2001-11-22
		From Hoda: The equation is: y" - 2y' + y = t et + 4 We need to use The method of Undetermined coefficients. I have tried assuming that the solution is Atet+Bet+C, but all I get is C=4 and I tried (At2+Bt+C)et+D, but again I get 0=0 when I calculate the first and second derivatives, so i get no information on the constants. Any suggestions? Answered by Harley Weston.
	Matrix		2001-11-21
		From Hoda: I have a question about matrix multiplication; well, actually, matrix division. I am assuming that matrices are divided the same as they are multiplied; that is, row by column. But what happens if you have to divide by zero? How does this affect the resulting matrix? Answered by Patrick Maidorn and Penny Nom.
	Cardinality of sets		2001-11-19
		From Tania: Show that the cardinality of P(X) (the power set of X) is equal to the cardinality of the set of all functions from X into {0,1}. Show that (the cardinality of the natural numbers set) |N| = |NxNxN|. Show that the cardinality of the set of prime numbers is the same as the cardinality of N+ Answered by Walter Whiteley.
	Number sequences		2001-11-17
		From Stephanie: My name is Stephanie. My grade 7 math class is studying number sequences and, to me, they make almost no sense at all. Here I wrote down 2 of the many problems I have for homework and was wondering if you could explain them to me (I have to find the next 3 numbers in each sequence.) It would be a big help! 10, 14, 18, 22, _, _, _. 12, 21, 39, 75, _, _, _. Answered by Penny Nom.
	Subsets of a countably infinite set		2001-11-14
		From Tania: How could I show (and explain to my son) that any countably infinite set has uncontably many infinite subsets of which any two have only a finite number of elements in common? Answered by Claude Tardif.
	Inequalities		2001-11-13
		From Pat: When writing the solution to an inequality, why is the solution written in set notation? {x/ } Answered by Penny Nom.
	2=the square root of (2 + the square root of (2 + the square root of (2 +...)))		2001-11-05
		From Cynthia: justify algebreically, that: 2=the square root of 2 + the square root of 2 + the square root of 2 + the square root of 2 + the square root of 2 + and so on, ....... Answered by Penny Nom.
	Applied geometry		2001-11-02
		From Jenny: Where can I find some hands-on activities for my Applied Geometry classes? I want to do more activities with them that allow us to get out of the classroom. However, I want to use activities that use only inexpensive equipment because I usually buy the equipment myself. Answered by Walter Whiteley.
	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.
	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.
	A geometric series		2001-10-24
		From Tashalee: The sum of the first 3 terms of a geometric series is 13. The sum of their reciprocal is 13/9. how do you find the first three terms? Answered by Penny Nom.
	Why quadratic for a second degree equation?		2001-10-20
		From Jana: Why do we use the word quadratic to describe second degree equations? Answered by Penny Nom.
	60 seconds in a minute		2001-10-11
		From Andy: I am a fourth grade teacher. Yesterday my students asked "Why are there 60 seconds in a minute?" Which also led to 60 minutes in an hour? I have had trouble determining why the number 60? Any help would be appreciated. Answered by Penny Nom.
	Ratio and proportion		2001-10-10
		From Steve: Where would you use a proportion and/or a ratio in a real life job or problem. Answered by Leeanne Boehm and Walter Whiteley.
	Who owns what pet?		2001-10-03
		From A parent: Don, Frank, Jenny, and Ken each come from one state, either Alaska, Maine, Montana, or Oklahoma. They each speak one primary language, either English, french, Russian, or Spanish. And they each have one of four pets, a chinchilla, a dog, a hamster, or a turtle. Figure out which language and what pet each of the four people have, using the following clues. . . . Answered by Judi McDonald.
	1+2+3+...+1000		2001-10-01
		From Louise: Find a quick way to add all Intergers (whole Numbers) between 1 and 1000? Answered by Walter Whiteley.
	Find the pattern		2001-09-26
		From A parent: MY SON HAD ON A WORKSHEET WHAT I HAVE LISTED BELOW, BUT WE CAN'T SEEM TO FIND THE PATTERN. MOST THE TIME WE CAN, BUT THIS ONE IS DIFFERENT. 6,___, 9,____,____,_____,_____,_____ Answered by Caude Tardif.
	Four sequences		2001-09-24
		From Nicole: I have a few questions I couldn't figure it out. So any help will be great to find the next three numbers or letters. Here's the patters... DEGHNORY, EHILMU, HIILMTU, BEILLMRUY,... 50, 33, 25, 20, 16, 14, 12,... 1777, 1795, 1818, 1819, 1820, 1822, 1836, 1837.. A,H,I,M,O,T,... Answered by Chris Fisher and Penny Nom.
	An egg shaped island		2001-09-22
		From Karen: I am a civil engineering designer trying to design an egg shaped island. I want a 30' radius at the top and a 40' radius at the bottom and the longest length of the egg to be 125'. Is there standard geometry for an egg shape? I am not held to exact radii or the length given. Answered by Chris Fisher.
	Counterclockwise		2001-09-14
		From Rolanda: When Descartes invented the coordinate system he decided to number them counter-clockwise. Why? Answered by Chris Fisher.
	Arithmetic sequences		2001-09-10
		From Rachel: I can't seem to figure out a problem that deals with arithmetic sequencing. This is the question: The 5th term in an arithmetic sequence is 1/2, and the 20th term is 7/8. Find the first three terms of the sequence. I attempted this problem with the formula: An = a + (n-1)d (where the n represents the nth term, a is the first term, and d represents the common difference) I keep getting -9.5 for the first number, and then 3/120 as the common difference between the numbers. But as I have figured it, the sequence is getting greater and greater, and my data does not go with the terms given. Answered by Penny Nom.
	The best of 7		2001-09-08
		From Michelle: Professional basketball, hockey, and baseball championships are decided on the best 4 out of 7 games. The first team to win four games wins the championship. In how many possible ways could the team win the championship series after winning the first game? Example: Game 1 2 3 4 5 6 7 Result W L L W W W Answered by Leeanne Boehm.
	Bisecting angles		2001-08-27
		From Monica: Ray QS is the bisector for angle PQR. Find the measure of angle PQS and PQR if the measure of angle SQR is 52 degrees. Answered by Penny Nom.
	A sequence		2001-08-25
		From Sharon: 1 11 21 1211 111221 312211 1311221 1113213211 31131211131221 13211311123113112211 What would be the next sequence of numbers? my name is sharon i work in customer service and a friend asked me to solve this. Answered by Walter Whiteley.
	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.
	A trig identity		2001-07-27
		From Jeff: prove this identity and show steps tan(x/2+pi/4)=secx+tanx Answered by Harley Weston.
	Generating uniquie 2 digit numbers		2001-07-16
		From Anthony: What methodology can I use to generate uniquie 2 digit numbers from unique 7 digit numbers. Of'course the total number of 7-digit numbers is not greater than 99. Answered by Penny Nom.
	Arclength of an ellipse		2001-07-03
		From A hobbyist: What is the equation (with the length of the arc as a variable) for one quadrant of the ellipse,... Answered by Claude tardif.
	Securing a plank in four dimensions		2001-06-06
		From Becca: If it takes two nails to secure a plank from rotating on a wall in the third spatial dimension, how many nails would it take if you were attempting to secure the board from rotating in the fourth spatial dimension? Answered by Walter Whiteley.
	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.
	SPRT		2001-05-24
		From A researcher: I have a medical-pharmaceutical study that says: SPRT (something to do with Secuential and Truncated). Do You know what it means S.P.R.T. and what it is? Answered by Ejaz Ahmed and Penny Nom.
	The diameter of an oval		2001-05-23
		From Tim: Is there a such thing as a diameter of a oval? If not, is there a way to get the circumference? Answered by Claude Tardif and Penny Nom.
	Harmonic numbers		2001-05-23
		From Leslie: The harmonic numbers Hk, k = 1,2,3.....are defined by Hk = 1 + 1/2 + 1/3....1/k I am trying to prove by mathematical induction: H2n >= 1 + n/2 , whenever n is a nonnegative integer. H8 = H23 >= 1 + 3/2 Can you help? Answered by Harley Weston.
	Circles, ellipses, parabolas and hyperbolas		2001-05-09
		From Colleen: How is an ellipse like a circle? In what way does an ellipse have a center? How is a hyperbola similar and different to an ellipse? How is a parabola similar a different to a circle ellipse and parabola? Answered by Pnny Nom.
	Tiling a floor		2001-05-01
		From Sarah: Cut out of paper or cardboard a quadrilateral having no two sides parallel, no two sides of equal length and no indentations. Can an endless floor be tiled with copies of such a figure? Answered by Claude Tardif.
	A sequence defined recursively		2001-05-01
		From A student: A sequence s is defined recursively as follows: s0=1 s1=2 sk=2sk-2 for all integers - Compute s2,s3,s4... to guess an explicit formula for the sequence sk. Answered by Penny Nom.
	A sequence of even terms		2001-04-29
		From A student: A sequence c is defined recursively as follows: c0 = 2 c1 = 4 c2 = 6 ck= 5ck-3 for all integers Prove that cn is even for all integers. Answered by Leeanne Boehm and 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.
	Geometry		2001-04-21
		From Rebecca: How do you prove the following: Let CD be an altitude of triangle ABC and assume that angle C=90 degrees. Let r1 and r2 be the inradii of triangle CAD and CBD, respectively, and show that r+r1+r2=CD, where r is the inradius of triangle ABC. Answered by Chris Fisher.
	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.
	An emergency response station		2001-03-29
		From Tara: Three cities lying on a straight line want to jointly build an emergency response station. The distance between each town and the station should be as short as possible, so it cannot be built on the line itself, but somewhere east or west. Also, the larger the population of a city, the greater the need to place the station closer to that city. You are to minimize the overall sum of the products of the populations of each city and the square of the distance between that city and the facility. City A is 6 miles from the road's origin, City B is 19 miles away from the origin, and City C is 47 miles from the origin. The populations are 18,000 for City A, 13,000 for City B, and 11,000 for City C. Where should the station be located? Answered by Claude Tardif and Penny Nom.
	An elliptic tunnel		2001-03-24
		From Janna: A tunnel is built under a river for a road 12m wide with a 2m sidewalk on either side. The top of the tunnel is semi-elliptical. A local bylaw stipulates that there must be a clearance of at least 3.6m at all points on the road. If the smallest possible ellipse is used, find the clearance at the center of the road. Answered by Harley Weston.
	The repetend in repeating decimals		2001-03-21
		From Sharon: What is the name for the bar over the repetend in repeating decimals? Also, what is the name of the long division "house"? Answered by Penny Nom.
	Timing with hour glasses		2001-03-20
		From Nathan: How can a chef use an 11 minute hour glass and a seven minute hour glass to time a vegtable that needs to be steamed for 15 minutes. Answered by Leeanne Boehm.
	4160		2001-03-07
		From Jessica: The product of two consecutive page numbers in this book is 4160. What are the page numbers? Answered by Penny Nom.
	Law of cosines		2001-02-20
		From Emily: I missed a few days of class and I can't figure out how to solve Law of Cosines problems. I have the notes and formulas but I can't figure out how to do the math involved to answer the problems. I am also getting confused about how to use degrees and seconds in the Law of Sine and Cosine. I can't seem to get the correct answers and I don't really know how to solve them and enter them into my TI 86. Answered by Harley Weston.
	Percentage increase		2001-02-17
		From Bob: If sales for jan 2001 are 154 vs 105 for 2000 - the increase total presented to my office is +46% - how does that compute. Please give me the equation. Answered by Penny Nom.
	Partitioning of an arbitrary line segment		2001-02-08
		From David: Did Euclid's Geometry include a construction for the regular partitioning of an arbitrary line segment? Answered by Chris Fisher.
	23 + 17 * 2 / 8 + 11 = 13		2001-02-02
		From David: My child is working through basic operations, and gave this problem: 23 + 17 * 2 / 8 + 11 = 13 The teacher wants the parenthesis to be put in the right places to come up with 13. Answered by Claude Tardif.
	Subsets of the natural numbers		2001-01-30
		From Christina: How do I explain why the set of natural numbers (N) cannot be equivalent to one of its finite subsets? Answered by Penny Nom.
	Crossing the dessert		2001-01-29
		From Zach: An Explorer needed to make a 5 day trip across a dessert. Each man with him could carry exactly 3 days food and water. For one man how many men will it take to cross the dessert? Answered by Claude Tardif.
	Geometric and arithmetic sequences		2001-01-26
		From Garry: what are the equations for geometric and arithmetic sequences? also, what are the equations for finding the sums of those series? Answered by Leeanne Boehm and Penny Nom.
	0,2,3,6,7,1,9,4,5,8		2001-01-23
		From Tami: What is the sequence of the numbers 0,2,3,6,7,1,9,4,5,8 Answered by Claude Tardif.
	The hypotenuse of a right triangle		2001-01-22
		From Phillipe: How do you find the hypotenuse of a right triangle? Answered by Penny Nom.
	Proportionality: direct and indirect		2001-01-18
		From Nancy Ellis: What is the difference between directly proportional and indirectly proportional? Answered by Leeanne Boehm.
	Polynomials and exponents		2001-01-15
		From A student: I am duing a project in math on polynomials and exponents. I need a real life usage of polynomials and exponents for my project. Answered by Penny Nom.
	Some terms in a sequence		2001-01-15
		From jamie: Please help as soon as possible! i am stuck with some terms in a sequence. the terms are 1st term=1, 2nd term=10, 3rd term=35, 4th term=84, 5th term=165, 6th term=286. can anyone tell me the formula for the nth term? n is term number Answered by Sukanta Pati.
	cot(arcsin 3/5)		2001-01-07
		From Jason: Find value. Assume that all angles are in Quadrant 1. cot(arcsin 3/5) Answered by Harley Weston.
	The city transit system		2001-01-07
		From Jacky: The city transit system carries an average of 9450 bus riders a day, for a fare of $1.75 each. The city wants to reduce car pollution by increasing ridership and to maximize the transit system's revenue at the same time. A survey indicates that the number of riders will increase by 150 for every $0.05 decrease in fare. Answered by Harley Weston.
	Derfs, Enajs and Sivads		2001-01-07
		From John and Norman: All Derfs are Enajs. One-third of all Enajs are Derfs. Half of all Sivads are Enajs. One Sivad is a Derf. Eight Sivads are Enajs. The number of Enajs is 90. How many Enajs are neither Derf nor Sivad? Answered by Penny Nom.
	A quarter-circle and two semi-circles		2000-12-31
		From Christopher: Inside the quarter-circle are two semi-circles with the same radius, (r). Which has a greater area, G or L? Answered by Penny Nom.
	An infinite series		2000-12-16
		From John: summation(n=1 to infinity)[n sin(1/(2n))]n Answered by Harley Weston.
	Direct and inverse variation		2000-12-12
		From Ashley: I'm stuck on this unit of direct and inverse variation..please and my problems and show me how to do each PLEASE!!! Assume that y varies directly as x If y= -4 when x = 2, find y when x= -6 Assume that y varies inversely as x If y =-4 when x=2, find y when x =-6 Answered by Penny Nom.
	A point that a group of lines pass through		2000-12-05
		From Ross: A point that a group of lines pass through is called a________? Answered by Chris Fisher.
	Triangles and trigonometry		2000-11-30
		From Mose: If I have a right triangle, and I know the lengths of all three sides, is there a formula that will allow me to determine the measurements of the 2 non right angles? Answered by Harley Weston.
	Power series representations		2000-11-27
		From Grace: Is there a systematic way of finding a power series representation of a function? I understand that you have to manipulate the function so that it is of the form 1/(1-x), but beyond that I am lost. Answered by Harley Weston.
	A piecewise linear equation		2000-11-24
		From Jacky: There is a light bulb and it is given that the light bulb cost $0.75 and the cost of operating it is $0.0081 per hour. From the information give, I came up with the linear equation: Let c be total cost and Let h be hours used. Therefore: c = 0.0081h + 0.75 represents the total cost of the light bulb and the electricity. However, the second part of the question added the fact that the light bulb will only last for 800 hours. If the light bulb is replaced as soon as it burns out exactly after every 800 hours, how can I write an equation that represents that? Is it possible? What would it look like on the graph. Answered by Harley Weston.
	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.
	Range of a function		2000-11-21
		From David Bell: Given a rational function such as f(x) = (8x-3)/(4x-1). How can the range be found. Answered by Penny Nom.
	Infinite Geometric Series		2000-11-10
		From Sam Carter: I ran into a problem when studying how to find the sum of an infinite geometric series. My math book attempts to explain the concept by giving formulas involving sigma and |r|, but it does not really explain how to go about finding the sum of an infinite geometric series. If you could either help me with this or point me in the direction of an informative website that could help me, I'd appreciate it. Answered by Harley Weston.
	Rhombuses		2000-11-07
		From Melissa: What in real life is the shape of a rhombus? Answered by Chris Fisher and Walter Whiteley.
	False Positives		2000-10-29
		From James: A rare disease infected 1 in 1000 people in the population. A test for the disease is accurate 99% of the time when given to an infected person and also when given to a heathy person. Fill out a two-tier tree diagram and find the probability of the false positive(i.e the conditional probabily of being healty even when tested postive by the test) Comment on the result? ... Answered by Penny Nom.
	Overlapping a circle and a square		2000-10-28
		From Jacky: A square with a dimension 20 by 20cm. and a quarter of the circle with the radius of 25cm (A quater of a circle is created by 2 cuts that are perpendicular bisectors of each other where the intersecting point is at the centre of the circle). With these 2 pieces, the 2 pieces are placed over each other in which the 90o angle of the quarter circle matches with one of the right angles on the square. Now, calculate the overlapping area of the 2 figures. Answered by Chris Fisher and Harley Weston.
	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.
	Assessment and portfolios relating to math		2000-10-24
		From Jackie: I will be assisting in a presentation for grades 4-6 on assessment and portfolios relating to math. If anyone has some ideas will love to hear them. I have checked out a few sites on the net Answered by Diane Hanson.
	A sequence question		2000-10-23
		From Chell: I have the following sequence: 4 16 37 58 89 145 42 20 I have no clue how to arrive at an answer. I've checked to see if it can be defined as an arithmetic or geometric series, and it can't. I've looked for primes and noticed that 37 and 89 are the only primes ... but from there I've lost. Nothing I've tried seems to work, so please help! Thanks a million!!!! Answered by Chris Fisher.
	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.
	Sunflower seeds		2000-10-09
		From A parent: Find the number of 3/4 pound of sunflower seeds that can be filled with 225 pounds of sunflower seeds Answered by Penny Nom.
	Maclaurin series again		2000-09-23
		From Jason Rasmussen: I suppose my confusion comes into play when I am trying to figure out where the xn term comes from. I know that the Power Series notation is directly related to the Geometric Series of the form sigma [ brn ] where the limit is b/(1-r) for convergence at | r | <1. Therefore, the function f(x) needs to somehow take the form of b/(1-(x-a)), which may take some manipulation, and by setting r = (x-a) and b = Cn, we get the Geometric Series converted to the Power Series. Taking the nth order derivative of the Power Series gives Cn = fn(a)/n!. There must be a gap in my knowledge somewhere because I cannot seem to make f(x) = ex take the form of f(x) = b/(1-(x-a)). Maybe I should have labelled my question as "middle" because it may be more of a personal problem with algebra and logarithms. Or, am I to assume that all functions can be represented by sigma [fn(a) * (x-a)n / n!]? Answered by Harley Weston.
	A Maclaurin series		2000-09-21
		From Jason Rasmussen: I have a question regarding power series notation for certain functions within the interval of convergence. Answered by Harley Weston.
	Arithmetic in base 5		2000-09-20
		From Lesley Emerson: my daughter is 9 and has been aske to solve the following in base 5 3+2 4+10 . . . Answered by Penny Nom.
	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.
	Tessellations		2000-09-17
		From Lindsay: What is the word that means a shape repeated over and over again to make something like a quilt pattern? Note: I'm pretty sure it is either a fractal or tesselation. Could it be that the pattern itself is a fractal but the entire quilt would be a tesselation? Answered by Chris Fisher.
	7 - - - - 77		2000-09-13
		From Peter: Does anyone know how to solve the following: 7 _ _ _ _ 77 ? I have to find the missing values. Answered by Chris Fisher and Walter Whiteley.
	The sum of the squares of 13 consecutive positive integers		2000-08-25
		From Wallace: Prove that it is not possible to have the sum of the squares of 13 consecutive positive integers be a square. Answered by Harley Weston.
	Covering 1, 1/2, 1/3,...		2000-08-22
		From Wallace: Consider the points 1, 1/2, 1/3, ... on the real number line. You are given five small bars, all of length p, which are to be placed on the number line such that all points will be covered. What is the minimum value of p that will allow you to do this? Answered by Penny Nom.
	Three consecutive odd integers		2000-08-18
		From Wallace: A six-digit integer XYXYXY, where X and Y are digits is equal to five times the product of three consecutive odd integers. Determine these three odd integers. Answered by Paul Betts.
	A semi-circle and a triangle		2000-07-28
		From Ben: A semi-circle and an isosceles triangle ABC have the same base AB and the same area. The equal angles in the triangle are BAC and CAB. I have to find the value of each of these angles. Answered by Harley Weston.
	Patterning and Sequencing		2000-07-05
		From Michael Jellis: What would be the next two terms? 1.0,0.5,0.6,0.75,0.8,___,____ please explain!!! I am completely baffled and need all the help I can get! Answered by Claude Tardif.
	Cairo tesselation and Archimedean duals		2000-06-21
		From Joyce DuVall: I am looking for a picture of the Cairo tesselation, and pictures of the Archimedean duals. Do you know of any good web sites or books? Answered by Penny Nom.
	A sequence		2000-06-16
		From Claire Hall: Can you find the formula for the pattern 4,12,24,40,60 Answered by AClaude Tardif.
	1+4+9+16+...n^2 = n(n+1)(2n+1)/6		2000-06-01
		From Shamus O'Toole: How do you derive that for the series 1+4+9+16+25.. that S(n)=(n(n+1)(2n+1))/6 Answered by Penny Nom.
	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.
	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.
	The number of seats in an auditorium		2000-05-16
		From David Evaska: There are 10 students in the first row of seats in an auditorium 12 in the second 14 in the third and 2 additional in each seat. The total number of rows is 40. I know the answer is 1960 can you please show me the formula step by step. Answered by Penny Nom.
	Looking for a pattern		2000-05-08
		From Laura: Yesterday, me teacher stumped me with a question. He talked to us about square units. He told us an area of 1 square unit produces 1 shape, an area of 2 sq.units produces 1 shape, an area of 3 sq.units produces 2 different shapes, an area of four square units produces 5 different shapes, and an area od five sq.units produces 12 different shapes. He left us there. He said we had to find how many different shapes an area of 1 sq. unit produces through how many different shapes an area of 15 sq.units produces. He said we could complete this "chart" by finding an equation. But, I can't find the equation. I think it may be a quadratic of some sort. My teacher told us to use the area(in sq.units) as X and the # of different shapes produced as Y. Now, what really is stumping me is I would have to have an equation so when X is Y, Y is 1 and when X is 2, Y is 1. I have also tried to see if I can complete a patter or something. The pattern I saw was 1,1,2,5,12. I can't make much sense of that pattern. Answered by Penny Nom.
	Area of an ellipse		2000-05-02
		From Kaushal Shah: How do I Calculate the area of a ellipse known the length of any related thing. Example, suppose if I know the length of latus rectum, major&minor axis etc. Answered by Walter Whiteley.
	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.
	Graphing cube roots		2000-04-27
		From Heather Jones: What do the graphs of cube roots look like? Answered by Walter Whiteley.
	Paying with silver		2000-04-26
		From Luther Jackson: A silver prospector is unable to pay his March rent in advance. He owned a bar of pure silver, 31 inches long, so he made the following arrangement with his landlady. He would cut the bar, he said into smaller pieces. On the first day of March he would give her and inch of the bar, and on each succeeding day he would add another inch to her amount of silver. She would keep this silver as security. At the end of the month, when the prospector expected to be able to pay his rent in full, she would return the pieces to him. . . . Answered by Claude Tardif and Penny Nom.
	Sample variance		2000-04-16
		From Jonathan Freeman: I was just reading your article entitled "A Note on Standard Deviation" I'm now teaching a unit on s.d. and my students were wondering why one uses a denominator of n for a population and n-1 for a sample. I saw in your article that this is because "[the quantity] tends to underestimate sigma... and other technical reasons." To which my students again asked... "Why?" Could you please elaborate a bit on the "other technical reasons" perhaps in terms a high school senior (or their teacher...) could understand? Answered by Harley Weston.
	Infinite sets		2000-04-12
		From Brian Provost: Here's the deal: There are an infinite amount of integers (1,2,3...). Agreed? There are an infinite amount of even integers, too (2,4,6...). Agreed? By convention, infinity equals infinity. Yet common sense tells us there are obviously more integers than there are even integers. Prove this to be true mathematically. Answered by Harley Weston.
	Geometric sequences		2000-04-11
		From Jodie: I am in a grade ten principles class and was taught how to do geometric sequences and series but no one in my class understood what we were taught. Our teacher is one of few to use the new curriculum which used to be the grade twelve curriculum. Could you please explain to me how to do geometric sequences and how to find the different terms and sums. Thank you very much! Answered by Harley Weston.
	Increasing the weight		2000-03-23
		From Lee Millard: A weight of dimension a, b is to have its weight increased by w% by bolting plates of the same material along the top and one side (but not at both ends). The top plate and side plate have the thickness, x. Find the thickness of the plates for a given weight increase of w%. 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.
	Completing a sequence		2000-03-17
		From David Grimmer: Complete the following sequence so that, after the first two terms, each successive term is the average of all the preceding terms. 20__ __ 28 __ __ Answered by Penny Nom.
	Angle of Intersection of Two Lines		2000-03-02
		From Veronica Patterson: I am having a real hard time trying to figure out this problem. Could you please help me! The homework question says to find the acute angle of intersection between the two lines y=3x+1 and y=(1/2)x-1. (It also says to use the results of a problem I had already figured out.) That problem was to use information from a picture shown that tan(theta sub1-theta sub2)= ((m sub2- m sub1)/(1+(m sub1 * m sub2))). I used the difference identity of tangent to figure out the answer. Any help on this problem would be greatly appreciated. Answered by Harley Weston.
	What's the next term?		2000-02-29
		From Meredith O'Neill: At this point, the whole family wants to know the answer. if possible an explanation. thanks a sequence ? 16,37,58,89,145 ?? Answered by Chris Fisher.
	Why counterclockwise?		2000-02-21
		From Drew: Why do the numbers of quadrants in a graph increase in a counter clockwise pattern? Why aren't they numbered increasingly in a clockwise pattern? Answered by Chris Fisher.
	Perimeter of an ellipse		2000-02-21
		From Kurtis Proffit: What is the formula for the perimeter or circumference of an ellipse? Answered by Chris Fisher.
	Number sense		2000-02-17
		From A college student: I am a college student and I am to answer the following question: Describe ways of telling by simple inspection when a fraction has a value close to 0; close to 1/2; and close to 1. I am to imagine that I am a 3rd grader answering this question. Any thoughts please? Answered by Penny Nom.
	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.
	100% on two tests		2000-02-01
		From Craig and Chelsea Bruzzone: A class of 35 students took a math test and a science test. 12 students got 100% on the math test. 9 students got 100% on the science test. There were 19 students who made less than 100% on both tests. How many students made 100% on both tests? Answered by Penny Nom.
	Percent of improvement		2000-01-30
		From Steve Quigg: In a 1998 survey, 21% polled responded favorably to a question. In 1999, 31% responded favorably. What is the percent of improvement? Answered by Harley Weston.
	zero		2000-01-01
		From Jason: What civilization first used zero? Answered by Penny Nom.
	Graph of a sine function		1999-12-23
		From Pierre: Given; amplitute:1 period: 540 Phase shift: 60 degree,right I am ask to right the equation: sin 2/3 (value -60degree) When I am asked to graph the equation, the period is mixing me up. Answered by Harley Weston.
	Approximations		1999-12-20
		From Adrian Valc: Long-time ago I red an article about surprizing (and in a way frustrating) results in math, for example the limit of a nicely defined infinite series which was believed to be a simple rational number, but later was determined to be a transcendent number that missed the rational value by an incredibly small amount (so for example the limit proved to be 2.75000...00137.. with a lot of 0's in between). I cannot find that article anymore, so i was wondering if you have any such examples, or you can point to any relevant information source? Answered by Chris Fisher.
	Comma as decimal separator		1999-12-18
		From Franck Menuge: Could somebody tell me the origin of the use of a 'comma' as a decimal separator and of a 'dot' for thousands in the French numeric system, ex.1.234,56 Is it only used in France or in other european coutries? Why is it different in the UK? Answered by Patrick Maidorn and 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.
	.400 in Baseball		1999-12-15
		From Nieve Nielson: I have several questions to ask about the probability of getting a .400 in baseball: What is the probability of a baseball player hitting a .400 in one game, considering that the hitter is up to bat four times? What is the probability of a baseball player hitting a .400 in a season, considering that there are 100 games in a season? With the first two questions in mind: Considering that baseball has been around for about 100 years, about how many people should hit .400 inthat time? Answered by Chris Fisher.
	Two conics		1999-12-07
		From Quinn: I know the formula to find the axis of symmetry of a conic section (I'm not sure what shape - circle for the first one??) is (-D/2A,-E/2C) but I obviously don't get how to calculate it, because when I check the answer it's wrong, but I'm so close!! For the following equations my teacher suggested to "divide the x term coefficient, D, by the x squared term coefficient before...do the same for y." 2x2+2y2-8x+12y+16=0 . . . Answered by Penny Nom.
	Bases other than 10		1999-12-06
		From Garret Magin: We are doing a lesson on numbers of other bases than 10. We are working with binary, octal, and Hexadecimal. I was wondering what is used to represent number of different bases other then 16? Does it just continue on with the alphabet and if so what happens when you get to Z. It would be a help if you could answer this because it is really bugging me. And none of the math teachers at my school could let me know. Answered by Claude Tardif and Patrick Maidorn.
	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.
	Selecting some players		1999-11-20
		From Korbin Brown: Roger Craig, during his term as team manager of the San Francisco Giants, received a strange communication from the team general manager, Al Rosen. Mr. Rosen told him to select 25 players according to this formula: 1/2 of the team had to be outfielders and infielders 1/4 of the team had to be starting pitchers 1/6 of the team had to be relief pitchers 1/8 of the team had to be catchers Roger was a bit confused by Al's request, yet complied anyway. How did he do it? Answered by Claude Tardif.
	Domain and Range of a Function		1999-11-14
		From Michelle Mellott: How do you find the range of the following function: 2y2/(y2+5y+6)?? I know the domain is x not equalled to -2, -3. How can one easily find the range? Answered by Harley Weston.
	Number sequences		1999-11-11
		From Justin Schessler: I CAN NOT figure out this sequence or how we continue this sequence... 3,2,6,5,15,14,___,___,___ Answered by Chris Fisher and Harley Weston.
	Inverses of functions		1999-11-01
		From Leanne Hickey: Let f(x) = 2x2 -3x + 2. Find f-1(4) given the fact that f(2) = 4. So the question is finding the inverse of 4, he said it's easier than it looks. Answered by Penny Nom.
	Ben's observation		1999-10-28
		From Emily Nghiem and Ben Rose: As a teacher at a school called Educere in Houston, I have a ninth-grade student who discovered the following shortcut last year as an eight-grader. What he noticed is that given any two consecutive integers (or n and n+1 for any rational number greater than or equal to 2), the difference between their squares was equal to the sum of the two numbers. . . Answered by Chris Fisher and 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.
	Piecewise functions.		1999-10-20
		From Jenny: How do you figure out a piecewise function by hand? e.x. ( 2x (if x is not equal to 0) f(x)=< ( 0 (if x is not equal to 0) Answered by Harley Weston.
	Percentage increase		1999-10-03
		From Ann Allen: I am a a student in the 12th grade. I need to know how to calclulate the following: A percentage increase from 2.0% to 9.5% is what percentage? Answered by Harley Weston.
	Notation		1999-09-03
		From Judy Gray: My name is Judy Gray. I guess the level on this would be about middle school, and I am an other!! I've been out of school for alot of years. I have a couple of questions, I guess. What does an equal (=) with a slash through it mean? I put intersects, but I think I'm wrong. What is the symbol of a small n? Only the symbol is wider. Example: If A = {1.2} B = {2,3} then what is A (n) B? Can you make sense out of that? What is the equation of the y-axis? Answered by Penny Nom.
	Cleaning an Ellipse		1999-07-29
		From Mark Salter: Hello hope some one can help. We need to clean an elipse and then paint it. We need to know the square foot of the job and the job is an elipse which rises 2 ft. is 12 ft wide and is 36 ft long. Answered by Harley Weston.
	A Weighty Problem		1999-06-17
		From A parent: When using a balance scale, weights can be placed on either side of the scale. For example, if a 10 pound weight provides a counter balance to an object and a 7 pound weight, then the object must weigh 3 pounds. What four weights can be used to weigh objects of 1, 2, 3 ... 38, 39, 40 pounds? Answered by Penny Nom.
	Base 2 to Base 10, conversion, convert		1999-05-08
		From Larry Bader: 101000112 is the same as what number in Base ten? a. 83 b. 128 c. 93 d. 326 e. 163 Answered by Penny Nom.
	Shape-preserving transformations		1999-05-04
		From J McAndrew: A shape preserves its shape if a rotation, translation or scaling is performed on it. Are these the only continuous transformations which have this property? These transformations if performed on the parts and then summed have the same effect as the transformation being applied to the whole; are these linear transformations? Who, and what area of mathematics has classified all transformations of this type completely? Answered by Chris Fisher.
	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.
	A Series		1999-04-20
		From Deepak Shrestha: Given the sequence an=e^(-n*Ln(n)), does the series converge and why? Answered by Harley Weston.
	Volume of oil in a tank		1999-04-17
		From Lars Waldemarsson: My problem is to get an equation for the depth of the oil in a gastank formed like a cylinder. The cylinder is in a horizontal position and by a stick you will be able to get the depth of the oil in the tank. All I need is an exmaple which I can build on. By this equation you will be able to get the volume of the oil if you know the depth. Answered by Harley Weston.
	Dividing a Circle		1999-04-12
		From Mike Kenedy: I am having trouble with a homework question for bonus marks. A Circle is continually divided by lines that do not intersect the center so that they produce the most pieces of circle. For example 1 line divides the circle into 2. 2 into 4. 3, however into 7. 4 into11 5 into 16 6 into 22 7 into 29 8 into 37 etc... I am stumped and cannot figure out the equation, though I'm sure it involves squares. Can you help? Answered by Penny Nom.
	Cross-sectional area of a cylinder		1999-04-12
		From Rebecca Connor: What is the formula to find the cross-sectional area of a cylinder? Answered by Chris Fisher.
	Linear programming and optimization		1999-04-09
		From Shams: What is Linear programming and optimization? Answered by Jack LeSage and Penny Nom.
	Percentages		1999-03-16
		From Beth Barton: If I have two figures and want to know the difference between them, in Percentage, how do I proceed with a calculation? Example: 67,800 - 56,000 = 11,800 What percentage does this difference represent? Answered by Jack LeSage.
	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.
	Reversing the direction of an inequality.		1999-03-06
		From Mallory White: If the Problem was -4a plus -5 is less than or equal to 14, why would you change the sign to greater than or equal to? Answered by Jack LeSage 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.
	Dig digs in the garden		1999-02-11
		From Katherine Shaw: A circular garden has an a radius of 8m. Dig, the dog, is tied up to a fence that runs round the outside of the garden. Dig was able to dig up all the garden, apart from an area of 64 square metres, which he couldn't reach. How long was his lead? Answered by Chris Fisher and Harley Weston.
	Cannonballs		1999-01-27
		From Roger King: How many cannonballs can be stacked in a triangular pyramid? Answered by Penny Nom.
	Place Value		1999-01-05
		From Reg: I work in a Section 27 classroom with various grades. I am looking for assistance on how to deliver a lesson on place value:decimal numbers keeping in mind that they need to see it (visual) to comprehend. I am looking for grade 4-6 level. Answered by Jack LeSage.
	Intersection of Planes		1998-12-03
		From Lindsay Fear: My name is Lindsay Fear. I am an OAC student (which is the Ontario equivalent to Grade 12 in most other states and provinces). I am in an Algebra and Geometry course and am currently studying a unit on equations of planes. Our teacher has given us this question that my friend and I have attempted several times, but we are still unable to solve it. My teacher has also suggested using the internet as a resource. The question is: Prove that a necessary condition that the three planes -x + ay + bz = 0 ax - y + cz = 0 bx + cy - z = 0 have a line in common is that a^2 + b^2 + c^2 + 2abc = 1 Answered by Walter Whiteley.
	Intersection of planes		1998-11-22
		From Dave Rasmussen: I am a teacher of secondary mathematics with a question about the uses of Three Dimensional Co-ordinate Geometry. I have been teaching my students to write equations of planes and lines, - to find the intersection of these and the distance between them. What I am having difficulty finding are good applications of these techniques to "real world" situations. Can anybody help me? Answered by Walter Whiteley and Harley Weston.
	What's the next term?		1998-11-12
		From Ilia: What the formula and explonation for formula for next patterns: 1) 1, 4, 10, 20, 35, 56, 84,... 2) 0, 6, 30, 90, 210, 420,... Thanks! Answered by Penny Nom.
	Two sides and a bisectrix.		1998-11-11
		From Victor Grinshtein: I am looking for someone who can tell me how to construct a triangle by 2 sides and a bisectrix using a compass and a ruler. Answered by Chris Fisher.
	Operations Research		1998-10-08
		From Lisa Barrett: What is the history of operations research and the study of linear programming? Answered by Judi McDonald.
	Dividing a Class		1998-10-01
		From Tom Barker: My eighth grade niece called with the following homework problem: A teacher wanted to divide her class into equally numbered groups. She tried to divide the class into groups of two, but was one student short. She tried to divide the class into groups of five, but was one student short. She tried to divide the class into groups of seven and was successful. What is the least number of students that were in her class? I know the answer is 49, but don't know how to prove it. I must be getting old if I can't solve eighth grade math problems. Your assistance would be appreciated. Answered by Penny Nom.
	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.
	Social Security Numbers		1998-07-07
		From Valerie Lucas: How many social security numbers are possible? the answer is 10^9 why isn't the answer 9^9? Answered by Harley Weston.
	Sequences and series		1998-05-27
		From Michael Le Francois: The sum of the first ten terms of an arithmetic series is 100 and the first term is 1. Find the 10th term. The common ratio in a certain geometric sequence is r=0.2 and the sum of the first four terms is 1248 find the first term. Answered by Penny Nom.
	The Fourth Dimension		1998-05-24
		From Whitney Page: Okay, here goes all my effort to try to explain shat I'm trying to ask of you. It's about something I read in a book called A WRINKLE IN TIME, by Madeline L'Engle. It's called tesser, or tesseract. It talks about first diminsion, a straight line, second diminsion, a flat square, and third diminsion, a square with sides, front and back, top and bottom. I can picture all of that. Then it says that fourth diminsion is when you square the three diminsional square. It also described the fourth diminsion as time. I can't figure out how that can be. Then it says... Answered by Chris Fisher.
	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.
	Seed Problem		1998-03-26
		From Jody A. Johnson: Seed Problem: The height of an amazing plant grown from a seed varies linearly with the time it has been in the ground. After six days it is 6cm tall and after 60 days it is 15.8m (1580 cm) tall. Write the particular equation giving the height as a function of time. Find the intercepts and explain them. What would be the height in one year? How long would it take for the plant to grow to a height of 1km? I'm having a problem with this equation. Could you please help. Thank you. Answered by Penny Nom.
	Matrices		1998-03-10
		From Ksya: A and B are matrices. If A^n=B^n, can we say A=B or det(A)=det(B) or det(A)^n=det(B)^n ? Any conditions ??? If B^(-1) is the inverse of B, where B is a matrices. Can we say [(B^(-1))^n][B^n]=I, where I is identity matrices? Any conditions??? Answered by Doug Farenick.
	Pay Phone Problem		1998-02-26
		From Shameq: Hi, I've been given a problem that I'm having some trouble with. I'd really appreciate any help. Here's the question (it's called the Pay Phone Problem) A pay phone will take only 10p, 20p, 50p, and £1 coins"(It's British). A woman has plenty of 10p and 20p coins. She has no other coins. She can put the coins into the pay phone in any order. INVESTIGATE the number of different ways, she could put the 10p and 20p coins into the pay phone. Answered by Penny Nom.
	Tessellations of non-polygons		1998-02-24
		From Ellen Goldwasser: Hi! My name is Ellen Goldwasser. I'm a seventh grade student and I'm doing a prodject on tessellation. My question is: why will certain shapes (not polygons) tessellate? Thanks for your help! Answered by Penny Nom.
	Tangrams		1998-02-24
		From Allison: Do you know the story behind the tangram? I know that it is a Chinese puzzle about 200 years old. If there is a story about its creation, I would love to share it with my 7th graders. Thanks. Answered by Diane Hanson and Penny Nom.
	Intersecting Lines.		1998-02-10
		From Erik Heppler: My typewriter frequently makes mistakes. Suppose I gave you the following system of equations to solve: 35.26X + 14.95Y = 28.35 187.3X + 79.43Y = 83.29 When I looked back, I realized that I meant to use 14.96 as the "Y" coefficient in the first equation instead of 14.95. Solving the system using 14.95 and then solving another system using 14.96 with all other values the same both times results in the intersection points (1776, -4186) and (-770, 1816) respectively. How can that be? Answered by Penny nom.
	Calculating the Intersection Point.		1997-12-10
		From Milton Parsons: Given 2 lines through (x1,y1),(x2,y2),and (x3,y3),(x4,y4). Can you give me a good formula for calculating the intersection point. I would greatly appreciate it.Thanks. Answered by Chris Fisher and Penny Nom.
	How many intersections?		1997-10-08
		From James: (a) A collection of eight points, no three collinear. If lines are drawn between each pair of these points, how many points of intersection would there be? (b) what would your answer have been in part (a) if there had been n points to start with? Answered by Chris Fisher.
	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.
	Graphing Inequalities of Conic Sections		1997-03-24
		From James Sheldon: I'm trying to graph Systems of Conic Sections with inequalities, but I'm running into problems on which area to shade: x^2+y^2 is greater than or equal to 16 xy > 4 So I graph these two equations, and then my teacher said to substitute a point into it but I'm still not sure how to do it... Answered by Penny Nom.
	Area Between Two Sectors		1997-03-02
		From Rebecca Henry: Points A,B,C,D,E,F are equally spaced on a unit circle. Arc CGE has a center A. Find the number of square units of area in the shaded region. Answered by Walter Whiteley.
	Some Circle Questions.		1997-02-25
		From Staci Vawser: A circle with a radius of 10m is drawn. A chord is drawn across the circle. How is the area that is formed between the chord and the arc calculated? Answered by Harley Weston.
	Foci of an Ellipse		1997-01-22
		From David Gilliam: How do I find the focii of the following equation? 4x^2 + 9y^2 = 36 Answered by Harley Weston.
	Common Area of two sectors.		1996-11-06
		From Lynda Mow: How do I find the area common to two intersecting circles of radii 8 ft and 10 ft if their common chord is 10 ft long? Answered by Penny Nom.
	Where do 2^x and x^2 intersect?		1996-07-23
		From Darin M Selfridge: The intersecting points of y=2^x and y=x^2, graphed along with x^2=2^x, are obviously three... (2,4), (4,16) and (?,?). I am having problems figuring out the value, and even an equation for the (?,?). Can you help? Answered by Harley Weston Chris Fisher.
	What are fractals and are they of any practical use?		1996-06-26
		From Ron: What are fractals and are they of any practical use? Answered by Chris Fisher.
	Converting to other bases		1996-02-06
		From Paul: Converting base 10 numbers to other bases Answered by Penny Nom.
	What is the golden section?		1995-09-17
		From Cindy: What is the golden section of a line? Answered by Denis Hanson.
	Quel est le 6e nombre dans la serie suivante		2010-08-13
		From jeff: Quel est le 6e nombre dans la serie suivante: 1,2,6,42,1806,... Answered by Stephen La Rocque and Claude Tardif.
	Deux nombres consécutifs		2010-01-18
		From Janot: Bonjour comment peut on faire pour démontrer que si deux nombres sont consécutifs, leur produit et leur somme sont premiers entre eux Merci de me mettre sur la voie , j'ai échoué avec Bezout. Answered by Claude Tardif.
	Le plus grand commun diviseur		2009-11-11
		From Katie: Question: Pendant mon cours de MAT 1300, mon enseignant m'a posé la question suivante: (a, b) = 12 (a², b) = 24 (b, 72) = ? Pouvez-vous m'aider s'il-vous-plaît? Answered by Claude Tardif.
	Le réservoir		2009-04-09
		From Myrianne: Le réservoir d'essence d'une petite voiture peut contenir 50 litres. En sachant que 1 dm3 équivaut à litre, donne les dimensions de deux prismes différents représentant ce réservoir. Answered by Claude Tardif.
	Une série géométrique		2008-11-23
		From anass: je vx savoire est ce kil existe la somme de (1/n^x) avec n variant de 0 jusk à infini nota: lorsk x=1et 2 la somme reste tjrs facile mé lorsquil depasse 3 c difficile et merci Answered by Pierre-Louis Gagnon.
	Logarithmique et semi logarithmique		2008-03-08
		From azaar: Je veux savoir comment passer d'un échelle linière à l'échelle logarithmique ou semi logarithmique ? Answered by Lierre-Louis Gagnon.
	Le symbole ∈ epsilon		2007-10-10
		From Cora: Je veux aider ma fille avec ses devoirs. C'est quoi le symbole qui semble un E, mais c'est un demi-circle? ie:X ∈ N Answered by Claude Tardif.
	addition et soustraction des heures, minutes, secondes		2006-11-22
		From Halnais: 13 h. 25 mn + 18 h. 06 mn 23 h. 31 mn + 19 h. 33 mn je ne me souviens plus très bien de ces opérations, faut-il additioner les heures à part puis les minutes, etc. pour les heures je crois qu'il ne faut pas dépasser 24 h. Pourriez-vous m'aider, et me donner le résultat, merci infiniment. Answered by Claude Tardif.
	Des exercices complémentaires		2006-02-26
		From Nathalie: Bonjour, mon fils est en 2e année dans une école de Montréal. Il éprouve des difficultés en mathématiques. Auriez-vous des sites à me suggérer dans lesquels je pourrait trouver des exercices complémentaires à lui faire faire. Answered by Claude Tardif.
	Inverse		2005-10-18
		From Pauline: Défi ! a et b désignent deux nombres distincts non nuls. Peut-on trouver un nombre à retrancher du numérateur et du dénominateur du quotien a/b pour obtenir son inverse b/a? Answered by Claude Tardif.
	exercice!		2005-09-28
		From Un eleve: soit x et y deux nomres réels telque: 1 ≤ x2-x*y+y2 ≤ 2 1) Montrer que: 2/9 ≤ x4+y4 ≤ 8 2) Montrer que: x2*n+y2*n ≥ 2/32*n telque n est un nombre entier naturel et n≥3. Answered by Chris Fisher.
	quel sont les plus grands diviseurs communs?		2005-09-07
		From Sylvain: quel sont les plus grands diviseurs communs? Answered by Claude Tardif.
	Opérations de base		2003-07-05
		From Anne-Marie: Je m'appelle Anne-Marie et je suis enseignante de 5e année à l'école Domaine des copains de Balmoral au Nouveau-Brunswick. Récemment, j'ai participé à un concours intitulé: Budweiser King Pack Nascar Hat Promo. Afin de réclamer le prix, qui est une casquette, je devais répondre à une question réglementaire. Il s'agissait d'une phrase mathématique qui se présentait comme suit: 4 x 26 - 24 / 8 = qui se lit: 4 fois 26 moins 24 divisé par 8 Answered by Claude Tardif.
	La somme de 51 nombres entiers consécutifs est 1785		2003-04-01
		From Katrine et Armand: La somme de 51 nombres entiers consécutifs est 1785, quels sont ces nombres? (indication : on rappelle que pour tout entier P, on a 1 + 2 + ....+ P = P (P + 1) / 2). Answered by Claude Tardif et Penny Nom.
	des conversions de bases différentes		2003-01-04
		From Christian: Je cherche désespérément la (les) règle(s) pour réussir des conversions de bases différentes : de base x vers base y. Answered by Claude Tardif.
	La bissectrice de l'angle ABC		2000-02-16
		From Laurent Gauthier: Est-ce redondant d'ecrire "angle ABC" avec un accent circonflexe sur le B? Peut-on ou devrait-on se contenter d'ecrire soit ABC (avec l'accent), soit l'angle ABC (sans accent) ? Le contexte dans lequel ceci apparait est le syntagme "la bissectrice de l'angle ABC", c'est-a-dire que je me demande si on devrait ecrire "la bissectrice ABC " (avec accent), "la bissectrice de l'angle ABC" (sans accent) ou "la bissectrice de l'angle ABC" (avec accent). Answered by Claude Tardif.
	Septante		1999-12-18
		From Guillaume Bessis: Pourqoui et depuis quand en France emploie-t-on l'expression 'soixante-dix' et non septante pour désigner 70 ? (idem pour 90 et nonante) Answered by Claude Tardif.
	La longueur des segments formant un triangle		1999-10-05
		From Michel Provencher: Connaissant la longueur des segments formant un triangle,comment détermine-t-on chacun de ses angles si: il S'agit d'un triangle rectangle Sachant que la somme des angles d'un triangle est de 180 degrés et sachant par conséquant qu'un des angle est de 90 degrés (triangle rectangle) il reste donc, 90 degrés à partager entre les 2 angles restant. Si les 2 segments formant l'angle droit sont de même longueur on obtient un angle de 45 degrés pour les angles restant soit 1/2 angle droit ce qui ne me pose évidement aucun problème. Quel relation, S'il y en a une, y a t-il entre la longueur de ces 2 segments et les angles restants. il S'agit d'un triangle quelconque Answered by Claude Tardif.
	les fractions		1998-02-24
		From Colette Huguenin: Bonjour je révise mes math de tout les secondaire et le livre louer la bibliothèque n'est pas entier voici le genre de problêmes qui me bloque (5 4/5+1/2)divisé 1/3 je sais que je dois commencer par la parenthèse mais...je fait quoi comme opération avec le 5? dois-je le multiplier ou l'additionner ou.......????? si je pouvais seulement avoir la base des fractions je redébloquerais surement Answered by Diane Hanson.

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