







A 50:1 ratio in a pint 
20200522 

From Steve: How much oil do I need to put in a pint if it's 50:1 ratio Answered by Harley Weston. 





Gravel for a French Drain 
20200417 

From Ray: Hello,
** I am wanting to add 2 French Drain's in my yard. The 1st drain will be 25 ft. long, 8 in wide and 18 in deep. The pipe I'm using is 4in. in diameter. I'm trying to figure out how many yards of clean gravel I will need for this project?
** The 2nd French Drain will be 100 ft in Length, 10in wide and 18 in deep. I will also be using the 4in in diameter pipe for this drain. I am needing to see how many yards of clean gravel, I'll need for this drain?
Any assistance would be greatly appreciated!! Thank you!! Answered by Harley Weston. 





Odds 
20191216 

From Craig: I’d like to know what are the odds of a lotto machine giving out a specific 4 digit number as a quick pick?
I know there are 10,000 possible 4 digit combinations. So let’s say the number is 3587 what are the odds the lotto machine spits it out EXACTLY that way on a quick pick? Answered by Penny Nom. 





Two people are clapping their hands 
20191206 

From Yukti: Two people are clapping their hands, but with different frequencies. Ramya claps her hands
17 times per 3 minutes, and Kumar claps his hands 31 times per 5 minutes. They start
clapping at the same time. How many times does each one clap before they clap together at
the same time again? Answered by Penny Nom. 





The volume of a pile of dirt 
20190401 

From Genevieve: We have a pile of dirt approximately 6 feet high by 15 feet wide by 80 feet long.
We need to know how many cubic yards of dirt are in this pile. Thank you Answered by Harley Weston. 





Percentages 
20190330 

From Mari: I am trying to find out what percentage of our worlds population does the youtuber
Pewdiepie have for subscribers? So he has 91 million subscribers and there are roughly
7.53 Billion people in the world. So what percent of our worlds population does Pewdiepie
have for subscribers? Am I asking this correctly? I am just curious for marketing reasons
and how much of the worlds market share does Pewdiepie have for his youtube
channel? I just do not know how to set up the problem to find the answer? Answered by Penny Nom. 





The volume of water in a pipe 
20190321 

From Abati: How can I calculate the volume of water in a pipe with below details;
Pipe diameter  6 inches
Length of pipe  127meters Answered by Penny Nom. 





Slope and percentage 
20190319 

From Tom: I need a slope of 2 Inches every 30 feet what is the percentage to put on my pipe lazer. thank you Answered by Penny Nom. 





Two intersecting tubes 
20180815 

From Tommy: Hi, I am trying to determine a mathematical model for two metal tubes joining at various degrees for weld.
For instance, if I am trying to join the end of a tube to the side of another at a 90 degree angle, it will be a simple profile cut out of the joining tube.
Where it gets tricky is if you want to join the new tube at a given angle.
It would be very helpful if you could give insight as to how I can solve this problem or an equation I could work off of.
Thanks for the help!! Answered by Edward Doolittle. 





Two spinners 
20180813 

From Atina: A spinner has four equal sectors and a number is written on each sector; 1, 2, 3 and 4. A twodigit number is formed by spinning two times. The number on the first spinning makes the first digit and the number on the second spinning makes the second digit. For example, 2 on the first spinning and 1 on the second spinning make the number 21.
(a) Give the sample space S for the experiment.
(b) Consider the following events : E = odd number; F = number smaller than 35; G = prime number.
Give the subset of outcomes in S that defines each of the events E, F, and G.
(c) Describe the following events in terms of E, F, and G and find the probabilities for the events.
• getting an even integer less than 35.
• getting an odd number or an prime.
• getting an even number greater than or equal to 35 that is a prime number. • an odd number smaller than 35 that is not a prime number.
(d) Are E and F mutually exclusive events? Give a reason for your answer. Answered by Penny Nom. 





Taking 6 pills 
20180529 

From Dave: My motives are simple, I want to get revenge on my brother who, unbeknown to me,
repeatedly cheated when we played online Scrabble! Can you help?  he has posed this
question knowing that I'll struggle to get the solution.
Question: He is taking 6 pills a day, if he takes the pills in a different order each day,
how long will it be before he takes the pills in the same order on the same date again?
I think leap years might come in to it!
Will I confess to using you guys?  I'll think about that one. Answered by Penny Nom. 





The number of truckloads to fill a hole 
20170618 

From Jennifer: How many full size truck bed pickup loads do in need to get to fill a hole that is 18' x 30' that is 4" deep? Answered by Penny Nom. 





3rd Grade math problem 
20170530 

From Angela: Following is a problem from my 3rd grader's homework assignment:
Solve. Draw a diagram to represent the situation.
Rachel has 20 oneinch beads. She wants to use all of them to make a square picture frame. What will be the length of each side?
Find Perimeter, Area, and Side Length Answered by Penny Nom. 





A function which is onto but not onetoone 
20170416 

From Avinash: Define a function f(x):N>N which is onto but not oneone.Where N is set of natural numbers. Answered by Penny Nom. 





Covering the ceiling of a garage 
20170220 

From DeAnna: I am trying to drape a 15 x 30 garage with yards of fabric. If the yard of fabric is 60 inches wide, would 10 1/4 yards be enough for my space? Answered by Penny Nom. 





A pie chart 
20161205 

From vickie: Determine the central angle needed to form a pie chart for the following housing characteristic data: 63% owner occupied, 27% renter occupied, and 10% vacant Answered by Penny Nom. 





Acres and miles 
20161130 

From Carolyn: If I am running a pipeline of 1,100 miles, how many one acre plots will it take to cover this distance?
Carolyn Answered by Penny Nom. 





A kinky curve 
20161006 

From tammie: Koch’s kinky curve is created by starting with a straight segment and replacing it with four segments, each 1/3 as long as the original segment. So, at the second stage the curve has three bends. At the next stage, each segment is replaced by four segments, and so on. How many bends does the curve have at the third stage? Answered by Penny Nom. 





A triple product 
20161003 

From sam: Let a and b are vectors such that
Vector a = (1,1,2)
Vector b = (2,1,1)
And let vector c be a unit vector such that triple product of a,b,c is
minimum . We have to find the value of c.
[Thoughts]
I thought triple product of a b, c means the volume occupied by
parallelepiped. And we have to do volume minimum Answered by Penny Nom. 





An equation involving pi 
20160626 

From Diaz: How would you solve :
( pie*X)/ 4 = pie/2
I have no idea.what to do! 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. 





Filling a pit with glass pebbles 
20160517 

From Sam: I need to know how many pounds of glass pebbles are needed to fill a 24 inch across circular fire pit, if 5 pounds covers 4"H x 4"W x2"D? Thank u for any assistance, Sam 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. 





Pizza delivery 
20160403 

From Andrew: Suppose you own a local pizza restaurant, Pizza with Pizzazz, and in order to compete with the big pizza chains in your area you are considering an advertising campaign offering customers a free pizza if their pizza is not delivered in 30 minutes or less. Even though your pizza restaurant is known for its fast and friendly delivery service, you are not sure if you can afford to give away too many pizzas for free. Looking over your past 12,421 pizza deliveries you find out 97% of the pizzas were delivered in 30 minutes or less.
Calculate the probability that all 100 randomly selected pizza deliveries will have been made in 30 minutes or less? Hint: Use the multiplication rule. (Round 4 decimals)
I'm really stumped on how exactly to do this problem. I don't need the answer just the steps broken down to show me how to get it!
It would be gladly appreciated if you could help! Answered by Penny Nom. 





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. 





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. 





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. 





Sierpinski Pyramid 
20151214 

From victor: Is a tetrix (a Sirpienski Pyramid/Tetrahedron) its own hyperplane?...alternatively, is it a hyperplane? Answered by Robert Dawson. 





The flight of a ping pong ball 
20151013 

From Abigail: Hello,
Wondering if there is a way to figure out the quadratic equation of half of a parabola?
Doing an assignment about finding quadratic equations for separate bounces of a ping pong ball, but the first bounce is incomplete (as the ball has presumably been dropped, hit the ground and then went on to make a complete bounce).
Please see attachment for references to the diagram that I am using.
Not sure whether I would have to look at it from a different perspective.
Thanks,
Abi Answered by Harley Weston. 





How can the probability be zero? 
20151013 

From anagha: Hi,
thank you for answering (beforehand)
The other day I was just thinking of circles and I came across this peculiar thing.
Most of'em say that there are infinite number of points on the circumference.
and, if it is true, if we spin the radius, the probability that it will point a a particular point is 1/infinity, right?
It didn't make any sense to me and so, I thought there might be an explanation or something of the kind...? Answered by Harley Weston. 





Mathematics 
20151013 

From anagha: Hi,
thank you for answering (beforehand)
The other day I was just thinking of circles and I came across this peculiar thing.
Most of'em say that there are infinite number of points on the circumference.
and, if it is true, if we spin the radius, the probability that it will point a a particular point is 1/infinity, right?
It didn't make any sense to me and so, I thought there might be an explanation or something of the kind...? Answered by Harley Weston. 





Is 22/7 is an irrational number? 
20150607 

From Sayak: Is 22/7 is an irrational number 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. 





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. 





Bricks around a fire pit 
20150305 

From Jayson: I have a round fire pit. It measures 25 inches in diameter. I have 12 inch long square bricks to go around it . My question is what degree do I cut the ends of these bricks to make them fit around this circle? The brick dimensions are 12"Lx6"Wx4"D. Answered by Harley Weston. 





Stopping distance 
20150211 

From Audrey: A Harley Davidson motor cycle weighing 650 lbs with a rider weighing 175 bs
was going 40 miles per hour. He had to make a sudden stop . Slammed on brakes. How long a distance for him to stop? 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. 





A piecewise graph 
20140510 

From Zoe: Lightning Energy charges residential users for each unit of electrical energy bought from them each quarter, according to the scale below:
0500 units cost 17 cents per unit
5001500 units cost $85 plus 10 cents for each unit in the excess of 500
1500 or more units cost $185 plus 9 cents for each unit in excess of 1500
Sketch a graph showing the charge C as a function of U for up to 2000 electricity units Answered by Penny Nom. 





The locus of a point 
20140404 

From srishti: A point P moves such that the difference between its distance from the origin and from the axis of x is always a constant c . what is the locus of the point? Answered by Penny Nom. 





Graphing piecewise functions 
20140329 

From Rayven: Hi! I'm in eighth grade, taking ninth grade algebra 1. I'm confused as to how to
graph piecewise functions. I know that you have already answered a question similar to this
(I did my research first) but it didn't completely help me on my homework. I have to graph
piecewise functions for the specified domains, and create a table for the absolute values.
I know that two bars around a number means absolute value (two bars around 2 makes it +2)
, but how do I graph and chart the absolute value for the following:
f(x)= x+3  for 5≤x≤3
And then graph and chart: (on a separate graph):
f(x)= {x if x≤0
{x+1 if x <0
thank you!
~Rayven Answered by Penny Nom. 





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 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. 





Two overlapping circles 
20130522 

From Alexandra: There are two overlapping circles. The two nonoverlapping regions have areas A and B.
As the area of overlap changes, the values of A and B also change.
Prove that no matter how big and small the overlap is, the difference between
A and B is always the same. Answered by Penny Nom. 





Cutting three sections of pipe 
20130516 

From Michael: A plumber cuts three sections of pipe from a 12’ length of ABS pipe, the lengths of the sections
are 33 3/8”, 56 5/8” and 39 7/8”. What is left over from the full length, if the saw cut is 1/8”
wide? 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 function with 3 asymptotes 
20121019 

From rimoshika: find a function that have 3 Asymptotic : y=x/y=sinx/x=1 Answered by Penny Nom. 





Three piles of top soil 
20121007 

From Steve: I need your help please, I am looking to purchase some top soil and keep getting conflicting answers.
There are 3 piles and here are the sizes;
Pile #1: 203 feet around and 21.29 feet high.
Pile #2: 195 feet around and 18.75 feet high.
Pile #3: 150 feet around and 17.98 feet high.
I look forward to hearing back from you asap.
Thank You!
Steve Answered by Harley Weston. 





Functions 
20120918 

From nayeem: I tried with many functions but I am not getting the exact values please help me
A give an example of a function whose domain equals the set of real numbers and whose range equals the set the set {1,0,1}?
B Give an example of a function whose domain equals (0,1)and whose range equals [0,1]
C.Give n example of a function whose is the set of positive integers and whose range is the set of positive even integers
D. Give an example of a function whose domain is the set of positive even integers and whose range is the set of positive odd integers
E give an example of function whose domain is the set of integers and whose range is the set of positive integers.
F. Give an example of function whose domain is the set of positive integers and whose range is the set of integers.
please show me the work
Please give me the trick of finding such functions Answered by Robert Dawson and Harley Weston. 





Functions 
20120918 

From nayeem: I tried with many functions but I am not getting the exact values please help me
A give an example of a function whose domain equals the set of real numbers and whose range equals the set the set {1,0,1}?
B Give an example of a function whose domain equals (0,1)and whose range equals [0,1]
C.Give n example of a function whose is the set of positive integers and whose range is the set of positive even integers
D. Give an example of a function whose domain is the set of positive even integers and whose range is the set of positive odd integers
E give an example of function whose domain is the set of integers and whose range is the set of positive integers.
F. Give an example of function whose domain is the set of positive integers and whose range is the set of integers.
please show me the work
Please give me the trick of finding such functions Answered by Robert Dawson and Harley Weston. 





The distance between overlapping circles 
20120726 

From Jeff: I have two circles of different size that overlap one another:
Circle #1 has an area(A) of 731,475, so I can calculate its radius as 482.6.
Circle #2 has an area(A) of 502,517, so I can calculate its radius as 400.
If I know that the area where they overlap is 179,271, how can I calculate the distance between the midpoints of these two circles? Answered by Chris Fisher. 





A pile of topsoil 
20120723 

From Perry: I have a pile of topsoil that is 42ft long and 16ft tall shaped like a cone how many yards of topsoil do I have. Answered by Penny Nom. 





A pie chart 
20120501 

From muhammad: How can i construct a pie chart on the following of the combunation of students:
Sos 50, Crs 25, Eng 100, Iss 75, Geo 150, Hist 10 Answered by Penny Nom. 





Two overlapping circles 
20120321 

From Monty: If you have a 3.75" radius circle overlapping a 5" radius circle with their centers 3" apart what would be the area of the nonoverlapped portion of the small circle? Answered by Penny Nom. 





The price per square inch of a pizza 
20120317 

From jordan: pizzaz pizza sells a small pizza for $10.99.it has a diameter 10 inches.what is th price per square inch ? Answered by Penny Nom. 





Building a tipi 
20120129 

From Lacy: Hi there!
We are building a tipi for our children. We want to build a large one about 15ft tall with a base of about 15 feet diameter. I am trying to figure out how much canvas we need to accomplish this. I graduated about 20 years ago and am struggling. Please help if you can. 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 pizzas 
20120123 

From kris: a pizza company wishes to put 4 medium pizzas in a box to sell as a party pack. The box they want to use the square and has dimensions of 60cm by 60cm. They need you to help them calculate the dimensions of the pizza that will fit in the box. Calculate the following: area, radius, diameter, circumference Answered by Penny Nom. 





A picture in a frame 
20120110 

From nnadozie: a picture, which measures 46cm by 38cm, is surrounded by a frame, which is 2cm wide, find the area of the frame. Answered by Penny Nom. 





A wire spiral 
20120107 

From Pinar: I am trying to help my daughter with very challenging maths questions which sometimes I get stuck
If someone help me with one of them I would appreciate it.
Jane is making a spiral out of wire. She bends the wire after 1 cm, then bends the wire
after 2cm, then 3cm and continues in this manner. After 4 bends she used 15 cm of wire
For each bend how many cm wire was used? After 6 bends how many cm wire will she have used?
How many bends will she have made if she uses 66 cm of wire?
I would appreciate if somebody would help me with this.
Thank you!
Pinar Answered by Penny Nom. 





The weight of 36 inch steel pipe 
20111222 

From Keith: What is the weight of 36 inch steel pipe 3/4 wall per foot in lbs. Answered by Penny Nom. 





An octagonal fire pit 
20110819 

From terry: i have a 18 ft diameter gravel circle laid down for a fire pit. i want to lay the paver stones out in a octagon pattern. How long would the sides of my octagon be to fit center on the 18 ft diameter of gravel base? Answered by Penny Nom. 





A pipe in a ditch 
20110519 

From Jim: How many cubic feet of stone will it take to fill to six inches around a 4 inch pipe in a ditch 128 ft long x 20 in wide? Answered by Penny Nom. 





pi + pi 
20110320 

From Sarah: what is pi + pi? Answered by Penny Nom. 





Slicing a rectangular parallelepiped 
20110223 

From tom: a) Pass a plane containing a vertex of a rectangular parallelepiped and a
diagonal of a face not containing that vertex to cut a pyramid from the
parallelepiped. What fraction of the volume of the parallelepiped is the
volume of the pyramid thus cut off?
b)Pass a plane through a cube of edge 8 in so that the section formed
will be a regular hexagon. Through each side of the hexagon pass two
planes, one plane containing one of the two vertices of the cube
which are farthest away from the plane of the hexagon, the other
plane containing the diagonally opposite vertex of the cube. Find the
volume of the solid bounded by these planes.
c)three of the edges of a rectangular parallelepiped that meet in a point
are also the lateral edges of a pyramid. What fraction of the parallelepiped
is this pyramid...?
you know the my only problem is how to illustrate this one...if only i
could ...can you help me....all I need is the drawing and I can do the rest
..it's fine if you'll only answer any of these but I'll be thankful if you
will do the three :).... Answered by Penny Nom. 





Area and volume of a parallelepiped 
20101214 

From ryan: Got a question, I'm really confused what the question mean and how the diagram would look like... someone please help... Here's the question.
The base of a parallelepiped is a rectangle 4m by 6m. If its lateral edge is 8m and is inclined at an angle 45 degrees to a 6m edge of the base, find the total area and volume of its parallelepiped.
My dilemma is what does it mean by the lateral edge of 8m is inclined at 45 degrees to a 6m edge of the base? Can someone post a diagram to help me solve the promble. Thanks in advance. Answered by Chris Fisher. 





Intersecting polygons 
20101117 

From Laura: How can I estimate the amount of intersection (area or better a normalized number) between two polygons if I have the cartesian coordinates of their vertices?
Thank you in advance,
regards,
Laura Answered by Robert Dawson. 





Bbippities, bops, and boos 
20101105 

From Stacey: six bippities equal three bops,and six bops equal two boos. How many
boos are there in one bippity,one bop, and one boo?? Answered by Stephen La Rocque. 





A taxi ride 
20100922 

From Jack: A taxi ride costs you $2 for the first km and 10 cents for each tenth of a km thereafter.
Sketch a graph of the total cost $C(x) for a ride of xkm, for 0 < x < 2. Hint: The
graph is not smooth.
How will I start this question off? I tried the table of values method, and then graphed it, but it comes out as smooth, Answered by Stephen La Rocque. 





Limits 
20100920 

From rodrigo: what's the limit of x+1/x1, when x tends to 1? Answered by Janice Cotcher. 





Constructing a tipi 
20100920 

From mike: we are thinking about making a lightweight tipi tent but we need to know what the angles and lengths of each side that we will need to cut. The height of the tipi wants to be about 2.2m span at the widest point wants to be about 3.2m we want to make it based upon a 6 sided(hexagon) shape thanks for your help Answered by Harley Weston. 





Pi 
20100726 

From Eden: I think that "pi" is an important number in math. I have learned this number's
approximate value since childhood but I haven't known how can it be got and
who find that number . So please help! Answered by Robert Dawson. 





A circular oil slick of uniform thickness 
20100522 

From Susan: Hi,
I have this problem on a homework assignment and just can't seem to figure it out:
A circular oil slick of uniform thickness is caused by a spill of 1 m^3 of oil. The thickness of the oil is decreasing at the rate of .001m/h. At what rate is the radius of the slick increasing when the radius is 8. Answered by Penny Nom. 





A conical pile of gravel 
20100515 

From Chuck: If I have a conical pile of gravel 50 feet across at the base and a height of 65 feet and
the slope of the side is approximately 60 degrees, how do I calculate the cubic yards? Answered by Robert Dawson. 





The diameter of a circle 
20100430 

From Jimmy: If I have a straight line with a known length and decide to make a circle out of this know length how would I calculate what the diameter of the circle would be Answered by Penny Nom. 





The width of a picture frame 
20100428 

From Daniel: The frame of a picture is 28 cm by 32 cm outside and is of uniform
width. What is the width of the frame if 200 cm ^2 shows? Answered by Penny Nom. 





A conical pile of gravel 
20100413 

From Chassity: The gravel pile is 120' around at the base and goes up 20' high at the peak. How many tons or yards of gravel in that pile? Answered by Penny Nom. 





Two overlapping circles 
20100412 

From Scott: There are two circles, big circle with radius R and small one with radius r. They intersect and overlap in such a way that the common area formed is 1/2 pi r^2 (half the area of the small circle). The Question is: suppose we have known the radius r of the small circle, and the distance between the two circle centers, what should the radius R of the large circle be? Answered by Chris Fisher. 





Two overlapping circles 
20100307 

From Hayden: I have two circles of equal size. The radiuses of the circles are 30ft. The two circles are positioned 40ft apart and I need to find the area where they overlap. Answered by Harley Weston and Tyler Wood. 





Odds and evens in an n by n+1 table 
20100121 

From Shankar: The boxes of an n * (n+1) table ( n rows and n+1 columns) are filled with integers.
Prove that one can cross out several columns ( not all of them !) so that after this operation
all the sums of the numbers in each row will be even. Answered by Robert Dawson. 





A circular photo in an octagonal frame 
20100113 

From Mike: I have a circle photo 18 and one quarter inches round. I want to cut frame for it in a octagon shape. What would the angle and the length of cut be?
Mike Answered by Robert Dawson. 





Trigonometry and picture hanging 
20100113 

From george: The top of a picture 1m high 0.8m from the ceiling. At a point on the ceiling directly in front of the picture, we wish to install a light so that the angle subtended by the picture equals to the angle of depression of the top of the picture. How far out from the wall should the light be installed? Answered by Penny Nom. 





Cows, pigs and ducks 
20100106 

From Eileen: There are 239 cows and pigs in a farm. The total number of cows and ducks in the farm is 767. There are 5 times as many ducks as pigs. If the farmer can sell each duck for $7.50, how much can he collect from the sale of all his ducks? Answered by Robert Dawson. 





The volume of a compost pile 
20091211 

From Tim: I have a pile of compost that is78 feet long by 18 feet wide at base by 9
feet tall to a point. At the width it looks like a triangle
I'm looking for the square yards
Thanks Answered by Penny Nom. 





Two adjacent pig pens 
20091204 

From alysia: A pig farmer wants to build two adjacent pens using 96 feet of fencing. He wants rectangular pens that share the short side and the overall length is to be six more than twice the width. What should be the dimensions of the overall pen? Answered by Penny Nom. 





Two overlapping circles 
20091119 

From Raraa: There are two identical circles . The edge of one circle is at the middle point of the other circle. There were overlapped . The area of the overlapped surface is 20000 square centimetres . How do I find the radius of the circle rounded to the nearest whole centimetre ? Answered by Penny Nom. 





Cables in a pipe 
20091113 

From john: how many 0.28 mm diameter cables will fit into a 19.05 mm diameter pipe Answered by Stephen La Rocque. 





Cutting a pipe at an arbitrary angle 
20091024 

From Carol: I have read your article on cutting pipe,etc. at a 45 degree angle. I need to develop
an equation and pattern for cutting any size pipe (3" to 7") to any degree. I don't
understand how to transfer the wave pattern to graph paper.
Thanks. Answered by Harley Weston. 





e^pi and pi^e 
20091022 

From Natalie: Question from natalie, a student:
Without using your calculator, prove which is bigger: e^pi or pi^e
we talked about ad absurdum in class, so I'm assuming that is how I approach this question, but since neither of them have a variable( like the examples we actually solved in class), I'm not quite sure how to solve it.... Answered by Harley Weston. 





$6.25 in nickels quaters and dimes 
20091010 

From miriam: a piggy bank contains $ 6.25 in nickles quaters and dimes.
there are 65 coins all together and there are four times as many nickles as quaters
find the number of coins of each kind Answered by Penny Nom. 





Ordering pizza for 162 people 
20091001 

From Jean: Need to know how to feed about 162 people 70 square inches of pizza at the lowest price.
22" Pizza is $9.95
16" Pizza is $5.25
12" Pizza is $2.99 Answered by Penny Nom. 





Friends in a class 
20090914 

From pran: it is known that among any group of three students in a class two of them are friends. the total number of students is 25. prove that there is a student who has at least 12 friends Answered by Claude Tardif. 





Chickens and pigs 
20090828 

From David: A farmer has a number of chickens and pigs. There are 24 heads and 80 ft.
How many pigs and how many chickens are there? Answered by Robert Dawson. 





A paper towel roll 
20090819 

From Jeff: I am making a spiral tube with paper that is 2" in dia. and 102" long
I will be using paper that is slit 3" wide how many lineal feet of paper will
I need to to cover the 102"
I will be using 3 rolls of paper that will over lap the other by half to make
a hard tube (paper core) in a roll of paper towels
Thanks Jeff Answered by Penny Nom. 





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. 





liquid in a 3/4 inch pipe 
20090630 

From junior: We are in dilemma at my job. We need to figure out the formula for how much water can our pipe hold. It's inside diameter is 13/16" and is 50ft. long? Answered by Robert Dawson. 





The surface area of a fire pit 
20090630 

From eric: whatw is the square footage of the inside wall of a fire pit 2 feet deep and five feet in diameter? I need to estimate both the floor and wall square footage to order bricks. Answered by Robert Dawson and Harley Weston. 





A gravel pile in my driveway 
20090513 

From Dean: The only place I have to deliver gravel is in my driveway. The driveway is 16 ft wide by 18 ft long. How much gravel can I order as to not exceed the boundaries of my driveway when the truck dumps the gravel onto my driveway?
I am assuming the angle of repose comes into play when calculating this elliptical pile? The maximum amount of gravel I need is 12 cubic yards. Answered by Robert Dawson. 





A six sided pyramid 
20090511 

From Karen: I am going to make my kids a six sided tipi (pyramid) I have a 5 foot tall central pole, and I would like the floor area to be 6 feet across. How do I work out what size to cut each fabric panel to make this happen? Answered by Harley Weston. 





Filling a container with water 
20090422 

From frank: With one house pipe it takes 8 hours to fill a container with water. How long will it take with 4 house pipes of the same size and the same water pressure and same container? Answered by Robert Dawson. 





15 pigs in 4 pens 
20090422 

From Melissa: A farmer has 15 pigs. He wants to put them all into 4 pens, have an
odd number of pigs in each pen, and have no pigs left over. Also, he
isn't thinking about having any for dinner, as they are his pets.
How does he do it? Answered by Robert Dawson. 





Pi 
20090421 

From Serena: Who invented pi? Answered by Robert Dawson and Stephen La Rocque. 





An octagonal shaped gravel pit 
20090416 

From Melissa: What is the square footage of a 7'3" square ocatogon with a height of 5 inches? I need to know how much pea gravel to buy for my sons gravel pit. Answered by Stephen La Rocque. 





How many times is 9 in pi? 
20090409 

From Serena: How many times is 9 in pi? Answered by Robert Dawson. 





An equation for a line with a changing slope 
20090321 

From Ben: Is there anyway to write an equation for a line with a changing slope.
e.g. A cell [hone company has a initial fee of 50$ paying for the first 100 minutes,
the rate then increases to 10 cents per minute, then at 500 minutes the rate is 5 cents
per minute.
If so please tell how.
Thanks Answered by Penny Nom. 





A 20 foot piece of pipe 
20090319 

From chris: How many 8 inch pieces can you get from a 20 ft. piece of pipe? Answered by Penny Nom. 





An octagonal landscaping frame 
20090301 

From Richard: Hi
I am trying to put landscape timbers down in octagon shape that measures 6
feet across and outside measures 360 degrees.. The timbers are 4 inches by 4
inches. I need to know at what angle to cut boards and at what length i need to
complete octagon.
Thanking you in advance for your kind assistance.
Richard :) Answered by Harley Weston. 





Triangles within triangles 
20090224 

From Mari: a large shaded triangle changes each day with a white triangle appearing
in the center of each shaded one. If this pattern continues, how many white
triangles will be there on the 6th day? On the 6th day, what fraction of
the large outer triangle will be white?THANKS! Answered by Robert Dawson. 





Percentage difference in pipe volumes 
20090222 

From mike: what is the % difference between a 3 inch diameter pipe compared to a 4 inch diameter pipe? and how do i find the answer? Answered by Penny Nom. 





A ¾ inch copper pipe 
20090222 

From Ray: Hi
Do you have a formula I can use for this problem? And how to use it.
Thank You
How many feet of ¾ inch copper pipe will it take to hold 3 gallons of water? Answered by Harley Weston. 





Gallons of water in a 3 mile pipe 
20090219 

From tim: I need to know how many gallons of water a 16" pipe that is 3 miles long holds? Answered by Penny Nom. 





y = p q^t 
20090212 

From Conor: y= p x (q (to the power t) ) ; y= 100 when t = 2 and y= 4 when t= 0
a) find p and q
b) hence find y when t=4 Answered by Stephen La Rocque. 





A piecewise function for monthly salary 
20090203 

From Josh: A sales rep for a drug company is paid on the following scale. His base salary is $1600 per month. He is also paid a commission of 2% of sales over $20,000. When his gross sales reach $30,000 he is then paid 4% on the amount above that until his sales reach $50,000 after which point his commission becomes 6%. His commission reaches 8% when his sales total goes over $100,000 for the month. Set up a piecewise function for the information above. Answered by Harley Weston. 





Concrete around a pipe 
20090114 

From Doug: How much concrete will i need for a hole that is 20 feet deep 20 inches in
diameter with a 8inch pipe in it. I need to know how much concrete
on the outside of the 8inch pipe. Answered by Penny Nom. 





The volume of a pipe elbow 
20081231 

From mhd: how i can find volume of the pipe elbow of 4inches? Answered by Stephen La Rocque. 





A spill of oil on a flat surface 
20081219 

From Phillip: Hello, my question is: If I spilled 25 gallons of diesel fuel on a flat surface how much area would the spill cover?
How would I mathematically figure it out?
Thanks! Answered by Robert Dawson and Harley Weston. 





The volume of a pipe 
20081210 

From Walter: What is the volume of a pipe 7.92 inches inside diameter and 22 km. long in cubic feet of water Answered by Robert Dawson and Harley Weston. 





Compatible numbers 
20081030 

From Paul: Use compatible numbers to estimate the quotient of 23.52 and 11.04 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. 





Concrete around a pipe 
20081008 

From mick: i am trying to find the area of concrete to be placed around a concrete pipe! Dimensions can be 12m wide by 5m wide by 7m deep and pipe been 8m by 600mm radius... Answered by Stephen La Rocque. 





What is the exact value of pi? 
20080927 

From mahesh: what is the exact value of pi.
22/7 is accurate value of pi, if not then how can i find out the exact pi value. Answered by Harley Weston. 





Cutting a pipe at an arbitrary angle 
20080920 

From John: from the original question Al asked about cutting a 200 diameter pipe in 45 degrees. can someone explain the math steps required to creating the graph. I am trying to do the same thing only using a 150 degree cut. Answered by Harley Weston. 





Pumping water into a tank 
20080913 

From nadha: A water pump can fill a tank at the rate of 750 litres per hour.A tank has a capacity of
9000 litres. Find the time needed to fill 7/15 of the tank? Answered by Stephen La Rocque. 





Grouping addends 
20080913 

From juan: how do you group the addends then find the sum: 2+4+6= Answered by Penny Nom. 





Cutting a pipe on a 45 degree angle 
20080912 

From Bakshani: how do you a mark a pipe 5 inch diameter and cut it to form a 45 degree angel Answered by Stephen La Rocque. 





The length of a pipe 
20080825 

From John: How many feet of one inch pipe would it take to hold 30 and 40 gallons of water?
Imperial gallons please. Answered by Penny Nom. 





Graphing a piecewise function 
20080812 

From Shanti: how do you graph a step function or piecewise function such as
u^2 if u is greater than or equal to 2 and less than 1
2 u if u is greater than or equal to 1 and less than 4 Answered by Penny Nom. 





Right Sided Limit of an Exponential Function 
20080729 

From joseph: I am trying to find the limit as X approaches 0 from the positive side of x to the sin of x
which look like this lim x^sinx
x>0+ Answered by Harley Weston. 





The size of a pipe 
20080629 

From payal: hi , i want to know the area of a pipe with 63.5 mm diameter and 3718 mm height . can u pls help me Answered by Harley Weston. 





What is a 1% slope? 
20080617 

From randy: trying to figure out percentage of slope lets say i have to run a pipe 80' at a 1%slope how much pitch is that? Answered by Harley Weston. 





A piecewise equation 
20080616 

From John: AT&T charges $39.99 for 450 minutes per month. It charges 45 cents per minute over the 450 minutes.
How can I make a piecewise equation of this problem? Answered by Penny Nom. 





The wedges in a circle graph 
20080518 

From Libby: I don't understand how to do this word problem:
The cafeteria workers distributed a survey to the student body asking students to pick 1 from a list of 5 choices for their favorite lunch. The circle graph below gives the results of the survey for the students who responded. What is the measure, in degrees, of the central angle for each choice?
And there is a pie chart that has food choices with these percentages: 25%, 20%, 15%, 10%, and 30% Answered by Leeanne Boehm and Penny Nom. 





Two overlapping circles 
20080426 

From Michelle: Two overlapping circles O and Q have the common chord AB (vertical line between the overlapping circles). If AB is 6 and circle O has a radius of length 4 (horizontal line going through the overlapping circles and touching the side of the circle) and circle Q has a radius of length 6, how long is OQ. Answered by Penny Nom and Walter Whiteley. 





The maximum area of a pizza slice 
20080412 

From charles: A slice of pizza in the form of a sector of a circle has a perimeter of 24 inches. what value for the radius of the pizza makes the slice largest[when o is the central angle in radians, the area of the sector is given by A= r^20/2and the length on the circle is given by s=r0 Answered by Harley Weston. 





Cutting a 200 diameter pipe at 45 degree angle 
20080410 

From Al: i want to cut a 200 diameter pipe in 45degrees. Can you demonstrate how to develop a flat rap around please Answered by Harley Weston. 





The cost before tax and shipping 
20080206 

From jonathan: Please explain how to solve this problem. I know you have to work backwards. If i have $125 to spend, how do I know the most I can spend before adding 6% tax and 9% shipping.(shipping is cost before tax) I can only figure this out by trial and error. I know there is a better way Answered by Penny Nom. 





Two spinners 
20080205 

From Kim: Zack has two spinners with numbers on them. the probability of spinning
a 7 on both spinners is 3/20. if the probability of spinning a 7 on the first
spinner alone is 1/4 what is the probability of getting a 7 on the second
spinner alone? Answered by Penny Nom. 





Bubbles trapped in the volumetric pipet 
20080131 

From Nursing: In determining the density of a liquid, a student left air bubbles trapped in the volumetric pipet. Did this give a density less than expected or greater than expected? Why? Answered by Penny Nom. 





Belledout pier 
20080128 

From Gina: I need to know how to find the total yards needed to fill a concrete pier that is 54"/ 108" and 26' deep.
That is...54" @ the top of the pier belled to 108" @ the bottom...26' deep. Answered by Stephen La Rocque. 





Pie graphs 
20080115 

From amarilis: explain why circle graphs are called pie graph or pie charts Answered by Stephen La Rocque. 





Pictographs 
20071211 

From eniyah: The title of my pictograph is Favorite pets. I have two columns. in my first column is the kind of pet and the second column is the numbers of students, the dogs have 16 student that like them and cats have ten students the likes them. each pictures equals 2 stodents my question is. i have to draw paictures to show the number of students for each row. the key says each symbol equals 2 students. since 16 divided by 2 is 8 can you show me how to make this in a graph Answered by Stephen La Rocque. 





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. 





A limit of the form 0 times infinity 
20071113 

From Russell: find the following limit
lim x((e^1/x) 1) as
x > infinity Answered by Penny Nom. 





Stopping distance and speed 
20071111 

From Joanna: The algebraic relation d=0.0056^2 ++ 0.14s models the relation between a vehicle's stopping distance d, in metres, and its speed s, in kilometres per hour.
(a) What is the fastest you could drive and still be able to stop within 80 m?
(b) What is the stopping distance for a car travelling at 120 km/h?
(c) Estimate the length of an average car. How many car lengths does the the stopping distance in (b) correspond to? Answered by Stephen La Rocque. 





l'Hospital's rule 
20071028 

From SWAPNA: Evaluate the following limit using L'Hospitals Rule
lim (sin x/x) ^ 1/(x^2)
x>0 Answered by Harley Weston. 





Surface area of an openended cone 
20071016 

From Lorne: What is the surface area of an open ended cone? Measured at 10' high,
16' diameter on the bottom and 2' diameter at the top. Answered by Stephen La Rocque. 





lim (1 2 cosx) / (sin(x pi/3)) 
20071015 

From hanan: lim (1 2 cosx) / (sin(x л/3)) Answered by Harley Weston. 





Roof trusses 
20071005 

From Mary: I need to know how algebra is used in making or designing of roof trusses for a house. I have to present a poster in class showing how algebra is used in daily jobs. My dad works at a truss company. Answered by Chris Langdon. 





Number of real solutions 
20071005 

From Sujith: The no of real solutions of the equations 1+x+x^2+x^3 = x^4+x^5 is ? Answered by Harley Weston. 





Liquid in a pipe 
20070905 

From christian: how many cubic feet are in a pipe that is 3" (inside diameter) and 459 feet long? Answered by Stephen la Rocque. 





The irrationality of PI 
20070807 

From Matthew: I have what I like to think of as a rather interesting question that I can't explain confidently for the life of me.
If we take a circle with a radius of 1 and we calculate the circumference, we can use 2 pi R.
Doing this calculation results in a circumference of 6.28318530717~ which goes on forever.
However, if you were to take a that same circle in the real world, say with radius 1cm and wrap a string around
it, and then measure the string, you don't get 6.28~, you get something like 6.2, a much more finite distance. The length
of the string is not an irrational number, like the math claims it to be. Answered by Claude Tardiff and Stephen La Rocque. 





Comparing flow rates of two pipes 
20070714 

From Kenneth: If two water pipes are 3 feet long, but one of them has a 1 foot diameter and the second has a 1 1/2 foot diameter, what simple mathematical method can be used to determine how much faster one pipe can drain water than the other pipe? Answered by Stephen La Rocque. 





Babylonian geometry 
20070617 

From marleen: The following problem and the solution were found on a Babylonian tablet dating from about 2600BC:
Problem:60 is the Circumference, 2 is the perpendicular, find the chord.
Solution:
Thou double 2 and get 4
Take 4 from 20, thou gettest 16
Square 16, thou gettest 256
Take 256 from 400, thou gettest 144
Whence the square root of 144, 12 is the chord.
Such is the procedure. Modern day mathematicians have reasoned that the Babylonian Mathematician who solved this problem assumed that the value of Pi is 3. By explaining in detail how the Babylonian Mathematician must have solved this problem, justify the reasoning of the modern mathematicians. Answered by Stephen La Rocque. 





Uses of pi 
20070508 

From Kari: How is pi used in real life? Answered by Penny Nom. 





What is the origin of pi? 
20070430 

From Aastha: from where has been tha value of "pi" derived? or what is the origin of "pi" Answered by Penny Nom. 





What is the Sales Tax? and Shipping? 
20070424 

From Mark: 1 Item $4020.44
1 Item $1749.86
1 Item $11455.62
Total 17,225.92
The sales tax and shipping is included in the total. The sales tax rate is 8.75%
What is the Sales Tax? and Shipping? Answered by Stephen La Rocque. 





Factor by grouping 
20070416 

From Vincent: How do you factor
the ( ) are exponents
4b4b(3)+ a(2)b  4a  ab(4)
I still don't understand if there is no a in 4b4b Answered by Penny Nom. 





Principia Mathematica 
20070412 

From victoria: i need help making a poster on emilie du chatelet a great mathematician can you describe
the newton principia because i know that she worked on it
thanks,
victoria Answered by Stephen La Rocque and Penny Nom. 





A pictograph 
20070314 

From Angie: I am confused! I have to include a title, labels, and a key: Here is the problem
Snickers 45
Kit Kats 65
Nerds 30
Kisses 50
Suckers 75
With the above information please help me make a candy pictograph
I would gladly like your help as my child is a second grader and can not tell me anything about a pictograph Answered by Penny Nom. 





What is pi? 
20070309 

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





What value of pi did the Indians use? 
20070306 

From gigi: What value of pi did the indians use? Answered by Penny Nom and Sara Ulmer. 





The grade 6 math curriculum 
20070224 

From Ajay: Do you have a list of topics a 6th grade students should learn in the 6th grade? I am "rusty" in math and would like to assist my son... Example: if an icetray has X cc of water and is split into 8 parts...what is the volume of each part...is this truly 6th grade level math? Answered by Pam Fowler and Penny Nom. 





Piecewise Functions 
20070209 

From Steph: h(x)={2 if x<0 {x+1 if 0< x <10 {1/2x+16 if x>10 PLEASE HELP Answered by Penny Nom. 





21 pigs and only 4 pig pens 
20070111 

From Emma: i was given this pig pen problem. if there are 21 pigs and only 4 pig pens how can you distribute the pigs into the pens and have an odd number of pigs in each pen. it doesn't seem possible to me. i need help! Answered by Haley Ess. 





How many gallons of water in 6600 feet of half inch pipe 
20070109 

From David: How many gallons of water in 6600 feet of half inch pipe Answered by Stephen La Rocque. 





Th pitch of a roof 
20061215 

From Rob: I am trying to determine how much to add for roof pitch. I guess the best way would be to use a right triangle as an example.
The base of the triangle is always 12 inches. The leg pointing straight up is a variable. I will say 6" in this example. By changing the variable how can i determine how much longer the hypotenuse than the base expressed in percent or decimal. Answered by Stephen La Rocque. 





Piecewise functions 
20061108 

From Kait: We discussed how to graph piecewise functions today and I'm very lost!! I'm sitting here staring at this problem that says: f(x){2x+1, if x <1 f(x){x+4, if x is greater than or equal to 1. Answered by Penny Nom. 





Piecewise functions 
20060924 

From Claudia: hi! i was just looking at a question by someone else about piecewise functions, but i still don't get it.
my problem is
g(x){x+2 if x <2}
g(x){2x  1 if x> or = 2} Answered by Penny Nom. 





How much water it will hold? 
20060920 

From Doug: I have thirty feet of piping that is two inches in diameter and I want to know how much water it will hold and the equation for solving the answer. Answered by Stephen La Rocque. 





If all of them work together, ... 
20060727 

From Kakron: Pipe A can fill in 20 mins and pipe B can fill in 30 mins and pipe C can empty the same in 40 mins. If all of them work together, find the time taken to fill the tank? Answered by Stephen La Rocque. 





Flipping a coin 
20060608 

From John: If a coin is flipped n times, where H is the number of heads after n flips, and T the number of tails, then will the quantity (HT) change signs infinitely often as n goes to infinity? Answered by Chris Fisher. 





Landscaping 
20060511 

From Luke: HOW MANY CUBIC YARDS OF CONCRETE WILL IT TAKE TO FILL UP A BOX 20FT.X20FT.X6IN DEEP?
HOW MANY CUBIC YARDS OF CONCRETE WILL IT TAKE; I HAVE A 12FT.IN DIAMETER POND AND I WANT TO PUT A 3FT.SIDEWALK AROUND THE OUTSIDE OF IT? Answered by Stephen La Rocque. 





Small pipes and large pipes 
20060509 

From geece: A large fresh water reservoir has two types of drainage system. Small pipes and large pipes. 6 large pipes, on their own, can drain the reservoir in 12 hours. 3 large pipes and 9 small pipes, at the same time, can drain the reservoir in 8 hours.
How long will 5 small pipes, on their own, take to drain the reservoir? Answered by Penny Nom. 





Cutting a piece of PVC pipe 
20060503 

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





The last slice of pizza 
20060427 

From Lori: I have a pizza. The radius is 10 inches long.The pizza was cut into 16 equal slices. When one slice was left, my sister and I both wanted it, so we agreed to cut it in half, but I like the crust more than she does, so we decided to cut it the "other way." In other words, the two pieces would not be symmetrical. The inside piece would contain all topping, and the outer piece would contain some topping and some crust.
How far up the radius from the center of the circle will I need to cut so we will both have an equal area of pizza? Answered by Stephen La Rocque. 





Marine shipping  fuel consumption 
20060426 

From Sandy: When a ship is 800 nautical miles from port its speed is reduced by 20%,
thereby reducing the daily fuel consumption by 42 tonnes and arriving in
port with 50 tonnes onboard. If the fuel consumption per hour is given
by the expression (0.136 + 0.001V^3) where V is speed in knots;
Estimate a) reduced consumption per day b) fuel onboard when speed reduced
c) normal consumption for 800 nautical mile voyage d) increase in steaming
time Answered by Stephen La Rocque. 





Which has more pizza? 
20060419 

From Kristine: Which has more area: a round pizza that is 16 inches in diameter or three square pieces of pizza that are 8.5 inches on each side? Answered by Stephen La Rocque. 





Overlapping area of two circles 
20060415 

From Jade: Given two identical circles where the radius (6 units) is the distance between the centers, what is the area of the overlapping region?
Answered by Stephen La Rocque. 





An epicycloid 
20060410 

From Sharon: What is the name of the curve formed by a point on the circumference of a circle that rolls on the outside of a fixed circle? This curve is used in the study of gears. Answered by Stephen La Rocque and Penny Nom. 





The cost of pizza 
20060328 

From Kristine: Use the formula for the area of a circle, A=3.14rsq, to determine which is a better deal: a 14in. pizza for $10.50 or a 16in. pizza for $11.95. Using 3.14 for pi Answered by Penny Nom. 





Piecewise functions 
20060321 

From Kris: First Problem:
Southeast Electric charges .09 cents per kilowatthour for the first 200 kWh.The company charges .11 cents per kilowatthour for all electrical usage in excess of 200 kWh. How many kilowatthours were used if a monthly electric bill was $57.06? The answer I came up with is 360, is that right? and also how do I set it up in an equation form?
Second Problem:
A construction worker earned $17 per hour for the first 40 hr of work and $25.50 per hour for work in excess of 40 hr. One week she earned $896.75. How much overtime did she work? I came up with 8.5 hrs overtime worked. Again I don't know how to set up the equation to come up with the answer.
I need some pointers on how to figure out story problems! If you have any suggestions that would help me out I would be very grateful. Answered by Penny Nom. 





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. 





The first six million digits of PI 
20060308 

From Lori: How many threes are there in the first six million digits of PI? Also how many nines? Answered by Stephen La Rocque. 





Related rates and an oil spill 
20060212 

From Brandon:
An Oil Tanker Spills 100,000 cubic meters of oil, which forms a slick that spreads on the water surface in a shape best modeled by a circular disc is increasing at a rate of 3m/min (it doesn't state what is increasing at 3m/min, so I'm assuming Radius until I can ask my teacher.) At t=T, the area of the "circular" slick reaches 100pi Sq. meters.
A) how fast is the area of the slick increasing at t=T
B)How fast is the thickness of the slick decreasing at t=T
C)Find the rate of change of the area of the slick with respect to the thickness at t=T.
Answered by Penny Nom. 





The diameter of a pipe 
20060127 

From An other:
I know the base length of my arc (10 inches)  I also know the height at the center to the arc (2 inches). I don't think the end is at the midpoint tho. How do I figure out how long the arc length is?
My question involves being able to cut a round pipe into an arc that is 10 inches wide and 2 inches tall. I need to know the smallest diameter pipe to buy in order to fulfill these requirements.
Answered by Penny Nom. 





A picture window 
20051114 

From Marcos: The length of a picture window is 2 feet longer than twice its width. If the diagonal of the window is 13 feet, find the dimensions of the window. Answered by Penny Nom. 





(x/1+x)^x 
20051023 

From A student: LIMIT x.>0 (x/1+x)^{x} how to solve it. Answered by Penny Nom. 





How many pixels are there to an inch? 
20051015 

From Fred: I want to know how many pixels there are to an inch. Answered by Penny. 





A 3dimensional pie shape 
20050917 

From Bill: Your site appeared in my search for the name of a 3dimensional pie shape. 2d would be a sector of a circle. As it it curved, I don't believe it is in a the polyhedra family. Can you help me find the mathematical term for it? Answered by Chris Fisher. 





I need to know the measurement of 75grams of spice into milliliters. 
20050916 

From Cyla: I don't know if this is possible but I need to know the measurement of 75grams of spice into milliliters. Even an approximation would be great. Answered by Penny Nom. 





A piecewise function 
20050915 

From Duncan: A child is assigned to your care and she has a headache. The parent has authorized the administration of Children's Tylenol. Read a box of Children's Tylenol (or any other similar drug) and find the directions for administration. Note the child's weight and the corresponding dosage. (Be sure the drug you choose has a minimum of 4 weight intervals.)
Answered by Penny Nom. 





Cows, chickens and pigs 
20050910 

From Markequetta: I was asked a question by a friend who refuses to give the right answer to a question that I answered wrong. So if you can help me that would be great! The level of my question is secondary I believe.
Question:
Cows cost: $10
Chickens cost: $0.50
Pigs cost: $3
You have to buy 100 animals and spend $100, so how many cows, chickens, and pigs do you have on your farm? Answered by Claude Tardif. 





L'hopital's rule 
20050515 

From Abraham: Find the limit of [(1/(x+4))(1/4)]/x as x approaches zero.
How do you use l"hopital's rule to find this limit. I know how to do it with multiplying everything by 4(x+4), and getting the answer, 1/16.But how do you apply derivatives with l'hopitals rule to this type of problem? Answered by Penny. 





How much sand is in a pile? 
20050416 

From Larry: I was wondering if there is a formula for determining how much sand would be in a pile. I am a student in medical school, and this is a bonus question for a test. I hope you can help me. Answered by Harley Weston. 





Two overlapping circles 
20050320 

From Safi: I have a problem to calculate the area of two overlapping circles because two circles are overlap then how i calculate the overlap area to subtract from the area of both circle. Answered by Penny Nom. 





If the mixture is 1 pint to 6 gal 
20050313 

From Trey: If the mixture is 1 pint to 6 gal. Do i use 4 pints to 24 gallons of gas Answered by Penny. 





21yd 2ft divided by 5=what? 
20050310 

From A student: 1gallon 3qt divided by 6= what?
21yd 2ft divided by 5=what? Answered by Penny Nom. 





1 pied linéaire 
20050218 

From Christiane: Pouvezvous m'indiquer 1 pied linéaire égale quoi? 3 pied....? Answered by Claude Tardif. 





A parallelepiped 
20040925 

From Aman: " If OA, OB, and OC are three edges of a parallelepiped where O is (0,0,0), A is (2,4,2), B is (3,6,1), and C is (4,0,1), find the coordinates of the other vertices of the parallelepiped.)" Answered by Penny Nom. 





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. 





f(x) = x4 if x<2 
20040921 

From Dani: Hi, my name is Dani. I'm in tenth grade Algebra 2, and I'm learning about a lot of different kinds of functions, and I can't quite seem to understand how every part of the piecewise function works. I understand most of it, I think, but I've been looking at an example in my math book, and I'm not sure how they got the answer they did. The part I don't understand reads: "Graph f(x) = x4 if x<2" and "Identify the domain and range." The picture in the book shows an open circle at (2,2), with an arrow going down and to the left with the slope being one. How did they get the open circle to be at (2,2), and why does the arrow point where it does? Answered by Penny Nom. 





Fabricating with pipe 
20040919 

From Gil: I need to fabricate a 10 section, 4" pipe circle with an inside diameter of 40". I would like to know what angles would apply and how to find them, Answered by Penny Nom. 





Pick a number greater than 1 
20040625 

From A student: I understand that when you pick a number greater than 1 and less than 10; multiply it by 7 and add 23, then add the digits of that number until you get a one digit number. Then multiply that number by 9, add the digits of that number until you get a one digit number, subtract 3 from that number and divide the difference by 3; that this process will always give you the result of 2. Does this have a name or theory for it as to why the answer will always be 2? Answered by Penny Nom. 





What is the name of a 3D rectangle? 
20040607 

From Jack: if a cube is a 3D square, what is the name of a 3D rectangle? 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. 





Pi 
20040510 

From Kim: I'm a 7th grader at Lakeside Middle School. And I was wondering if you can answer a question for me for my math project. I'm doing a project on pi, and my teacher said to ask an expert like you to ask about how you would use the subject, pi, in real life usage. How would you use pi in real life usage? Answered by Penny Nom. 





Water in a pipe 
20040425 

From Marlean: How much water would be in a 480 foot one inch inside diameter pipe?? In imperial gallons please. thanking you in advance for your help in this matter.
Answered by Penny Nom. 





Logarithms 
20040201 

From A student: Where did the word logarithmic come from? Where/whom did it originate? Answered by Harley Weston. 





Divisibility by 2 or 5 or both 
20031030 

From Abdu: How many positive integers less than 1,001 are divisible by either 2 or 5 or both? Answered by Penny Nom. 





The volume of an earthen pit 
20030912 

From Bruce: This shape would occur at the four corners of a rectangular shaped earthen pit with sloping sides (1:1.5). Depth is 14'. Top dimensions are 170' by 158'. After calculating the easy volume components of this shape, we are left with the end corner pieces. 21' base, 14' height, side hypotenuse 25.24' and corner diagonal 32.83'. We're confused. Thank you for any help you may provide. Answered by Penny Nom. 





Graphing a piecewise function 
20030824 

From Amber: How do i begin to graph a piecewise function, absolute function or step function? Answered by Penny Nom. 





Spacing the spindles for a railing 
20030606 

From Jennifer:
Scott is a homebuilder. He builds railings in which he places spindles. Spindles ar evertical posts taht are equally spaced beneath a horizontal bar. Scott would like a mathematical model to help him determine the amount of space to put between each spindle. The railing must follow the following criteria: The spaces between each spindle must be equal except for the ones at either end. Theses spaces are smaller. They are half the width of a spindle less than the other spaces. The number of spindles needs to be minimized since spindles are costly. Help Scott determine what width of space to use between the spindles. Create a mathematical model to determine the width of space between each spindle in termso f the number of spindles. Use an 8' (96") railing that has 2 1/2" wide spindles. Explain your thinking. For safety reasons the maximum width of a space is 4" Generalize you model to determine the width of spaces for total railing of length L and spindle width s Answered by Penny Nom. 





The volume of air flowing in windpipes 
20030502 

From James: The volume of air flowing in windpipes is given by V=kpR^{4}, where k is a constant, p is the pressure difference at each end, R is the radius. The radius will decrease with increased pressure, according to the formula: R_{o}  R = cp, where R_{o} is the windpipe radius when p=0 & c is a positive constant. R is restricted such that: 0 < 0.5*R_{o} < R < R_{o}, find the factor by which the radius of the windpipe contracts to give maximum flow? Answered by Penny Nom. 





Chopping trees 
20030419 

From Tamara:
The master needs some of the trees (twenty, to be exact) at the back of his spooky old mansion cleared to make way for a new evil laboratory, so he decides to send some his slaves to do the work for him. He initially sends out four of his men, armed with axes, to chop the trees down. Due to the fact he is very impatient, every ten minutes he sends out another man to help with the work. Assuming that it takes one man 30 minutes to chop down 1/3 of a tree, how long till all twenty trees are chopped down? Answered by Penny Nom. 





Divide a circle in 8 equal pieces 
20030404 

From Naomi: I have to divide a circle in 8 equal pieces but can only cut 3 times can you please help me Answered by Penny Nom. 





Friends and enemies 
20030324 

From Becky:
Consider a room that contains six people. Any two people are either friends of each other, or they are enemies. A. Argue why there are three people, all who are friends, or there are at least three people, all who are enemies
B. Rephrase the situation using graph terminology, using all of these terms correctly: vertex, edge, graph, complement, clique, independent set, and bipartite. Answered by Penny Nom. 





Cubic yards in a gravel pile 
20030110 

From Ron: I am looking to find a way to measure gravel piles to get yards. They are generaly not square.it would be like pouring sand out of a bag into a pile. they generaly are concave in dimension. can you help. I have attached a picture to show a small scale what I am working on is in much larger volume. Answered by Harley Weston. 





What really is pi? 
20020905 

From Rachel: what really is pi? 3.1444 Answered by Penny Nom. 





Addends can be grouped differently but the sum does not change 
20020903 

From Jodia: I have been searching the web for over an hour & a half now for the answer to the following question: The _____ states that addends can be grouped differently but the sum does not change. Answered by Penny Nom. 





The circumference of a 72 
20020814 

From Linda: What is the circumference of a 72" diameter circle? Answered by Penny Nom. 





A rope around a post 
20020715 

From Nic: My daughter who is in the 10th grade asked me this ?, you have a pole 45 inches high, 22inches around. You have a rope 1/2 thick, how many feet of rope would you use to go from top bottom of pole to top. Answered by Penny Nom. 





Pigs in pens 
20020710 

From Shannon: A farmer has 21 pigs and 4 pens, he must put an odd number of pigs in each pen, how does he do it? Answered by Penny Nom and Chris Fisher. 





Overlapping circles 
20020529 

From Naman: There are two circles, big circle with radius R and small one with radius r. They intersect and overlap in such a way that the common area formed is 1/2 pi r^{ 2} (half the area of the small circle) If r=1, find the Radius of the big circle (R)? Answered by Harley Weston. 





An Olympiad problem 
20020423 

From Aurora: I wrote a mathematical Olympiad the other day and there was one question that I could not work out. The question was If ab = 1, bc =2, cd =3, de =4 and ea = 6, what does a + b + c + d +e = It was a multiple choice and the answers were : 43/6; 47/6; 49/6; 53/6; 61/6 The correct answer was 61/6, but how can do you get to that answer? Answered by Anrei Volodin. 





A probability problem 
20020323 

From Kate: If I have a spinner and then spinner has the numbers 1,2,3,4 on it and it is spun 3 times, what is the probability that the spinner will stop on 4,3,and 1 ? In that order? Answered by Leeanne Boehm. 





Shipping charges 
20020219 

From Sohail: A mail order company charges a fixed fee for shipping merchandise that weighs 1 pound or less, plus an additional fee for each pound over 1 pound. If there shipping charge for 5 pounds is $4.80, and for 12 pounds is $6.20, find the fixed fee and the additional fee. Answered by Penny Nom. 





Diameter of a pipe 
20020216 

From Landry: I am trying to calculate the dia. of a pipe 60 inches long that will hold a gallon of water. What is the formula? Answered by Penny Nom. 





Zeta[2]=(Pi^{2})/6 
20020202 

From alex: Can you please tell me a proof that Zeta[2]=(Pi^{2})/6 Answered by Chris Fisher. 





Nickles, dimes, quarters and fifty cent pieces 
20020108 

From A parent: The total for all coins counted is $4,564.50 The last coin added to the pile is a 50 cent piece There are 8 times as many 50 cent pieces as there are quarters There are 6 times as many dimes as nickles How many of each are there? Answered by Penny Nom. 





Maple trees and pine trees 
20020106 

From A student: A team of scientists found that in a forest there was four maple trees for every nine pine trees.How many maple were there if they counted 45 more pine than maples? Answered by Penny Nom. 





2/3 vs 3/4 
20020102 

From Julia: So, here's my question. Some of the problems they've had to do starts off with two fractions, and they have to tell whether the two fractions are:  The first one is greater than the second one
 The first one is less than the second one, or
 They are equal.
One day my son had the problem of 2/3 vs 3/4. Without drawing out a pie chart, how in the world can a child "eyeball" a problem like this and tell what the correct answer is? I've also tried to teach about making common denominators, but that's going over his head at this point. Answered by Denis Hanson and Harley Weston. 





Piles of coins 
20011205 

From A student: Sharon has less than 20 coins. When she puts them in piles of 5, she has 1 left over. When she put them in piles of 3, she also has 1 left over. How many coins does Sharon have? Answered by Penny Nom. 





L'Hopital's Rule 
20011125 

From Mike: I'm a high school senior. I'm in ap calculus and was wondering if you know the proof of L'Hopital's Rule? Our teacher said he has never been able to find it in a math book and was unable to derive it himself. Answered by Claude Tardif. 





The "pi" of a circle in hyperbolic space 
20011119 

From Alex: How can you find the "pi" of a circle in hyperbolic space (or is it the same). I would like to know because our environment is hyperbolic and if the "pi" of hyperbolic space is irrational, it would follow that space is non discrete. I would greatly appreciate any help in this question. Answered by Walter Whiteley. 





Is the tree a pine tree? 
20011027 

From Kate: Suppose Stock Brokers tell the truth 2/5 of the time, and 1/3 of the trees in a given forest are Pine. If 4 Stock Brokers say that a certain tree in that forest is Pine, what is the probability that the tree is indeed a Pine tree? Answered by Penny Nom. 





The best of 7 
20010908 

From Michelle: Professional basketball, hockey, and baseball championships are decided on the best 4 out of 7 games. The first team to win four games wins the championship. In how many possible ways could the team win the championship series after winning the first game?
Example:
Game 1 2 3 4 5 6 7
Result W L L W W W
Answered by Leeanne Boehm. 





Sharing a donut 
20010906 

From Amanda: You have invited 11 people over to your house one day, and your friends are hungry. You go into the kitchen and find out you only have 1 donut (with a hole in the middle). In order to feed 12 people (including you), you must cut the donut into 12 pieces with only using a straight knife and cutting 3 times. This is NOT a trick question. Answered by Claude Tardif. 





e^pi > pi^e 
20010727 

From Dusty: What book(s) contain a proof that e^{Pi} > Pi^{e}? I think it might be in Problems in Analysis published by SpringerVerlag but I have not been able to check. Answered by Chris Fisher. 





Some irrational numbers 
20010703 

From Kellie:
 Is it possible to write pi as a fraction?
 Is it possible to write the square root of 2 as a fraction.. Explain why?
Answered by Harley Weston. 





Pi 
20010524 

From Mary: Where does the term pi come from and how many digits are actually in pi? Answered by Penny Nom. 





A pile of sand 
20010514 

From Gul:
 Sand for use on icy roads is stored in a conical pile 14.2 m high and with a base diameter of 34.4 m
 calculate the volume of the pile
 if one sander can take 6.9 m of sand, how many sanders can be filled from the pile?
Answered by Penny Nom. 





Typing a project 
20010501 

From Tom: Two students have to type a project. One can do it in 2 hours. It would take the other student three hours. They have 2 type writers. How fast can they finish by working simultaneously? Answered by Claude Tardif. 





Dots on squared paper 
20010330 

From Tom: Consider some squared paper with lines 1cm. apart and dots where the lines cross. Place squares whose sides are whole numbers of centimetres on the paper in such a way that the sides of the squares always lie along the lines on the paper. For each square, find (a)the number of points inside the squares; (b)the number of points on the square and (c)the area of the square. How are these quantities related? Answered by Leeanne Boehm and Penny Nom. 





Airflow in windpipes 
20010325 

From Ena: The volume of air flowing in windpipes is given by V=kpR^{4}, where k is a constant, p is the pressure difference at each end, R is the radius. The radius will decrease with increased pressure, according to the formula: Ro  R = cp, where Ro is the windpipe radius when p=0 & c is a positive constant. R is restricted such that: 0 < 0.5*Ro < R < Ro, find the factor by which the radius of the windpipe contracts to give maximum flow? Answered by Harley Weston. 





Factoring 
20010322 

From Kaleena: Factor this equation: 5x^{7}10x^{5}+4x^{3}8x Answered by Harley Weston. 





The nth place of pi 
20010227 

From Andrew: I have always wondered; is it possible to find the value of an irrational number, such as (phi) at it's nth decimal place??? You would plug the decimal place into the formula and the value would be given at the specified decimal place. When we look at the expression { (sqr 5 + 1)/2 } we are in a sense visualising the number in it's entirety, so the formula may include elements of the above expression in some form. Answered by Claude Tardif. 





A merchant from Pisa 
20010211 

From A student: A merchand doing business is Lucca doubled his money there and spent 12 denarii. On leaving, he went to Florence, where he also doubled his mone and spent 12 denarii. Returning home to Pisa, he there doubled his money and again spent 12 denarii, nothing remaining. How much did he have in the beginning? Answered by Claude Tardif. 





A limit using l'hopital's rule 
20001213 

From Wassim: I need to know how to solve the: limits of (x ( to the power lamda) 1 )/LAMDA when lamda tends to zero ( the answer is that the functional form is ln x) and I still don't know how using hopital rule leads to this answer. Answered by Harley Weston. 





Pizza delivery 
20001207 

From Meghan: 3 men give 10 dollars each to a pizza deliver driver and when he gets back to his work the manager says to the pizza driver the bill was actually 25 dollar so he has to returns 5 dollars. on his way to the mens house he the driver decides to kept 2 dollars for himself and he gives 1 dollar back to each of the men. So each one of the men actually paid 9 dollars. but 9 times 3 is 27 plus the other 2 that the driver took equals 29 so where did the other dollar go. Answered by Harley Weston. 





A 16 slice pizza 
20001130 

From A student: What is 5/8 of a 16 slice pizza? Answered by Penny Nom. 





A piecewise linear equation 
20001124 

From Jacky: There is a light bulb and it is given that the light bulb cost $0.75 and the cost of operating it is $0.0081 per hour. From the information give, I came up with the linear equation: Let c be total cost and Let h be hours used. Therefore: c = 0.0081h + 0.75 represents the total cost of the light bulb and the electricity. However, the second part of the question added the fact that the light bulb will only last for 800 hours. If the light bulb is replaced as soon as it burns out exactly after every 800 hours, how can I write an equation that represents that? Is it possible? What would it look like on the graph. Answered by Harley Weston. 





Pillows and Cushions 
20000927 

From Fiona:
The following problem was given to grade eleven algebra students as a homework assignment. To manufacture cushions and pillows, a firm uses two machines A and B. The time required on each machine is shown. Machine A is available for one full shift of 9.6 hours. Machine B is available for parts of two shifts for a total of 10.5 hours each day. Answered by Harley Weston. 





Six typists 
20000819 

From Paula Duncan: If it takes a typist 4.5 hours to type 860 words, how many hours would it take 6 typist to do 16800 words? Answered by Penny Nom. 





L'Hospital's Rule 
20000719 

From Dan Krymkowski: The limit of the following as x goes to infinity is 2*y. Y is a constant. lim 2*x*log(x/(xy)) = 2*y Answered by Harley Weston. 





Pi to 5 decimal places 
20000603 

From Emily: The question is find the value for pi to 5 decimal places???? Answered by Penny Nom. 





Two calculus problems 
20000501 

From Kaushal Shah: How Do WE Integrate the following Functions,  Integral xtanx dx
 How was natural base "e" discovered and why e=2.7.......
Answered by Claude Tardif. 





Pi 
20000222 

From Shelley Collier: Numbers that can be written in the form p/q where p and q are integers, (q not 0), are known as rational numbers. What you are missing is that p and q must be integers. The fact that Pi is irrational means that you can't have a circle with both the circumference and diameter being integers. In fact you can't even have the circumference and diameter both rational since the quotient of two rationals is again a rational. Answered by Claude Tardif and Penny Nom. 





Counting guppies 
20000126 

From Sarah Albaugh: Out of 200 fish, 99% are guppies. How many guppies must be removed to have 98% of the remaining fish to be guppies? Answered by Penny Nom. 





A roll of paper 
20000115 

From Richard: I have a roll of paper, wrapped around a corrugate core, whos diameter is 10.750 in. The outer diameter of the roll is approx. 60 in. The thickness of the paper is .014 in. I am trying to find out how much linear feet of paper is left on the roll, given only the diameter of paper remaining on the core. Answered by Chris Fisher and Harley Weston. 





Three dimensional rectangle 
20000111 

From Dennis Murphy: I would like to find out the name of a Three dimensional rectangle. Answered by Harley Weston. 





Advanced Calculus 
19991207 

From Kay: Hi, my name is Kay. Please helpthese problems are driving me crazzzzy!!!! Your help would be greatly appreciated!  Let a,b be contained in R, a
 .
. . Answered by Claude Tardif. 





A pictograph 
19991028 

From Ali: Please tell me how to make a pictograph.I am 2 grade student. Answered by Penny Nom. 





Cutting a board into 8 equal pieces 
19991021 

From Brittany: Jamie wanted a board cut into 8 equal pieces. The Lucas Lumber Co. charges 60 cents for cutting a board into 4 equal pieces. How much will it charge for cutting Jamie's board? Answered by Claude Tardif. 





Piecewise functions. 
19991020 

From Jenny: How do you figure out a piecewise function by hand? e.x. ( 2x (if x is not equal to 0) f(x)=< ( 0 (if x is not equal to 0) Answered by Harley Weston. 





l'Hospital's Rule 
19991018 

From Yannick Gigandet: How can I solve these two limits :  lim when n approches 1 of n[a^{1/n} 1]
 lim when x approches 0 of (e^{ax}  e^{bx}) / x
Thanks for the answer! Answered by Harley Weston. 





Six toothpicks 
19990914 

From Maddie: The book asks: Using 6 toothpicks represent the number 17. I am studying expressions to represent a number. ex.) (2+4)4x4=96. Answered by Penny Nom. 





Circles, cirmcuference and area 
19990516 

From Stephen Ehrler: I would appreciate if you could please tell me if what I discovered here is something or my ignorance? I noticed that a circle with r radii has the folling characteristic. r = [2 * ( pi * r^{2} / pi * 2r)] The equation states that the ratio of a circles area over its circumfrence = 1/2 that of the circles radii. It works every time. Did you know this ? Is it some kind of therom and can it be used for any thing? I thought this was intresting and would appreciate any input you may have. Thank you. Answered by Chris Fisher. 





Shopping at Wegman's 
19990422 

From Stan: Joanne, Steve, Pat, Alice, Joan, and Bill go to Wegman's at the same time. Joanne buys 2 gal of milk, 1 dozen oranges, 8 apples, and 2 lb. of ground beef, paying a total of $13.24. Steve buys 3 qts. of milk, 5 lbs. of ground beef, 10 lb. of potatoes, and 2 bags of mixed vegetables, paying a total of $16.95. Pat buys 3 gal. of milk, 2 dozen oranges, 1 dozen apples, 5 lb. of potatoes, and 5 bags of mixed vegetables, paying a total of $25.09. .... Find the cost of: 1 qt. of milk, one orange, one apple one lb. of ground beef, one lb. of potatoes, and one bag of mixed vegetables. Answered by Penny Nom. 





Pi/4 
19990404 

From Daniela Annarella: What is the 30th digit of pi(1/4) after the decimal point? Answered by Harley Weston. 





John Napier and e 
19990206 

From Shimin: I would like to ask about the exact definition of e, its history (like how John Napier came about discovering it) and its applications in problems and real life situations. Thank you! Answered by Chris Fisher. 





Math Olympics 
19990119 

From Kim Brandson: I am trying to put on a Math Olympics for K5 students in my district. Any ideas? Resources? Suggestions? Answered by Jack LeSage. 





Logs 
19981021 

From Benny: What does log means? How come we have to use log Answered by Chris Fisher. 





Rational and Irrational Numbers 
19980919 

From Ri: I am trying to explain rational & irrational numbers to my niece who is grade 7 and am having difficulties. Could you please explain the difference between rational & irrational numbers. Thank you Ri Answered by Penny Nom. 





Cutting a Pizza 
19980909 

From Woody: what is the greatest number of pieces of pizza you can form if you use five straight cuts to cut the pizza? answer given is 16. please draw a diagram of the answer. thanks, woody Answered by Penny Nom. 





Pi 
19971031 

From Ryan McKinnon: What Is Pi? Answered by Chris Fisher. 





A Question About Pi. 
19970708 

From Mike Chan: I have read the section Repeating Decimals in your data base. It mention that 1/17 has at most only 16 repeating digits. But, why does "pi" have an infinite number of digits (and not repeating ). Answered by Penny Nom. 





Triangles, The Pythagorean Theorem and Pizzas. 
19970223 

From Sherryle Mathis: I am a graduating senior presently teaching geometry as part of my student teaching. I will do my CUP on Right Triangles and Pythagorean theorem. I am looking for a fun activity as part of my unit plan. Answered by Walter Whiteley. 





Approximating pi. 
19961104 

From Ben Dixon: How do you calculate Pi? Do you have to somehow combine the equation for a circle with the formula for the circumference? Answered by Chris Fisher. 





e^(i*pi) = 1 
19960219 

From Matt Schneider: Why is e^(i*pi) = 1? Answered by Harley Weston. 





Combien de bonds auratil besoin 
20120410 

From zachary: Un lapin fait toujours un bond de 3m suivi d'un bond de 5m. S'il maintient ce rythme de combien de bonds auratil besoin pour franchir une distance de 584m ?? Answered by Claude Tardif. 





Une piscine 
20091104 

From kemayou: Dans un de ces problèmes,ma fille se trouve face à cette question,et je ne parviens pas à l'aider,pourriezvous nous donner un petit coup de pouce?
Voici l'énoncé:Un jardin a 22m de long et 8m de large.Au centre du jardin,on a fait construire une piscine dont le périmètre est de 44m.La surface restante est couverte de gazon.
La question est :exprimer en fonction de x la longueur de cette piscine.
Dans l'attente de votre réponse,recevez nos salutations distinguées.
Merci.Mme kemayou Answered by Claude Tardif. 





Un empilement de spheres 
20020416 

From Sébastien: Lorsque j'etais encore a l'universite je me souviens qu'un prof nous avez dit, sans le demontrer (ce n'est pas bien du tout de sa part) que l'espace minimal qui existe dans un empilement de spheres est de l'ordre de 26% Voici plusieurs jours que je cherche a resoudre ce probleme de geometrie, et je n'arrive meme pas a trouver comment l'aborder. Answered by Claude Tardif. 





Recherhce sur pi et exponentielle 
20010317 

From Cyril: étudiant a la fac de sciences de montpellier je cherche des informations concernant la demonstration suivante: "comment prouver que pi et exponentielle sont irrationnels?" Answered by Claude Tardif. 





Calculer la hauteur de chute de cette pierre 
20001216 

From Marcus: Une pierre tombe au fond d'un puit, à 5 secondes on entend un son (de la pierre). Calculer la hauteur de chute de cette pierre en tenant compte de la vitesse du son = 340m.s^{1} Il faut savoir que pour la chute libre v= g.t ; h = 1/2 g.t^{2} ; v = 2g.h g intensité du champs de pesanteur = 10 ; h hauteur de chute. Answered by Claude tardif. 





logarithme neperien 
19991110 

From Louise Kieffer: D'où provient la valeur e ( 2,7....) des logarithmes népériens ? Answered by Claude Tardif. 

