







Finding the area of a regular polygon 
20070504 

From Dana: We are trying to figure the square footage of a tetradecagon....sort of a round house with 14 sides that are 8 ft' in length. It has a height of 9 ft. How do we figure the square footage of this? Answered by Stephen La Rocque. 





The surface area of a dome 
20181218 

From Chithrabhanu: If a dom dia is 4.552 and the height is 1.21 what is the surface area? Answered by Penny Nom. 





The area and weight of sod 
20181211 

From Susan: I have equipment that will cut sod 30 inches across and 75 Feet in length?
how much will this be in square foot age ? Yards? Approximate weight? Answered by Penny Nom. 





A puzzling equation 
20181204 

From Manny: Hello,
Can you explain why this is wrong:
1 = (1)^3 = (1)^{6/2} = ((1)^6)^{1/2} = (1)^{1/2} = 1 ??
Thank you Answered by Penny Nom. 





The price of eggs rises 10 cents per dozen 
20181110 

From Maddie: Hi! I'm currently struggling with a word problem that says:
"If the price of eggs rises 10 cents per dozen, one will be able to get 2 dozen fewer eggs with $6.00 than was possible at the lower price. What is the lower price?
We are working on completing the square and all of the problems I've done so far in this chapter require using that method. If possible and needed, could you explain how to set up the equation?
Thank you so much! I appreciate all your help!! Answered by Penny Nom. 





Why 1/2 in the area of a circular sector? 
20181026 

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. 





Why 1/3 in the volume of a cone? 
20181020 

From Keith: In the formula for the volume of a pyramid, Volume = 1/3 * base * height, where does the 1/3 come from, intuitively? Answered by Penny Nom. 





The area of a trapezoid 
20180924 

From An other: AB272 feet: AC 690 feet; CD330 Feet; DA669Feet Calculate the area in feet and Acres. Answered by Penny Nom. 





Two curves 
20180923 

From Megan: How do i find the interception points of xy=2 and y=x+3? Many thanks! Answered by Penny Nom. 





The pointslope equation for a line 
20180923 

From Sally: The equation of the line in pointslope form for the line passing through the point ( 4, 6) and parallel to the line y = 6x + 2. Describe the steps. Answered by Penny Nom. 





Predicting the number of fish in a lake 
20180916 

From April: A researcher catches 30 fish in a pond, attaches a marker to their fin and releases them. The next day she places a large net in the water and catches 9 fish. 3 have the marker attached to their fin. Can she predict the number of fish in the pond???
Thank you Answered by Penny Nom. 





A locus of points 
20180903 

From Ericka: Find the locus of points three times as far from (0,4) as from (2,0) Answered by Penny Nom. 





5 mm of water over 1 hectare 
20180810 

From Joyce: Please help me with this question.
How many tonnes of water fell on 1 hectare of land during a rainfall of 5mm? Answered by Penny Nom. 





The surface area of a levee 
20180704 

From John: Figuring out the surface area in sq. Ft. Of a levee
Height:10’
Top of levee width: 6’
Width of base (from toe to toe): 40’
Length of levee: 1,250’ Answered by Penny Nom. 





The product of two numbers 
20180619 

From amie: the product of two numbers is 108.when the larger number is divided by the smaller number the quotient is 3. What are the number.tnx Answered by Penny Nom. 





The domain of f(g(x)) 
20180618 

From Joshua: What are the restrictions of the domain of f(g(x))? Answered by Penny Nom. 





The number of terms in an arithmetic sequence 
20180615 

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 area, radius and slant height of a cone 
20180518 

From joette: If you have a cone how to find the slant height when given the area and radius? Answered by Penny Nom. 





Rods,poles and perches 
20180513 

From roy: i have some land and its measured in rods poles and perches
how cann i convert to understand it more Answered by Penny Nom. 





Two expressions for the perimeter of a a rectangle 
20180513 

From Slayde: A rectangular house has one side 4 metres longer than the other. Create two different expressions for its perimeter. The expressions should be given in factorised and expanded form. Answered by Penny Nom. 





Gauss' Addition of whole numbers. 
20180430 

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. 





Spreading soil over 10 acres 
20180429 

From Joe: If you have 54000 cubic yards of soil and want to spread it over 10 acres of land, by how many inches would the ground level rise? Answered by Penny Nom. 





A rectangular prism with rounded corners 
20180425 

From Jackie: Rectangular prism that is 40 by 20 with rounded corners with a radius of 2.5.
What would the surface area be? Answered by Penny Nom. 





More on the curvature of the Earth 
20180423 

From will: the formula for figuring the earth's curve goes against logic, looking at a fixed point and backup 1mi. the point drops 8" then 16" in the next mi. and 32" in the third mi. why shouldn't it be 24" why is the 8" per mi. squared can you tell me in laymens terms why this is it goes against logic it would seem the correct wat would be to add up 8" per mile as you back up from the fixed point 8" 16" 24" 32" not 8/16/32/64" Answered by Harley Weston. 





A volume expression for a pyramid 
20180423 

From Shaheer: Do a three sided pyramid and a square pyramid have the same formula if you want to calculate the volume? Answered by Penny Nom. 





How to find the area of triangle? 
20180419 

From g.a: how to find the area of triangle Answered by Penny Nom. 





The sides of a circle 
20180410 

From Reid: Hello,
I recently was wondering about whether or not a circle has an infinite number of sides, and I ended up searching it on your website. I saw that you guys found the question to be too ambiguous or something of that nature, and I thought about your process of reasoning involving vertices and such. I soon realized that I may have come up with the solution to the question, but I want to confirm it with you guys. Allow me to explain:
A circle, unlike any other typical 2 dimensional polygon, can sustain an infinite number of straight lines coming in contact with only one point on it. A square, for example, cannot. A square only has 4 locations that can sustain a such a line, each of those being its corners. The flat edge of a square cannot support a tangential line, because the line would either be crossing the edge of the square or coming into contact with multiple points along its edge.
This concept is consistent in every 2 dimensional polygon: pentagons sustain 5 locations for tangential lines, hexagons 6, nonagons 9, etc.
The reason a circle has an infinite number of sides is simply the fact that it must have an infinite number of "corners", assuming it can be defined as a polygon like any of the shapes I described above.
Corners can only exist assuming there is two sides coming into contact with one another.
If there is an infinite number of corners in the circle, which is apparent due to the above reasoning, there must be an infinite number of sides coming into contact with each other.
Thus, a circle is a polygon that consists of an infinite number of sides coming into contact with each other.
Please review this reasoning and let me know if it is solid.
Thank you! Answered by Penny Nom. 





A circle problem 
20180330 

From ahamed: the diameters of a circle AB and CD intersect each other at O perpendicularly. Then a chord DF is drawn. AB and DF intersect at E. DE=6cn and EF=2cm.find the area of thw circle Answered by Penny Nom. 





The volume of a tent with a hexagonal base 
20180327 

From shohel: A tent has its base in the shape of a regular hexagon whose sides are 10m . If the height of the tent is 12m , then find its volume. Answered by Penny Nom. 





Distance between a chord and its arc on a circle 
20180323 

From Doug: Specifically, what is the subject distance for the Earth orbiting for 27 days. Assume the orbit of the Earth to be a circle have a 93 million mile radius. Assume the angle of arc to be (27/365) x 360 degrees. Thank you. Answered by Penny Nom. 





Walking a fraction of a mile 
20180320 

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. 





The sum and difference of two numbers 
20180313 

From samima: Two numbers have a difference of 0.85 and the sum 1.What are the numbers? Answered by Penny Nom. 





The dimensions of a rectangle 
20180303 

From Mia: A wire of length 36cm is bent to form a rectangle.
Find the dimensions of the rectangle. Answered by Penny Nom. 





Expand (5x9)(5x+9) 
20180301 

From adil: expand the following:
(5x9)(5x+9) Answered by Penny Nom. 





The perimeter of a square 
20180225 

From Alicia: What's the perimeter of a square with 441cm square Answered by Penny Nom. 





Dividing a region in half 
20180224 

From mandy: There is a line through the origin that divides the region bounded by the parabola y=4x−5x2y=4x−5x2 and the xaxis into two regions with equal area. What is the slope of that line? Answered by Penny Nom. 





The slope of a line 
20180222 

From Steve: my current slope is 6%. I want to know how many inches higher I will be at 18'
Thanks Answered by Penny Nom. 





A footballer angle 
20180214 

From Kim: Two goal posts are 8m apart. A footballer is 34m from one post and 38m from the other. Within what angle must he kick the ball if he is to score a goal. Answered by Penny Nom. 





Related rates 
20180211 

From angelo: hi admin please help me answer this question. thank you!
At a certain instant of time, the angle A of a triangle ABC is 60 degrees and increasing at the rate of 5degrees per second, the side AB is 10cm and increasing at the rate of 1cm per second, and side AC is 16cm and decreasing at the rate of 1/2 cm per second. Find the rate of change of side AB? Answered by Penny Nom. 





Water in a cone 
20180210 

From Shuvo: The diagram shows a vertical crosssection of a container in the form
of an inverted cone of height 60 cm and base radius 20 cm. The circular
base is held horizontal and uppermost. Water is pursed into the
container at a constant rate of 40 cm3/s.
Show that, when the depth of water in the container is x cm, the
volume of the water in the container is (πx^3)/27 cm3.
Find the rate of increase of "x" at the instant when "x" = 2. Answered by Penny Nom. 





Positive and negative values of a function 
20180130 

From Grayson: f(x)=x^6x^4
Interval: ( negative infinity, negative one )
Test Value: negative two
Function Value f(x): positive forty eight
Interval: ( negative one, zero )
Test Value: negative one
Function Value f(x): zero
Interval: ( zero, positive one )
Test Value: positive one
Function Value f(x): zero
Interval: ( positive one, positive infinity )
Test Value: positive two
Function Value f(x): positive forty eight
What is the sign of f(x) for each Interval? Answered by Penny Nom. 





The sum and difference of two numbers 
20180125 

From Ali:
Hello,
I was looking at the original question that was posted and answered by
your team:
http://mathcentral.uregina.ca/QQ/database/QQ.09.07/s/donna1.html
I used the 7 and 4 as example and not looking for 39 per original
question:
A=7
B=4
7+ 4 =11 and 74 = 3
We end up with 11 +3 = 14
A= 14/2 give use 7
B = how do you solve for B or 4 with out knowing anything about 3 or any other numbers ?
Thank you
Ali Answered by Penny Nom. 





The equation of a line 
20180123 

From Gloria: Write the equation of a line in standard form through the point (1, 6) and perpendicular to the line 2x –y = 9. Answered by Penny Nom. 





y as an expression in terms of x 
20180120 

From Mark: What is y as an expression in terms of x ? Answered by pennt. 





Profit margin and markup 
20180118 

From Oyewumi: Mr A sold a car to Mr B at 20% profit margin and Mr B sold the car to Mr C at 30% markup on cost. If Mr C got the car at $x.
1. How much did Mr A buy the car in terms of x.
2. How much did Mr A buy the car if x is $2800000 Answered by Penny Nom. 





When are the hands of a clock perpendicular? 
20180111 

From Nazrul: How many times in a day are the hands of a clock perpendicular to each other? How can I find the times? Please help me. Answered by Penny Nom. 





A fraction of a mile 
20180106 

From Sierra: There are 5280 feet in a mile. what fraction of a mile is represented by 660 feet? Answered by Penny Nom. 





A puzzling sequence 
20171219 

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. 





Needing the area of an irregular Pentagon 
20171206 

From Dale: I'm needing to find the square footage of an irregular pentagon.
I've seen the other questions similar to this one, but without a great deal of difficulty can't get you the angle degrees, or the length between opposing angles.
I'm hoping that a different bit of information can help. So here goes:
The longest side is 67ft long.
One of its legs is 39ft long, and the other is 18ft long.
The leg off of the other end of the 39ft leg is 35ft long.
The leg off of the other end of the 18ft is 49ft long, and meets the other end of the 35ft side.
The information that I DO have, which I'm hoping makes the difference, is that the 39ft and the 18ft sides are parallel.
Also, while the angles at each end of the 67ft side are not right angles, they are fairly close to it,
approximately 80 degrees at the 39 ft side corner, and 100 degrees at the 18ft side corner.
Dale. Answered by Harley Weston. 





Heat equation 
20171123 

From Max: What does du\dt=a(triangle)^2u mean. Can it be solved for t. Answered by Penny Nom. 





How many miles did he drive in one hour? 
20171121 

From Ava: Graham drove 42 1/3 Miles in 1 1/3 hours. How many miles did he drive in one hour? Answered by Penny Nom. 





An expression for the area of a triangle 
20171119 

From hari: why is area of a triangle drawn from centre of a circle i.e radii forming the sides is
1/2 *r^2 sin theta where r is radius Answered by Penny Nom. 





Splitting twice 
20171111 

From Terry: 4 people are splitting 1/3 of something. 1 is to receive twice as much as the other 3. what it the fractional interest for each? Answered by Penny Nom. 





The graph of graph y= 2x1 
20171111 

From Natividad: How do you graph y= 2x1? Answered by Penny Nom. 





Surface area of a hemisphere 
20171028 

From Shaina: If the total surface area of a hemisphere be 36.22/7 cm then its radius will be 3 cm is it true or false Answered by Penny Nom. 





f(x)=x^26x find f(x2) 
20171027 

From Kenneth: f(x)=x^26x find f(x2) Answered by Penny Nom. 





The distance between the origin and a moving point on a graph 
20171016 

From Paulina: Find the rate of change of the distance between the origin and a moving point on the graph of y=x^2 +1 if dx/dt=2 centimeters per second Answered by Penny Nom. 





The volume of a cone without calculus 
20171002 

From Akash: How to find the volume of a cone without the knowledge of calculus? Answered by Penny Nom. 





The square root of 6 is irrational 
20171002 

From John: http://mathcentral.uregina.ca/QQ/database/QQ.09.06/sylvia1.html
In the initial assumption of that proof, root 6 is assumed to be a/b where a and b have no common factors, but why does having a common factor make it irrational? Answered by Penny Nom. 





Four multiples of 10 
20170923 

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. 





The surface area of a sphere 
20170917 

From penny: The surface area of a sphere is 1519.76cm. Taking 3.14 , find the radius of sphere Answered by Penny Nom. 





Quadrilateral ABCD is inscribed in a circle 
20170911 

From Joie: Quadrilateral ABCD is inscribed in a circle such that side DA is the diameter. AB=2m., BC=4m., CD=6m., angle BAD=75.93degrees. Find the area of the quadrilateral. Answered by Penny Nom. 





The volume of an attic 
20170907 

From paul: trying to determine volume of an attic base is rectangular 29 ft by 37 ft
peak runs parallel to longest base side and is 7 ft long
roof lines run from each end of the peak to the respective corners
the peak is 3.5 ft above the base
(so seen from above there are 5 visible lines: the peak and 1 line to each of the 4 corners) Answered by Harley. 





The perimeter of a sector of a circle 
20170811 

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. 





Teams of 4 from 20 people 
20170804 

From Christopher: math team has 20 people on the team but only 4 can enter the competition. The team captain has to pick 4 of them but he knows that he cannot put James, Bill or Todd on the team with one another or there will be problems. what would the formula be to find the solution to how many possible team combinations the are Answered by Penny Nom. 





3 consecutive multiples of 11 
20170722 

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. 





The equation of a circle 
20170703 

From Chen: Find the center radius and equation of a circle in standard form given the following conditions:
1. Tangent to 3x+2y=0 at the point (0,0) and passing through (1,1) and (6,0) Answered by Penny Nom. 





The surface area of a hexagonal pyramid 
20170616 

From Emilie: Hello, I need help with this question:
A pyramid has a regular hexagonal base with side lengths of 4 and a slant height of 6. Find the total area of the pyramid.
Thank you in advance if you can help me... Answered by Penny Nom. 





The maximum area of a rectangle with a given perimeter 
20170602 

From Bob: How would I go about finding the maximum area of a rectangle given its perimeter (20m, for example)? Answered by Penny Nom. 





Two wires between two buildings 
20170511 

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. 





Canada's population as a percentage 
20170511 

From bethmarie: What percentage of the world population (7.5 billion) is Canada's population (36 million).
Thank you very much! Answered by Penny Nom. 





Slicing an inverted bowl at various heights 
20170430 

From Joel: Find a formula to calculate the circumferences of an inverted bowl at various heights.
E.g. Take an inverted bowl with a diameter of "x" cm and a depth / height of "y" cm.
How can I calculate the circumferences at distances of various heights above the base?
Alternately, what would be the formula to calculate the distance of the line segment resulting from a line which intersects both sides of a parabola in which that line is drawn parallel to the tangent of the vertex of the parabola at any given distance from the vertex? Answered by Penny Nom. 





1 acre as a 2 foot wide strip of land 
20170425 

From alan: How can one convert 2 acres (a square  area) of land into a strip of land that is 2 feet wide and (?) feet long? Answered by Penny Nom. 





The length of a train 
20170424 

From Stefano: If a freight train is coming towards you and you were traveling at 85 miles an hour and it takes 35 seconds for the train to pass you how long is the train
Figure 50mph for train Answered by Penny Nom. 





Forming a cone from a circle 
20170415 

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. 





Why does 10x10x10 give 1,000.0000000000001? 
20170412 

From Randolph: Hi, On your calculator I found that a box 10 by 10 by 10 inches has a volume of 1,000.0000000000001 cubic inches. Can you explain the numeral 1 thirteen places past the decimal? Thanks, Randy Answered by Penny Nom. 





The height of a isosceles trapezoid 
20170403 

From Riham: Hi
How can I find the height in an isosceles trapezoid if I have the measurements of all of its sides ?
Thank u in advance. Answered by Penny Nom. 





The sum and difference of two numbers 
20170320 

From Olivia: The sum of two numbers is 87 and their difference is 29. What are the two numbers Answered by Penny Nom. 





2^a, 2^b, 1^1 and 1^0 
20170317 

From Émile: If you had 2^a = 4 and 2^b = 4 you could assume that a = b right? Yet we can observe that 1^1 and 1^0 both equal 1, yet 1 = 0 isn't true. So if given a log base 1 number 1 the would the answer be 1 AND 0? Answered by Penny Nom. 





The ratio of two ages 
20170315 

From Angel: The sum of Keith's age and Alan's age is 36. Four years ago, the ratio of Keith's age to Alan's age was 4:3. Find the ratio of their present age Answered by Penny Nom. 





What is the grade of the incline? 
20170312 

From Jon: If I am climbing 16 feet in elevation over 80 feet horizontal. What is the grade of the incline Answered by Penny Nom. 





More on calculating the area (acreage) of a foursided lot 
20170306 

From Kerri:
Can you please show the formula used to calculate areas as provided on this page:
Calculating the area (acreage) of a foursided lot Answered by Penny Nom. 





The inside diameter of a silo 
20170228 

From JOHN: I need to find the inside diameter of a cement silo with an outside circumference
118 ft and a wall thickness of 7 inches. thank you John Kerr. Answered by Penny Nom. 





The volume of a slab 
20170121 

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 average rate of change of cot(t) 
20170118 

From Brianna: Hello!
It's been a while since I've taken a math course, and I'm stuck on a problem in my calculus course.
The question is this:
Find the average rate of change of the function over the given interval.
h(t)=cot(t) a) [5pi/4, 7pi/4] Answered by Penny Nom. 





One millionth of one percent of 90,000,000,000 
20170116 

From Gene: What absolute number is one millionth of one percent of 90,000,000,000 Answered by Penny Nom. 





8^3/2(2+2) 
20170113 

From Mary: 8^3/2(2+2) Answered by Penny Nom. 





Water leaking from a trough 
20161228 

From Kathryn: A trough is 6 m long, and has uniform crosssection of an equilateral triangle with sides 1 m.
Water leaks from the bottom of the trough, at a constant rate of 0.1 m3/min.
Find the rate at which the water level is falling when the water is 0.2m deep. Answered by Penny Nom. 





20+30*0+1=? 
20161226 

From Mr: 20+30*0+1=? Answered by Penny Nom. 





Two concentric circles 
20161221 

From shrestha: Two concentric circles have radii of 14 cm and 7 cm respectively. Find the area of space between them. Answered by Penny Nom. 





The inverse of y=x^2+x+c 
20161221 

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) 
20161221 

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(x2) not a function?
Suggest a domain restriction which would ensure that the inverse is a function.
Thank You :) Answered by Penny Nom. 





The area and radius of a circle 
20161219 

From india: How do you find the radius of a circle if only the area is given to you? Answered by Penny Nom. 





980 cubic yards of dirt 
20161217 

From Jondi: I am trying to visualize 980 cubic yards of dirt by using a metaphor.
Would this be the size of a car?
A fire engine?
A semitrailer?
How many trucks would you need to haul away 980 yards of dirt? Answered by Penny Nom. 





1/1cosine(2x)  1/1+ cos(2x) 
20161214 

From Sean: 1/1cosine(2x)  1/1+ cos(2x) Answered by Penny Nom. 





How far apart are the boats? 
20161213 

From Halley: Two boats leave port at the same time. Boat A travels east at a speed of 12 km/hr. Boat B travels southwest at a speed of 14 km/hr. After two hours, how far apart are the boats? North is 0 degrees. How do I figure this out.
Thanks Answered by Penny Nom. 





Profit and loss on two shirts 
20161206 

From Mahesh: A man purchases one shirt and one TShirt for Rs. 6000. He sells the shirt at a profit of 20% and TShirt at a loss of 10%, as a result he gains 2% on whole transaction. what is the cost price of the TShirt ? Answered by Penny Nom. 





Gallons and cubic inches 
20161205 

From Theresa: If I did not know the cubic inches in a liquid gallon how would I find it?
In other words what is the formula for this? Answered by Penny Nom. 





The amount of material remaining on a roll 
20161111 

From Yoh:
Question from Yoh:
Hello,
I am trying to find impressions on a roll (either full roll or partial).
Let's say I have the following information.
 Outer Diameter of roll
 Inner Diameter of roll (cardboard core)
 thickness per layer
 Each cut off length (impression length)
Now let's say a roll has a 40in outer diameter, the cardboard core has a 3.75in diameter and a thickness of .002. Each impression has a cut off of 14inches.
With this the roll will have approximately 2,700 impressions. How would I find the remaining impressions if the outer diameter of the roll is only 6.5inches?
Thank you. Answered by Penny Nom. 





The derivative of the inverse of a function 
20161028 

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. 





y = mx + c and Ax + By + C = 0 
20161018 

From Erick: please explain to me how to convert an equation from the form y=mx+c to Ax+By+C=o form. Answered by Penny Nom. 





The degree of 2x + 7 
20161017 

From Deejay: How about when the given has no degree and the other has a constant only, For example 2x + 7,
where's the leading term and what is its leading coefficient? Answered by Penny Nom. 





The equation of a line 
20161001 

From Miriam: write the equation of the line that passes through (6,7) and is perpendicular to 3x+5y=0 Answered by Penny Nom. 





The equation of a circle 
20160930 

From Trent: write the equation of circle B with center B(2,3) that passes through (1,2) Answered by Penny Nom. 





Two equations 
20160917 

From Nilesh: How to solve (xy)^1/2 + 3(xy) = 30 ; xy + 3(xy) = 11? Answered by Penny Nom. 





The radius of a coffee cup 
20160912 

From Brett: What is inside radius, in centimeters of a coffee cup if it holds 350g of coffee when filled to a depth of 9.5 cm? Assume coffee has the same density of water, 1.00g/cm3. A numeric value is expected and not an expression. Answered by Penny Nom. 





The equation of a ski slope 
20160831 

From Hannah: The information provided is
A ski slope has a slope of 0.2. You start at an altitude of 10,000ft.
Then the question is "Write the equation giving altitude (a) as a function of horizontal distance moved (d).
I know this is probably a very simple question but I didn't take a math class my senior year and now I'm a freshman in college, so some of it is very frustrating to me.
Any help is much appreciated, thank you! Answered by Penny Nom. 





The dimensions of a rectangle 
20160831 

From Hazym: How do I find the length(which is 15m longer than the breadth) and the breadth of a rectangle just by its perimeter which is 70 m? Answered by Penny Nom. 





Covering an octagonal region with sand 
20160813 

From Lynn: How much sand is needed to fill a 20 ft. wide octagon area 6 inches deep? Answered by Penny Nom. 





The area of a circle 
20160812 

From sandeep: if circumference of a circle is πd what is the area? Answered by Penny Nom. 





The diameter of a cylindrical tin 
20160804 

From Scott: a cylindrical tin is 15 inches high and holds 5 gallons of paint when it is full. Find the diameter of the tin.
(1 gallon = 0.1605 cubic feet) Answered by Penny Nom. 





The dimensions of a rectangle 
20160725 

From Krunox: A rectangle is twice as long as it is wide. Its perimeter (the sum of the lengths of its sides) is 60 cm. Find its length and width. Answered by Penny Nom. 





The number of sides of a polygon 
20160723 

From Shriya: All the angles of a polygon are either 155° or 140°.
There are twice as many angles of 155 °or 140°.
Find the number of sides of the polygon Answered by Penny Nom. 





A congruence theorem for two right angled triangles 
20160717 

From Sayari: Hello.
Is it possible for two right angled triangles to have the same length of base and height and a different hypotenuse? If not so, then why in the congruence criteria RHS the hypotenuse is given more importance? It can also be like 'two triangles are congruent if they are right angled and have the same base and height.'
Thank You. Answered by Penny Nom. 





The composition of a function with itself 
20160717 

From Mel: If f(1 + 3x) = 1 * x, solve f(f(x)) Answered by Penny Nom. 





Triakis 
20160627 

From Gordon: Some authorities treat "triakis" (and related terms "dyakis", "tetrakis", etc.) as attached prefixes; others treat them as separate adjectives. Thus I see one of the Catalan solids described as both "triakistetrahedron" and "triakis tetrahedron". Which usage is correct? Answered by Chris Fisher. 





Subsets 
20160626 

From Kats: How Many sub sets are in set k={6,7,3} Answered by Penny Nom. 





Cubic feet of soil 
20160619 

From H: A garden is 8 ft x 7 ft that needs to raised 6 inch's How many cubic feet of soil required ? What am I missing ?
Thanks
H Answered by Penny Nom. 





Profit 
20160615 

From Toyia: 12.87 profit from 21.99 sale. What is the percentage that was taken off the 21.99 Answered by Penny Nom. 





A barn roof 
20160529 

From Joe: Is it possible to build a barn roof (irregular pentagon?) with a 12' base and the other 4 sides 4' each? Thanks. Answered by Penny Nom. 





A cylinder in a cube 
20160525 

From Sonia: A cylinder has the same height and diameter as the sides of a cube use 3.14~ which has the greater volume Answered by Penny Nom. 





The area of a 4sided lot 
20160525 

From prasad: How to find area of a land whose sides are 41ft,33ft,32.3ft and 33.2 ft. Pl give me the formula and proof. Answered by Penny Nom. 





Two pieces of rope 
20160521 

From Render: Fred cuts a 12 inch piece of rope. Then he cuts a second piece of rope that is 3/2 longer than the first piece. Is the second piece shorter or longer than the first piece? Explain. Answered by Penny Nom. 





A trough with a triangular cross section 
20160521 

From Clarice: A trough having an equilateral triangle end sections has sides equal to 0.4 m and 7m long.what is the volume of the liquid in the container if the depth of the water is one half the depth of the trough? Answered by Penny Nom. 





The volume of a truncated rectangular pyramidal pond 
20160513 

From Paul: How do you calculate a partially filled truncated rectangular pyramid if you always know the bottom rectangle, the maximum height top rectangle perimeter, but have a varying height. Similar to filling up a pond you know the current height and dimensions at the max rectangle how do you calculate it half full i.e. 10x30 outside perimeter with a 2x8 base and a max height of 6ft how do you calculate it at 3ft without remeasuring the top perimeter.
Thanks,
Paul Answered by Harley Weston. 





A pair of equations with fractions 
20160511 

From tiya: hello, i want to know how to solve this question.
m/6+2n/3=6
m/10=2n/5=2 Answered by Penny Nom. 





Solve 2^2x + 3(2^x)  4 = 0 
20160427 

From Lloyd: Solve the equation 2^2x + 3(2^x)  4 = 0 Answered by Penny Nom. 





The inverse function for f(x)=2x^2+5x 
20160423 

From Ashini: The inverse function for f(x)=2x^2+5x Answered by Penny Nom. 





A sector of a circle 
20160421 

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. 





15.86 acres 
20160421 

From Ronald: If a rectangular piece of land is 1320 ft. on one side, how many feet would be required on the other side to equal 15.86 acres? Answered by Penny Nom. 





A square of side length 4x3 units 
20160420 

From Bryan: Find an expression that represents the area of a square with side length 4x3 Answered by Penny Nom. 





The derivative of x! 
20160416 

From Sang: How to find the derivative of x! and integral of x! Answered by Penny Nom. 





tan15° 
20160411 

From JOHN: find the exact value of tan15° in surd form. Answered by Penny Nom. 





Filling a hole with 14 tons of rock 
20160408 

From Barry: If I had 14 tons of inch and one half sized aggregate rock, how large of a square or rectangular shaped hole would I need to hold that amount? Answered by Penny Nom. 





The last two digits of a phone number 
20160403 

From Joshua: I want to find the last two digits of a phone number whose first eight numbers of a ten digit phone numbers are known. Answered by Penny Nom. 





The volume of a cone 
20160331 

From Odum: Find the volume of a cone with radius 6.5cm and height 12.6cm Answered by Penny Nom. 





The volume of a box with a hexagonal base 
20160327 

From Frank: how many gallons of water in an 8" hexagon shaped box. 6" sides x 12.5" high ? The walls are 1" thick , beveled @ 30 degrees, so inside dimensions are 6" Answered by Penny Nom. 





Travelling in a spacecraft 
20160325 

From julie: if i was travelling in a spacecraft at the speed of light and i turned on my headlight would i see the beam ? Answered by Robert Dawson. 





A rotating schedule for a softball team 
20160325 

From Caroline: I couldn't find a similar question, hopefully there isn't one!
I have a softball team of 18 people (7 girls and 11 boys), but am limiting each game to 13 players (6 girls and 7 boys). The season is 10 games long. How do I create a rotating schedule which allows members to play evenly? I tried separating the boys and girls to create rotation for each but I got confused. Some are unable to attend all games but for the simplicity of a rotation schedule can you please help? Answered by Robert Dawson and Victoria West. 





The inverse of a function 
20160320 

From Billy: f(x) = Square root(x^2 + 2x)
What is the inverse? Answered by Penny Nom. 





The perimeter of a rectangle 
20160317 

From Linda: Noel correctly adds the length of three sides of a rectangle and gets 88 cm her brother Ryan correctly adds the lengths of three sides of the same rectangle and gets 80cm. What is the number of cm in the perimeter of the rectangle Answered by Penny Nom. 





A block wall 
20160315 

From Robert: I have a wall 40 ft. long and 4 ft. tall as well as another one that is 30 ft by 3.5 ft. tall that I am trying to build. how many 6 inch by 12 inch landscaping blocks do I need? Answered by Penny Nom. 





The sides of a triangle 
20160315 

From Hitarth: Why we cannot construct a triangle ofngiven sides 5cm,5cm and 10cm? Answered by Penny Nom. 





Angles 
20160312 

From Laurynn: What are angles in general (please include the 'angle of incline')
Thank you
Laurynn Answered by Penny Nom. 





The integral of a sum 
20160310 

From Rahul: How to solve definite integral of a sum. The specific problem is as follows,
Integral of ( 1+ sum of x^k, k=1 to k=n), x=0 to x=b *dx.
The answer is b + sum of b^(k)/k, k=2, to k=n+1. I understand only the integral
of first term. But integral of the sum I do not understand at all. Answered by Penny Nom. 





The area of a rectangle 
20160303 

From Lucas: The area of a rectangle is given by A=x2+18x+72
use factoring to find an expression for the dimensions of the rectangle.
if the area of the rectangle is 7 square feet, what are the possible values of x?
what are the dimensions of a rectangle? Answered by Penny Nom. 





Corrosion inhibitor in a pipeline 
20160302 

From Edu: I have a 12 in pipeline and 5 miles long. I need to coat it with corrosion inhibitor how much chemical will I need Answered by Penny Nom. 





A rectangular prism 
20160302 

From Paula: Trying to help with a math problem. I don't know how to set up the equation for this.
A rectangular prism has a volume of 7.875m3rd and a height of 3.5 m. What is the area of the base of the prism?
Thanks for your help! Answered by Penny Nom. 





An algebra problem with a sphere 
20160229 

From Sania: If the number of square centimeters on the surface area of a sphere is equal to the number of cubic centimeters in its volume find its diameter Answered by Penny Nom. 





10800 sq. ft equal approx what part of an acre? 
20160227 

From David: 10800 sq. ft equal approx what part of an acre Answered by Penny Nom. 





The sum of the angles of a triangle 
20160224 

From Sophia: Does every triangle add up to 180 degrees? (Such as a unique triangle) Answered by Penny Nom. 





The weight of some dirt 
20160224 

From Michael: How many tons of dirt are in a triangle 14M x10M x 8.1M x .8M deep? Answered by Penny Nom. 





The domain and range of a function 
20160219 

From Genius: State the domain and range
g(x)=x(x1) Answered by Penny Nom. 





The interior and external angles of a regular polygon 
20160217 

From percy: a regular polygon has n sides .The size of each interior angle is eight times the size of each exterior angle .
1.find the size of each exterior angle
2.calculate the value of n Answered by Penny Nom. 





The equation of a vertical line 
20160207 

From Kagiso: The equation for a vertical line that goes through the point (7; 3) is? Answered by Penny Nom. 





The midpoints of the sides of a quadrilateral 
20160205 

From Andrea: The segments, joining, in order the midpoints of consecutive sides of a quadrilateral form a parallelogram. Answered by Penny Nom. 





The height of a triangle 
20160203 

From Brooklyn: How do I figure out the height of a triangle when it only tells me the base of he triangle? And vice versa. Answered by Penny Nom. 





The diagonals of a polygon 
20160129 

From Sofia: What are diagonals and if you drew an octagon and drew all the diagonals how many would there be? Please explain because this is pretty confusing! Thank you! Answered by Harley Weston. 





Consecutive angles of a parallelogram 
20160128 

From Hanna: The consecutive angles of a parallelogram measures Answered by Penny Nom. 





The range of a function with a finite domain 
20160125 

From Hannah: Solve y=(1⁄4)x1 if the domain is (4,2,0,2,4).
I don't get how to do this. Can anyone help? Answered by Penny Nom. 





A system of linear equations 
20160124 

From kareem: my name is kareem
and i am a student i have a math puzzle and i tried to solved it but it always have same mistake
xy=9
x+z=12
zn=14
y+n=2 Answered by Penny Nom. 





Fractions of two quantities 
20160122 

From Melody: Kate ate 1/4 of her orange. Ben ate 2/4 of his banana. Did Kate and Ben eat 3/4 of theit fruit? Explain. Answered by Penny Nom. 





The perimeter of a square 
20160116 

From dennis: If I have eleven Square Acres, what would the perimeter dimensions be? Answered by Penny Nom. 





A limit of a rational function 
20160116 

From selvamani: F (x) = x^3+3x^29x2 / x^3x6 and limit x tends to 2, f (x) exist then limit x tends to 2, f (x) is equal to ? How to answer this problem. Answered by Penny Nom. 





Complex numbers in standard form 
20160115 

From Michael: express the following complex numbers in standard form (2+3i)+(52i) Answered by Penny Nom. 





The range of a function defined piecewise 
20160113 

From sarah:
f(x)={x2, x<2
{x^24, 2_<x_<2
{x+2, x>2
find the range Answered by Penny Nom. 





The perimeter of a triangular plot of land 
20160111 

From Janelle: I need to fence off 6.5 acres. The plot is triangular shape. How many feet would I be fencing off? Answered by Penny Nom. 





The area of a rectangle 
20160108 

From ranjan: if we make a rectangle with a 100cm of wire, then its area will be? Answered by Penny Nom. 





Two transport companies 
20160106 

From Brynleigh: The Sugar Sweet Company will choose from two companies to transport its sugar
to market. The first company charges $5096 to rent trucks plus an additional fee of
$200.75 for each ton of sugar. The second company charges $5500
to rent trucks plus an additional fee of $175.50 for each ton of sugar.
For what amount of sugar do the two companies charge the same?
What is the cost when the two companies charge the same? Answered by Penny Nom. 





A graph of the water level of a river 
20160105 

From emoni: Suppose that the water level of a river is 34 feet and that it is receding at a rate of 0.5 foot per day. Answered by Penny Nom. 





The height of a parabolic arc 
20151230 

From Tom: Is there an algebraic means to determine the highest point of a parabolic arc if the base and perimeter are known? Answered by Penny Nom. 





Strings of characters 
20151228 

From Ali: If I have an app and offer a two, three and four digits name and it can be only number, letters or both?
I want to know how many options will I have for each?
For example
the two digits: aa, 11, a1 or 1a
the three digits: 111, a2a, 222
the four digits: 1111, 2ge3 or 1234
So if I used all the letters and all the numbers but nothing starts with a zero
How can I calculate them separately? Or what's the result for each?
Thank you
Ali Answered by Penny Nom. 





A diameter of a circle 
20151227 

From sahil: Find the equation of diameter of circle x2 +y26x +2y8 which passes through the origin. Answered by Penny Nom. 





The angles of a triangle 
20151217 

From Faith: Does the measure of angle determine the length of its side? For example two angles are congruent then the sides are also congruent because from my understanding the angle determine the shape of triangle. Answered by Penny Nom. 





Proof that an erroneous algebraic statement is false 
20151214 

From Berteanu: I need help with this proposition:
"It exists x a real number that for every y real number 5*x2*y*y=1
This is false.
Let x be from R.
And I need an y real number that 5*x2*y*y!=1
Please,could you help me? Answered by Penny Nom. 





The line of intersection of two planes 
20151209 

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. 





Drawing an arc 
20151204 

From hassan: how to draw a curve long 1m with an angle of 22.5? Answered by Penny Nom. 





The height of a truncated cone 
20151204 

From Jack: I need to build a truncated cone that has a top of30 inches and a base of 64 inches . The sides need to be at a 64.5 degree angle. This will determine the height. Can this be calculated? Answered by Penny Nom. 





The sweep angle of a video camera 
20151125 

From Franc: a television camera is 30ft from the sideline of a basketball court 94 ft long. The camera is located 7 ft from the mid court. through what angle must it sweep in order to cover all action on the court? Answered by Penny Nom. 





The range of f(x)=(2x+2)/(x1) 
20151125 

From Nazrul: f : R to R is a function which is defined by f(x)=(2x+2)/(x1).
Is f(x) an onto function? Please explain.
What is the range of this function?
Thank you very much for your previous help. Answered by Harley Weston. 





How much does the Earth curve over a one foot distance? 
20151124 

From Sean: Hi, I am trying to figure out how much the earth curves over a one foot distance. I'd like to be able to draw the exact arc on a piece of paper. I am an artist and am looking to make glass vessels with the exact curvature of the earth. I read on your site that it curves approximately 8 inches per mile. can I just use simple ratios to break it down into inches?? Thank you so much for your help. Answered by Harley Weston. 





The measure of an angle in terms of its complement 
20151122 

From Pam: Can you please help me so I can help my daughter the equation is the measure of angle v is 4 time the measure of its complement what is the measure of angle v when the equation is 4x+x=90 Answered by Penny Nom. 





20 million as a percentage of 7.3 billion 
20151118 

From Nick: Based on the estimate of the worlds current population (7.3 billion people), I'm trying to work out what percentage of that figure 20 million people would amount to?
(Apologies in advance that I've no idea if the 7.3 billion figure is an American Billion or UK billion)
Thanks for any help.
Nick. Answered by Penny Nom. 





The area of a domed roof 
20151113 

From Brandon: I have a tank with a 13' radius that has a domed roof of 3.5' tall How do I figure out the area in SQFT? Answered by Penny Nom. 





A concrete container 
20151112 

From Karstin: The exterior of a concrete container will be 10 feet by 8 feet by 4 feet tall. The walls and the bottom are 6 inches thick. What will it cost to construct it if concrete is $98.95/cubic yard? Answered by Penny Nom. 





Roof Square footage 
20151111 

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. 





The derivative of x^1/3 
20151108 

From omar: hi can help me
am teacher ask me about x^1/3 Derivation definition . Answered by Penny Nom. 





The domain of cos2x/(sinx2) 
20151102 

From Ameen: Find the domain of:
f(x) = cos2x/(sinx2) Answered by Penny Nom. 





The sum of two repeating decimals 
20151022 

From Kaitlin: Here is the question I am struggling with:
Is the sum of two repeating decimals always repeating decimal? Explain your answer and give an example.
I answered this question thinking that no you cannot but only when adding 0.9 repeating, but my professor said this was incorrect.
Thanks for the help!
Kaitlin Answered by Penny Nom. 





The length of a rectangle 
20150926 

From Tris: Hi,
I'm trying to figure out the length of a rectangle but i forgot how. So, the width is
5cm and the perimeter is 34cm. Answered by Penny Nom. 





Order of operations 
20150912 

From Tanisha: I would just like to double check if something like 5x squared times 4x cubed equals 20x to the power of 5??
It's just that we were told you can only answer an equation like this if the base is the same...so does that mean the x part or the whole thing like 5x?
I'm sorry if that didn't make sense!
Thank you for your help!! Answered by Penny Nom. 





The diameter and circumference of a circle 
20150901 

From Tracey: Hello,
I own a custom workroom, I am figuring out fabric quantities or an estimate. When
at the job site, I forgot to measure the diameter of the semi circle shape that I have to
make a cushion for!!!
If the circumference of the semi circle is 165" what would the diameter be, maybe half
this measurement????
I appreciate any help...I basically need the width from left to right to see if I can fit
the cushion on one width of fabric that is 52" wide! Answered by Penny Nom. 





The distance over a Quonset 
20150820 

From jane: total base of hemisphere is 30 ft
apex height is 20 feet
what is total length over dome Answered by Penny Nom. 





Parallelogram area 
20150804 

From Nigel: To find the area of a parallelogram you multiply the base by the height of the parallogram, the height being determined by an imaginary line drawn at right angles to the base. However if I made a parallelogram with joints at each corner and maipulated it to an upright position where the base and sides were at 90 degrees to each other,, I could then simply multiply the base times the height to get the area. Since the sloping side of the parallelogram does not vary in my imaginary jointed model, why can I not simply multiply the base by the sloping side to get the area in the same way that I multiply the base times the height of a square to find its area ? I cannot find the answer to this on the internet although I have searched. Answered by Chris Fisher. 





Why is the area of square not conserved when it changes to a rhombus? 
20150628 

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. 





1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 x 0 + 1 = ? 
20150618 

From Sharon: 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 x 0 + 1 = ?
I got 1 as my answer despite BODMAS making it 12 because logic tells
me I ought to place brackets around the first set of repeated addition. Could you
please clarify this for me? Thank you 😊 Answered by Harley Weston. 





2^48  1 
20150613 

From Soham: The number 2^481 is divisible by two numbers between 60 and 70. The sum of
the two numbers is? Answered by Penny Nom. 





The amount before profit and overhead 
20150612 

From kelly: I have an existing amount of $22,750.00. this includes the profit at 10% and overhead at 10%.
How do I remove the profit and overhead in order to come up with the original starting figure? Answered by Penny Nom. 





The surface area of a triangular prism 
20150603 

From Alex: Find the surface area of a triangular prism with Isoceles triangles and dimensions 4 feet by 6 feet Answered by Penny Nom. 





The volume of a pipe 
20150602 

From gordon: What is the formula to find out how many gallon of water in a length of pipe tried your answer on 8inch at 50feet did not work out Answered by Penny Nom. 





A pentagon inscribed in a circle 
20150530 

From Victoria: find the area of a regular pentagon inscribed in a circle with radius 3 units Answered by Penny Nom. 





The perimeter of a rectangle 
20150528 

From Imran: The length of a rectangle is x+3 centimetres.
The width of the rectangle is x1 centimetres.
Find an expression in terms of x for the perimeter of the rectangle.
The perimeter of a rectangle The perimeter of a rectangle
Give your expressions in it's simplest form.
The perimeter of a rectangle The perimeter of a rectangle
Thank You. Answered by Penny Nom. 





Prove that you cannot factor x squared + 5 
20150528 

From lily: the question is: prove that you cannot factor x squared + 5 Answered by Robert Dawson. 





The perimeter of a quarter circle 
20150521 

From Bethany: The perimeter of a quarter circle is 3.57. What is the quarter circle's radius? Answered by Penny Nom. 





The intersection of a plane and a cone 
20150516 

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. 





A pile of mulch 
20150515 

From Justin: I have a pile of mulch that measures 19 feet wide at the bottom and has a height of 6 feet. I need to know how many yards of mulch I have.
Please help and help with the formula for further use. Thank you! Answered by Penny Nom. 





An angle of depression problem 
20150514 

From haxir: find the height of the balloon directly above a town if the measure of angle of depression of another town 5km from the first town is 20°!6` Answered by Penny Nom. 





A word problem 
20150508 

From JAMES: A businessman bought a number of similar articles for a total of sh. 6000. Three of the articles turned out to be defective with no resale value. He sold the remaining articles at 12.5% each above the cost price making a total profit of sh 480. How many articles had he bought? Answered by Penny Nom. 





The surface area of a hemisphere 
20150505 

From Mandy: How can I show that the total surface are of any solid hemisphere is 75% of the area of the full sphere? Answered by Penny Nom. 





The method of elimination 
20150501 

From oreanna:
Question from oreanna, a student:
How do u solve 2x+9y=3
7x4y=25 in elimination Answered by Penny Nom. 





Filling a pool with dirt 
20150501 

From Mike: I have a hole which a 24 ft pool in it is 10" deep in the the centre and goes to 1" inch at the edge want to fill it in with dirt how many yards of dirt would I need to fill it in Answered by Penny Nom. 





The volume of a sphere 
20150430 

From Cassidy: How do you find the radius of a sphere that has volume 36pI? Answered by Penny Nom. 





The volume of a cube 
20150430 

From megan: What's the volume of a cube with a side length of 6? Answered by Penny Nom. 





The surface area of a cut pipe 
20150427 

From ARUN: dear Sir,
please advise me , how to calculate the surface area of a pipe with diameter of 630 mm and thickness of 67 mm which is cut in a angle of 22.5 degree.
please show me how to calculate the surface area of the pipe which cut in an angle.
Thanking you. Answered by Harley Weston. 





A piecewise function 
20150425 

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. 





Locating the center of a circle that forms an arc 
20150423 

From Ken:
Find the Cartesian coordinates of the center of an arc with the given location of the beginning and end points and radius length. Not the midpoint of the circumference but the actual point that the arc
is drawn around.
I know their are two answers depending on the direction of the arc. Unless we assume that all arcs are drawn counter clock wise.
Thanks
Ken
Answered by Harley Weston. 





Two cars approaching an intersection 
20150416 

From Engabu: Car A is traveling west at 50km/h & car B is traveling north at 60km/h. both are headed for the intersection of the two roads. At what rate are the cars approaching each other when car A is 3km & car B is 4km from the intersection? Answered by Penny Nom. 





Two airplanes 
20150414 

From john: two planes leave an airport at the same time, one going northwest (N35*W)at 400 mph and the other going east at 332 mph. How far apart are the planes after 4 hours to the nearest mile? Answered by Penny Nom. 





The area of a circle given the circumference 
20150412 

From F: How do you find the area of a circumference of 6?
Thanks. Answered by Penny Nom. 





The perimeter of a quarter circle 
20150410 

From Riley: How do you find the perimeter of a quarter circle when the radius is 56? Answered by Penny Nom. 





On what day of the week did 1994 begin? 
20150405 

From tayyaba: there were 365 days in the year 1993
the first day of the year was friday.
on what day of the week did 1994 begin? Answered by Penny Nom. 





The weight of a steel block 
20150404 

From Mark: the weight of a steel cube 37 inches X 28 inches X 7 inches Answered by Penny Nom. 





n^2 is a multiple of 100 
20150330 

From Rahul: I have to prove that n^2 is a multiple of 100 is necessary or
Sufficient condition (or both) for n being multiple of 10 Answered by Penny Nom. 





The game of 24 
20150328 

From Suzanne: I love this game! Cannot figure out 4,9,10,16 to equal 24? Help! Answered by Penny Nom and Claude Tardif. 





The weight of two dogs 
20150317 

From Renee: Darlene's dog weighed 5 times as much as Leah's dog. Together, the dogs
weighed 84 pounds. How much did each dog weigh?
Write an equation and solve Answered by Penny Nom. 





A cone of maximum volume 
20150316 

From Mary: I have to use a 8 1/2 inch by 11 inch piece of paper to make a cone that will hold the maximum amount of ice cream possible by only filling it to the top of the cone. I am then supposed to write a function for the volume of my cone and use my graphing calculator to determine the radius and height of the circle. I am so confused, and other than being able to cut the paper into the circle, I do not know where to start. Thank you for your help! Mary Answered by Robert Dawson. 





The height of an equilateral triangle 
20150312 

From anna: I am anna and i am in 7th grade.
i am trying to find the height of and equilateral triangle, all sides equaling 4 inches Answered by Penny Nom. 





The area of a quadrilateral 
20150311 

From Joel: Diagonal ac of quadrilateral ABCD is 60cm and the lengths of perpendiculars to
It from the opposite vertices are 4.2cm and 5.8 cm find the area of the quadrilateral
ABCD Answered by Penny Nom. 





Angles of elevation and depression 
20150308 

From Timmy: Joel is walking down a street and sees a 115 ft tall building in front of him. He stops 190 feet from the base of the building at the tip of the building's shadow. Round answers to three decimal places.
A. If there was a piece of rope from the top of the building to Joel, how long would it be?
B. What is the angle of elevation from Joel to the top of the building?
C. Margaret says that she could find the angle of depression from the top of the building to Joel by subtracting the angle of elevation from 90°. Is she correct? Explain. Answered by Penny Nom. 





A man is standing on top of a building 
20150306 

From kiki: a man of height 1.5m standing on top of a building of height 48.5m views another building across the square. he observe that the angle of depression of the bottom of the building is 40 degrees and the angle of depression of the top of the building is 5 degrees. Both buildings stand on the same level
a) calculate the distance of the man from the base of the building across the square measured along the line of sight Answered by Penny Nom. 





Solve x=r(tsin(t)) for t 
20150228 

From David: I don't know how to write the function of t(x) by x=r(tsin(t)).
Can you teach me that? Answered by Harley Weston. 





The radius of a cylinder 
20150226 

From Rose: Hi. I want to know how to find the radius of cylinder.
When I have height (35cm) and area of the curved surface(880sq.cm).
I know the formula is 2πr(h+r). But I can't understand how to find it's radius.
Please help me. I really need your help. Answered by Penny Nom. 





A limit 
20150219 

From genc: Lim (27x^31) / (3x1)
X> 1/3 Answered by Harley Weston. 





The center and radius of a circle 
20150206 

From ariana: I need to find the center and the radius of this circle. I don't know how to put 9/2
than square it into a fraction.
x^2 + 2x + y^2 +9y=5 Answered by Penny Nom. 





The volume of a cone 
20150205 

From Linda: How do you calculate the volume of a cone that is 25cm high and has an angle of 20 degrees? Answered by Penny Nom. 





Ratio of gas to oil 
20150202 

From Chris: I would like to find the gas oil ratio for a 2 cycle engine.
I have the gallons of gas and the ounces of oil used by
the engine, but I want to find what the ratio is. For example
I used 5.675 gallons of gas and 5 ounces oil what is the ratio?
Please explain step by step, and I understand there are 128oz in
a gallon. Answered by Harley Weston. 





128/(16)/(2) 
20150128 

From jackie: 128/(16)/(2) I was wondering if you can show me how to work this question out Answered by Harley Weston. 





Scheduling meetings with pairs of people 
20150122 

From Jacey: I am trying to figure out a formula/system to pair up a list of people so they meet with each other every month, but they rotate who they meet with. Right now I have 13 people and I would like to just type in their names and then have the system put each person with someone else every month and rotate so no one gets the same person twice. Can this be done? Answered by Victoria West. 





The game of 24 
20150121 

From aaron: 24 game whants me to use 11 14 5 and 9 to make 24 allowed (+  dividing and multiplying) Answered by Penny Nom. 





The height of a building 
20150120 

From Emily: A man 2m high observes the angle of elevation to the top of the building to be 70 degrees. And the angle of depression to the bottom of the building to be 19 degrees. How tall is the building? Answered by Robert Dawson. 





The length of a roll of paper 
20150112 

From Peggy: roll of paper 3ft wide and roll equals 500 sq ft how long would the roll be? Answered by Penny Nom. 





A difference quotient 
20150112 

From Sasha: Simplify the difference quotient
f(x) − f(a)/ xa
if x ≠ a.
f(x) = x^3 − 12
Answered by Penny Nom. 





The volume of a lake 
20150110 

From Peter: If a lake is 8 acres in size and 10 feet deep how many gallons of water does it contain Answered by Penny Nom. 





Selling items at a reduced price 
20150109 

From Kent: I have an item I sell for $19.95 and make a profit of $10.97 for each sale.
If I reduce the price to $14.97, my profit is $5.99 each sale.
Is there a formula to determine how many more I would need to sell
at $5.99 per sale to make the same net cash (profit) as selling at $10.97 per sale? Answered by Penny Nom. 





The units digit of a prime 
20150108 

From Patricia: Every prime number greater than 10 has a digit in the ones place that is included in which set of numbers below 1 3 7 9 or 1 3 7 or 0 2 4 5 6 8 or 1 3 5 9 Answered by Walter Whiteley. 





The degree of a polynomial 
20150105 

From Nichole: How do I determine the degree of polynomials? I've searched this on sites but they are
all so confusing! Is there a simple explanation or way to find what the degree is? Some
examples are: 6x^4 10x^2yz^5 and 3m^2n^710m^8. I also have to say that I am
under the impression that this symbol ^ means the number after it is an exponent. Answered by Robert Dawson and Harley Weston. 





1.5% of 1 trillion 
20141230 

From Kgosi: How much is 1.5% of 1 trillion? Answered by Penny Nom. 





Curvature of the Earth 
20141229 

From Jimmy: Both batteries died in my scientific calculator and I have lost my formula for the heigth of the curvature of the earth between two points on the surface. I used degrees and miles. I only had to enter the distance between the two points on the surface and the formula gave me the hieght the earth raised between the two points. Answered by Robert Dawson. 





The perimeter of a quarter circle 
20141226 

From Maisy: This is the question that I got for a math worksheet.
The radius of a quarter circle is 5 miles. What is the quarter circle's perimeter?
Use 3.14 for pi. Answered by Penny Nom. 





A line segment of length root 5 
20141215 

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. 





Planar curves 
20141213 

From ann: what does planar curve mean in your definition of a cone? Answered by Penny Nom. 





30% profit 
20141205 

From Lyn: I would like to know a formula that I would use on a standard calculator to calculate a 30% profit margin on an item.
If I purchased an item at $7.70 how would I calculate 30% profit for me, not just 30% mark up? Answered by Penny Nom. 





1999 equations in 1999 unknowns 
20141128 

From Subrahmanya: Solve the following system of 1999 equations in 1999 unknowns :
x1+x2+x3=0, x2+x3+x4=0……., x1997+x1998+x1999=0,
x1998+x1999+x1=0, x1999+x1+x2=0.
(in x1,x2,...................,x1999 the numbers 1,2,.............,1999 are subscripts) Answered by Penny Nom. 





What is 20 and 3/5 of 10? 
20141126 

From Jeannine: What is 20 and 3/5 of 10? Question is written exactly this way.
Is this 20 3/5 times 10 (103/5 times 10), or is it 20 and (3/5 times 10)? Answered by Penny Nom. 





Doubling the dimensions of a cone 
20141121 

From Hannah: If the volume of a cone of height 10 cm is 261.8 cm3, show that this
volume is increased by a factor of 8 if the dimensions of the cone are doubled. Answered by Penny Nom. 





(x3)^2(x+3)^2 
20141113 

From Bernice: (x3)^2(x+3)^2 Answered by Penny Nom. 





What is 3 squared? 
20141112 

From Christine: On a math test, it said "What is 3 squared?" It did NOT say "What's is (3)squared"
The teacher's explanation is that if there are no brackets or parenthesis, you ALWAYS square the number first then do the negative, so the answer should be 9, but I can't find anywhere that confirms this.
Help please. Answered by Robert Dawson. 





Two quadratic polynomials 
20141028 

From khushboo: The zeroes of a quadratic polynomial x^2+ax+b are 'c' and 'd'
and the zeroes of a quadratic polynomial x^2+cx+d=0 are 'a' and 'b'.
find the numerical value of a+b+c+d where a, b, c and d are non zero integers. Answered by Penny Nom. 





A 10foot piece of PVC pipe 
20141021 

From David: A plumber has a 10foot piece of PVC pipe. How many 9/5foot pieces can be cut from the 10foot piece ? Answered by Penny Nom. 





Sieve of Eratosthenes 
20141003 

From Hope: using Sieve of Eratosthenes to determine for in instance prime numbers between 1 to 200, to what nth number should i stop?, 4th, which is 11 or what? Answered by Robert Dawson. 





The perimeter of a parcel of land 
20140918 

From Shirley: What is the perimeter of a parcel of land that is 564 acres square Answered by Penny Nom. 





A tangent to a curve passing through a point not on the graph 
20140915 

From Aquilah: For the curve y = x2 + 3x, find the equations of all tangent lines for this graph
that also go through the point (3, 14). Answered by Penny Nom. 





The diagonals of a cube 
20140904 

From Rukshanth: How many diagonals does a cube have? Answered by Harley Weston. 





The sum of two numbers is 52 
20140901 

From Blake: The sum of two numbers is 52 and the difference is 10. What are the numbers? i used to be real good at this stuff? Answered by Penny Nom. 





The perimeter of a triangle 
20140821 

From Phyllis: What is the perimeter of a five acre triangle with one side being 250 feet and the second side would be at a 90 degree angle.
Thank you. Answered by Penny Nom. 





The equation of a circle 
20140814 

From jennifer: hi there My name is Jennifer and residing in Denmark. I am a student and I wrote to you because i am having trouble in finding out the equation for the circle using
(xa)^2 + (yb)^2 =3D r^2.The diameter of this circle is d=3D 44,514 cm.
I have attached a drawing of my problem..thanks Answered by Penny Nom. 





Ratios ond percents 
20140813 

From aswathi: if the ratio of cost price and selling price of an article is be as 10:11,the percentage of profit is Answered by Tyler Wood. 





The area of a quadrilateral 
20140806 

From Rahul: find the area of the quadrilateral whose side measure9cm,40cm,28cm,15cm and in which the angle between the first 2 sides is a right angle Answered by Penny Nom. 





The area of a kite 
20140804 

From Janis: How do you calculate the area of a kite with the diagonals 24cm and 48cm? Answered by Chris Fisher and Penny Nom. 





Expand and simplify [x3][x+3] 
20140716 

From symion: Expand and simplify [x3][x+3] Answered by Penny Nom. 





A 5 sided lot 
20140710 

From mia: have the feet numbers of three sides, but the forth side is in a "V" so it has two figures.
Question: can i add the two figures of the "v" together to get one figure, so then I would have the figures for all four sides. Answered by Harley Weston. 





A ladder against a wall 
20140709 

From thabo: A ladder 6.5m long,leans against a wall so that the top of the ladder is 4.8m from the ground.what is the angle of elevation of the ladder to the top of the wall Answered by Penny Nom. 





The method of elimination 
20140705 

From leo: please explain how can i solve this problem
3x6y=38
6x9y=44
using elimination and simultaneous method thank you :) Answered by Penny Nom. 





The width of a rectangle 
20140702 

From john: if the area of a rectangular field is 90 sq. m and its length its is 19 m find its width Answered by Penny Nom. 





A triangle on the surface of the Earth 
20140626 

From Christine: A, B and C are three towns, the bearing of B and C from A being 310 degrees and 220 degrees, and their distances from A are 510km and 700km respectively. Find the bearing of B from C to the nearest minute. Answered by Robert Dawson. 





50+913 multiplied by 2= 
20140625 

From Adrian: 50+913 multiplied by 2= Answered by Penny Nom. 





An oval pool 
20140621 

From steve: I have a 16' x 28' oval pool that is buried 24" deep inground. The dig site is dug
2' wider all the way around the pool. I need to back fill this area with stone. I want to fill this area with 6 to 8"
of stone. How many tons of stone will this take?
Thanks you
Steve Answered by Penny Nom. 





The number of standard deviations 
20140615 

From Dawn: Suppose that, at a certain college, the average weight of all male students is 160 pounds with a standard deviation of 30 pounds. A certain male student weighs 145 pounds. Determine how many SD's his weight is above or below average. Answered by Penny Nom. 





Profit 
20140614 

From roudha: find the profit of one item if it was bought for AED 180 and sold for
AED 275. assume that the additional costs are AED 25 . Answered by Penny Nom. 





The area of a circle of circumference 32.69 meters 
20140611 

From coco: Find the area of a circle with a circumference of 32.69 meters. Answered by Penny Nom. 





Bags of sand 
20140606 

From Robert: We have a section that is 20ft long by 14ft wide and 4inches deep, the bags of sand are
.5 cubic ft. How many bags of sand do we need to fill this space evenly. Answered by Penny Nom. 





The volume of a wedge 
20140521 

From steve: I need to figure the volume of a wedge / right triangle, the dimensions of the right triangle is L1(10'5"), L2 (10'6"), H (14'9.5") height of L1 is 0'0" height at intersect L2/H is 3'3" Answered by Penny Nom. 





The equation of a line 
20140516 

From Michael: Find the equation of a line that passes through (2,1); the sum of the x and yintercepts is 2. (There are two answers) Answered by Penny Nom. 





A schedule for 2 teams of 10 
20140507 

From John: How can I set up a schedule for 2 teams of 10 on a team to play each individually against each other over a 10 day span at 10 different course with 10 different start times each day. I was looking to not repeat any competition. As an example, Team A would consist of players 110, Team B would consist of players 1120. I would want to have 10 start times a day for 10 days where a member of team A plays a member of team B each day without repeating any matches and any of the same courses and not repeating any of the same start times. Any help in this would be GREATLY appreciated!!!! Answered by Victoria West. 





A cone of vision 
20140429 

From David: It is known that a fish in water looking up has a 97 degree "cone" of vision that sees "through" the surface of the water. If a fish lies 4 inches below the surface, the cone forms a window (circle) smaller than if a fish lies 8 inches below the surface. What is the ratio of inches of depth to the radius of the circle on the surface that is its visual window? Answered by Penny Nom. 





Profit and loss 
20140429 

From Anoushka: A man sells two tables of the same price. On one he makes a profit of 10 percent and on the other he suffers a loss of 10 percent.Find his loss or gain percent on the whole transaction. Answered by Robert Dawson. 





A triangular chicken pen 
20140427 

From Cierra: Margaret has two lengths of fence, 20 meters and 24 meters, for two sides of a triangular chicken pen. The third side will be on the north side of the barn. One fence length makes a 75° angle with the barn. How many different pens can she build if one fence is attached at the corner of the barn? What are all the possible lengths for the barn side of the pen?
Not sure what they are asking here... please show step by step what to do! Thank you so much! Answered by Penny Nom. 





The volume and radius of a sphere 
20140427 

From grace: How do you find the radius of a sphere when all you know is the volume? Answered by Penny Nom. 





The derivative of sin(x) 
20140426 

From Lucky: f(x)=Sin(x), by first principle its f'(x)...show me how to solve such problem. Answered by Penny Nom. 





What was the selling price? 
20140425 

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 quadratic equation given the roots 
20140423 

From Sarah: How do you find the quadratic formula when you're given just the roots ... X=3 X= 1/3
Thanks ! Answered by Robert Dawson. 





Golf for 6 
20140421 

From barbara: We are a group of 6 golfers. We play in groups of 3 for 5 days.
How can I arrange the groups that everybody plays with everybody else at least once?
Thanks. Answered by Victoria West. 





Golf with 3 teams of 20 
20140421 

From Joshua: Thank in advance for this great service
Golf  new  3 teams of 20  to create 20 unique groups of 3
For example use 3 teams of 3
1a 2a 3a
1b 2b 3b
1c 2c 3c
So groups are
1a 1b 1c
2a 2b 2c
3a 3b 3c
Groups can only have one a, one and one c  and that combo should be unique Answered by Victoria West. 





Barrels of oil 
20140416 

From daryl: Looking for an accurate number to use when calculating barrels per inch in a a tank with the following dimensions:
Nominal diameter  15'6", nominal height  16ft, nominal capacity  500 barrels. These are commonly referred to as 500x16 tanks.
Currently we are using 2.6 barrels per inch. We need 180 barrels for a full load so I'm trying to figure out how many total inches I need to load 180 bbl. This has been a matter of debate for some time. Thanks for your help. Answered by Harley Weston. 





The surface area of a circular dome 
20140410 

From Shafiqah: Is this a dome's surface area formula??
{{2 × π r × h square units}}
Is the surface area of the floor for the dome is calculate too in this formula?
Thanks for answering. =) Answered by Robert Dawson and Penny Nom. 





The sides of a triangle 
20140406 

From Michael: I am supposed to sove for the length of side "b" of an irregular triangle. I am given the following:
Side a: 65'
Side b: Find this length
Side c: 50'
Angle A: unknown
Angle B: unknown
Angle C: 52 degrees
I am supposed to use the law of cosines to solve for side "b" and my teacher
says there is no mistake in the "givens" for the problem. I do not see how
this can be done using the law of cosines and i have not figured out how to sove for
angle B to use the law of cosines. Answered by Penny Nom. 





The Pythagorean Theorem 
20140330 

From brenae: The Pythagorean Theorem, what is it? Answered by Penny Nom. 





A schedule for 6 people 
20140329 

From John: How do I set up a schedule where six people are here for ten of twenty days.
Arranged in rotating groups of three, so everyone works with everyone else.
Everyone works with everyone else at least once and everyone works ten days. Answered by Victoria West. 





Curvature of the Earth 
20140328 

From Max:
Recently I read the answer to a question proposed by someone on this site.
The question : What is the rate of curvature per mile on Earth?
The answer given : Use Pythagoras' Theorem to solve for the answer, given a 1 mile side
and a side as the radius. The hypotenuse minus the radius is your answer of drop/mile or curve/mile.
My conjecture : Why go through all of that work if the distance is one? Something like
{1/diameter} would would fine for such a problem. Seems like a lot of work for no reason.
I understand the practical application of Pythagoras' Theorem in this certain situation, as you would need
to use a^2+b^2=c^2 for any distance greater than one [mile]..
It just seems excessive and unnecessary if you're solving for curve / one mile. Answered by Robert Dawson. 





A table of values 
20140327 

From Marisol: A table value X 0,1,2,3,4,5,6 and Y 3,7,11,15,19,23,27 . what relationship of X to Y is represent by which equation? A . y= 4x. B y =x+3 . C y =4x+3 or . D y =4x3 Answered by Penny Nom. 





Two overlapping arcs in a square 
20140315 

From Jean: I have a square with side 4 cm. There are two overlapping arcs going from vertex to diagonal vertex. The other two vertices are the center of the arcs, which are shaded. How do I find the area of the shaded arcs? The overlapping arcs when shaded resemble a long thin football
Thank you for your help. Answered by Penny Nom and Walter Whiteley. 





The angle of depression 
20140308 

From Ranger_minor: A woman of height 1.4 metres standing
on the top of a building 34.6 metres high
views a tree some distance away.
she observes that the angle of depression of the bottom of the tree
is 35 degrees and the angle of depression of the top of the tree
is 29 degrees.
assume that the building and the tree are on level ground :
1). calculate the distance of the woman
from the top of the tree measured along her line of sight. Answered by Penny Nom. 





The equation of a circle 
20140307 

From Balraj: I have to draw a circle x^2+y^2 =8x . please tell me how to understand these coordinates ? please elaborate , on how to understand these types of equations. Answered by Penny Nom. 





The diameter of the base of a cone 
20140223 

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. 





Three investment partners sharing the profit 
20140222 

From Ayatullah: Hello;
We are three partners and bought a property at 2050000 and sold at 2300000.
Details of investment of the partners
X= 1500000
Y= 400000
Z = 150000
My questions are
1) How could i calculate percentage of investment of each partner?
2) How could i deduct 30% commission from each partner in profit?
3) How could i distribute the profit amongst the partners?
Thanks in advance Answered by Penny Nom. 





The growth of a tree 
20140216 

From Emily: If a tree is 10 ft tall after 2 years and 25 ft tall after 5 yrs , find the rate of change of growth
Of the tree if y is the height in ft and x is the number of years. Answered by Penny Nom. 





The grade of a road as a percent 
20140214 

From Emily: What is the grade of the road shown below expressed as a percent rounded to one decimal place?
Rise is 40feet
Run is 380 feet Answered by Penny Nom. 





The volume of a cone 
20140208 

From hibba: why is the volume of right circular cone divided by 3? Answered by Penny Nom. 





A triangle has angels in the extended ratio of 2:5:8 
20140206 

From Rubina: a triangle has angels in the extended ratio of 2:5:8. find the measure of
all three angles? Answered by Penny Nom. 





Order of operations 
20140204 

From Alex: Hi there,i got problem with order of operation.Can you please help to find a solution for this?
Thank u beforehand
63(7+2)+(2+4)/34. Answered by Penny Nom. 





The volume of a frustum 
20140202 

From mike: volume of frustum R23", r 18", h 16" Answered by Penny Nom. 





Conics 
20140201 

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. 





$9.50 in coins 
20140115 

From dana: you have $9.50 in coins. it has twice as many nickels as quarters and three times as many dimes as nickels. how many of each coin do you have? Answered by Penny Nom. 





On what day of the week was July 4, 1904? 
20140111 

From Madi: Hi guys,
I have a question. July 4, 1903, was a Tuesday. On what day of the
week was July 4, 1904? If you could give me an equation that would
work for any question like this, that would be GREAT!
Your fellow math scholar (in training),
Madi Answered by Penny Nom. 





When would one flip the inequality sign? 
20140109 

From Natasha: Would one flip the inequality symbol in this equation: (explain why)
(9a)/(9) > 81
And please explain in what circumstances one would flip the inequality sign
THANKS! Answered by Penny Nom. 





Profit as a percentage 
20140104 

From Dane: If i brought a card for £5 and sold it for £10 what is my profit percentage? 50% or 100% Answered by Penny Nom. 





25% profit 
20140102 

From Finn: Hello,
The question is all about buyandsell business.
Problem:
Pencil  $6 for whole sale price
$8 if I sell the item
How do I get the 25% profit? (you can change the whole sale price and the retail price[if i sell the item])
if I buy the pencil at 24 pieces and sell it at 24 pieces. Answered by Penny Nom. 





The slope of the line y=2x+5 
20131229 

From victoria: what is the slope of the line with the equation y=2x+5 Answered by Penny Nom. 





Can 100r^281z^2 be factored? 
20131208 

From Rosa: Can 100r^281z^2 be factored? Answered by Penny Nom. 





Fractions and square roots 
20131204 

From arionne: How do you solve a square root with improper fractions like 121 over 49 Answered by Penny Nom. 





What is the slope of this line? 
20131201 

From Charlene: What is the slope of this line? Answered by Penny Nom. 





How many cords of wood is this? 
20131117 

From melody: 5.5 ft wide and 24ft long and 10ft wide how many cords of wood is this? Answered by Penny Nom. 





A sloped concrete wall 
20131030 

From Brad: We are planning on pouring concrete in a wall form that is sloped. One end is 73 inches tall, and it tapers to 24 inches tall over a distance of 348 inches. It is flat on bottom and sides and is 12 inches thick. Thanks. Answered by Penny Nom. 





The perimeter of a rectangle 
20131024 

From sana: if the length is given 70 m and the breadth is given as 40 m find the perimeter of the rectangle Answered by Penny Nom. 





The domain of a derivative 
20131010 

From Renee: I am looking to find the domain of a derivative of a radical function,
one such as: f(x) = the square root of (8 − x).
I am kind of unclear on how domains work for derivative.
I don't understand how you take a function's domain and use that to
find the derivative's domain.
Thanks! Answered by Penny Nom. 





A line through (5, 1) 
20131008 

From allison: find an equation in standard form for line passing through point (5,1) and perpendicular to line x=4 Answered by Penny Nom. 





A triangle problem 
20131002 

From raneem: ABC is a triangle in which : BC=20cm. M(<B) =29 and m(<C)=73 . D is the midpoint of BC
Find the length Of AB and AD approximated to 2 decimal places Answered by Penny Nom. 





Two teams of 4 playing 4 rounds of golf 
20130929 

From Tom: We would like to play a ryder cup format with two teams of 4 playing 4 rounds of golf. Three of the rounds would be pairs playing each other and one round would be singles. How can we set up the foursomes so we balance the number of times we play with every other golfer. Answered by Victoria West. 





Price, revenue and profit 
20130922 

From lorraine: What price maximizes revenue? What price maximizes profit?
The only data I'm given is total output, total revenue, and total cost.
I'm not sure how to set up a formula Answered by Penny Nom. 





The number of cords on a pile of wood 
20130918 

From Gary: a cord of wood is 4 feet by 4 feet by 8 feet, how much wood is a row that is 16 in by 5 foot by 32 feet? Answered by Penny Nom. 





If the earth was made of a ball of string 
20130918 

From Tammy: My 9 year old son asked me a question and I have no idea how to work it out! Please can you help?
If the earth was made of a ball of string and you unravelled the string how long would it be? Assuming the string is 5mm thick. Answered by Penny Nom. 





Using trig to find the height of a hill 
20130814 

From Anna: From the top of a hill, the angles of depression of two successive milestones on a level road, which leads straight away from the hill, are 5degrees and 15degrees respectively. Fine the height of the hill.
Suggestion: BE is drawn perpendicular to AD. Find BE, then BD, finally CD.
Thanks :) Answered by Penny Nom. 





A system of equations 
20130813 

From Nina: 3x2y=8
x+3y=5
What is the solution of the system of equations Answered by Penny Nom. 





An equation in slopeintercept form 
20130812 

From Brittney: write an equation in slopeintercept form of the line that is parallel to the grapg of y=3/4x+6 passes through 8,5 Answered by Penny Nom. 





Four equations 
20130808 

From may: HI how to solve this 4 equations?
A+C = 0
4A+B8C+D=1
3A+16C8D=29
12A+3B+16D=5 Answered by Robert Dawson. 





Practical uses of trigonometry 
20130806 

From tharindu: use of trigonometry Answered by Penny Nom. 





The angle of elevation of the sun 
20130703 

From Maurice: A vertical pole with a length of 7m cast a shadow with a length of 5m. Calculate the angle of elevation of the sun and include a diagram. Answered by Penny Nom. 





a cubeb cubea+b= ? 
20130616 

From saryu: a cubeb cubea+b= ?
find the answer Answered by Penny Nom. 





(4 4cos^4 x)/(sin^2 x) 
20130518 

From Agnes: How I can solve this question :
Simplify (4 4cos^4 x)/(sin^2 x) and write in terms of sin x Answered by Penny Nom. 





The surface of a solid 
20130507 

From mustafa: I am doing a research paper on solid surface applications . Part of the project is to find four at least 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 solid surface are used in our world today and I really can't find anything.. Thanking you in advance, mustafa Answered by Penny Nom. 





Profit margin 
20130506 

From Arron: I have the retail price of $45.50. This price reflects a gross profit margin of 47%. How do I calculate the original cost of the item? Answered by Penny Nom. 





Points of intersection 
20130502 

From Bianca: Find the sets of values of k for which the line y=kx4 intersects the curve y=x^22x at two distinct points. Answered by Penny Nom. 





Bags of premixed concrete 
20130412 

From Bruce: Hello there,
I need two cubic yards of concrete for a playgound I am
installing for my kids. That much i have figured out. I am stumped
over the number of 25kg bags of premixed concrete i will need
to accomplish my goal.
Your help would be greatly appreciated.
Thanks
Bruce Answered by Harley Weston. 





The equation of a line 
20130404 

From Miranda: My coordinates provided are (6, 6) and (8, 9) and i need to put this into ax=bx=c format. I remember the equation to find the slope of y2y1/x2x1 to get the slope. However when i put that back into the y=mx+b format it still leaves me with a lot of variables. Please help :) Answered by Penny Nom. 





A gravel pile in the shape of a triangular pyramid 
20130404 

From Casey: Hello
Right now I am stuck and I feel embarrassed because I feel like the answer is so easy I should know it.
I am working on a project and need to find a volume of gravel it will take to occupy this triangular prism like area. I am not sure what formulas I should use whether it be that for the volume of a pyramid or something more complex? Basically it forms a right triangle at one side then from there all points slope to one singular point about 10412mm away.
I am attaching a picture drawn up in paint with the actual dimensions to clear up any confusion.
Thank you for any help.
Casey Answered by Penny Nom. 





Question 
20130404 

From Casey: Hello
Right now I am stuck and I feel embarrassed because I feel like the answer is so easy I should know it.
I am working on a project and need to find a volume of gravel it will take to occupy this triangular prism like area. I am not sure what formulas I should use whether it be that for the volume of a pyramid or something more complex? Basically it forms a right triangle at one side then from there all points slope to one singular point about 10412mm away.
I am attaching a picture drawn up in paint with the actual dimensions to clear up any confusion.
Thank you for any help.
Casey Answered by Penny Nom. 





We can't write sinx and cosx as a finite polynomial. 
20130331 

From rimoshika: prove that we can't write sinx and cosx as a finite polynomial. Answered by Walter Whiteley. 





A markup followed by a discount 
20130323 

From edward: A shopkeeper marks his goods to gain 35%. He allows 10% discount for cash payment. What is his profit percent when he sells the goods for cash? Answered by Penny Nom. 





Percent profit: State exam question 
20130312 

From tony: which is the correct way to figure 30% profit?
1)
1000 product
500 labor
50 permit
1550 total cost
1550x1.3=2015
2)
1000 product
500 labor
50 permit
1550 total cost
1.3=.7
1550/.7=2214 Answered by Harley Weston. 





state exam question 
20130312 

From tony: which is the correct way to figure 30% profit?
1)
1000 product
500 labor
50 permit
1550 total cost
1550x1.3=2015
2)
1000 product
500 labor
50 permit
1550 total cost
1.3=.7
1550/.7=2214 Answered by Harley Weston. 





A messy arithmetic expression 
20130224 

From niiaryee: (((((5^2*4^3)1/5+9^3/3)+(25+(4*5)/15)^210)/10/2)3))))) Answered by Penny Nom. 





The tangent to a circle at a point on the circle 
20130222 

From Andrew: What is the equation of the line tangent to the circle with equation x^2+y^2=25 at the point (4,3) Answered by Penny Nom. 





Your profit should be 20% of your cost 
20130221 

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. 





Related rates 
20130217 

From Ishaak: A hemispherical bowl is filled with water at a uniform rate. When the height of water is h cm the volume is π(rh^21/3 h^3 )cm^3, where r s the radius. Find the rate at which the water level is rising when it is half way to the top, given that r = 6 and the bowl fills in 1 minute. Answered by Penny Nom. 





The continuity of f(x,y)=ln(x^2+y^2) 
20130217 

From anu: the question says we have to find the points in the plane where the function is continuous:
f(x,y)=ln(x^2+y^2) . here we aren't given a particular point (x,y) where we have to check a function's
continuity.
what is to be done if we have to check continuity over the whole domain of the function?
please help . Answered by Harley Weston. 





The equation of a circle 
20130211 

From mhd: Complete the equation of the circle centered at(0,4) with radius 3 Answered by Penny Nom. 





4*4+4*4+44*4=??? 
20130206 

From Jacky: 4*4+4*4+44*4=??? Answered by Penny Nom. 





What is the domain of f(x)=sin(ln(x))/ln(x)? 
20130206 

From Behrooz: Hi, the following problem may be interesting:
What is the domain of f(x)=sin(ln(x))/ln(x)?
Be careful, domain is not obvious.
Best regards
Behrooz Answered by Penny Nom. 





The fourth side of an irregular polygon 
20130201 

From Emran: I have a irregular polygon. I know 3 of the 4 sides, and 2 of the angles. AB is 285, BC is 149, and CD is 310. Angle B is 135 degrees. and Angle C is 45 degrees. Is there a formula to solve for the final side? Thanks. Answered by Penny Nom. 





We have 2 teams of 6 couples each that play 6 games 
20130125 

From Denise: We put together a game night where we have 2 teams of 6 couples each that play 6 games. We haven't been able to figure out an arrangement that allows each couple to play each game with a different couple from the opposite team (i.e. Team A couples play every game with a different couple from Team B). Is this possible? It works with 2 teams of 5 couples each. Answered by Chris Fisher. 





Maximize profit 
20130119 

From Chris: A firm has the following total revenue and total cost function.
TR=100x2x^2
TC=1/3x^35x^2+30x
Where x=output
Find the output level to minimize profit and the level of profit achieved at this output. Answered by Penny Nom. 





The weight of a pipe full of water 
20130116 

From joe: how do you figure out the weight of a pipe full of water Answered by Harley Weston. 





A shed roof 
20130112 

From christine: A roof on a shed is 7.3 ft wide has an incline of 20 degrees what is the height? Answered by Penny Nom. 





3x6)+(12divided by2)8= ? 
20121217 

From christina: hi my question that's been bothering me is what's
(3x6)+(12divided by2)8= ????? Answered by Penny Nom. 





If n is odd, then n^2  3 is even 
20121211 

From Tracy: Prove the statement:
For all integers n, if n is odd, then n2  3 is even. Answered by Penny Nom. 





The angles of elevation and depression 
20121203 

From Chelsey: a person on a balcony of one building looks towards a second building. if the angle of elevation to the top of the second building is 25 degrees, the angle of depression to the bottom of the second building is 17 degrees, and the balcony of the first building is 22 feet above the ground, what is the height of the second building? Answered by Penny Nom. 





Two quadratic equations 
20121122 

From fahmie: graph and solve the intersection of the following equations:
x^2+y^2=4
x^2+2y=4 Answered by Penny Nom. 





Difference of squares 
20121119 

From Qelibar: Please factorise x^2y^2  4 Answered by Penny Nom. 





The square of any odd number, decreased by 1, is divisible by 8 
20121116 

From bailey: Prove that the square of any odd number, decreased by 1, is divisible by 8 Answered by Penny Nom. 





How much should I price the earrings? 
20121113 

From Sharon: I want to sell some earrings and make a $12.00 profit on them I have to pay a
35% commission on them. How much should I price the earrings? Answered by Penny Nom. 





4+4x5+4= ? 
20121031 

From Bob: 4+4x5+4= ? Answered by Harley Weston. 





How fast is the distance between the aircraft and the car increasing? 
20121024 

From Steven: At a certain instant an aircraft flying due east at 240 miles per hour passes directly over a car traveling due southeast at 60 miles per hour on a straight, level road. If the aircraft is flying at an altitude of .5mile, how fast is the distance between the aircraft and the car increasing 36 seconds after the aircraft passes directly over the car? Answered by Penny Nom. 





Composition of functions and one to one 
20121017 

From Ariana: If f o g are one to one function,does it follow that g is one to one? Give reasons for your answers Answered by Penny Nom. 





The degree measure of the central arc of a circle 
20121017 

From Crystal: On a circle with radius of 12 cm is an arc of length 20 cm. What is the degree measure of the central angle used to make this arc? Answered by Penny Nom. 





Profit 
20121005 

From kathie: find the profit income is $500 expenses $120 Answered by Penny Nom. 





Profit and discount 
20120924 

From ally: A wholesaler purchased a wheat for $150 per tonne.He sold it at $170 per tonne.Calculate the percentage profit to (1 decimal place)if the wholesaler offered a 12% discount on the selling price.What could be the new selling price? Answered by Penny Nom. 





A profit of 35% 
20120907 

From Jack: If a product cost me $10.00 and I want a profit of 35% what is my sell price? How do I figure the sale price to make a 35% profit on the sale? Answered by Penny Nom. 





The volume of a sphere 
20120818 

From Rohit: why isn't volume of a sphere = Area of a semicircle x the circumference.
i.e. if we revolve a semicircle around its axis we get a sphere Answered by Penny Nom. 





5 + 5 + 5  5 + 5 + 5  5 + 5 x 0 = 
20120729 

From Tom: 5 + 5 + 5  5 + 5 + 5  5 + 5 x 0 = Answered by Harley Weston. 





John's electronic store 
20120725 

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 volume of revolution 
20120715 

From Tewodros: Let f(x) = e^x and g(x) = x^1/2 both be defined on [0,1]. Consider the region bounded by f(x), g(x), x = 0, x = 1. Rotate this region about the yaxis and determine the volume using the shell method. Answered by Harley Weston. 





The angular elevation of the sun 
20120714 

From VINEET: WHAT IS ANGULAR ELEVATION OF THE SUM Answered by Penny Nom. 





A cylinder is to be filled with peas. 
20120612 

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. 





93(2+6)/62*5 
20120608 

From Sammi: Hi there,
I am doing a practice test for my admittance into a college accounting program
and I am really confused by this equation.
The answer I got was way off what the test answer sheet says it should be.
The question is
93(2+6)/62*5
If you could explain how the answer beccomes 35 that would be greatly apprciated!!
Thank you! Answered by Robert Dawson. 





Multiples 
20120528 

From Kenneth: If I understand correctly , a multiple is a product of two numbers. For example some of the multiples of 6 are 6, 12, 18, 24, 30, etc. I just multiplied 6 by 1, 2, 3, 4, 5, etc.
Are the multiples of a fraction, for example, 2/3, determined in the same way? Are they 2/3, 4/3, 6/3, 8/3, 10/3, etc., or are they instead, 2/3, 4/6, 6/9, 8/12, 10/15, etc.?
Or do fractions have no multiples? Answered by Penny Nom. 





Sharing the profit 
20120514 

From Mafiza: A and B started a business by investing $6000 and $8000 respectively. At the end of the year, a profit of $2100 is made. How much amount will A get as his share of profit? Answered by Penny Nom. 





An equation of the form y=mx 
20120417 

From Samiya: what would be an equation of the form y=mx with the points (2, 6) and (1, 3) for the line? Answered by Penny Nom. 





Profit as a percent 
20120414 

From Anson: The cost price of a CD is $50 and its marked price is $105. If the
selling price is $88, find the profit percent. Answered by Penny Nom. 





The spread of a rumor 
20120409 

From Roohi: The function f(t) = a/(1+3e^(bt)) has also been used to model the spread of a rumor. Suppose that a= 70 and b=3 0.2. Compute f(2), the percentage of the population that has heard the rumor after 2 hours. Compute f'(2) and describe what it represents. Compute lim t approaches infinity and describe what it represents. Answered by Penny Nom. 





The period T of a pendulum 
20120327 

From Ashley: The period T of a pendulum is given in terms of its length, l, by T=2pi sqrt(l/g) where g is the acceleration due to gravity(a constant)
a. find dT/dl
b. what is the sign of dT/dl
c. what does the sign of dT/dl tell you about the period of the pendulums? Answered by Penny Nom. 





The equation of a line 
20120326 

From Danielle: Hello, could you help me figure out what the equation of the line is in the form of Ax+By=C with the points (2,0) and (0,3)?
Thank You! Answered by Penny Nom. 





A vertical line passing through (10,4) 
20120316 

From Isabelle: Hi! My question is this:
Write the equation of each line described:
A vertical line passing through (10,4)
I would really appreciate your help!
Thanks,
Isabelle Answered by Penny Nom. 





An increase/decrease in profit 
20120313 

From Thanikasalam: It is understood that increase/decrease in profit for current year compared to the previous year is done by the formula (xy)/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/y1
* = (xy)/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. 





A storage box with a slanted roof 
20120213 

From Sophia: Hi!
I have another problem.
The diagram shows a side view of a box which is used to store small logs of
wood for burning in a fire place. The slopping lid has an overhand of 15cm.
a) Calculate the total length of the slopping lid to the nearest cm.
b) When the lid is open above ground will the end of the lid be?
P.S. Please see attached. Answered by Penny Nom. 





The curvature of the earth 
20120208 

From sean: Question from sean, a student:
Two people 1.8 metres tall walk directly away from each other until they can no longer see each other (due to the curvature of the earth, which has a radius of about 6378 km).
A) Find a function relating the height of two identical objects with the distance between them using the scenario above as an example.
B) Sketch this function (you may use Graphmatica if you wish). Over what domain and range does the function exist?
C) Describe this relation in practical terms. Answered by Harley Weston. 





Two sectors of a circle 
20120203 

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. 





1 + 3 + 3^2 ...+3^(n1) = 3^n  1/2 
20120127 

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^(n1) = 3^n  1/2
This equation was used to find the number of white triangles in the Sierpinski Triangle Answered by Walter Whiteley. 





Four apples and two oranges cost Rs. 30... 
20120113 

From nasr: Four apples and two oranges cost Rs. 30, and one apple and 3 oranges costs Rs.15.How much does each apple and each oranges cost? Answered by Harley Weston. 





A volume of revolution 
20120111 

From john: find volume of solid generated by revolving the region in the first quadrant bounded by the curve y squared=x cubed, the line x=4 and the xaxis about the line y=8. The answer in the back of the book is 704 pi divided by5 Answered by Penny Nom. 





Sum and difference of squares 
20111231 

From Anne: Se x e y săo números reais distintos, entăo:
a) (x^2 + y^2) / (x  y) = x + y
b) (x^2 + y^2) / (x  y) = x  y
c) (x^2  y^2) / (x  y) = x + y
d) (x^2  y^2) / (x  y) = x  y
e) Nenhuma das alternativas anteriores é verdadeira. Answered by Harley Weston. 





Three sides of a triangle 
20111224 

From saba: the three sides of a triangular lot have lengths 10,11and 13cm,respectively.
find the measure of its largest angle and the area of the lot? Answered by Penny Nom. 





The volume of a cylinder 
20111222 

From luke: what is the volume of a cylinder that is 30 mm in diameter and 70 cm high?
can you please write the equation out in full for me to help understand it better. thanks Answered by Penny Nom. 





The number of digits in a number base m 
20111222 

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. 





Water is flowing into a cup 
20111219 

From Tim: A cup has a radius of 2" at the bottom and 6" on the top. It is 10" high. 4 Minutes ago, water started pouring at 10 cubic " per minute. How fast was the water level rising 4 minutes ago? How fast is the water level rising now? What will the rate be when the glass is full? Answered by Penny Nom. 





A cube of ice is melting 
20111205 

From Emily: a cube of ice (i.e.) each side is of the same length) is melting at a rate such that the length of each side is decreasing at a rate of 5cm per hour. how fast is the volume of the cube decreasing (in cubic cm per hour) at the instant the length of each side is 25cm? Answered by Penny Nom. 





Water pouring into a conical tank 
20111121 

From Patience: Hi my name is patience and I'm having a problem with this question.
Water pours into a conical tank of semi vertical angle 30 degrees at the rate of 4 cm^3/s, where h is the depth of the water at time t. At what rate is the water rising in the tank when h = 10 cm?
Thank you Answered by Penny Nom. 





The slope of a line 
20111110 

From Sara: Line k lies in the xyplane.
The xintercept of line k is 4.
And line k passes through the midpoint of the line segment whose endpoints are (2,9) and (2,0).
What is the slope of line k?
Give the answer as a fraction. Answered by Penny Nom. 





What was the cost price of the article? 
20111110 

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 area of a circle 
20111017 

From Winney: If the diameter of a semicircle is 3 feet what is the area. Answered by Penny Nom. 





One central circle and three tangent circles 
20111016 

From Margaret: You have one central circle and three or more circles tangent to the outside of the circle of varying radii. You know the x,y coordinates of the centers of the other circles. If you now remove that central circle (and pretend you never knew where it was), can you calculate its center in x,y coordinates? Answered by Chris Fisher. 





A reservoir has the shape of an inverted cone 
20111003 

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. 





A hemispherical bowl with a lead ball inside 
20110927 

From Jean: "(a) Water is being poured into a hemispherical bowl of radius 3 inch
at the rate of 1 inch^3/s. How fast is the water level rising when the
water is 1 inch deep ?
(b) In (a), suppose that the bowl contains a lead ball 2 inch in
diameter, and find how fast the water level is rising when the ball is
half submerged." Answered by Penny Nom. 





Composition of functions 
20110905 

From Jenna: Let f(x)=x^21 and g(x)=12x. Find the indicated values.
1. f(g(1)) and g(f(1))
Thanks,
Jenna Answered by Penny Nom. 





The height of a fluid in a horizontal tank 
20110724 

From jason: Same set up as many others, cylindrical tank on its side, but I am interested in defining the change in volume and/or fluid level as a function of time at a constant volumetric outflow. I plan on hooking a pump to the tank so "gpms' will be constant. I have a couple different sized tanks and pumps so I want a general equation. Thanks for your help. Answered by Harley Weston. 





A reel of paper 
20110603 

From keith: if a full reel of paper has 7750 metres on it with a diameter of 1240mm and a core diameter of 100mm how can work out the thickness of each strip of paper therefore allowing me to work out the metreage of the roll when its half in diameter at say 620mm Answered by Penny Nom. 





A rational number 
20110517 

From owais: according to definition of irrational number "a number which cannot be
expressed in p/q form is called irrational number"
square root of 2 is a irrational number but if i round off the digit correct
to two decimal places so it becomes 1.41 and we can easily convert
into p/q form so it is a rational number ??? Answered by Penny Nom. 





Dividing the profits 
20110419 

From Tracy: I need to know how to come up with the answers to the following problems. I need to be able to show my work. So can you help me on how to come up with the answers to questions like these. Thanks.
Three individuals form a partnership and agree to divide the profits equally. X invests
$9,000, Y invests $7,000, Z invests $4,000. If the profits are $4,800, how much less
does x receive compared to having the profits divided in proportion to the amounts
invested by X, Y, and Z?
In printing an article of 48,000 words, a printer decides to use two sizes of type. Using the
larger type, a printed page contains 1,800 words. Using a smaller type, a page contains
2,400 words. The article is allotted 21 full pages in a magazine. How many pages must be
in smaller type? ___________
thank you Answered by Penny Nom. 





The equation of a sphere 
20110416 

From kanika: equation of sphere and how to know its center Answered by Penny Nom. 





Coefficient of variation 
20110414 

From Braden: When determining coefficient of variation (CV) or %CV is it possible to calculate %CV for two variables? For instance can %CV be used to determine the precision of 5 data points on a graph using the X and Y coordinates? or does %CV need to be determined for each variable separately? Answered by Robert Dawson. 





PEDMAS 
20110410 

From Ross: 48 ÷ 2 (9+3)
Is the answer 2 or 288? Answered by Harley Weston. 





Eliminate y 
20110407 

From Lynn: 2x + y = 8
y + 3z =5
z + 2w =1
5w + 3x = 9
Form three equations with y eliminated Answered by Penny Nom. 





A conical container and a spherical balloon 
20110406 

From Steven: Water is running out of a conical container 12 feet in diameter and 8 feet deep (vertex down) and filling a spherical balloon.
At the instant the depth of the water in the cone is 4 feet, the radius of the sphere is approximately 4 feet.
The rate of change of the depth of the water in the cone at the instant is approximately ______________ times the rate of change of the radius of the balloon. Answered by Penny Nom. 





Administration costs and profit 
20110405 

From brian: Hi , If I have direct job costs of $100. and my administration is 20 % and I want to make a 15 % profit , how would I calculate the administration and profit and what would be the total of each be and also the final total?
Thanks,
Brian Answered by Penny Nom. 





Two ships 
20110405 

From Gevork: Ship A is sailing due south at 16 mph. At the same time, a second ship B, 32 miles south of A, is sailing due east at 12 mph.
(a) at what rate are they approaching or separating at the end of one hour?
(b) At what rate are they approaching or separating at the end of two hours?
(c) When do they cease to approach each other and how far apart are they at that instant. Answered by Penny Nom. 





The rate of change of the area of a parallelogram 
20110405 

From Gevork: Let a parallelogram have sides of 8 and 12 and let vertex angle A be decreasing at a rate of 2degrees per minute. Find the rate of change of the area of the parallelogram when angle A equals 30 degrees. Answered by Penny Nom. 





I need to make $1000 profit 
20110328 

From Kat: I need to make $1000 profit selling plants for $3 each. My direct cost is $2 per plant and my overhead is $5oo. How many pots (plants = 1 per pot) do I need to make $1000? Answered by Penny Nom. 





What is x to the power of 0? 
20110323 

From Jason: What is x to the power of 0? Answered by Robert Dawson. 





(3x+4y)^2  (2xy)^2 
20110316 

From Taiwo: pls could some one help me with this question? thanks as lot
factorize:
(3x+4y)^2  (2xy)^2 Answered by Penny Nom. 





A family of circles 
20110301 

From steffi: Find the equation of the family of the circle passing through the the point of intersection of x^2+ y^2 4x28=0 and x^2 +y^2 4x20+52=0; the member tangent to x=7. Answered by Penny Nom. 





A camera's line of sight 
20110226 

From MJ: A rocket that is rising vertically is being tracked by a ground level camera located 3 mi from the point of blast off when the rocket is 2 mi high its speed is 400mph At what rate is the (acute) angle between the horizontal and the camera's line of sight changing Answered by Penny Nom. 





Prove sin x = sin (pi  x) 
20110215 

From Janet: Prove sin x = sin (pi  x) Answered by Penny Nom. 





The equation of a sphere 
20110209 

From kelly: what is the equation of a sphere if one of it's diameters has a giving end point of (4,4,4), (8,8,8)? Answered by Penny Nom. 





(7cubed * 8(exponent6))exponent 6 
20110129 

From Shalaine: What is the exponential form of (7cubed•8(exponent6))exponent 6? Answered by Penny Nom. 





Profit as a percentage 
20110117 

From Connie: I am trying to determine the profit margin on selected items.
ex: A bottle of juice costs me $.70, I sell it at $3.75. How can I determine what my profit percentage is? Answered by Penny Nom. 





Identify each polynomial by its degree and number of terms 
20110110 

From betty: Write in standard form and identify each polynomial by its degree and number of terms. How do you do this? Answered by Penny Nom. 





If ac = bc ... 
20110104 

From jamielle: if ac=bc, then a is not equal to b, c is not equal to zero Answered by Penny Nom. 





Profit as a percent 
20101219 

From gaurav: In the following, which calculation is right to calculate the profit percent.
if profit is 20% 100*1.2 = 120
if profit is 20% 100/0.8 = 125? Answered by Penny Nom. 





Angle of elevation 
20101210 

From PANKAJ: angle of elevation of the sun perpendicular72 and base 88 find angle Answered by Penny Nom. 





The rate of change of (8e^3x)+(27 e^3x) 
20101123 

From Aleo: I am unable to solve this problem:
Find the rate of change of (8e^3x)+(27 e^3x), with respect to x when x= 0.5 Answered by Penny Nom. 





A 35% profit 
20101119 

From Ana: You have a stamp collection and make a 35% profit by selling it on EBay for $2700. Find the original cost of the collection by using the formula:New value × 100 / 100 + percent change = Original value Answered by Stephen La Rocque. 





How far must the pitcher travel to get to the ball? 
20101104 

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. 





What is the speed of each car? 
20101104 

From Jennifer: two cars are 420 miles apart and traveling towards each other along the same road. They meet in 3.5 hours. One car is traveling 15mph slower than the other. What is the speed of each car?
This must be solved using a system of equation, I have no idea? Answered by Stephen La Rocque. 





I want to make a 50% profit 
20101029 

From Debbie: If my cost on an item is $32.00 and I want to make a 50% profit What would the retail be? Answered by Penny Nom. 





Two algebraic expressions 
20101029 

From chaptay: what is the difference between x(n^2) and x(n)^2 Answered by Penny Nom. 





The game of 24 
20101026 

From gabrielle: What is the answer using the numbers 0 0 0 0 (trig and calc are
allowed, all math is allowed) in the game 24? Answered by Claude Tardif. 





Powers 
20101020 

From dylan: how do you write 20736 in exponential form .same for 1728 and 50625.
is there a formula to figure out how to express large know numbers in exponential form. Answered by Penny Nom. 





The equation of a circle 
20101020 

From Silvan: Hi, I just want to find the x,y values for the circumference of a circle...
Lets take a clock having its centre at (0,0) in a graph.
I just want to know how to find the (x,y) coordinates for the curved path or the surface of the circle..
Is there any formula to directly align the curved path or the circumference of the circle in a graph for a known radius of a circle..
I feel it will be useful for me to draw a clock in a graph... :) Answered by Penny Nom. 





The distance between the origin and a moving point 
20100924 

From Norma: I am having problems with this question
find the rate of change of the distance between the origin and a moving point on the graph of the function below if dx/dt=5 cm/sec
y=x^2+2 Answered by Penny Nom. 





20% profit on the selling price 
20100924 

From ata: My cost is 100 and I want to make 20% profit on my selling price (not 20% of the cost). So, what should be calculation formula? Let's say my cost is 493.71 and I want to make 53.28% profit on the selling price; so how to determine the selling price? Answered by Penny Nom. 





Elimination and substitution 
20100918 

From Lauren: Solve one using the method of substitution and the other with the method of elimination.
v
a. y=5x+4
x=2y+1
b. 4x+3y=7
6x3y=13 Answered by Penny Nom. 





A building and a flag pole 
20100909 

From paul: A flag pole and a building stand on the same horizontal level. From the point p at the bottom of the building,the angle of elevation of the top t of the flag pole is 65 degrees. From the top q of the building the angle of elevation of the point t is 25 degrees.If the building is20 meters high. Calculate the distance pt Answered by Penny Nom. 





Percentage improvement 
20100826 

From shahrukh: Hi...
We had a web page that was taking 12 secs to load. Now it loads in 3 secs.
What is the percentage of improvement or how much faster is it working now.
TO me it looks like it is working 3 times faster or there is a 300% improvement in the loading time.
However my client says its ((123)/12*)100 = 75% improved. Which seems illogical on the face of it.
Thanks for your help
Shahrukh Answered by Robert Dawson and Chris Fisher. 





What is 2^2? 
20100825 

From alex: I know that (2)^2 is 4 but what is 2^2? Answered by Robert Dawson and Penny Nom. 





How many labels are left on a roll? 
20100813 

From Melissa: Is there a simple way to calculate how many labels are left on a roll? I thought there was a way to look at the individual label length, the label thickness and the core diameter and then measure the overall diameter to calculate how many pieces were left, but I'm struggling. I've seen a tool before I thought we called it a circle calculator, but those parameters were all that I needed to input to spit out the correct count. I never saw what was behind the scenes for this calculation. Ie factoring in revolutions or the number of pieces on each layer, etc. Please let me know if you have any suggestions. Any assistance will be greatly appreciated!!! Thanks! Answered by Penny Nom and Tyler Wood. 





A fruit seller 
20100731 

From Nazrul: 5% of total number of fruits of a fruit seller has been rotten and also 5% of them has been damaged during transportation. What is the percentage profit by which he sells the rest so that he profit 20% as a whole? Answered by Penny Nom. 





Thickness of sand 
20100707 

From RHONDA: In an 18 x 33 ft area how much is 4 yards of sand in inches to cover this area. Answered by Penny Nom. 





Volume of a styrofoam cup 
20100623 

From Stacy: how do you find the volume of a truncated cup with height of 3, top diameter of 2.5, and a bottom diameter of 2 Answered by Penny Nom. 





Selling price, cost and profit 
20100622 

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 number of gallons of water in a basement 
20100523 

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. 





Difference of cubes 
20100522 

From Anad: how can we prove a^3  b^3 is equal to (ab)(a^2+ab+b^2)? Answered by Penny Nom. 





Line of sight 
20100506 

From David: I live in St. Joseph, Michigan and there is an ongoing argument regarding lineofsight over the horizon.
Standing on a 200 foot high bluff here, people swear they can see the top of the Willis (nee Sears) Tower in Chicago, which is about 1653 feet high.
It is my contention that this is actually a "refracted reflection" and not directlineofsight.
So, to settle the argument, I'd sure like some simple explanation for this, even ifand I hope notI am incorrect.
David Answered by Harley Weston. 





The rate of change of y with respect to x 
20100429 

From Tom: I just had a quick calc question about wording that wasn't ever
addressed in class. When the book says "the rate of change of y with
respect to x", should it be considered how fast y is changing in
comparison to x?
I ask because the textbook says that "y is changing 3 times faster than x,
so the rate of change of y with respect to x is 3." I'm use to rate being
like velocity, as in units of distance per units of time. All we're told
in class is that it's the slope of the tangent line, I was hoping you
could clarify for me what exactly is meant by the wording of a "rate of
change of something with respect to something else". More specifically, what
"rate" and "with respect to" mean within this context?
Thanks for your time Answered by Harley Weston. 





The height of a flag shaft 
20100425 

From Sarah: A man standing 20metres away from a tower observes the angles of elevation to the top and bottom of a flag shaft standing on the tower as 62degrees and 60degrees respectively. Calculate the height of the flag shaft.' Answered by Penny Nom. 





Profit 
20100421 

From joyann: a Raleigh road runner 16" unisex bike which cost $892 was sold for $1052.56 calculate
A. the profit made on the bike
B. the percentage profit Answered by Penny Nom. 





Exactly two lines of symmetry 
20100411 

From debbie: i am looking for a quadrilateral with exactly two lines of symmetry. please help! thank you. Answered by Tyler Wood. 





The area of a field of view 
20100407 

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. 





Fitting a sofa through a doorway 
20100406 

From Yvonne: Hi, I would be most grateful if you could help me, because I have no idea how to work this out! I am moving from a house to a flat, and the doors in the flat are 70 cm wide. I have a sofa 88 x 88 x 215. Will it go through the door if we tip it sideways at an angle?
Thanks, Yvonne Beck Answered by Robert Dawson. 





A system of equations 
20100330 

From samantha: the equations of two lines are 6xy=4 and y=4x +2.what is the value of x in the solution for this system of equations? Answered by Penny Nom. 





The sides of a 306090 triangle 
20100329 

From maris: Find the sides of a 306090 triangle whose perimeter is 6. The solution must use systems of equations using 3 variables. Answered by Penny Nom. 





The area of a polygon 
20100328 

From John: Question from John, a student:
How do you find the area of a polygon with any given amount of sides? Answered by Harley Weston. 





The height of a hill 
20100326 

From Amber: A surveying team determines the height of a hill by placing a 12foot pole at the top
of the hill and measuring the angles of elevation to the bottom and to the top of the pole.
They find the angels of elevation. Describe how to find the height of the hill. Answered by Penny Nom. 





A radio tower 
20100326 

From Alex: The height of a radio tower is 450 feet, and the ground on one side of the tower slopes upward at an angle of 10 degrees. How long should a guy wire be if it is to connect to the top of the tower and be secured at a point on the sloped side 110 feet from the base of the tower? Answered by Harley Weston. 





A roll of paper 
20100325 

From keith: how many yds of paper for a roll with a width of 6.875 and a core of 3 in and a diameter of 40in? Answered by Robert Dawson. 





The angle of intersection between two lines 
20100325 

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. 





Modelling the roof of a house 
20100323 

From Sandi: This question has been haunting my dreams at night. It states the cross section of the roof of a house is modelled by the function y= 5\12x12+5, where y>0 or y. Now I'm suppose to graph the function. b) Find the slope, height, length of sides, and base of the isosceles triangle. c)Explain what transformation must be applied to the graph of y=x to obtain the graph of y= 5\12x12+5, where y>0 or y=0. 1st I put the equation into my calculator and graphed it. I got 10 for the height. We have had 2 sub teachers this past week. The first one told me the height should be 12 the other one told me 5. So I'm really confused. If I use my 10 units as height and the Pythagorean Theorem I get my sides to be 26 units the base 48 and my slope I calc to be 5/12. Both teachers are pretty sure I'm wrong and they are right but we all have different answers. Please help put this problem to rest so I can rest soundly at night. Thank you for your time. Answered by Penny Nom. 





A quadrilateral with 4 known sides and 1 known angle 
20100319 

From samuel: Name: Samuel
Status: Student
I have a quadrilateral with 4 known sides and 1 known angle, and I'm trying to evaluate the other angles of my quadrilateral.
By the law of cosines, I can easily find my opposite angle (using the diagonal as a basis for the equation).
However, to find the two remaining angles, I have found no other way so far than to use the other diagonal, which can be found with the equation attached (from geometry atlas).
Is there any simpler way? Answered by Robert Dawson and Harley Weston. 





Cooling 
20100307 

From Lori: If a house is always at 20 degrees celsius.
Water (tea) boils at 100 degrees celsius.
5 minutes later the tea was 70 degrees celsius.
Use an equation to predict the temperature after 20 minutes. Answered by Tyler Wood. 





Prove A intersect B =X iff A = X and B = X 
20100306 

From Gloria: how would you prove A intersect B =X iff A = X and B = X Answered by Tyler Wood. 





How many CDs and videos did the store sell? 
20100301 

From dawn: A used book store started selling CDs and videos. In the first week,the store sold 40 used CDs and videos,at 4.00
per CD and 6.00 per video.The sales for both CDs and videos totaled 180.00 she wrote a system of equations to represent the situation.Then she graph the system of equations
thanks Dawn Answered by Tyler Wood. 





The test for some disease is 99% accurate 
20100224 

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. 





15% profit 
20100221 

From daviann: calculate the cost price,given
selling price=$304
percentage profit=15%
what is the answer? Answered by Penny Nom. 





The angle at which the road is inclined 
20100210 

From abeth: a mountain road drops 5 m for every 22 m of road. Calculate the angle at which the road is inclined to the horizontal to the nearest degree. Answered by Penny Nom. 





Order of operations 
20100207 

From addie: (3+10) x 10  8 x 4 = Answered by Penny Nom. 





Everything in a cube 2 miles long? 
20100131 

From Naresh: in a book, i got to read this :
Is it possible to pack the entire population of earth and everything that was created by
humankind in a cube whose edges are 2 miles long ?
Is it possible? Thanks. Answered by Stephen La Rocque. 





The height of a roof 
20100131 

From carl: Width of my roof I am building is 5M at baseline, and the pitch is 40%.
What will the height be, and how can I work this out in the future. Answered by Penny Nom. 





1^3 + 2^3 + 3^3 +4^3 ... n^3 = ? 
20100129 

From ireimaima: Hi..
Can u please help me with this question..
I find that when i test eg: n=2 for n (n+1) /4,
it seems that it does not giving me the right answer of 1^3 + 2^3 = 9
but 3/2... i'm confuse..can u please help me..thanks so much
Prove that:
1^3 + 2^3 + 3^3 +4^3………………………………..n^3 = n (n+1) /4 Answered by Penny Nom. 





Solving a triangle 
20100125 

From Paige: how do i solve a triangle with one angle of 73 degrees,
one angle of 32 degrees, and one side of 23cm? Answered by Harley Weston. 





Angle of incline 
20100120 

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. 





A proof by induction 
20100112 

From Bhavya: Prove by induction that if Xi >= 0 for all i, then
(Summation Xi from 1 to n)^2 >= Summation Xi^2 from 1 to n Answered by Penny Nom. 





A proof involving real numbers 
20100111 

From Amper: Let a,b is an element of real numbers, and suppose that for every x>0 we have a is lesser than or equal to b+x.
(a) Show that a is lesser than or equal to b.
(b) Show that it does not follow that a is lesser than b.
i'm feeling bad of having no idea with this, hope i you can help me. GRACIAS!! Answered by Penny Nom. 





Profit increase from 10% to 15% 
20100103 

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. 





A trig question 
20091215 

From A trig question: Hey, my name is Candle
I'm in academic math10 and am stuck on my trig... one question I thought I had right because i used the cosine law I got wrong and can't figure out why... here's a copy of the question. (i guessed it was D... but my teacher said it's B)
Thanks
Candle Answered by Robert Dawson. 





A 4 digit number 
20091215 

From Lisa: Billy Club was assigned the task of putting numbers on
all the playground balls used during daily recess. Billy
will number the balls using the following rules:
1. It will be a 4digit number.
2. The digit in the thousands place will be a 1 or a 2.
3. The digit in the hundreds place will be a 2, 4, or 6.
4. The digit in the tens place will be an odd number.
5. The digit in the ones place will be greater than six.
How many balls can Billy number if he follows these rules? Answered by Robert Dawson. 





A telephone pole on a slope 
20091214 

From Marissa: A 10 meter telephone pole casts a 17 meter shadow directly down a slope when the angle of elevation of the sun is 42 degrees. Find the angle of elevation of the ground. Its a law of sines problem. Answered by Penny Nom. 





e = m c^2 
20091209 

From Jim: Please explain the following formula:
E=MC2 (squared) Answered by Robert Dawson. 





Game of 24 
20091209 

From Tony: Checked out all of the previous inquiries into the crazed game, and found none with these particular numbers: 1, 4, 6, 7. I've tried every method I can think of, please Help! Tks. Answered by Robert Dawson, Penny Nom and Claude tardif. 





How fast is the distance between the two cars decreasing? 
20091208 

From Jenny: Two cares are on a collision course toward point P. The paths of the two cars make a 30 degree angle with each other. The first car is 40 km from P, and traveling toward P at 16 km/hour. The second car is 50 km from P, traveling at 20 km/hour. How fast is the (straight line) distance between the two cars decreasing. (Hint: Law of Cosines) Answered by Harley Weston. 





(9  x^2)/(x  3) 
20091204 

From Sandy: 9x^2/x3
I need to know how to solve this.
Thanks Answered by Penny Nom. 





(24x3)+(7x8)(20/5)+(4x7) 
20091201 

From Marilyn: (24x3)+(7x8)(20/5)+(4x7)
Thought I had the answer but the form says no. Could you solve it for me please. Answered by Penny Nom. 





Three angles and one side of a triangle 
20091116 

From Esther: How do i find the sides of an acute triangle if i know the angels are 60,45,75 and i only know one side which is 10? Thanks! Answered by Penny Nom. 





Maximize profit 
20091114 

From Willie: Profit is the difference between Total Revenue and Total Cost.
Therefore, to MAXIMIZE PROFIT you must maximize Total Revenue.
True or False? Explain answer. Answered by Penny Nom. 





At what rate are the people moving apart? 
20091101 

From saira: A man starts walking north at 4 ft/s from a point P. 5 minutes later a woman starts walking south at 5 ft/s from a point 500 ft due east of P. At what rate are the people moving apart 15 minute after the woman starts walking ? Answered by Harley Weston. 





A linear system 
20091020 

From marissa: Solve this linear system
2xy=5
3x+y=9 Answered by Penny Nom. 





Proof that the root of 27 is irrational 
20091018 

From Scarlet: How do you prove that the square root of 27 is irrational? Answered by Victoria West. 





A right triangle 
20091012 

From Josseph: A right triangle has an area of 84ft sq. and a hypotenuse 25ft long. What are the lengths of the other two sides? Answered by Penny Nom. 





Game of 24 
20091002 

From trami: game of 24 by using 4 7 7 1? Answered by Claude Tardif. 





Prove by induction 
20091002 

From Anonymous: How can you prove the following by induction:
Any fraction (A / B), where 0 < (A / B) < 1, can be expressed as a finite sum
(1 / c(1)) + (1 / c(2)) + (1 / c(3)) + ... + (1 / c(k)),
where c(1), c(2), ..., c(k) are natural numbers greater than 0.
[ex. (20 / 99) = (1 / 9) + (1 / 11)] Answered by Claude Tardif. 





4 squared and (4) squared 
20090929 

From Andrea: Is 4 squared the same as (4) squared? I am thinking the first is 16 and the second is +16. I am trying to clarify for my students. Answered by Penny Nom. 





Evaluating x^2 + (yz  3)^2 
20090928 

From Kathy: My daughter and I are having trouble solving this equation:
x²+ (yz – 3)²
if x=4,y=2 and z=0
We are having difficulty with the x² part of the equation. Thanks Answered by Penny Nom. 





How many terms are there in this sequence? 
20090928 

From tabby: How many terms are there in this sequence?
5,1,3,...,111 Answered by Penny Nom. 





Probability 
20090927 

From Ed: My mother died 3 years to the day after her daughter died. what are the odds of that happening by chance? thanks Answered by Chris Fisher. 





Order of operations 
20090924 

From aman: my question is regarding the fact
i have a formula which looks like this :
(ratio 1 + ratio 2 divided by 2)
so my question is do i add first then divide by 2 or do it all together Answered by Penny Nom. 





5 x 8 + 6 divided 6  12 x 2 
20090924 

From Susan: 5 x 8 + 6 divided 6  12 x 2. I am not sure of the rules of operation for this type of question Answered by Penny Nom. 





Two equations in two unknowns 
20090918 

From Citizen: x+3y=7
x+4y=7 Answered by Penny Nom. 





The method of substitution 
20090917 

From laura: ok! i really need help with this question plz help!!
x=  4y +5
x+2y = 7 Answered by Penny Nom. 





A trillion grains of rice 
20090914 

From akaila: can 1trillion rice grains fit in a classroom with the area of 144.4m3 Answered by Penny Nom. 





Simultaneous equations 
20090828 

From onias: solve 3/a  2/b = 1/2 , 5/a + 3/b = 29/12 Answered by Robert Dawson. 





y=2x+1 and y=2x1 
20090828 

From MARICELA: Need help of how to work this problems
y=2x+1 and y=2x1
First of all what is the difference?
Second I think is easy just to work with the X y with the line in the middle
but how do you get the numbers for each side. Answered by Penny Nom. 





The game of 24 
20090827 

From ANITA: Help I'm suppose to be a math expert, yet I can not yield 24 from the numbers 8,4,9,9, using each only once. HELP Answered by Penny Nom. 





An antiderivative problem 
20090813 

From Indrajit: ∫4e^x + 6e^x/(9e^x + 4e^x)dx = Ax + Bloge(9e2x  4) + C
then A=?......B=?.....C=?
plz solve it...."^" stands for "to the power of".... Answered by Harley Weston. 





The leaning tower of Pisa 
20090809 

From MF: Would you have any idea how the 'latitude of 44 degrees N" has anything to do with this question and how I would apply it?
The leaning tower of Pisa leans toward the south at an angle of 5.5 degrees. One day near noon its shadow was measured to be 84.02 m long and the angle of elevation from the tip of the shadow to the top of the tower was measured as 32.0 degrees. To answer the question, assume that the tower is like a pole stuck in the ground, it has negligible width. Also, it is important to know that Pisa Italy is at a latitude of approx 44 degrees North because this affects the direction of the shadow.) Answered by Stephen La Rocque. 





Eye Height Level Found from Visual Angle 
20090807 

From Jolie: Hello,
I am trying to figure out what height from the ground a person's eyes are if they have a 12 degree visual angle to a screen that is 58cm away from their eyes?
Thank you. Answered by Janice Cotcher. 





Highest Common Factor of Two Polynomials 
20090728 

From Nazrul: If x+a be the h.c.f. of x^2+px+q and x^2+mx+n, how can I prove that (pm)a=qn. Answered by Robert J. Dawson & Janice Cotcher. 





Inequalities Proof 
20090724 

From ABOU: good morning.......a b c are real positive no zero......proof that
sq root(2a/(a+b))+sq root(2b/(b+c))+sq root(2c/(c+a))inferior or equal 3
thank you Answered by Janice Cotcher. 





Properties of Natural Numbers 
20090724 

From nazrul: If m,n,k are natural number how can I prove that (m+n)k=mk+nk. In the proof the properties of natural number should be used. Answered by Janice Cotcher. 





Proof of a Unique Solution 
20090724 

From muele: Find matrix A such that A is not invertible, and
b such that Ax=b has a unique solution Answered by Robert J. Dawson. 





Selling fish 
20090722 

From Hemantee: A fishmonger bought 150kg of fish. he sold 70%of it at the price of Rs90 per kg and the rest at Rs 75 per kg. he made a profit of 42.5 per cent. how much did he pay for the fish. Answered by Penny Nom. 





Profit as a percentage 
20090715 

From Jay: If I buy an item for $3.00 and sell it for $6.00. What is my percentage of profit? Answered by Penny Nom. 





A roll of paper 
20090705 

From mark: is there a simple way of finding out how much is left on a roll of paper. i have read similiar questions and answers on here but all seem very complicated and not being very good at maths does not help me much. some are in inches and all have different figures to mine so if i give my figures hopefully i wil understand it better. the radius of the cardboard core is 52.25mm, the radius of the paper at 2000 linear meters is 158.625mm. the thickness is 0.17mm. when nearing the end of the paper how do i work out how much is left in a simple way. thank you in advance for any help you can give me Answered by Harley Weston. 





Coffee scoops per cup 
20090629 

From charity: if my coffee machine takes 10 scoops for every six cups, how many scoops do i need for 4 cups.
each scoops equals one tbls(.25 oz) Answered by Penny Nom. 





Prove that the set of all positive odd integers is an infinite set 
20090620 

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. 





A difference quotient 
20090617 

From Sue: When s(x)=x^3+x, compute and simplify the difference quotient s(x+h)s(x)/h. Answered by Harley Weston. 





The product of gradients between 2 perpendiculars lines 
20090611 

From Alister: how do i prove that the product of gradients between 2 perpendiculars lines equal to 1.... Answered by Penny Nom. 





Vectors and the Law of Cosine 
20090608 

From lauren: once force of 20 pounds and one force of 15 pounds act on a body at the same point so that the resultant force is 19 pounds. Find, to the nearest degree, the angle between the two original forces Answered by Janice Cotcher. 





Profit margin 
20090526 

From andreya: what is the profit margin of a business that spends $200 in order to make $1000 Answered by Penny Nom. 





Game of 24 
20090522 

From Sam: Using the numbers 7, 3, 2, and 2, how do you get the number 24? Answered by Claude Tardif and Harley Weston. 





Maximum profit 
20090511 

From Sally: a manufacturer of dresses charges $90 per dress up to 100 units and the average production cost is $60 per dress. to encourage larger orders the company will drop the price per dress by .10 for orders in excess of 100. I need to find the largest order the company should allow with the special discount to realize maximum profit. Answered by Harley Weston. 





A 6 team social softball league 
20090502 

From Don: Hi
We have a 6 team social softball league with only two fields. Each team
plays two games each Saturday. We have three time slots 10:00, 12:00
and 2:00 We play for 11 Saturdays and than have a 2 weekend playoff.
All teams prefer double headers vs the split at 10:00and 2:00. How do we
schedule as balanced a schedule as possible and minmize the splits ?
Thanks
Don Answered by Laura Morrison and Victoria West. 





Game of 24 
20090502 

From Barbara: using the numbers 1,3 7 and 9 only once how do you get the answer of 24 Answered by Claude Tardif. 





The sum of the roots of a quartic 
20090421 

From dave: This is a algebra problem that i am confused about:
The sum of the roots of x^4x^3+5x^2+4=0 is:
i tried graphing it, but it shows that there are no roots, but the answer is 1. are they wrong? Answered by Penny Nom. 





12 oz. cup 
20090419 

From Tom: I am a ceramic teacher and wanted my students to make a 12 oz. cup, what formula should we use? Answered by Chris Fisher. 





Exponential form 
20090416 

From Pete: Hi,
How do you express ³√h^4 in exponential form. I am having a lot of
trouble with this one.
thanks
Pete Answered by Stephen La Rocque. 





The axiom of choice and constructibe sets 
20090410 

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. 





Game of 24 
20090408 

From Joe: How do you get 24 using 6,9,10,10 once. Its called the 24 game.
Joe Answered by Harley Weston. 





Multiplication of polynomials 
20090407 

From Carla: I am struggling to understand Multiplication of Polynomials. No matter how hard I try to understand Multiplication of Polynomials, I just can't get it!
The problem that I am trying to solve is this :
3x^3y(y + 2 x^2 + x) Answered by Robert Dawson. 





Game of 24 
20090405 

From Ramona: math 24 using 16, 9, 20, 7 Answered by Penny Nom. 





Profit as a percent 
20090326 

From Danny: If I have something that cost me .38 and I want to sell it for $1.00 what is my profit % on this item Answered by Robert Dawson. 





The rate of change of the volume of a sphere 
20090325 

From Kaylin: why the rate of change of volume of a sphere is not constant even though dr/dt is constant? Answered by Walter Whiteley. 





The optimal retail price for a cake 
20090325 

From Shawn: Your neighbours operate a successful bake shop. One of their specialties is a cream covered cake. They buy them from a supplier for $6 a cake. Their store sells 200 a week for $10 each. They can raise the price, but for every 50cent increase, 7 less cakes are sold. The supplier is unhappy with the sales, so if less than 165 cakes are sold, the cost of the cakes increases to $7.50. What is the optimal retail price per cake, and what is the bakeshop's total weekly profit? Answered by Robert Dawson. 





The sides of a parallelogram 
20090317 

From Sami: If ABCD is a parallelogram, prove that line AB is congruent to line CD. Clearly state your reasons and conjectures. Answered by Penny Nom. 





The midpoints of two sides of a triangle 
20090317 

From Manis: Prove that the line joining the midpoint of two sides of a triangle is parallel to the third and half of it. Answered by Robert Dawson. 





Related rates 
20090314 

From Jeevitha: The side of an equilateral triangle decreases at the rate of 2 cm/s.
At what rate is the area decreasing when the area is 100cm^2? Answered by Stephen La Rocque. 





Related rates 
20090309 

From Megan: A plane flying with a constant speed of 330 km/h passes over a ground radar station at an altitude of 3 km and climbs at an angle of 30°. At what rate is the distance from the plane to the radar station increasing a minute later? Answered by Harley Weston. 





The game of 24 
20090301 

From Jeff: My son in the 5th grade was given a problem for extra credit and could use parents help. He was given the numbers 21, 13, 9, 6 and asked to use each number only once by +, , /, x the numbers in any order to obtain an answer of 24. Answered by Harley Weston. 





Collecting an army 
20090225 

From bevaz: Question from bevaz, a student:
A ruler orders his chamberlain to collect an army from 30 houses. The servant goes to the first house alone and collects one man. At each house after that he takes the same number of men as he has already collected, so at the second house he goes with one other and so on. How many men did he collect in all? Answered by Penny Nom. 





Find the resultant of this displacement pair 
20090222 

From katydidit: Find the resultant of this displacement pair:
500 miles at 75 degrees east of north and
1500 miles at 20 degrees west of south.
How do I graph this and how do I solve this problem? Answered by Penny Nom. 





Angle of depression 
20090218 

From Meeka: An aircraft flying at an altitude of 2000m is approaching an airport.
If the angle of depression of the airport is 5 degrees, what is the distance from the plane to the airport measured along the ground?
Round your answer to the nearest tenth of a kilometer. Answered by Robert Dawson. 





A rectangular park 
20090206 

From Debbie: A park named Writer's Rectangle opened in town. When asked about the dimensions of the rectangle, the city planner, responded with these clues: The diagonals of the rectangular park plus its longer sides together measure seven times one of the shorter sides. The length of one diagonal is 250 m longer than one of the shorter sides. Use this information to find the area of the park. Answered by Stephen La Rocque. 





How much did the statue originally cost him? 
20090206 

From Debra: Jim is able to sell a handcarved statue for $670 which was a 35% profit over his cost. How much ded he statue originally cost him? Answered by Penny Nom. 





The substitution method 
20090206 

From amber: Pleasse help me with this problem
x+y=2
y2x=1 Answered by Penny Nom. 





Calculating markup 
20090203 

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. 





How fast is the visible surface of the earth decreasing? 
20090124 

From Ray: A dive bomber loss altitude at a rate of 400 mph. How fast is the visible surface of the earth decreasing when the bomber is one mile high? Answered by Harley Weston. 





In the shadow of a flagpole 
20090122 

From La: How fast is the length of the shadow of an 18 foot flagpole growing when the angle of elevation of the sun is 45 degrees and is decreasing at a rate of 10 degrees per hour? Answered by Harley Weston. 





Factor x^2  y^2 
20090120 

From Shell: complete Factor: x^2y^2 Answered by Penny Nom. 





Negative rate of change 
20090112 

From hemanshu: when i have to find rate of change of decrease in any value my ans comes in negative why?????????? Answered by Penny Nom. 





A Tshirt fundraiser 
20090111 

From Andre: Lou's class is selling Tshirts for a fundraiser. The supplier charges 750$ for the initial design and the setup plus 5$ for each imprinted shirt. The students sell the shirts for 15$ each.
a)How many Tshirts do the students need to sell to break even?
b)How much profit will the students make if they sell 150 shirts? Answered by Harley Weston. 





The table of values for y=3x10 
20090109 

From Jade: How can I know the value of x for y=3x10 in this table of values pls. include the deatails
if x=2 y=16
if x=3 y=1
but how if y=2 what is x Answered by Penny Nom. 





30% profit 
20090106 

From bob: this is a basic question that I just can't get thru my head.
I know all my cost for a product, if I want to sell at a given profit can I divide by a given
number, example for 30 % divide by .7 or do I multiply?
Is there a simple answer for this? Sure would make my work a lot easier.
Thank you for your time
Puzzled in Ohio Answered by Penny Nom. 





The sum of the roots of a quartic 
20090103 

From peter: How do you find the roots of an equation without graphing? like, i have a problem that says what is the sum of the roots of x^4x^3+5x^2+4=0. Answered by Harley Weston. 





System of equations  comparison method 
20090102 

From nick: Hi, I am doing a project on system of equations by using comparison method,
but for some reason or another, i can't seem to find any information on the
comparison method at all. So, please would you help me by giving me a website
that you know of that has some information on my method. And, if you know the
answer, can you please tell me why or when do we use system of equations by
using comparison method?
Thank You Answered by Robert Dawson. 





The area of a triangle 
20081223 

From ashiya: Hi,
I have attached figure of the triangle, Can you please help to find the area of Triangle ABC.
Thanks.
Ashiya Answered by Stephen La Rocque. 





Coefficient of variation 
20081217 

From JR: I have read your reponses regarding the coeffcient of variation (CV) and find them very useful. I still have a question about interpreting the CV. Let's that the CV of sample #1 is 3% and that of sample #2 is 12%. Can I report that Sample #2 is 4 times more variable than sample #1? Thanks in advance! Answered by Robert Dawson. 





The angle between two lines 
20081217 

From abhi: how to calculate the angle between two lines, given the length of the lines..
angle should vary from 0  360 in the counterclockwise direction Answered by Robert Dawson and Harley Weston. 





Do all square numbers have an odd number or factors? 
20081211 

From Amy: Do all square numbers have an odd number or factors? Answered by Victoria West. 





Related rates 
20081126 

From Lyudmyla: How fast is the volume of a cone increasing when the radius of its base is 2 cm and growing at a rate of 0.4 cm/s, and its height is 5 cm and growing at a rate of 0.1 cm/s? Answered by Harley Weston. 





The game of 24 
20081124 

From Davey: this has us all stumped. 5 ,5 ,7 ,and9 = 24. Oh may you assist in ending
our brain pain Answered by Penny Nom. 





Profit as a percentage 
20081121 

From Nomar: Cost Price is $ 556,109.64 and Selling price is $ 1,020,936.00, What is the Profit Percentage? Answered by Harley Weston. 





The path of a small sailboat 
20081119 

From jane: a sailor in a small sailboat encounters shifting winds. she sails 2.00 km East
then 3.40 km North East, then an additional distance in an unknown direction. Her final position
is 6.68 km directly east of the starting point. find the magnitude & direction
of the third leg of the voyage. Answered by Harley Weston. 





Factoring 
20081119 

From Neji: How do you factor (yz) (y+z) (y^4+y^2z^2+z^4) and get (y+z)(y^2yz+z^2) (yz) (y^2+yz+z^2) as the answer? Answered by Harley Weston. 





How far are the boats apart? 
20081114 

From dom: Two boats leave port at the same time. They leave at 150 degree angle. One boat travels at 10mph and the other at 20mph. After two hours how far are the boats apart? Answered by Penny Nom. 





What is 5x+3y=24? 
20081113 

From Robert: What is 5x+3y=24??????? Answered by Stephen La Rocque. 





The angles and sides of a triangle 
20081113 

From JAMIE: a triangle with a side(b)37m an angle(C)70degrees and (a)79m find values of angles A and B and length of side c Answered by Stephen La Rocque. 





How fast is the distance between the airplanes decreasing? 
20081110 

From Crystal: At a certain instant, airplane A is flying a level course at 500 mph. At the same time, airplane B is straight above airplane A and flying at the rate of 700 mph. On a course that intercepts A's course at a point C that is 4 miles from B and 2 miles from A. At the instant in question, how fast is the distance between the airplanes decreasing? Answered by Harley Weston. 





Melting ice on a hemisphere 
20081020 

From heather: The top of a silo is the shape of a hemishere of diameter 20 ft. if it is coated uniformly with a layer of ice, and if the thickness is decreasing at a rate of 1/4 in/hr, how fast is the volume of ice changing when the ice is 2 inches thick? Answered by Penny Nom. 





How much does Luc pay for his tools?? 
20081020 

From imran: Luc makes $1 profit on each tool he sells. Marc makes a $2 profit while paying $5 less for his tools than Luc. Marc thus makes $6 more profit for every $100 invested. How much does Luc pay for his tools?? Answered by Penny Nom. 





An arithmetic series 
20081017 

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. 





Related rates 
20081016 

From Gisela: As sand leaks out of a hole in a container, it forms a conical pile whose
altitude is always the same as its radius. If the height of the pile is increasing
at a rate of 6 in/min, find the rate at which the sand is leaking out when the
altitude is 10in. Answered by Penny Nom. 





The rate of change of the volume of a cone 
20081015 

From Barbara: Suppose that both the radius r and height h of a circular cone change at a rate of 2 cm/s.
How fast is the volume of the cone increasing when r = 10 and h = 20? Answered by Harley Weston. 





The average rate of change of gasoline used 
20081006 

From JHulie: What is the average rate of change of gasoline used, measured in miles per gallons
if you travel 212 miles, then you fill your gas tank up again and it takes 10.8 gallons.
If you designate your change in distance as 212 miles and your change in gallons as 10.8? Answered by Penny Nom. 





The vertex of a parabola 
20080930 

From Anne: How do you find the vertex of the function f(x)=x squared+7x6 Answered by Penny Nom. 





Lines that pass through a point 
20080930 

From Abigail: what is the name for a point that a group of lines pass through that contains the letters c e n p i l? Answered by Penny Nom. 





z(z+1)x(x+1) / zx 
20080930 

From sylvia: z(z+1)x(x+1) / zx
HOW DO I SIMPLIFY THIS Answered by Penny Nom. 





a(a+1)  b(b+1) 
20080930 

From Shaun: I need to factor (ab) out of the following: a(a+1)  b(b+1). I know it is simple but I cannot remember how. Answered by Penny Nom. 





How tall is the wall? 
20080929 

From ash: you and bob are separated by a tall wall you stand 10 feet further from the wall
than bob your angle of elevation is 37 degrees and his 44 degrees
how tall is the wall? Answered by Penny Nom. 





Number of factors 
20080918 

From Austin: I am stuck on finding what type of number has exactly two factors and
what type of number has an odd number of factors? I need some examples. Answered by Penny Nom. 





The volume of a box 
20080916 

From Andre: volume of the box cubic centimeters
____ X _____ X ______ X =_______
The length is 8.5 Width is 3.4 Answered by Penny Nom. 





The nth term of a sequence 
20080913 

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. 





Angle of elevation 
20080909 

From kristy: A man on the tenth floor of a building shouts down to a person on the street. If the angle of elevation from the street to the man in the building is 35° and the man in the building is 40 feet up, about how far away from the building is the person on the street? Answered by Penny Nom. 





The height of a tree 
20080909 

From danice: At a certain time of day, the angle of elevation of the sun is 30°. A tree has a shadow that is 25 feet long. Find the height of the tree to the nearest foot. Answered by Penny Nom. 





A security camera 
20080907 

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. 





Mathematical induction 
20080905 

From James: I need to prove a problem by induction regarding the Triangle Inequality. The problem is
abs(a1 + a2 +...+an) <= abs(a1) + abs(a2) +...+ abs(an). Answered by Victoria West. 





A line parallel to y= 1/2x + 5 
20080903 

From Michelle: Find the equation of a line parallel to y= 1/2x + 5 if the required line passes through ( 3,4) Answered by Penny Nom. 





A roof angle 
20080830 

From carla: Use vectors to find the angle in the attached diagram Answered by Chris Fisher and Stephen La Rocque. 





A cubic equation 
20080825 

From RAM: The following Cubic Eqn should have three roots  what are they?
x^327=0 Answered by Penny Nom. 





Radii and Chords Create a NonRight Triangle 
20080822 

From Beary: AOC is a diameter of circle O. Line AB is 12, and lines OA and OC (the radii) are 10. Find the length of line BO and chord BC. Answered by Janice Cotcher. 





Simplifying Algebraic Expressions 
20080822 

From Jacky: x^2y^2+4x+4y Answered by Penny Nom. 





Trough Filling with Water 
20080821 

From lanny: a triangular trough is 10 feet long, 6 feet across the top, and 3 feet deep. if water flows at the rate of 12 cubic inches per minute, find how fast the surface is rising when the water is 6 inches deep. Answered by Janice Cotcher. 





The game of 24 
20080820 

From Tasha: I have four numbers a 6, a 6 a 5 and a 3, i can add subtract divide or multiply these numbers in anyway but i have to use all of them and call only use them once i have to come up with a total of 24 Answered by Penny Nom. 





Factoring x^2 + 729 
20080819 

From peter: hello I,am having trouble factorising a polynomial into polynomial factors
with real coefficients please can you help the polynomial is x^2+729 Answered by Harley Weston. 





Solving for Shared Height of Two Right Triangles 
20080817 

From Heidi: find the height of a triangle, which can be split into two right triangles, but the base (50m) is not split equally in half. one end of the base is 40 degrees, while the other is 30 degrees. Answered by Janice Cotcher. 





BEDMAS 
20080812 

From Rebecca: I have 3 questions.
1) I don't really understand BEDMAS.Im going in to the 6th grade and im
kind of nervis about it.?
2)When you're doing BEDMAS what does the small 3 or 2 above the
other numerals mean?
3)How would you answer this:5+2 x 9  9 x 12= ?? Answered by Janice Cotcher. 





Arclength and sectorangle 
20080806 

From Benson: If chord length, radius are given, How to find the sector angle and arclength Answered by Janice Cotcher. 





Find the product of 2^35 and 5^38 in sci. notation. 
20080803 

From Peter: I am preparing for a competition and a lot of the noncalculator problems are like find the product of 2^35 and 5^38 in sci. notation. How would you do that? Answered by Penny Nom. 





The product of the digits of a four digit number 
20080726 

From Pete: I am a student preparing for a competition and this was one of the prep problems: The product of the digits of a four digit number is 6x5x4x3x2x1. how many such numbers are there with this property? Answered by Stephen La Rocque. 





Proofs 
20080726 

From Taylor: when doing a proof, how do i figure out the steps in which i find the statements? i find the reasons pretty easily but i do not understand how to get the proving part. that would be great if you can help me! Thanks Answered by Victoria West. 





Alpha level 
20080723 

From anonymous: What is the advantage of using an alpha level of .01 versus a level of .05, What is the disadvantage of using a smaller alpha level? Answered by Janice Cotcher. 





The number of digits in a really big exponent 
20080721 

From Pete: how would you find the number of digits in a really big exponent without a calculator? Answered by Penny Nom. 





Four Positive Integers 
20080720 

From william: let a, b, c and n be positive integers. If a+b+c=(19)(97) and a+n=bn=c/n, compute the value of a. Answered by Janice Cotcher. 





Number of factors 
20080720 

From pete: how do you find the number of factors in a really big number without using a factoring program or listing the out? Answered by Penny Nom. 





solving four simultaneous equations 
20080718 

From Muhammad: 2B2C+4E=1
A+B+C+D=0
2B2C2D+E=0
B+C+4D2E=0 Answered by Janice Cotcher. 





Does the sequence 1 2 4 8 16 32 etc have a name? 
20080717 

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. 





Express as a function of x 
20080714 

From Rita: Express the area A of an isosceles right triangle as a function of x of one of the two equal sides.
NOTE: I always see the phrase "Express as a function of x" in math textbooks.
What exactly does that phrase mean?
I also have seen it written as "Express in terms of x." Answered by Penny Nom. 





Profit as a percentage 
20080708 

From ANNORIS: Question from annoris, a student:
How to calculate percent of profits using step by step division formula.
I know how to get the profit.
Selling cost was $15.00
Cost amount was $10.00
Total profits its $ 5.00.
But i do not know how to get the percent because i dont know how to divide to well . Can you helppppppp me ? Answered by Penny Nom. 





A net profit of 4% on a sales volume of $100 million 
20080707 

From Muriel: If a firm has a net profit of 4% on a sales volume of $100 million and the
company has instituted logistics programs that result in cost savings of
$1 million, what equivalent sales increase would be required to equal such
a cost savings?
What I do know is that the net profit % has increased from 4% to 5% and
the profit has gone from $4,000,000 to $5,000,000 but I have no idea what
the formula is to figure out how much sales would have to increase to
result in that same profit. Answered by Janice Cotcher. 





Sum and product of the roots of a quadratic 
20080703 

From Gautam: If a and b are the roots of x^2+px+1=0 and c and d are the roots of
x^2+qx+1=0
prove that
(ac)(bc)(a+d)(b+d)=q^2p^2
Regards
Gautam Answered by Harley Weston. 





The sum of the digits of twodigit number is 9 
20080701 

From Audrey: the sum of the digits of twodigit number is 9. if the digits are reversed, the new number if 63 greater than the original number. find the number. Answered by Penny Nom. 





Slope and rate of change 
20080623 

From Lee: What is the difference between a slope and a rate of change? Answered by Stephen La Rocque. 





111...111 * 2003 
20080623 

From Peggy: Number a = 111...111 formed by 2003 1's. Find the sum of the digits of the number 2003 * a. Answered by Penny Nom. 





The sum of the digits of a number 
20080623 

From Ben: Question: Using mathematical induction, prove that if the sum of the digits of a number is divisible by three, then the number itself is also divisible by 3. Answered by Penny Nom. 





30% profit 
20080619 

From Julie: how do i calculate the price per person that will return a 30% profit on the sales revenue generated? Answered by Penny Nom. 





Cows and chickens 
20080616 

From damebochie: I got this problem and want to write a system of equation for it:
Farmer Joe has cows and chickens on his farm. One day he count 76 legs and 24 heads. How many cows and how many chickens are on the farm? write a system of equations and solve.
I don't have any problem to solve it, but I just can;t see how I am going to write this system of equation.
Thank you so much for helping? Answered by Harley Weston. 





The rate of change in the depth of the water 
20080612 

From Liz: A rectangular pool 50ft long and 30ft. wide has a depth of 8 ft. for the first 20 ft. for its length and a depth of 3 ft. on the last 20ft. of its length and tapers linearly for the 10 ft in the middle of its length. the pool is being filled with water at the rate of 3ftcubed/ min
at what rate is the depth of the water in the pool increasing after 15 hours? Answered by Harley Weston. 





Guy wires for a tower 
20080519 

From larissa: a radio tower 500 feet high is located on the side of a hill ( the hill has an inclination to the horizontal of 5 degrees.) How long should two guy wires be if they are connected to the top of the tower and are secured at two points 100 feet directly above ( up the hill ) and directly below the base of the tower? Answered by Penny Nom. 





Selling price 
20080510 

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. 





How many presses should be used? 
20080504 

From Sarah: Hi! I am in Calculus and this problem is on my study guide and i just cant figure it out!?
A printing company had eight presses, each of which can print 300 copies per hour. It costs $5.00 to set up each press for a run and 12.5+6n dollars to run n presses for an hour. How many presses should be used to print 6000 copies most profitably? Let h equal the number of hours used to print the 6000 copies. Answered by Harley Weston. 





A bowl is the shape of a hemisphere 
20080428 

From josh: a bowl is the shape of a hemisphere with diameter 30 cm and water is poured into the bowl to a height h cm. how do i find the volume of the water in the bowl Answered by Harley Weston. 





A volume of revolution 
20080424 

From Sabahat: Hi, i have a region enclosed by both axes, the line x=2 and the curve y=1/8 x2 + 2 is rotated about the yaxis to form a solid . How can i find the volume of this solid?. (Please note that y equation is read as y =1 over 8 times x square plus 2.) I will be really grateful if you answer this question. :) Answered by Harley Weston. 





Why does 2^2 = 4 when 2 * 2 = 4? 
20080422 

From blaine: Why does 2^2 = 4 when 2 * 2 = 4? Answered by Penny Nom. 





The three sides of a triangle 
20080416 

From Bridgett: The sum of the lengths of any 2 sides of a triangle must be greater than the third side. If the triangle has one side that is 11 CM, and the second side of the triangle is 4 cm less than twice the third side, what lengths do the 2nd and 3rd side have to be?
between 00000000 and 99999999 Answered by Stephen La Rocque. 





How many bags of mulch? 
20080407 

From MJ: I have an area that is 35' X 50' and I want to cover it with 2" of mulch.
Do I take length X Width X depth? Bags of mulch are sold in 2 or 3 cubic feet per bag.....I just want to know how
to do the math. can you please send me the equation? Answered by Penny Nom. 





A volume of revolution 
20080404 

From ted: Consider the region bounded by y=x^2 + 1, y=53x and y=5. Sketch and
shade the given region; then set up but dont evaluate teh integrals to find
the following:
a) The volume of the solid generated by rotating the region about the line
y=5
b) the volume of the solid generated by rotating the region about the yaxis Answered by Penny Nom. 





How many bags of cement do I need 
20080330 

From Joe: How many bags of cement do I need if I want to extend my carport 6 inches all around?
The carport is 15ft. x 15ft. and the existing slab is 4 inches thick. Answered by Harley Weston. 





The average rate of change 
20080329 

From Tom: For the function x/3x1 find the average rate of change between the interval x=1 and x=5? Answered by Harley Weston. 





A car tire full of concrete 
20080327 

From robert: I want to build a volleyball net support. I am using a car tire 24"odx16"id filled with concrete. how much will this weigh? thanks Answered by Penny Nom. 





The product of the roots 
20080319 

From Rebecca: Determine the product of the roots of the equation
(x1)(x2) + (x2)(x5)=0 Answered by Penny Nom. 





The sum and product of the roots of a quadratic 
20080316 

From Katelyn: Write the quadratic equation....
Sum of the roots = 16
Product of the roots = 80 Answered by Penny Nom. 





A roll of paper 
20080305 

From Sheik: How I Convert My Roll Weight Into Meters?
Roll Width : 241mm
Thickness : 56gsm
Weight :81 Kg Answered by Harley Weston. 





The profit was what percent of the cost? 
20080229 

From sierra: The profit was what percent of the cost?
Here is some more of that whole problem.
Selling Price$26.60
Discount$6.65
Sale Price after the Discount$19.95
The Profit$5.95 Answered by Penny Nom. 





A proof in geometry 
20080227 

From Kimberly: I'm trying to write a proof for the following: If all altitudes are equal in an equilateral triangle then all sides are equal. Answered by Stephen La Rocque and Penny Nom. 





What number has exactly 51 divisors? 
20080226 

From Lisa: What number has a Tau which equals 51? In other words, what number has exactly 51 divisors? It must be a square of some kind! Answered by Penny Nom, Victoria West and Harley Weston. 





10  3 + 2 
20080221 

From Amrit: what 103+2
is it 5 or 9 Answered by Penny Nom. 





The slope intercept form of a line 
20080217 

From chris: find the slope and y intercept of the line (2x+4)3y=11(x1)
is this equation in slope point form. Answered by Penny Nom. 





The length of the third side of a triangle 
20080216 

From mary: I have an angle of 72 degrees and each of the sides are 5' long. What is the distance from each of the ends of the 5 feet to form a triangle. Answered by Stephen La Rocque. 





5x^2  45 
20080211 

From Tiana: factor:
5x^2  45 Answered by Stephen La Rocque. 





What percent profit is this? 
20080207 

From Vanessa: Mrs Henderson buys a chair for $215.00 and later sell the chair for $336.00 what percent
profit is this? Answered by Penny Nom. 





Total profit 
20080203 

From Rhonda: I help to manage a concession stand. We sell a variety of items. Some have a profit of 60%, some 80%, etc. We have done nothing scientific to choose our prices. We just try to stay in the ballpark of schools around us. Our administrator wants to pay those that run the concession stand a percent of what is in the cash box after startup money is taken out. We have some gathered some data (not much) on how many of each item we sell and can certainly calculate percent profit. Is the profit for the entire concession stand a weighed average? I'm thinking (% profit on candy)(number candy sold) + (percent profit nachos)(number nachos sold) + (percent profit pop)(number pop sold), etc. Will this work? Does the AMOUNT of profit for these different items need to be figuredin? Hmmm. . . Answered by Victoria West and Harley Weston. 





Sum and difference of cubes 
20080130 

From Amanda: It has been a really long time since I was in Algebra and I can't remember how to factor cubes such as x^3 +81 or subtracting/adding fractions with variables such as [1/(x+h)+2][1/x+2]. Please help!!! Answered by Penny Nom. 





The volume of a tank 
20080127 

From Fred: A cubic tank holds 1,000 kilograms of water what are the dimensions of the tank in meters? Answered by Harley Weston. 





Find the slope of the line with equation 73y=2x 
20080123 

From nell: Find the slope of the line with equation 73y=2x Answered by Stephen La Rocque. 





Out of school applications of Pythagoras Theorem 
20080123 

From Laura: Hi,
I am currently working on a math summative in which I have to choose a real life subject and relate it back to the material in my grade 12 math class. I find the history and discovery behind the Pythagorean Theorem and Identity very interesting, but I have yet to find a reallife application of the equations. Yes, I know they are used for finding distances, heights etc., but realistically, how many people actually use it in those situations? Very few. I was hoping for a new application. Is the pythagorean theorem (sin^2x + cos^2x = 1) even applicable? Thank you,
Laura Answered by Harley Weston. 





A parallelogram and a rhombus 
20080122 

From miguel: i have a problem proving a parallelogram a rhombus.. if a diagonal of a parallelogram bisects an angle
of the parallelogram , then its a rhombus
prove Answered by Stephen La Rocque and Walter Whiteley. 





1/2, 1/2, 3/8, 1/4, 5/32, 3/32, 7/128 
20080122 

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. 





The equation of a line 
20080120 

From Sara: The question is:
Write the equation of a line that is parallel to y=3x2 through the point (5,9).
I think the correct equation for this is y=3x+24.
But I have to write it in standard form, and I can't seem to figure out how to do that. Please answer soon! Thanks! Answered by Stephen La Rocque and Penny Nom. 





The line through (22 ;1) and (23, 2) 
20080120 

From Zachery: i have a slope that equals 1/1 and my coordinates are (22;1) and (23;2) and i am trying to change it into the equation y=mx+b and the farthest that i've gotten is y=1x_ (i can not find out how to find b.) So i was wondering if you could help me find out what b is because i have got no clue!!!!! Answered by Penny Nom. 





The game of 24 
20080117 

From Raina: I have four numbers 3 3 9 5 that need to equal 24 using addition subtraction multipliction and division and I'm so stuck. Answered by Chris Langdon, Stephen La Rocque and Claude Tardif. 





The angles of a triangle given the three sides 
20080117 

From Lucy: Is there a way to find the angles of a triangle just by knowing the lengths of it's sides?
It seems like the would be a relationship between the two, but I'm not sure. Answered by Stephen La Rocque and Harley Weston. 





Explaining the factoring for the difference of cubes 
20080116 

From Bill: A student asked me where did the "difference of cubes" and "sum of cubes" come from. I did not have an answer for her. She is very bright and understands how they work but wanted to know where they derived from. Any help you can offer would be great. Thanks Answered by Stephen La Rocque. 





Two solutions using the law of sines 
20080114 

From Kate: I am working on the Law of Sines and I have a problem that says: Find a value for b so that the triangle has 2 solutions.
I am given that A = 36 degrees and a = 5. Now, I learned that for a triangle to have 2 solutions, h < a < b.
BUT...my answer key says the answer is: 5 < b < 5/sin 36. I can't figure out how to make this fit with h < a < b. Answered by Harley Weston. 





How far is the jet from the lighthouse? 
20080107 

From Natalie: Question: A ship spots a lighthouse that is 53m high, at an angle of elevation of 7 degrees that is directly north of the ship. The same ship spots a jet travelling N62E at an altitude of 1500m with an angle of elevation of 15 degrees. How far is the jet from the lighthouse?
Natalie Answered by Harley Weston. 





The standard normal distribution 
20071229 

From GEORGE: Statistics texts state that in a normal distribution, 1 standard deviation covers 68%, 2SD 95% 3SD 99.7%. However, on looking at the tables for normal curve areas, the percentage for a z value of 1 is 84.13. 68 % of values are covered at a z value of 0.47. The discrepancies exist even for other values but are smaller. So why is the rule of thumb so different from the Table for Normal Curve areas? Answered by Harley Weston. 





Profit percentage (markup and margin) 
20071218 

From Laura: If my husband says he sold $11,000 worth of tools and made $1400 on the deal, what is the percent of profit? Answered by Stephen La Rocque. 





How many houses must they paint? 
20071212 

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. 





System of equations 
20071206 

From Jenn: change the equation,xy=4 to form y=mx+b
the solution to the system of equations y=2x and y=x+3 is Answered by Stephen La Rocque. 





Chicken and goat feet 
20071205 

From Kim: Old McDonald raises goats and chickens. The animals have a total of
100 heads adn 360 feet. How many goats and how many chickens does Mr.
McDonald have? Answered by Stephen La Rocque and Penny Nom. 





(322 x 5) divided by 2 + 8 
20071128 

From Kim: Solve
(322 x 5) divided by 2 + 8 Answered by Leeanne Boehm. 





A curve sketch 
20071122 

From Ahson: Find critical points, determine the monotonicity and concavity and sketch
a graph of f(x) with any local maximum, local minimum and inflection
points labeled:
1. f(x) = x^4  x^3  3x^2 + 1 Answered by Harley Weston. 





Bundles of wood 
20071119 

From Darcy: When you purchase a "bundle" of wood at the store, it is marked .75 cubic feet. What is the formula for figuring out that measurement for cubic feet and what fraction of a true cord of wood (128 cubic feet) is it. I would appreciate the formula so I can build a spreadsheet to help my secretaries and myself be in compliance to the law when selling firewood. Thanks. Answered by Harley Weston. 





Confidence level 
20071119 

From Fara: It is common for public opinion polls to have a " confidence level" of 95%, meaning
that there is a 0.95 probability that the poll results are accurate within the claimed margins of error.
If six different organizations conduct independent polls, what is the probability that all
six of them are accurate within the claimed margins of error? Does the results suggest that
with a confidence level of 95%, we can expect that almost all polls will be within the claimed
margin of error? Answered by Harley Weston. 





Find the radius of a circle given the center and a point on the circle 
20071118 

From Raymund: Find the radius if the center is at (0, 5) and one point on the circle is (2,3) Answered by Stephen La Rocque. 





Expand (a^4  b^4) 
20071117 

From Saif: how would you expand (a^4  b^4) ??? Answered by Stephen La Rocque and Victoria West. 





A geometric proof 
20071116 

From Julie: Prove that tangents to a circle at the endpoints of a diameter are parallel. State what is given, what is to be proved, and your plan of proof. Then write a twocolumn proof. Answered by Walter Whiteley. 





Why do they use the letter b in y=mx+b? 
20071115 

From virginia: why do they use the letter b in y=mx+b?
im asking this because my math teacher said he will give extra points to anyone who finds this out first
and i was hoping you guys would be the ones who could help. Answered by Penny Nom. 





Maximize his profit 
20071112 

From apoorva: During the summer months Terry makes and sells necklaces on the beach. Last summer he sold the necklaces for $10 each and his sales averaged 20 per day. When he increased the price by $1, he found that he lost two sales per day.
a. Find the demand function, assuming it is linear.
b. If the material for each necklace costs Terry $6, what should the selling price be to maximize his profit? Answered by Penny Nom. 





6 consecutive multiples of 6 
20071111 

From jeff: find 6 consecutive multiples of 6 whose sum is the least common multiple of 13 and 18 Answered by Penny Nom. 





Questions of the Month 
20071101 

From Judith: Where would I find comprehensive questions, that cover the majority of skills in a unit such as number sense, to use as "Questions of the Month"? Answered by Victoria West. 





The rate of change of the concentration of a solution 
20071030 

From Nicholas: A barrel initially has two kg of salt dissolved in twenty liters of water. If water flows in the rate of 0.4 liters per minute and the wellmixed salt water solution flow out at the same rate, how much salt is present after 8 minutes?
I tried working backwards given the answer but I can't seen to get their answer of ~1.7kg. Any help would be great! Thanks Answered by Harley Weston. 





Two mirrors 
20071024 

From Peter: The reflecting surfaces of two intersecting flat mirrors are at an angle θ (0° < θ < 90°). For a light ray that strikes the horizontal mirror, show that the emerging ray will intersect the incident ray at an angle β = 180° – 2θ. Answered by Stephen La Rocque. 





Turn 81 into the power of three 
20071022 

From Victoria: I do not understand how to turn 81 into the power of three. Answered by Penny Nom. 





Maximize profit 
20071022 

From Dina: A meat market purchases steak from a local meat packinghouse. The meat is purchased on Monday at a price of $2 per pound, and the meat market sells the steak for $3 per pound. Any steak left over at the end of the week is sold to a local Zoo for $0.50 per pound. The demand for steak and the probabilities of occurrence are as follows:
Demand Probability
20 10%
21 10%
22 15%
23 20%
24 20%
25 15%
26 10%
Determine the amount of stock to maximize the profit. Draw the graph and explain. Answered by Penny Nom. 





The rate of change of the area of a triangle 
20071022 

From Ahlee: So my question is:
The included angle of the two sides of a constant equal length s of an isosceles triangle is ϑ.
(a) Show that the area of the triangle is given by A=1/2s^2 sinϑ
(b) If ϑ is increasing at the rate of 1/2 radian per minute, find the rate of change of the area when ϑ=pi/6 and ϑ=pi/3.
(c) Explain why the rate of change of the area of a triangle is not constant even though dϑ/dt is constant Answered by Penny Nom. 





Order of operations 
20071017 

From Devon: What function precedes the other? ie; 18  4 x2 = Answered by Penny Nom. 





Four triangles in a square 
20071015 

From Kristina: A square with side lengths of 6 cm is divided into 3 right triangles and a larger isosceles triangle. If the three right triangles have equal area, find the exact area of the isosceles triangle. Answered by Stephen La Rocque. 





15 divided by 5a 
20071012 

From Susan: Is "5a" considered an expression to be solved first, or do you simply go in PEMDAS order with the 15 divided by 5 in the following problem: Evaluate when a = 2 15 divided by 5a Answered by Penny Nom. 





How much water is in a hose? 
20071012 

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. 





The average rate of change of a function 
20071011 

From vern: Find the average rate of change of the function over the given interval. Compare this average rate of change with the instantaneous rates of change at the endpoints of the interval. f(X)=sinX for the inverval [0,pi/6]? Answered by Harley Weston. 





Substitution method 
20071011 

From Kevin: 3xx+2y=36y=11 Answered by Stephen La Rocque. 





Area of a quadrilateral 
20071010 

From Courtney: how would i find the area of a quadrilateral..
the sides are a (/) is 6cm, b (—) is 9 cm, and c (\) is 7 cm..
the angle between a and b is 140 degrees and b and c is 115 degrees.. Answered by Stephen La Rocque. 





Simplifying algebraic expressions 
20071009 

From Sakeena: (2^2*3)^x+1/2^2x*3x Answered by Stephen La Rocque. 





Solving four simultaneous equations (system of four linear equations) 
20071007 

From Johan: I need some help in solving this question
x + 2y  3z + 4w = 12
2x + 2y  2z + 3w = 10
0 + y + z + 0 = 1
x  y + z  2w = 4 Answered by Stephen La Rocque. 





Solving arithmetic problems in the right order (BEDMAS) 
20071005 

From Kim: 3+4x2(10 divided by 5)= what? Answered by Penny Nom. 





Maximizing profits II 
20071005 

From a student: Suppose there are three firms with the same demand function. The function is Q=100040P. Each firm also a a cost function.
Firm 1: 4000+5Q,
Firm 2: 3000+5Q,
Firm 3: 3000+7Q.
What price should each firm charge if it wants to maximize profits. Answered by Harley Weston. 





Maximizing profit 
20071005 

From a student: Use the following equation to demonstrate how a firm that produces at MR=MC can also maximize its total profit. The equations to use are
P=1705Q
TC=40+50Q+5Q^2 Answered by Harley Weston. 





y squared over 3 times 8 over y 
20070930 

From John: y squared over 3 times 8 over y Answered by Stephen La Rocque. 





The area of a roof 
20070927 

From RANDY: I have an area of roof. It's in a sort of triangle.
it's 25' across the top
30' at each edge
86' across the bottom Answered by Stephen La Rocque. 





The game of 24 
20070927 

From Amanda: I'm really stumped on a 24 math game question from math class. The numbers are 7,11,17,and 20. Help?? Answered by Claude Tardif. 





Cubic meters, square feet and office space 
20070925 

From Kathryn: Can someone please help and let me know how do you convert 11 cubic meters into square footage? Answered by Steve La Rocque and Harley Weston. 





Prove that any two consecutive integers are relativley prime. 
20070918 

From Michael: Im not very good at proofs and I was wandering if you would be able to help me with the following question:
Prove that any two consecutive integers is relativley prime.
Thanks a million. Answered by Penny Nom. 





A 5 by 5 checkerboard 
20070917 

From Darren: Hi, I'm Darren and i have some questions to ask you about this problem:
In a 5 by 5 checkerboard : how many 2 by 2 squares are there,
what other sizes of squares do you need to count and how many of of each size of squares
can you find; how many squares did you find in all Answered by Victoria West. 





Two equations in two unknowns 
20070914 

From CAMEILA: NEED T0 SOLVE THIS EQUATION
Y = 2X + 6
Y + 6 = 2x Answered by Stephen La Rocque. 





The area of half a circle 
20070914 

From Heather: We need the formula for area of half circle please explain where each number comes from. Answered by Penny Nom. 





The slope of a line 
20070906 

From Danielle: Hello. I need some help with this: i am supposed to find the equation of a line with a point
(2/3,5) and (5/6,4) the answer in the book says y=6x+1. My question is how did they get
for the slope? Answered by Penny Nom. 





How many two digit numbers contain at least one 7? 
20070906 

From Janet: How many two digit numbers contain at least one number seven? Answered by Penny Nom. 





Fractions, ratios and percentages all mixed together 
20070829 

From Charon: Example: x : 1/4% :: 9 3/5 : 1/200 Answered by Stephen La Rocque. 





Twocolumn proof for a circle geometry problem 
20070824 

From Kendra: i have to prove that tangents to a circle at the endpoints of a diatmeter are parallel by stating whats given, whats to prove and a plane, then write a two column proof i dont understand this Answered by Stephen La Rocque. 





A geometry problem 
20070820 

From samhita: ABC is a triangle. Let D be a point on side BC produced beyond B such that BD=BA. Let M be the midpoint of AC. The bisector of angle ABC meets DM at P. Prove that angle BAP=angle ACB. Answered by Chris Fisher. 





The length of the third side of a triangle 
20070815 

From Brooklyn: What is the equation to find the length of the third side of a triangle if you have the length of A, B, and the angles(s)? Answered by Stephen La Rocque. 





Twenty dining tables 
20070813 

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. 





Induction  divisibility 
20070804 

From Jerry: How would you prove that for any positive integer n, the value of the expression 3^(2n+2)  8n 9 is divisible by 64. Answered by Chris Fisher and Penny Nom. 





What fraction of the letters of the alphabet is each word? 
20070802 

From Clayton: How do I figure this out, the math question has the answers but I have no idea how to get it.
my Mom can't figure it out either.
What fraction of the letters of the alphabet are each word
Man = 3/26
Glasses = 7/26
Integrity = 1/4
computer = 2/9 Answered by Paul Betts and Harley Weston. 





The height of a pole 
20070802 

From lalaine: Hi, this is my problem..
From a point 50.2 m to the pole, a student measured the angle of elevation to the top of the pole to be 32°. Find the height of the pole if the student's height from his feet to his eyes is about 4 ft. Answered by Penny Nom. 





Multiplcation of two negative numbers 
20070726 

From Brett: Someone asked a question about multiplication and division of two negative numbers yielding a positive result here:
http://mathcentral.uregina.ca/qq/database/QQ.09.99/butler1.html I was not fully happy with the explanation b/c I want to give me daughter a realworld example and I can't seem to find one.
The following illustrates why multiplying negative numbers has become difficult to explain:
2 X 2 = 4
(4)(2)024
In this example we start with 2 and then want 2 more of them.
When we move across the number line from 2 to our answer, which is four, we have moved only 2 units to the right.
2 X 2 = 4
(4)(2)024
In this example we start with 2 and then want 2 more of them.
When we move across the number line from 2 to our answer, which is four, we have moved 6 units to the right.
How can the phenomenon of multiplying two negative numbers being more powerful than multiplying two positive numbers be explained?
Brett Answered by Stephen La Rocque and Harley Weston. 





Simplifying an algebraic fraction expression 
20070725 

From Jessica: How do I simplify b/(b^{2}25) + 5/(b+5)  6/b? Answered by Stephen La Rocque. 





Angle of depression 
20070723 

From joyce: hello,
here is my problem......
As you stand on a bridge w/c is 100 ft. above the water
you are looking @ an approaching barge.
If the A of top of the front of the bridge is 29.04 degrees
and the angle of depression of the rear is 17.36 degrees .
Find the length of the barge? Answered by Harley Weston. 





What fraction of the company does Mary own? 
20070718 

From Bridget: Sam and Mary each owned onehalf stock in a printing company. Sam sold 2/3 of his stock to Mary. What fractional part of the printing business does Mary now own? Answered by Stephen La Rocque. 





Angle of depression (declination) between sailboat observations 
20070718 

From Joyce: From a cliff 150 ft above a lake, we see a boat sailing directly towards us.
The angle of depression of the boat is seen to be 5 degrees and 7 inches and
11 degrees and 18 inches. Find the distance sailed between observations. Answered by Stephen La Rocque. 





Angle of inclination from the horizontal 
20070718 

From Joyce: In flying upward for 1260 yards along a straight inclined path airplane rises
156 yards. Find the climbing angle
( the angle of inclination from the horizontal)
Thank you in advance Answered by Stephen La Rocque. 





Calculating the area (acreage) of a four sided lot 
20070718 

From A property owner: I have a real estate property and the lot size is something I need to find out. I know the lengths of the four sides, but it isn't a rectangle, it is an odd shape. How do I find the acreage? Answered by Stephen La Rocque. 





Height of a tower from two observations 
20070716 

From joyce: An observer wishes to determine the height of a tower. He takes sight @
the top of the tower from A & B w/c are 5oft. apart @
the elevation on a direct line w/ the tower.
The vertical angle @ point A is 30 degrees & the point B is 40 degrees.
What is the height of the tower?
Find the value of x in angle tangent 40 degrees and 30 degrees?
Show the solution of the value of x? Answered by Stephen La Rocque. 





Height of an antenna (angle of elevation) 
20070716 

From Fhay: An antenna stands on the edge of the top of a 52 story building from a point 320 ft. from the base of the building, the angle of elevation to the top of the antenna is 64 degrees in each story is 12 ft. high. Find the height of the antenna Answered by Stephen La Rocque. 





The two towers (angles of elevation trigonometry) 
20070714 

From joyce: The angle of elevation of tower B from the top of tower A is 28 degrees
and the angle of elevation of the top of tower A from the base is 46 degrees
Find the height of tower A if tower B is 120 m high? Answered by Stephen La Rocque. 





Proving a quadrilateral is a rectangle 
20070714 

From Sonja: I was having this discussion with another teacher and we need a third opinion. When you are trying to prove a quadrilateral is a rectangle which method should you use:
 Prove the shape is a parallelogram by doing slope 4 times by stating that parallel lines have equal slopes. Then proving a right angle by stating that perpendicular lines have negative reciprocal slopes.
 Doing the slope 4 times and stating that the shape is a rectangle because opposite sides are parallel because of equal slopes and it contains a right angle because of negative reciprocal slopes.
I guess the real question is do you have to first state that the shape is a parallelogram? Answered by Stephen La Rocque. 





Any regular polygon inscribed in a circle 
20070712 

From DJ: Circle with r=12" is inscribed in a regular octagon. What is the length of each octagon segment?
Note: Our answer works for any regular polygon inscribed in any circle. Answered by Stephen La Rocque. 





Grams of vodka 
20070710 

From Andrew: milliliters to grams..vodka 80 proof? Answered by Stephen La Rocque. 





Derivative of a Function 
20070709 

From Bob: What is the derivative of the function a sub n = [n/(n+1)]^n ? Answered by Stephen La Rocque. 





Proof that any side of a triangle is less than half the perimeter. 
20070707 

From Omkar: Any side of a triangle is smaller than half of its perimeter, prove this in short ? Answered by Stephen La Rocque. 





Splitting the profits unequally 
20070627 

From Maci: We recently hosted a fundraiser.
Not everyone will receive a whole share of the profits
because they did not participate the entire time.
Several will receive only 1/2 or 1/3 share.
How do I divide the profits? Answered by Stephen La Rocque. 





Selling price and revenue 
20070624 

From nick: hello, this is my first time asking for help from this website in which by the way, i think is great for everyone. My question is as follows... the relationship between the selling price of a sleeping bag, s dollars, and the revenue at that selling price, r(s) dollars is represented by the function: r(s)= 10s^2+1500s
evaluate, interpret, and compare: a) r(29.95) Answered by Stephen La Rocque and Penny Nom. 





Simplifying complex denominators 
20070621 

From Krys: How do I simplify completely?
((4+i ) / (3+i ))  ((2i ) / (5i )) Answered by Stephen La Rocque. 





Simplifying a quartic rational expression using long division 
20070614 

From Megan: x+2/12x^4+17x^3+0x^2+8x40= Answered by Stephen La Rocque and Penny Nom. 





Angles of depression 
20070613 

From Phonda: The pilot of a small private plane can look forward and see the control tower for a small airstrip. Beyond that is a large factory that is 3 milies from the airstrip. The angles of depression are 12.5 degrees and 4.8 degrees respectively.
Find the airplane's altitude, to the nearest ten feet. Answered by Stephen La Rocque. 





The area of a quadrilateral 
20070610 

From Lucy: Calculate the area of the quadrilateral ABCD.
AB= 4.1cm, BC = 7.6cm, AD= 5.4 cm, CD= ?
Angle ABC = 117, Angle ADC = 62.
Give your answer correct to 3 significant figures. Answered by Stephen La Rocque and Penny Nom. 





The law of sines 
20070609 

From Felicia: A parallelogram has one side that is 12.0 cm and one angle that is 65°. The shorter diagonal is 25.0 cm. To the nearest tenth of a centimetre, how long is the other side of the parallelogram? Use the sine law. Answered by Penny Nom. 





Rate of change of distance between the clock hands 
20070605 

From Jonathan: A certain Clock has a minute hand with a length of 4 inches long and an hour hand with a length of 3 inches long. How fast is the distance between tips of these hands changing at 9:00? Answered by Stephen La Rocque. 





What happens when you have zero's on both sides? 
20070605 

From Lily: On the substitution method what happens when you have zero's on both
sides of the equation? Is that considered no solution or infinitely many? Answered by Stephen La Rocque and Penny Nom. 





Area of an isosceles triangle 
20070601 

From Josh: In a previous question answered by Sue regarding the area of a regular polygon you gave a formula for the area of an isosceles. My question is how did you get this formula? Can you please explain to mean the process that you used to get that formula?
Thanks Answered by Stephen La Rocque. 





The intersection of two planes 
20070531 

From Sarim: How to find a intersection of two planes? Answered by Penny Nom. 





Fractions, decimals and profit 
20070529 

From fatima: how can i change a fraction into a decimal and how do i change a
decimal into a fraction................
anther question please what does making a profit have
to do with percentage change!!!!!! Answered by Penny Nom. 





System of equations 
20070524 

From Chris: Find all real solutions (x,y,z,w) of the system of equations:
2y= x + x/17, 2z= y + y/17, 2w = z + z/17, 2x= w + w/17 Answered by Penny Nom. 





Find the sample size needed 
20070513 

From Mini: Find the sample size needed to be 98% confident thata marketing survey on the proportion of shoppers who use the internet for holiday shopping is accurate within a margin of error of 0.02. Assume that the conditions for a binomial distribution are met, and that a current estimate for a sample proportion does not exist. Answered by Penny Nom. 





Find the equation of a line passing through two given points 
20070512 

From Kenzie: I am having problems solving an equation of the line passing through (2,4) and (6,0) Answered by Penny Nom and Stephen La Rocque. 





Angle of Elevation 
20070510 

From Micky: Two Buildings are on opposite sides of a street 40 feet wide.
The taller of the two buildings is 580 feet tall. The angle of depression
from the top of the tallest building to the shorter building across the
street is 57 degrees. Find the height of the shorter building. Answered by Stephen La Rocque. 





Are proofs important in geometry? 
20070507 

From BJ: Are proofs very important to know how to do?
My daughter has been in Geometry & the teacher skipped proofs. Answered by Penny Nom. 





What is the square root of 729 to the third power? 
20070425 

From Tori: What is the square root of 729 to the third power? Answered by Penny Nom. 





The size of a freezer 
20070423 

From Jacqui: How many can packages can fit? I have a freezer that is 7cf. But
it contains a little tray component. The freezer measurements without the
tray is(bear with me, I'm not good with LxWxD) 23 across x 16 W x 25
deep (I'm assuming depth) and the tray is 8 across x 16 w x 15 D. We are
trying to see how many 9 L x 6 W x 3.5 D packages can fit in the freezer.
Please help me. I'm getting app. 60. I need 84 to be able to fit. Answered by Penny Nom. 





Ax + By = C 
20070418 

From Diana: find an equation in general form Ax + By = C with the following properties passing through points (a,b) and (2a, 2b) Answered by Penny Nom. 





The area of a heptagon 
20070414 

From Chantel: Would you be able to tell me the formula to work out the area of a
heptagon? thank you. Answered by Stephen La Rocque. 





The angle of depression 
20070414 

From MaryBeth: Two towers are 30 m apart. From the 15th floor, 40 m up, find the angle of depression to the base of the taller tower? I think the answer is 53, but the answer book says 37. Answered by Penny Nom. 





Intersection of a line and a circle 
20070412 

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. 





A volume of revolution 
20070408 

From christina: find the volume of the solid formed when region bounded by y=x/3, y=2
and the yaxis. it is revolved about the xaxis.
the assignment was to use both the washer method and the shell method
but when i solved for the volume, i got different answers.
i think my shell method is wrong because i know i'm having difficulties
with using "dy" instead of "dx"
here's my work so far: Answered by Penny Nom. 





3 divided by 3 to it's fifth root 
20070406 

From Annie: How do I transform the equation 3 divided by 3 to it's fifth root to simple radical form
(getting the radical out of the denominator)? Answered by Penny Nom. 





How much did it originally cost? 
20070404 

From Megan: My question is simple:
"Jim is able to sell a handcarved statue for $650 which was a 35% profit over his cost. How much did ie originally cost?"
I don't even know where to start could you help? Answered by Penny Nom. 





Game of 24 
20070404 

From teri: How do you find the answer of 24 by using 12,24,7 and 2 only once. Answered by Stephen La Rocque. 





Using the "difference of squares" formula how do I compute 27 * 33? 
20070402 

From Sarah: Using the "difference of squares" formula how do I compute 27 * 33? Answered by Penny Nom. 





Is the inverse of a function always a function? 
20070329 

From San: Is the inverse of a function always a function? Please justify. Thank You! Answered by Penny Nom. 





Factoring a trinomial 
20070327 

From Kim: Hi, could you please help me solve this.
3x(squared) +20x  7 Answered by Leeanne Boehm. 





The distance between two fire towers 
20070323 

From tony: Two fire towers are 30km apart, tower A is due west of tower B. A fire is spotted from the towers, and the bearing from A and B are N76degreesE and N56degreesW, respectively. Find the distance from the fire to the straight line connecting tower A to tower B. Answered by Stephen La Rocque. 





Graphing a line 
20070323 

From mitchell: Graph each equation.
y = 2x + 4 Answered by Jaymi Peterson and Haley Ess. 





The law of cosines 
20070323 

From chetna: Q 1) In triangle LMN, l=7, m=5 , n=4. find ANGLE N.
After applying the rule and substituting values i'm getting
Cos n= 58/40. Is there something wrong. The answer at the back of the book is 34 degrees. Answered by Penny Nom. 





Angles of depression 
20070321 

From romaine: a woman of height 1.4m standing on top of a building of height 34.6m veiws a tree some distance away.
she observes that the angle of depression of the bottom of the tree is 35 degrees, and the angle of depression of the top
of the tree is 29 degrees. assume that the building and the tree is on level ground.
(a) calculate the distance of the woman from the top of the tree measured along her line of sight.
(b) determine the height of the tree. Answered by Stephen La Rocque. 





Angle of elevation 
20070313 

From Joslyn: A ship at sea sights a 12m high lighthouse on a cliff which is 80m above sea level.
If the angle of elevation to the top of the lighthouse is 27 degrees, calculate the distance from the ship to the shore. Answered by Haley Ess. 





What is pi? 
20070309 

From Billy: What is pi? Answered by Jaymi Peterson and Sara Ulmer. 





At what rate is the area of the triangle changing? 
20070224 

From mac: two sticks 3.5 feet long are hinged together and are stood up to form an isosceles triangle with the floor. The sticks slide apart, and at the moment when the triangle is equilateral, the angle is increasing at the rate of 1/3 radian/sec. At what rate is the area of the triangle increasing or decreasing at that moment? Mac Answered by Penny Nom. 





Find the area of the triangle 
20070220 

From Christina: Graph the function f(X)= x+1/x1 and graph the tangent line to the function at the points A:(2,3) and B:(1,0). The point of intersection of the two tangent lines is C. Find the area of the triangle ABC. Answered by Stephen La Rocque. 





Surface Area of a cone 
20070219 

From Cari: I am doing a math project. I am very confused on how to find the surface area of a cone. I have looked at other equtions but i still don't understand. How do you find the surface area of a cone that has a 15cm length and a 3.5cm radius? Answered by Penny Nom. 





Factoring polynomials 
20070214 

From Joe: I am in the eighth grade, and we are learning the equivalent of Algebra 2. I have no ides how to factor (x2)(x^21)6x6 You help is most aprreciated. Thank you! Joe Answered by Stephen La Rocque. 





The surface area of a dome 
20070211 

From chris: I need to figure the surface area of a dome which is 96" across and 48" tall. Could you help please? Thanks! Answered by Penny Nom and Melanie Tyrer. 





Large exponents 
20070209 

From Nick: I am trying to figure out an extremely large number. It relates to the estimated number of bacterial divisions in 12775 generations of bacteria. The problem I need to solve is: 2^12775 or 2 to the power of 12,775. Answered by Stephen La Rocque and Penny Nom. 





The area for a pentagon 
20070209 

From nicole: how do you find the area for a pentagon Answered by Stephen La Rocque. 





The capacity of a tank 
20070208 

From lorn: what is the capacity of a tank height is 110 feet diameter is 24 feet Answered by Brennan Yaremko. 





An even positive integer cubed minus four times the number 
20070207 

From Rachael: I can't figure out the proof or the method to get the proof for this question: any even positive integer cubed minus four times the number is divisible by 48 Answered by Haley Ess and Penny Nom. 





How to calculate margin of profit???? 
20070203 

From A student: If cost price is Rs. 100/ and our selling price is 139/. I want to know the gross profit & how much margin in this???? Answered by Penny Nom. 





The volume of a cone 
20070131 

From ajay: WHY VOLUME OF CONE IS ONE THIRD OF THE VOLUME OF CYLINDER? Answered by Penny Nom. 





The height of an isosceles triangle 
20070127 

From Brendan: I need to find the height of an isosceles triangle whose angles are 52, 52 and 76 degrees. The base is 100, and the two equal sides are unknown. How would I go about this? Answered by Stephen La Rocque. 





The area of a ellipse 
20070125 

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. 





An algebra exercise 
20070124 

From Clara: Given x + 2y = 2 and x  2y = 18, find: a) x^2  4y^2 b) x^2 + 4y^2 Answered by Stephen La Rocque and Penny Nom. 





What is the point of intersection of two sides of a polygon? 
20070123 

From Tyler: What is the point of intersection of two sides of a polygon? Answered by Stephen La Rocque. 





Is 2^2 = 4 or 4? 
20070123 

From Joan: Is 2 squared, when written without parentheses around the 2, 4 or could this correctly be solved by squaring 2 (2 x 2) for an answer of 4? Or, to correctly get an answer of 4, would the problem have to read (2) squared? Answered by Stephen La Rocque. 





Maximizing profit 
20070123 

From Denise: Total Profit= Total RevenueTotal Cost P(x)=R(x)C(x) Where x is the number of units sold. Find the maximum profit and the number of units that must be sold in order to get that profit. R(x)=5x C(x)=.001x^2+1.2x+60 Answered by Stephen La Rocque. 





Calculating a person's volume 
20070120 

From James: Hi i am currently trying to calculate my volume. I have tried to do this using a tank of water and measuring the difference. i worked out that my volume is 112 litres. my question is that i want to make a box that would hold my volume and so i need to convert it into centimeters. i know that there are 100 cm^2 in a litre. if i divide this by 4 i would be 91x91x91ft. is this simply to do with density. if so how could i make this more realistic? Answered by Stephen La Rocque. 





A formula for figuring a tanks volume at various levels 
20070120 

From Dave: I know there has to be a general formula to figure out a tanks volume where as you know the total volume but you need to know what it will hold at various levels measured in 1/8th inches in depth and that you may be able to plug this formula into a program like say excel and thus create a chart unique to that tank. But for the lack of me I can not figure it out. Answered by Stephen La Rocque. 





Irregular multi sided polygon 
20070120 

From Graham: I have an irregular polygon. I know the length of all the sides and know approximately all the internal angles. Is there a formula or table that can calculate the area for me? Answered by Steve La Rocque, Chris Fisher and Penny Nom. 





The area of an irregular pentagon 
20070118 

From Ranjit: I would like to find the area of an irregular pentagon where the total perimeter is 1000m. Is there a Heron's formula for this? Answered by Stephen La Rocque. 





Answer to skill testing question 
20070118 

From Mike: This question was on a ballot. Is the right answer 36 or 1? 5+21X6= Answered by Stephen La Rocque. 





Points of intersection 
20070118 

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. 





The height of a triangle 
20070117 

From Sharon: I am needing to determine the height of a triangle with a 50 ft base and one side is 40 ft the other side being 30 ft. Answered by Penny Nom. 





The volume of a frustum of a pyramid 
20070117 

From Sam: Find the volume of a frustum of a pyramid with square base of side b, square top of side a, and height h. Answered by Penny Nom. 





The volume of a sphere 
20070116 

From Anshul: How to prove or find the volume of sphere? Answered by Harley Weston. 





Where do the medians of a triangle meet? 
20070102 

From Brittany: Where do the medians of a triangle meet? 1. Inside the triangle v 2. On the traingle 3. Outside the traingle Answered by Stephen La Rocque. 





Prove that square root of 3 is irrational. 
20061221 

From Humera: Prove that square root of 3 is irrational. Answered by Stephen La Rocque. 





The product of of two rotations 
20061217 

From Katie: Is the product of of two rotations over a different center point always a translation? Answered by Walter Whiteley. 





cos(n)pi = (1)^n 
20061214 

From Idrees: How can I prove the following: cos(n)pi = (1)^n Answered by Steve La Rocque. 





The absolute value of imaginary and complex numbers 
20061211 

From Keith: i don't get how to find the absolute value of imaginary and complex numbers here is an examples from the text book the answers are given but they don't show the work so i can follow along just show me the work please and explain how it is done
problem 3+4i Answered by Stephen La Rocque and Penny Nom. 





Factoring m^49^n 
20061207 

From Josh: I can not figure out how to completely factor m^49^n. Answered by Penny Nom. 





The volume of an irregular tetrahedron 
20061206 

From Hai Van: Could you please show me the way to calculate the volume of an irregular tetrahedron Answered by Penny Nom. 





Star of Bethlehem 
20061205 

From Stephen: I need to construct a star for a Christmas play being done at our church. I want it to be a fourpointed star. The top and side points should be 12 inches long and the bottom point 24 inches. It will be flat on the back but raised on the front with lights inside for illumination. Each point will be made of two triangles with a ridge in the center. I would like the width of the rays at the center (widest point or center of star) to be about five inches and the center ridge at this same point to be raised about two inches from the flat back. I need to know the dimensions and angles of each of the 8 triangles that make up the star so that all of them meet properly at the center of the star so as to have the correct height from the flat back. Answered by Penny Nom. 





The height of a triangle 
20061201 

From Jeni: I need to know how to figure out the height of a triangle when all I know are the sides and base. The sides are 5 and the base is 8 What do I do? Answered by Penny Nom. 





The game of 24 
20061128 

From John: Math 24 with 9, 8, 4, 2? Answered by Stephen La Rocque and Penny Nom. 





What proportion of cups of coffee have at least one defect 
20061128 

From Ayman: coffee machine may be defective since it dispenses the wrong amount of coffee (C) & or the wrong amount of suger ( S ) the probability of these defects are P(C) = 0.05, P(S) = 0.04 & P( C&S ) = 0.01 find 1 what proportion of cups of coffee have at least one defect 2 what proportion of cups of coffee have no defect Answered by Penny Nom. 





Percentages 
20061123 

From Hyaqcinth: I just do not understand percentages...if the cost of a product is $1.20, how can I make a profit of 55% ? how do I calculate this problem? Answered by Stephen La Rocque. 





Profit margin 
20061122 

From Kris: I just started a new sales position and need to calculate profit margins based on my cost of a given product. For example I have a piece of equipment that costs me $102,077.73. I need to figure a profit margin of 18% from cost to arrive at my sale price. What is the best way to do this? Answered by Penny Nom. 





Factors 
20061122 

From Jacqueline: Why do the numbers 16,36,48,60,64,90 and 100 have an odd number of factors? Answered by Stephen La Rocque and Penny Nom. 





Composition of functions 
20061119 

From RJ: Let f0(x) = 2/2x and fn+1 = f0 o fn for n greater than or equal to 0. Find a formula for fn and prove it by mathematical induction. Recall that o represents function composition. i.e., (f o g)(x) = f(g(x)). Answered by Stephen La Rocque. 





A particle moving along a curve 
20061118 

From Rachel: a particle is moving along the curve whose equation is: (xy^3)/(1+y^2)=8/5 assume the xcoordinate is increasing at the rate of 6 units per second when the particle is at the point (1,2). a. at what rate is the ycoordinate of the point changing at that instant? b. is the particle rising or falling at that instant? Answered by Penny Nom. 





Composition of functions 
20061118 

From Oryan: Given f(x)=2x^3 and g(x)4x5, find g(f(1)) Answered by Stephen La Rocque. 





An aircraft and a missile 
20061118 

From Sarah: an aircraft is flying at a constant altitude with a constant speed of 600mph. an antiaircraft missile is fired on a straight line perpendicular to the flight path of the aircraft so that it will hit the aircraft at a point P. at that instant the aircraft is 2 miles from the impact point P the missile is 4 miles from P and flying at 1200 mph. at that instant, how rapidly is the distance between missile and aircraft decreasing? Answered by Stephen La Rocque. 





Wheat is poured on a conical pile 
20061117 

From Rachel: wheat is poured through a chute at the rate of 10 cubic feet per minute and falls in a conical pile whose bottom radius is always half the altitude. how fast will the circumference of the base be increasing when the pile is 8 feet high? Answered by Penny Nom. 





A system of equations 
20061113 

From Katrina: solve the system of equations using either the substitution or the elimination method. 2x3y= 12 and 4x+6y=15 Answered by Penny Nom. 





The rate of change of the perimeter of a square 
20061107 

From Karli: Find the rate of change of the perimeter of a square with respect to its area. Answered by Stephen La Rocque. 





A boat is being pulled towards a dock. 
20061106 

From Cassie: A boat is being pulled towards a dock. If the rope is being pulled in at 3 feet per second, how fast is the distance between the dock and the boat decreasing when it is 30 feet from the dock? Answered by Penny Nom. 





Profit margin 
20061104 

From Beverly: Our costs to make a product is $73.00. We want to sell this product and make a 30 percent profit margin. What is the selling price? What is the simple formula to follow? Is there a chart we can go to that shows us these percentage of profit breakdowns Answered by Penny Nom. 





Selling Price using Profit Margin 
20061029 

From Chris: What is the selling price of my inventory, find using the profit margin? Inventory A costs $2,300. The profit margin is 55% Inventory B cost is $4,500. The profit margin is 210%. Answered by Penny Nom. 





An odd number of factors 
20061028 

From Anthony: What is the common name used for numbers that have an odd number of factors? This answer should be a two word answer only. Answered by Stephen La Rocque. 





How much labor should the firm employ? 
20061028 

From Christy: A dressmaking firm has a production function of Q=LL(squared)/800. Q is the number of dresses per week and L is the number of labor hours per week. Additional cost of hiring an extra hour of labor is $20. The fixed selling price is P=$40. How much labor should the firm employ? What is the resulting output and profit? I am having a difficult time with this, HELP! Answered by Stephen La Rocque. 





(a^(1/3) – b^(1/3)) ( a^(2/3) + a^(1/3)b^(1/3) + b^(2/3)) 
20061024 

From Julie: (a^{1/3} – b^{1/3}) ( a^{2/3} + a^{1/3}b^{1/3} + b^{2/3}) Answered by Haley Ess. 





The area of a regular octagon 
20061022 

From Farhana: I have a regular octagon with sides of 0.8m and I need to find the area, Answered by Karen McIver and Penny Nom. 





The height of a triangle as a function 
20061019 

From Ryan: Let 2s denote the length of the side of an equilateral triangle. Express the height of the triangle as a function of s Answered by Penny Nom. 





How fast is the water level rising when the water is 1 meter deep? 
20061019 

From Don: The cross section of a 5meter trough is an isosceles trapezoid with a 2meter lower base, a 3meter upper base and an altitude of 2 meters. Water is running into the trough at a rate of 1 cubic meter per minute. How fast is the water level rising when the water is 1 meter deep? Answered by Stephen La Rocque. 





(2324/4)525+214 
20061015 

From Sherin: (2324/4)525+214 Answered by Penny Nom. 





A proof by induction 
20061002 

From Zamira: i'm studying induction but i don't get how to proof that 1+2+2^2+2^3+...+2^(n1) = (2^n)  1. Answered by Penny Nom. 





Prove that 2nCn is less than 4n, for all positive integers n? 
20061001 

From Anna: How can I prove that 2nCn is less than 4n, for all positive integers n? Answered by Penny Nom. 





Family of lines 
20060929 

From Sasha: could a "Family of Lines" have both parallel and intersecting equations that aren't related directly but otherwise related by each other to create a curve Answered by Chris Fisher. 





BEDMAS 
20060924 

From Partick: if you have a question like this (4)(4)+(4)+4 how do you solve it step by step Answered by Penny Nom. 





How many items must the company produce to begin to make a profit? 
20060924 

From Devon: The profit a manufacturing company makes can be found using the formula
P=120n  n^2  2200
How many items must the company produce to begin to make a profit? Answered by Stephen La Rocque. 





Parameters 
20060915 

From Chase: What is the meaning of the word "parameters" when used in reference to Algebra. Answered by Penny Nom. 





what is 8+(2)(5)/4(1)4(2+3) 
20060908 

From Jordan: what is 8+(2)(5)/4(1)4(2+3) Answered by Paul Betts. 





The velocity of a pendulum, part II 
20060907 

From Erin: We saw the question in your database about the velocity of a pendulum swinging.....It is the same exact question....but there is another question......it says....
"estimate the instantaneous rate of change of d with respect to t when t = 1.5. At this time, is the pendulum moving toward or away from the wall? Explain." Answered by Harley Weston. 





The lower half of a sphere 
20060830 

From Yvette: I am interested in finding out how to represent the lower half of a sphere in the form of z=f(x,y) with r=2 and a centre point (3,1). Answered by Stephen La Rocque and Penny Nom. 





16X27+32÷426 
20060820 

From Amanda: The question was 16X27+32÷426. Answered by Stephen La Rocque. 





Points of intersection 
20060820 

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 
20060818 

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. 





The development of trigonometry 
20060815 

From Eugene: Can you please give the exact time line of trigonometry. Answered by Penny Nom. 





1/x + 1/y 
20060811 

From Sonya: what is 1/x+1/y = ? is it equal to 1/x+y or what? Answered by Penny Nom. 





A problem with exponents 
20060809 

From A student: (8a to the negative 2 b cube c to the negative 4/4a squared b to the negative 3 c squared) to the negative 2 Answered by Stephen La Rocque. 





Order of operations 
20060629 

From Jaden:
(1) A triangle has vertices at (3,3) (7,3) and (2,5). What is the area of the triangle?
Is there a way of doing this so that you dont have to graph it? If the x axis is horizontal can i say it is the base and the yaxis is horizontal meaning the height. Would I be able to do this...3 to 7>9 spaces, 3 to 5>7 spaces9(7)63/2=31.5
(2) A cube has a surface area of 54 square centimeters. What is the volume of the cube in cubic centimeters?
Answered by Stephen La Rocque. 





Order of Operations 
20060629 

From Marcy: I have been having problems with this skill testing question. I know the rules of operation but I don't understand why they would put it in brackets. Can you help me. I have two answers but I would like to know which one is right. Im having a disagreement with a friend over this matter. Thank you so much
[ (20 + 82  6) ÷ 16 ] x 14 Answered by Steve La Rocque and Paul Betts. 





Marking out a circle 
20060628 

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. 





A trig problem 
20060624 

From Greg: A and B are two towers, B being 4 km due east of A. The true bearings of a flagpole, C, from A and B are α east of north and α west of north respectively. The true bearings of a second flagpole, D, from A and B are (α + β) east of north and (α  β) west of north respectively. Assuming A, B, C, and D are on level ground, and that α = 25, β = 10, find the distance between C and D. Answered by Penny Nom. 





The chord length of a polygon 
20060614 

From Krishna: I have to find out the chord length of a polygon  Tetradecagon ! The Radius of the Circle is 11.5 Cms. The Circle is intersepted by 14 arcs. Then how to find out the chord length? Answered by Stephen La Rocque. 





A volume of revolution 
20060607 

From Colleen: Find the exact volume in cubic units generated by rotating a region, R, around the
yaxis, given that R is the region bounded by the curve y = x^{3} and the lines x = 1 and
y = 8. Answered by Penny Nom. 





The coefficient of variation 
20060520 

From Glenn: What is the correct formula for coefficient of variation for a binomial distribution? Answered by Penny Nom. 





More on the game of 24 
20060505 

From Kathy's daughter: My daughter's 5th grade class plays the 24 math game. She came home
the other day with a real stumper! The numbers on the card are 5,5,2,and 6.
The rules say you must use every number,you may only use a number once,you
can only add, subtract, multiply and/or divide and the answer is 24. Can you
help!!!! No one where I work has been able to figure this one. Answered by Paul Betts and Penny Nom. 





Proof by induction 
20060424 

From Meshaal: Find an expression for:
13+5  7 + 9  11 + ... + (1)^(n1) * (2n1)
and prove that it is correct.
Answered by Stephen La Rocque. 





Geometry proof 
20060423 

From Jade: From a point P outside a circle with centre O, tangents are drawn to meet the circle at A and B.
a) Prove that PO is the right bisector of the chord AB.
b) Prove that Answered by Stephen La Rocque. 





What is the original cost? 
20060419 

From Charlie: Selling a piece of furniture for $670 and the profit is 35%. What is the original cost? Answered by Stephen La Rocque. 





Proving a summation formula by induction 
20060419 

From Sharon: Prove by induction that the sum of all values 2^i from i=1 to n equals 2^(n+1)  2 for n > 1. Answered by Stephen La Rocque. 





How do you round off 89,100? 
20060419 

From Jeannie: My home work says to round each number to the place of the underlined digit. It has 89,100. The underlined number is 9. What do I do? Answered by Stephen La Rocque. 





What is the cost price? 
20060414 

From Purushotham: If the selling price is 120 and the profit is 20%, what is the cost price? Answered by Stephen La Rocque. 





A proof by induction 
20060409 

From Sharon: prove by induction: For every n>1, show that
2 + 7 + 12 + ...+ (5n3) = n(5n1)/2 Answered by Penny Nom. 





Given three angles and a side 
20060409 

From Jon: How do you figure out the length of all sides of a scalene triangle if given the measure of all angles, and one side? Answered by Stephen La Rocque. 





An octagon shaped soffit 
20060408 

From Ken: I am trying to make an octagon shaped soffit in my ceiling and need help figuring how to divide the circle on the ceiling into an octagon
The circle is 7 foot in diameter. Answered by Penny Nom. 





The average of monthly averages 
20060406 

From Ray: I have the averages of some data in percentages. the data is rather large, how can i find the average of these averages without going back to the original data? Is there a Factor or Constant that i could multiply or devide or add and get the average of these averages without resorting to the raw data. Answered by Steve La Rocque and Harley Weston. 





A table of values 
20060328 

From Cindy: Create a table of values for each of the following functions: y=5x, y=52, and y=5x. I dont know to do this. Answered by Stephen La Rocque. 





given that p is a prime and pa^n, prove that p^na^n 
20060324 

From Janna: given that p is a prime and pa^{n}, prove that p^{n}a^{n} Answered by Stephen La Rocque. 





How far from Earth is Neptune? 
20060321 

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. 





BEDMAS 
20060321 

From Andie: It's been a long time since I've used bedmas. I'm still confused as to what the answer to this question would be.
30  (2 x 9) + (15/3)= Answered by Penny Nom. 





Three towns are located at the vertices of an equilateral triangle 
20060320 

From A student: three towns are located at the vertices of an equilateral triangle. The towns are 8, 5, and 3 miles, respectively, from a store. How far apart are the towns? Answered by Chris Fisher. 





The day of the week 
20060319 

From Neil:
A friend of mine has an excellent memory for dates and events that occurred on that date, but his party piece is the ability to tell you the day of the week that fell of any given date. This talent is all the more extraordinary because the answer comes back in less than 2 seconds (often under 1 second). By his own admission he is no mathematician.
Now his memory and knowledge are without question, but I challenged him that because of its diversity this party piece could not be based upon memory, but on mathematics. I believe that with the correct mathematical approach and the use of a common algorithm, anyone with a basic mathematical mind can do this in their head.
Answered by Chris Fisher. 





Gross profit as a percentage 
20060318 

From Mark: How do I calculate the gross profit by percentage on and a product I purchased for $23.80 marked up 45% sold for $34.51 = profit of $10.71 GP by percentage???????? Answered by Penny Nom. 





The square footage of an area in my backyard 
20060317 

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. 





9, 8, 7 and 2 in the game of 24 
20060317 

From Alana: I just began student teaching in a 5th grade math class and found that the students play 24 in class, a game that I used to play in elementary school. The students choose a card which shows 4 numbers and then have to use any combination of addition, subtraction, multiplication, and division to reach 24. There was one card that we found that seems to have all of us stumped. The four numbers are 9, 8, 7 and 2. Can you figure out how to make 24 with those? Thanks so much for your help! Answered by Claude Tardif. 





A proof by contraposition 
20060316 

From Eban:
1)by mathematical induction prove that 1^{2} + 3^{2 }+ 5^{2 }+ ...... + (2k1)^{2} = (1/3)k(2k1)(2k+1) for all positive integers k.
2)show that the contrapositive of the following statement is true. if 1 + M^{7} is even, then M is odd.
Answered by Stephen La Rocque. 





Profit 
20060311 

From Wendy: If I have a product I have bought for 33.58 and I mark it up by 30% sell at 43.65 how do I work out the gross profit. Answered by Penny Nom. 





Factor 
20060308 

From Brad: Factor:
x^{3} + 64m^{3} and 125p^{3}  q^{6} Answered by Penny Nom. 





The meaning of numbers 
20060303 

From John: I'm having a philosophical debate on the meaning of numbers, equations, or the world of math in general. Would it be possible if you could help me by giving me a resource that talks about it or if you have your own opinion I would be most grateful. Answered by Harley weston. 





Profit 
20060225 

From Vernessa: ABC company wants to sell enough products to earn a profit of $40,000, if unit sales are $10 and variable costs $8 , fixed cost $80,000 how many units must be sold to earn a profit of $40,000. Answered by Penny Nom. 





Victor's profit 
20060213 

From Millie: victor is trying to make money buying and selling cars. he saved up and buys a car for $2500 and then sells it for $4327.he then buys another car using 2/3 of his profit and sells it for twice what he paid for it. how much money did victor make during these transactions? Answered by Steve La Rocque. 





Proof by induction 
20060210 

From Victoria:
how do i prove by induction on n that
n
Σ 1/i(i+1) = n/(n+1)
i=1
for all positive integers n
Answered by Penny Nom. 





Prove that p^n >= (p!)/(pn)! 
20060202 

From Rhydian:
PROVE:
p^{n} >= (p!)/(pn)!
Answered by Penny Nom. 





More on the game of 24 
20060202 

From Cathy: 10,16,9,4 this numbers have to equal up to 24. we can't figure it out. Answered by Claude Tardif. 





BEDMAS 
20060131 

From Janielle: What Do All the Letters In BEDMAS Stand for? Answered by Penny. 





How do you find the angles in a triangle? 
20060127 

From Keith: How do you find the angles in a triangle if you know the lengths of the sides? Answered by Chris Fisher and Penny Nom. 





Our client wants to make 25% from their sale... 
20060124 

From Noelle: I need to figure out how to figure pricing for our clients. If our client wants to make 25% from their sale and they purchase it from me for $35.95, how do I figure what their cost is? Answered by Penny Nom. 





One boundary of a pond is parabolic in shape. 
20060120 

From Glenn: One boundary of a pond is parabolic in shape. The boundary passes through the points A(20,45), B(40,40) and E(30,35). The equation of the parabola is of the form y=ax2+bx+c. Find the equation of the parabola and the coordinates of the vertex of the parabola. Any assistance you could provide would be greatly appreciated. Answered by Penny Nom. 





3x^4  81 
20060102 

From Julio: How can I factor the following?:
3x^{4}  81 Answered by Penny Nom. 





Simultaneous Equations 
20051221 

From Matt: I have these two equations,
336 = 60a + 10b
and
432 = 84a + 6b
Am I right in saying both a and b are 4.8? Answered by Penny Nom. 





The game of 24 with 7, 5, 5 and 4 
20051218 

From Nicole: i was playing the 24 game the other day. you get 4 digits and you have to turn them into 24. You can use addition, subtraction, division, and multiplication. You have to use all the numbers but you can only use each number once. an example is 2 4 4 1 the answer is (2x4)(41)=24. I got stuck on one. The numbers were 7 5 5 4 . Answered by Penny Nom. 





The sum of the angels in a triangle 
20051125 

From Rachel: how do you prove, without knowing any of the measurements or degrees, that the three angles of a triangle equal 180? what are the steps for proving that? Answered by Penny Nom. 





BEDMAS 
20051124 

From Judy: My name is Judy and I am a grade 6 teacher.
We have just started our lessons on the order of operations and my students have asked me why we have BEDMAS and what is the logic to it.
Is there a reason that that we do math in this particular order?
Who invented this rule or how was it decided on and when? Answered by Walter Whiteley. 





An isosceles triangle 
20051114 

From Chris: PX and QY are attitudes of acute triangle PQR, and Z is the midpoint of PQ. Can you write a proof that triangle XYZ is isosceles? Answered by Chri Fisher. 





fog 
20051112 

From Janice: I am having problem with the (fog) function
(fog) (x). Given f(x)= 2x^{2} ; g(x)= 34x Answered by Penny Nom. 





Coefficient of variation 
20051019 

From Jan: I am currently teaching the coefficient of variation and am wondering if there are some guidelines as to the interpretation of this statistic. I understand that it measures the variation in a variable relative to the mean  but what is the cut off for "too much" variation expressed in this way???
Answered by Andrei Volodin and Penny Nom. 





The coefficient of thermal expansion for steel 
20051014 

From Jim:
Is the following statement true?
“The coefficient of thermal expansion for steel is 0.00000645in/in/deg. Doesn't sound like much but when you run out the numbers it comes to .405504 ft/mile/deg. Still doesn't sound like much, only about 5". Then multiply by 40 degrees and you get a piece of rail that has grown by 16.22 feet in that one mile. It's not at all unusual for the rail temp to go from say, 40 deg to 80 deg on a spring or fall day. Remember that on a sunny day, the rail temp can be significantly higher than the air temp as well."
I ran the math and came up with an answer closer to 16 inches, instead of 16 feet. Which is closer to being correct?
Answered by Penny Nom. 





The game of 24 
20051010 

From Kim and Chris: My 4th grade son came home with a math game called 24 game. In it each card has 4 numbers on it. Each number can only be used once, in any order, using multiplication, subtraction, division, or addition. We are stuck on one and wondered if you could help. The four numbers are: 9, 9, 9, 9. And they must equal 24. Any clues? Answered by Claude Tardif. 





Prove that a rhombus' diagonals are perpendicular 
20051002 

From Tania: How do you prove that a rhombus' diagonals are perpendicular using the 2 column proof method? Answered by Walter Whiteley. 





A system of equations 
20050902 

From Gina: How do you interpret the solution of a system of equations by the corresponding graph? Demonstrate your answer by the use of an example. Answered by Penny Nom. 





BEDMAS 
20050901 

From A student: I am a student and am wondering about the answer to this question.
56/2(31)
is the answer 7?
Answered by Harley Weston. 





Proof by induction? 
20050810 

From Peter:
I am a lecturer and am having a problem with the following Proof by
Induction.
If
(N x N x N x N) + (4 x N x N x N) + (3 x N x N) + (N) = 4000
Prove that N is even!
Answered by Chris Fisher and Penny Nom. 





Profit of more than 100% of cost 
20050622 

From sam: I know I can work out what percentage profit I am making by : profit/cost x 100, and I can work out up to 99% profit (the way I currently calculate it is profit x 1.99) But how do I work out any amount over 100%, say for instance I have something that costs me $0.52 that I wish to sell for 250% profit? Answered by Penny Nom. 





20% profit 
20050612 

From Shawn: If I know that I will be paid, say, $150.00, for labor, and I want to make
20% profit on what I pay for the labor, what is the calculation and factoring
process?
I see it like this
(x*.2)+x = 150
but I don't know how to factor it out from there. Answered by Penny Nom. 





The sum of the digits of 2^100 
20050611 

From Richard: The sum of the digits was calculated for the number 2100, then the sum of the digits was calculated for the resulting number and so on, until a single digit is left. Answered by Penny Nom. 





y = x+2 and y = 2x  1 
20050503 

From Kimberley: Question:
y=x+2
y=2x1 Answered by Penny Nom. 





40% profit 
20050419 

From Carol: Could you please tell me the formula to calculate for example a 25% profit on cost.
I.e a sandwich cost .75p for the cost of ingredients, I wish to make a 40% profit on that cost so what do I multiply and divide it by to arrive at the selling price in order to achieve a 40% profit? Answered by Penny Nom. 





A flaw in a problem 
20050415 

From Bryce:
Question:
(x^{2}x^{2}) = (x^{2}x^{2})
x(xx) = (x+x)(xx) [divide both sides by (xx)]
x = x + x
x = 2x [divide both sides by x]
2 = x/x = 1
Where is the flaw in this problem?
Answered by Paul Betts. 





Dimensions of a roof 
20050318 

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. 





The game of 24 
20050110 

From Manny: HI  my daughter and I are being driven crazy by the following "24" question 7,7,3,3. She's good at the game (well, better than I am) and her teacher gave her this one. Any insight would be appreciated! Answered by Claude Tardif. 





Profit 
20050110 

From Abraham: The profit a coat manufacturer makes each day is modeled by the equation P(x)=x2+120x2000, where P is the profit and x is the price for each coat sold.For what values of x does the company make a profit?
I don 't understand this problem(how to do it) and hope you can help me. Answered by Penny Nom. 





An isosceles triangle 
20050103 

From Abraham: The question is,"Triangle ABC is not isosceles.Prove that if altitude BD were drawn, it would not bisect AC."My question is If an altitude is drawn wouldn\'t that mean automatically its isosceles because, In a triangle the sides opposite congruent angles(in this case the right angles)are congruent? What am I thinking wrong? Answered by Harley Weston. 





2^9833 days from today 
20041226 

From Pauline: Today is Monday, 1 October 2001. What day of the week will be 29833 days from today? Answered by Penny Nom. 





A geometric proof 
20041211 

From Hanna: Given: ABCD is a quadrilateral;
Prove: ABCD is a parallelogram Answered by Penny Nom. 





"a" cubed minus "b" cubed 
20041202 

From Denise: "a"cubed minus "b"cubed equal (ab) times
("a"squared plus "ab" plus "b"squared)?
I know this is a formula, but why is it true? Answered by Penny. 





The substitution method 
20041128 

From A student: I Was working and i ran into this problem can you help me solve it using the substitution method?
3x2y=10
x+5y=27 Answered by Penny Nom. 





Proof by induction 
20041120 

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) = 2n1 x 3 (equation 1)
Equation 1 must be proven using mathematical induction. This is where I am having a problem. Answered by Penny Nom. 





Order of operations 
20041110 

From Andrew: I'm trying to solve this question, and I can't seem to remember the rules back from my high school days.
(40 x 8 ) / 2 + 55  15 =
Can you help me with the answer? Answered by Harley Weston. 





Bedmas 
20041109 

From Fariha: i have a single line question and am not sure of the method
it would be appreciated if u could send me a method and a solution Q : 1 + 9 / 2 + 5 * 1000
would this be solved by BEDMAS? if not, why? Answered by Penny Nom. 





Solving triangles 
20041030 

From Allen: Solve the following triangles.
Given
1. B = 20 Degrees, a = 25, b = 16
2. A = 35 Degrees, b = 2, c = 3
3. A = 32 Degrees, C = 44, c = 20 Answered by Harley Weston. 





Bedmas 
20041030 

From Gina: I am just curious whether Bedmas would be used in the following question as it is not in the typical Bedmas format.
Multiply 12 x 24
Add 26
Divide by 2
Subtract 7
Would we go about doing it in the sequence it is given or in Bedmas ? Answered by Penny Nom. 





Maximize income 
20041024 

From Connie: A company that sells x units of a product generates an income (I, in dollars) which is a function of x. The income generated is described by the equation
I = (1/2)x^2 + 100x.
Discuss how to determine the number of units that must be sold so that the company can maximize its income. What is the maximum income? Answered by Penny Nom. 





Solve for a and t 
20041023 

From Justin: How do I solve for "a" and "t" in the equations:
1000t= 4000 + 2000t + (1/2)at^2
1000=2000 + at Answered by Penny Nom. 





A rate of change problem 
20041015 

From Frank: Find the rate of change of the distance between the origin and a moving point on the graph of y = x(squared) + 1 if dx/dt = 2 centimeters per second. Answered by Penny Nom. 





Accelerating to the speed of light 
20040930 

From Lars: How long time would it take to accelerate up to the speed of light with an acceleration speed similar to 0100 seconds in 5 seconds? Answered by Penny Nom. 





A theorem involving a trapezoid 
20040929 

From Abraham: Given:Trapezoid ROSE with diagonals RS and EO intersecting at point M
Prove:Diagonals RS and EO do not bisect each other. Answered by Harley Weston. 





The volume of a pile of mulch 
20040922 

From Sam: Is there a formula to determine the cubic feet of something in a pile. IE I need to determine the cubic feet of a pile of mulch. The pile comes to a peak, so the length and width decrease as the pile increases. Answered by Penny Nom. 





The method of substitution 
20040920 

From Kayla: y=x1
y=2x3 Answered by Harley Weston. 





The game of 24 
20040916 

From Angelica: how can you make 24 out of 7,7,6,5? Answered by Claude Tardif. 





The game of 24 
20040914 

From Alan: I was playing that math 24 game and i cant get 21,14,2,2 to equal 24 Answered by Claude Tardif. 





The 24 game 
20040909 

From Erik: Ive spent around 40 hours on this one problem. I need help. 3,3,7,7 Answered by Claide Tardif. 





Order of operations 
20040904 

From Leanne: 6 + 3  2 x 3 = Answered by Claude Tardif. 





50/5x  y 
20040822 

From Rick: Niece has a question that was marked wrong but we are unable to determine how the teacher calculated and arrived at the answer? The problem was as follows:
50 / 5x  y =
x=5
y=1 Answered by Harley Weston and Leeanne Boehm. 





an integer with three factors 
20040803 

From A student: What is the probability that a randomly chosen 3 digit number has exactly 3 factors Answered by Penny Nom. 





The law of sines 
20040801 

From Joy: How do you solve this? Do you solve this triangle using the law of sines of the law of cosines? (ASA)
A=120DEG. B=40DEG c=35 cm
I keep getting different answers. Answered by Penny Nom. 





Rate of change problems 
20040801 

From Jim: I just want to check a couple average rate of change problems because i just guessed on how to do them. Can you tell me how to do them?
the question says if f(x) = sqrt(x + 3), find f( x + rx). I got sqrt( x + rx + 3)
the other two are : f(x)= 3x1 (f(x)  f(1)) / (x1) ... I GOT 3 &
f(x)= x^3  x (f(x)  f(1)) / (x1) ... I GOT x^2 + x Answered by Penny Nom. 





Factoring 
20040719 

From A student: Factor completely:
3x3  24y3
54x6 + 16y3
16xy  4x  4y  1
0.09x2  0.16y2 Answered by Penny Nom. 





A proof in geometry 
20040716 

From An: Im taking a geometry course for the summer , and we just started to learn about proofs for about one week. Today in class, we started to do this one proof but didnt finish it because class ended. the problem is as follows. Answered by Penny Nom. 





The Number of the Beast 
20040613 

From A Heinlein reader: Most people who have an interest in mathmatics are familiar with Robert Heinlein's novel "The Number of the Beast", where 666, or ((6 to the 6th power) to the 6th power) equals 1.0315 times 10 to the 28th power, which in the novel is the number of parallel universes in the cosmos. My question is what would the number of parallel universes be if you grouped 666 the other way: (6 to the power of (6 to 6th power)). I have tried this on my calculator, but it won"t register that high. Answered by Penny Nom. 





The game of 24 
20040604 

From Samantha: i have the game 24 (the one where you have to use multiplication, division, addition, and subtraction to get to the answer 24) I was playing when i came across the 4 numbers 20, 17, 7, 11 and i cant seem to get 24. Answered by Claude Tardif. 





Finding bearings 
20040524 

From James: This question is about finding bearings. A boat race starts from point A, goes North to Point B, a distance of 1000 meters. The course is triangular. The bearing from point B to point C is South 70degrees West. The distance from Point B to point C is 1500 meters. Find the course bearing from C to A.
Answered by Penny Nom. 





Angles of elevation and depression 
20040518 

From Anjum: what is the difference between an angle of elevation and angle of depression? Answered by Penny Nom. 





Three dice 
20040510 

From A student: If one has 3, 6 sided dice what is the probability of the numbers that are rolled to total 4 through 10 inclusively?
Subsequent to this, what is the probability to do this consecutively...say 3 times? Answered by Peny Nom. 





3x squared  27 / x + 3 
20040504 

From Stef: 3x squared  27 / x + 3 Answered by Penny Nom. 





