







One part in 10^x 
20190626 

From Jim: What is the meaning of the phrase ‘one part in 10x” where the x is an exponent? I have seen these examples: “...better than one part in 10x” and “...to within one part in 10x.” Answered by Penny Nom. 





Pennies, nickels, dimes, and quarters 
20190509 

From william: Ann has 177 coins (pennies, nickels, dimes, and quarters)
Her total value is $19.90
She has the same number of nickels as dimes.
She has the same number of quarters as dimes.
How many of each does she have? Answered by Penny Nom. 





Weighing stars and hearts 
20190225 

From Zach: Two stars and one heart weigh 38 units. One star and one heart weigh 27 units what is the weight of each? Answered by Penny Nom. 





Margin with commission as part of selling price 
20190213 

From Anni: I need to find selling price to put us at 24% margin.
15% commission is based on selling price and is included in our cost.
I'm trying to do it excel and keep getting a circular reference.
Total cost= cost + commission (15% of selling price)
Selling price=total cost + 24% margin Answered by Penny Nom. 





Converting decimals to common fractions 
20180508 

From Ruth: what does the 0 represent in .018 versus the decimal .180? As in, changing these to fractions? Thank you. 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. 





Nickels, dimes, and quarters 
20180420 

From Patti: A copy machine accepts nickels, dimes, and quarters. After 1 hour, there are 30 coins total, and their value is $5.10. How many nickels, quarters, and dimes are in the machine? (Hint: There are exactly five different solutions.) Answered by Penny Nom. 





A circle inscribed in a quarter circle 
20180416 

From abhijeet: ABC is a quarter circle and a smaller circle is inscribed in it. if AB = 1cm then find the radius of smaller circle 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. 





1/4 acre of land 
20180315 

From Jean: I have 1/4 acre of land.it is square.what should the measurement be for each side be in feet Answered by Penny Nom. 





Heat equation 
20171123 

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





Renting an electric cart 
20170107 

From Desiree: Vacation Rentals rents electric carts for travel on their grounds. The economy plan rents
carts for $26 per day and the premium plan rents a carts for $12 per day plus a one time fee of $126.05
For how many whole days would it be cheaper to rent from the economy plan then from the premium plan? 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. 





A road trip word problem 
20160410 

From Marc: While on a road trip I imagined this random word problem. Suppose I start a trip of 75 miles. My initial speed is 75 miles per hour. After every mile traveled I decrease my speed by one mile per hour. After the first mile I decrease my speed to 74 miles per hour and so on for each subsequent mile traveled. How long will it take to complete the 75 mile journey? Answered by Penny Nom. 





Compressed Earth blocks 
20160302 

From John: how many 14"x10"x4" blocks do I need for a 1300sq foot house 8 foot high 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. 





Prove the earth is round 
20160130 

From Kevin: Working on a project for a science fair.
To prove the earth is round without the ability to get way above the surface.
How could we set up and experiment to see the curve.
My thought is using a telescope at the beach?
Form what we see so far the curve is 8 inches per mile?
So thought is set up a telescope and a target 1 mile away? Answered by Robert Dawson and Chris Fisher. 





The perimeter of a one quarter acre square 
20160115 

From Kerry: If you have a perfect square that is one quarter of an acre what are the length of the sides and how do you arrive at the solution? thank you, Kerry. Answered by Penny Nom. 





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. 





Partitions into distinct parts 
20150919 

From Brian: Looking for a formula where I can type in a number, 17 for example, and using the numbers 1 through 17 (1, 2, 3, 4 etc....), to come up with all possible combinations, when added, that will equal 17. And each number can only be used once. I've tried a few search engines but my computer stares at me blankly and scratches its head :/. Answered by Chris Fisher. 





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 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. 





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. 





An arc subtended at the center of the Earth 
20140720 

From Abhinav: Meerut is 60 km from Delhi. Find the nearest second the angle subtended at the center of the earth by the arc joining these two points,earth being regarded as a sphere of 5940 km radius. Answered by Penny Nom. 





Quarters 
20140704 

From kamal: how many quarters in the sum of 8 and 12 ? 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. 





A model of the sun and the Earth 
20140614 

From Lynn: There is a model of the sun that is 2 1/2 inches in diameter. This is the only clue we have! How far away is the earth from this model? Answered by Penny Nom. 





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 cable around the Earth 
20140313 

From fikile: By how much must an equatorial cable be extended in order that it runs 1meter above the ground? Answered by Penny Nom. 





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. 





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. 





Restricted partitions 
20130325 

From vidya: I am having a series of numbers eg.( 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15)
I can take any 5 digits eg(15,10,8,6,5) and it should not repeat and the summation should be any predefined static value . eg(44)
That is (15+10+8+6+5=44) . How many summation series will result 44 ?
My problem is how to find this using a formula or any other simpler automation method is there instead of checking one by one all the combinations.
Plz do help me... Thnks in advance Answered by Chris Fisher. 





Cumulative Frequency Math Question 
20130320 

From Primadonna:
Hi,
Please help me solve this question.
Thank you so much.
The cumulative frequency table below shows the length of time that 30 students spent text messaging on a weekend.
Minutes Used 
Cumulative Frequency 
3140 
2 
3150 
5 
3160 
10 
3170 
19 
3180 
30 
Which 10minute interval contains the first quartile?
(1) 31–40
(2) 41–50
(3) 51–60
(4) 61–70 Answered by Penny Nom. 





Row echelon form 
20130315 

From Shawn: Please help me put matrix in row echelon form:
1 9 8 0
5 8 1 35
1 4 1 17 Answered by Penny Nom. 





A chart for y=mx+b 
20130311 

From jacinda: how to make a chart for y=mx+b Answered by Penny Nom. 





The zeros of a fourth degree polynomial 
20130123 

From Dakota: My problem has multiple steps and I have done everything but the last one. 8The original problem is f(x)=x^45x^3+7x^2+3x10 and I have to find the zeros of the equation. I used synthetic substitution like my teacher taught us to get the equation of x^33x^2+x+5=0 but now I don't know how to get the zeros of that equation, or solve it. Answered by Penny Nom. 





A bipartite graph 
20121029 

From A student: Suppose that G be a bipartite graph with maximum degree of k.
Prove that:
1)Exists a Kregular bipartite graph that G be subgraph it(H) Answered by Claude Tardif. 





A tank with an inner walled compartment 
20121012 

From don: I have a tank 20 feet diameter, 19' 8" tall with an inner walled compartment that has a 7' 6" radius arc with in the tank. I need to figure out the volume of the inner area and the volume of the larger area. Answered by Harley Weston. 





Points per quarter 
20120514 

From debbie: A basketball team scores 216 points in 8 quarters . Find the teams point per quarters rate 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. 





A circle inscribed in a quarter circle 
20120220 

From sonam: ABC is a quarter circle and a circle is inscribed in it and if AB=1cm than find radius of a small circle. 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. 





A quartic polynomial that is a perfect square 
20120205 

From archit: If P(x)=x^4+ax^3+bx^28x+1 is a perfect square then (a+b)=? Answered by Penny Nom. 





Two shapes 
20120106 

From muhammad: Question from muhammad, a student:
a boy has two pieces of wire each 99cm long .he bends them into the shapes shown below.calculate the radius of each figure,giving each answer to two decimal places.figures are one is semicircle and other on is half of the semicircle. Answered by Harley Weston. 





The perimeter of a quarter circle 
20111110 

From sierra: how do you figure the perimeter of a quarter circle that has a radius of 12 Answered by Penny Nom. 





Decartes' circle theorem 
20110907 

From Joseph: Given 3 circles of diameters 50, 55, and 60 units,
Place them externally tangent.
What is the diameter of the outer circumscribing circle,
tangent to all 3 circles? I can attach a pdf if this description is not clear.
Not urgent, this has nothing to do with current assignments,
just wondering if I have developed the best methods? Answered by Chris Fisher. 





A tangent to the earth 
20110903 

From Vickram: I have a math problem regarding tangent and circle. My example is as
follows: if a long flat ruler measuring 1500 miles is placed on top of earth
which has a radius of 3960 miles what part (length) of the tangential ruler
will actually be touching the earth and what two parts will not? Answered by Chris Fisher. 





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. 





The perimeter of a quarter circle 
20101215 

From kim: how do you figure the perimeter of a quarter circle that has a radius of 7 inches? I would like to have the explanation of how you figure it out. Thank you Answered by Penny Nom. 





The angles in an mgon and genrealizations 
20101016 

From Michael: Hello:
In answer to a student's question, someone named Penny from
your organization provided a proof that the sum of the interior
angles of a triangle in the plane is pi radians (or 180 degrees).
I am interested (and I'm sure many other people would be too) in
3 potential generalizations of this basic fact in plane geometry: Answered by Walter Whiteley. 





Area on a dart board 
20101011 

From Robert: A dart board consists of concentric circles and line segment. the radius of the bull's eye is 4 inches and each ring surrounding the bull's eye is 3 inches wide.
a) what is the area of the bull's eye
b) what percent is the bull's eye.
hint there are 4 rings and the bull's eye is divided into 4 (90) degree angles (meaning 1/2 up and down) (1/2 left to right. Answered by Stephen La Rocque. 





Factoring cubics and quartics 
20100929 

From Tori: How do you factor these types of questions:
* x^3  4x^2  x + 4
*2x^3  3x^2  4x  6
*x^4  15x^2  16 Answered by Robert Dawson. 





The volume of earth to be moved 
20100729 

From Michael: Volume of earth moved @ 500' across, 1 to 3 degree slope, 30' deep X 50' across at the bottom. Answered by Stephen La Rocque and Harley Weston. 





Curvature of the Earth 
20100529 

From grant: if you have 2 plumb structures 10ft. tall, how far apart will they be when they are 1 inch out of parallel at the top Answered by Tyler Wood. 





A quartic equation 
20100518 

From Austin: Z^410z^2=9 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. 





If a third is a fourth of a number, what is the number? 
20100408 

From larry: If a third is a fourth of a number, what is the number? Answered by Penny Nom. 





If the earth were covered completely with water 
20100225 

From don: If the earth were covered completely with water (over Everest) how many gallons would it be?? 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. 





Matt has 40 coins 
20091118 

From Amy: Matt has 40 coins(nickels, dimes, and quarters). The total amount is $4.05. He has 7
more nickels than dimes. How many quarters does he have? Answered by Penny Nom. 





The integral of sqrt(x) * ln(x) 
20091012 

From Oana: Hi! Can you tell me please how much is : ∫ (√x * ln x) ? Answered by Penny Nom. 





Dart teams 
20090918 

From Sally: I have 14 dart teams. Each team has a home bar.Usually it is one week home, the next week away. I have 3 locations that have one board only, yet have 2 teams at each location. I have one location that has 2 dart boards, and 3 teams. The last location have 3 dart boards and 4 teams.Can you make me a schedule that will be home and away, and every teams plays each other twice. In case you are wondering, the bars sponsor the teams.Thank you. Sally Answered by Robert Dawson. 





Helen has twice as many dimes as nickles. 
20090908 

From Dan: Helen has twice as many dimes as nickles. She has 5 more quarters than nickles. She has $4.75. How many nickles does she have? I know she has 14 dimes, 7 nickles and 12 quarters. How do you put this into an algebra equation? Answered by Stephen La Rocque. 





Nickels, dimes and quarters 
20090902 

From danielle: In changing a $5 bill, Sarah received nine more dimes than nickles and seven fewer quarters than dimes. How many coins of each type did she receive? Answered by Penny Nom. 





Fourth and fifth degree polynomials 
20090820 

From Evin: hello.i am a student . ax^4+bx^3+cx^2+dx+e=0 x=? i want to learn the solution or formula of equations of the fourth and fifth degree...PLEASE Answered by Robert Dawson. 





Nickels, dimes and quarters 
20090525 

From Amy: Coming from South Africa I find working with nickels, dimes and quarters confusing.
How many dimes are in a nickel and how many quarters are in a dime? Answered by Penny Nom. 





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. 





Fractional part 
20090401 

From Galina: What fractional part of eight is eight hundredths Answered by Stephen La Rocque. 





Partial derivatives 
20090117 

From Meghan: I have a question I've been working at for a while with maxima/minima of partial derivatives.
"Postal rules require that the length + girth of a package (dimensions x, y, l) cannot exceed 84 inches in order to be mailed.
Find the dimensions of the rectangular package of greatest volume that can be mailed.
(84 = length + girth = l + 2x + 2y)" Answered by Harley Weston. 





(a x b) intersect (b x a) 
20090108 

From sean: is it possible to have two sets such that
n((a X b) intersect (b X a) =3 Answered by Harley Weston. 





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. 





Partial variation 
20081103 

From Diamond: what are the 2 parts of partial variation? Answered by Penny Nom. 





Nickels, dimes and quarters 
20081027 

From val: I would like help working out a math word problem. A collection of 30 coins worth $5.50 consists of nickels, dimes, and quarters. There are twice as many dimes as nickels. How many quarters. Could you teach me how to find this formula? Answered by Penny Nom. 





Integration 
20081017 

From hazela: integration of
x sinx cosnx Answered by Harley Weston. 





Art and Integers 
20080917 

From pamela: how do artists use integers? Answered by Janice Cotcher. 





Cubic yards and quarts 
20080916 

From Mary: I need 2 yards of soil, how many quarts is this? Answered by Penny Nom. 





A string around the world 
20080818 

From Terry: I heard this on T.V. and was wondering if it was true. Place a string around
the world, you would need 25,000 miles of string. If you raised the string
off of the ground by 1 foot all the way around. How much more string
would you need? Answered by Penny Nom. 





The weight of a cubic yard of dirt 
20080721 

From Robert: I need to know how many pounds of dirt is in a cubic yard Answered by Penny Nom. 





How far away is the horizon? 
20080613 

From Ali: A plane is 10km above the earths surface, and you want to know how far away the horizon is, you know that the radius of the earth is about 6400km, how far away is the horizon along the earth's curved surface. My teacher has drawn a diagram; a circle representing the earth with one vertex at the center of the earth, another vertex outside the cirlce representing the plane (the distance between the earth and plane is 10km) and the last one is on the circle representing the horizon. Could you please explain how I would solve this problem, thanks! Answered by Penny Nom. 





Throwing a ball on the moon 
20080521 

From leria: equation for motion of moon is h=2.67t^2 + vt + s
equation for earth h=16t + vt + s
Suppose you are on an outpost on the moon and Jan is back on Earth. Both people toss a ball from a height of 96 feet with an initial velocity of 16 feet per second. How much longer will your ball stay in motion on the moon than Jan's on the earth?
Math Central,
I'm having a difficult time understanding which numbers to plug into the formula. Answered by Stephen La Rocque. 





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. 





Distance seen 
20080318 

From Nev: formule: Distance Seen
S = 1.225 x square root of H
S = Distance seen in Miles
H = Height in Feet
What dose 1.225 Relate To ? Answered by Stephen La Rocque. 





Integration by parts 
20080130 

From seth: hi i really dont understand integr
ation by parts. for example, the integral(t^2sintdt. i have u=t^2 and v'=sint also u'=t^/3 v=cost
for the formula i have uvintegralvu' dx this is all well and good but i cant get it right. Answered by Harley Weston. 





A large concrete shape 
20080116 

From Keith: what is the cubic yards of an area that is not a perfect 1/4 circle?
The dimensions are 100ft. x 60ft. x 125ft. curcumferal arch x 3ft. depth? Answered by Stephen La Rocque. 





Partial fractions 
20080106 

From taiwo: i copied the question below from john bird's higher engineering mathematics
fourth edition (pg 19) after solving all the partial fraction questions from the book
except this:
x^3 + 4^2 + 20x  7 over (x1)^2 (x^+8). i will appreciate it if you help me out so i can
know whether their answer is correct. thanks alot Answered by Harley Weston. 





Partitioning a clock face 
20071219 

From Kim: Using a clock with a regular circular faced dial, draw two straight lines such that the sum
of the numbers in each of the three areas is equal. Answered by The team at Math Central. 





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. 





Dividing a circle 
20071123 

From matt: hi. can you please send me a diagram of how to draw 3 lines in a circle to get 8 sections. Answered by Stephen La Rocque. 





Motion along a line 
20071002 

From Claudette: If the position function of a particle is x(t) = sin^2(2t), find the distance that the particle travels from t = 0 to t = 2 Answered by Harley Weston. 





Three circles 
20070929 

From Kevin: 3 given circles of R80, R56 & R24 are all in contact. The 2 smaller ones are inscribed in the big one.
Find by calculation or graphically (both if possible) the radiusof a 3rd circle which will be in contact with all 3 given circles. Answered by Chris Fisher. 





A place value chart 
20070912 

From glenwood: draw a million chart then place the following numbers in the proper place.
one hundred and nine million, seven hundred and twentythree Answered by Penny Nom. 





A problem concerning the medians of a triangle 
20070801 

From leeja: In a triangle ABC the sides BC and AC are given. It is also known that
the medians to these sides are perpendicular to each other. Calculate the
length of AB in terms of the other two given sides. Answered by Chris Fisher. 





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. 





Who was the mathematician that united algebra and geometry? 
20070508 

From Victor: who was the mathematician that united algebra and geometry Answered by Penny Nom. 





How many yards of soil is 55 quarts? 
20070320 

From Claudette: Costco sells bags of dirt in the quantity "55 quarts".. This makes no sense to me.
How many yards of soil is 55 quarts?
Thanks! Answered by Stephen La Rocque. 





Nickels, dimes and quarters 
20070318 

From Alexandra: Ellen has two more nickels than dimes and three more quarters than nickels. She has $3.35 in all. How many coins of each type does she have? Answered by Penny Nom. 





Nickels, dimes and quarters 
20070205 

From Avinash: Mary has 48 coins made up of nickels, dimes and quarters with a total value of $5.10. She has 4 more dimes than nickels and quarters combined. How many coins of each kind does she have? Use matrix to solve the system Answered by Stephen La Rocque. 





Integration 
20070202 

From Jenna: How do I integrate ( ln(x) ) / ( x^2 ) ? Answered by Penny Nom and Claude Tardif. 





Upper Quartiles 
20070126 

From Jamie: I see you have a question about Q3 with even numbers but what about odd numbers? I have a problem with 19 numbers 36,45,49,53,55,56,59,61,62,65,67,70,75,81,82,86,89,94,99. Is there anyway the answer could be 81.5 because every time I do it I get 82 and my teacher tells me that is wrong. So in conclusion how do you do it? Answered by Penny Nom. 





Word problem 
20061022 

From Sabrina: Thomas bought a badminton racquet and paid for it in quarters. If Thomas had used nickels and dimes, he would have needed 20 more dimes than quarters and one more than twice as many nickels as quarters. How much much did the badminton racquet cost? Answered by Stephen La Rocque. 





Plotting coordinates on a number plane 
20060908 

From Victor: I need to plot coordinates (0,2), (2,2), (2,0), and (0,0) on a number or coordinates plane, I am not sure how to do this, and get lost after the first point, can you please help? Answered by Penny Nom. 





Designing a garage 
20060608 

From A builder: I'm currently designing a garage and came upon this interesting math problem. I've tried using various methods to solve it but have so far been unsuccessful. I've included a picture as its far easier to show you my question than explain it verbally. I realize it could be done by trial and error but i'm looking for a real solution. Answered by Stephen La Rocque and Penny Nom. 





The distance to the moon from earth 
20060519 

From Maira: Using trigonometric functions first, show how to find the distance to the moon from earth and then find the radius of the moon. Answered by Stephen La Rocque. 





A triangle problem 
20060518 

From Jim: Right angle triangle with a hypotenuse of 20 units.
Square inside the triangle with sides of 4 units, the square shares two sides with both legs of the triangle, and the corner touches the hypotenuse limiting the triangles size. Answered by Penny Nom. 





Can one divide a circle into 4.5 parts 
20060330 

From Chris: If it is possible, can one divide a circle into say, 4.5 parts (with 4 equal parts and a half part)?
Or for that matter, for any integer, n, into n/2 parts as above?] Answered by Walter Whiteley. 





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. 





Quarts, liters cubic yards and soil 
20060319 

From Kathy: I am trying to find out how many quarts of dirt there are in a yard of dirt. The local flower store sells bags of dirt that are 20 quarts or 22 liters for $1.25 and another store sells a yard of dirt for $25.00. Which is the better deal? Answered by Penny Nom. 





What names are known for the quarter circle shape? 
20060306 

From Christina: What names are known for the quarter circle shape? Answered by Stephen La Rocque and Penny Nom. 





Outliers in a box and whisker plot 
20060219 

From A student: i need help on determining if their is an outlier...i know how to find the median and the lower quartile and the upper quartile..but i don't understand about the outliers....please tell me if their is an outlier in this problem....the numbers are...63,88,89,89,95,98,99,99,100,100 Answered by Penny Nom. 





Polar to Cartesian coordinates 
20060115 

From Linden: How do you convert six units at 30 degrees Polar Coordinate into a Cartesian Coordinate? Answered by Penny Nom. 





A sheet metal cone 
20051205 

From Laura: I am an art student and in the process of making a cone out of sheet metal. I am unable to work out the template I need to produce my final cone. The dimensions I have are that the final cone will be 58mm high and will have a diameter of 102mm. Answered by Penny Nom. 





Factoring quartics 
20051113 

From Kyle: How do I factor y^{4} + y^{2} +1?? I think the answer is (y^{2} + y + 1)(y^{2}  y + 1), but I'm not sure how to get that... Answered by Chris Fisher. 





The volume of the earth in gallons 
20050818 

From Daniel: I would like to know how to find the volume of the Earth in gallons. Answered by Penny Nom. 





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. 





Difference in latitude 
20050405 

From Gretel: Assuming the the earth is a sphere of radius 6378 kilometers, what is the difference in latitude of two cities, one of which is 400 kilometers due north of the other? 500 kilometers? Answered by Penny Nom. 





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. 





Perfecting an ideal gambling system 
20050306 

From Gaz: I am a screenwriter, currently in the fortunate position of having the development of a Screenplay funded by the South Australian Film Corporation. The (anti)hero of this screenplay is a statistician whose life is falling apart around him, thanks in part to his obsession with perfecting an "ideal" gambling system. Answered by Andrei Volodin. 





Stewart's Theorem 
20050117 

From Amy: In triangle ABC, AB=4, AC=6 and AD=5, where D is the midpoint of BC. Determine BC. Answered by Chris Fisher. 





Converting coordinates 
20041025 

From Allen: I am trying to help my son with his home, but I don't remember these conversions. Please help.
1. Convert the following coordinates
Cartesian x = 7, y = 24
2. Convert the following coordinates
Polar r = 4, theta = pi / 3 Answered by Penny Nom. 





A partial derivative 
20040319 

From Penny Nom: Is it possible to differentiate the following equation, if so could
you please explain.
S=SQRT(T(5/X^2))
I would like the derivative of S with respect to X. Answered by Harley Weston. 





How far can you see? 
20031215 

From Judy:
How far apart, assuming no obstacles, can two people stand and still see each other?
i know this deals with the curvature of earth, but i can't figure out the formulas involved.
Answered by Chris Fisher. 





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. 





Integrating e^x sin(x) 
20030503 

From Lech: I am having trouble integrating the following expression by parts: ex sin(x) I used the integrator at http://www.integrals.com/ to find the solution, ? 1/2 ex cos(x) + 1/2 ex sin(x). This is easy to confirm by differentiation, however I am confounded as how to arrive at the answer. Answered by Penny Nom and Claude Tardif. 





Hidden by the curvature of the Earth 
20030423 

From Shirley: There are 2 six foot men. What would the distance be between them before one could not be seen because of the curvature of the earth? Answered by Penny Nom. 





Two intersecting graphs 
20030423 

From Patty:
a) graph the equation x^{2}  y  4 = 0
x^{2} + y^{2} = 9 on the same set of coordinate axes. I did not have a problem with this. The problem is part (b) of the question ask: Find all solutions of the system in part (a) algebraically. Express answers in decimal form, accurate to two decimal places. Answered by Penny Nom. 





Wrap a rope around the equator 
20030212 

From Ali: If you take a rope and wrap it around the equator and then overlap it 6ft. and cut off the extra then you loosen it up so the ends meet how far would it stand off the ground? Answered by Penny Nom. 





A penny, a nickel, a dime, a quarter, and a loonie 
20030121 

From Blaine: I have 5 coins: a penny, a nickel, a dime, a quarter, and a loonie. How many different amounts of money could I pay using any combination of these coins? Answered by Penny Nom. 





Two problems 
20021014 

From Eva:
a) How many different equivalence relations can be defined on the set X={a,b,c,d}? b)Show that 6 divides the product of any 3 consecutive integers. I know it is true that 6 divides the product of any 3 consecutive integers. However, i have problem showing the proof. Answered by Leeanne Boehm and Penny Nom. 





The entire earths' population would fit in the state of Texas 
20020918 

From Roz: I have been told that the entire earths' population would fit in the state of Texas and each person would have 1/2 acre. Is this true. Answered by Chris Fisher. 





Ratios and weights on Neptune 
20020603 

From Janice: The ratio of an object's weight on earth to it's weight on Neptune is 5:7. How much would a person who weighs 150 pounds on earth weigh on Neptune. Answered by Penny Nom. 





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. 





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. 





Box and Whisker plots 
20011119 

From Rod: In our Prealgebra course, we have been studying Box and Whisker plots. Recently, we learned how to decide whether a data point is an outlier or not. The book (Math Thematics, McDougall Littell) gave a process by which we find the interquartile range, then multiply by 1.5. We add this number to the upper quartile, and any points above this are considered to be outliers. We also subtract the number from the lower quartile for the same effect. My question: where does this 1.5 originate? Is this the standard for locating outliers, or can we choose any number (that seems reasonable, like 2 or 1.8 for example) to multiply with the Interquartile range? If it is a standard, were outliers simply defined via this process, or did statisticians use empirical evidence to suggest that 1.5 is somehow optimal for deciding whether data points are valid or not? Answered by Penny Nom. 





A 3 dimensional 5 pointed star 
20011108 

From Kent: I am looking for a formula that will give me a layout for a 3 dimensional 5 pointed star. I want to form it out of sheet metal, using 5 polygons and soldering them at the apex. Can you please help me with this? I would like to be able to give the formula the height of the star from the bottom two points to the top point and also how deep the star is. Thank you very much! Answered by Judi McDonald. 





Dividing a circle 
20011017 

From Ahmeen: I am having a hard time figuring out how a circle can be divided into 11 equal parts with only 4 cut allowed? My teacher gave this to us and I still can't cut my pie into eleven equal parts with only four cuts. Answered by Walter Whiteley. 





When will the ship disappear? 
20011010 

From Stacy: If the sail of a ship were a 100 ft. tall and you were a mouse at the edge of the shore looking out at it, how far out would the ship be when it disappears? ( your eye level is level with the water.) Answered by Harley Weston. 





The 100 chart 
20010928 

From Nich: Am I suppose to use the 100 chart for these questions. Question One: I am a 2 digit number my tens digit is 2 more than my one digit my 1 digit is between 4 & 6. What # am I ? Question Two: I am a 2 digit # I am greater than 40 but less than 60 my tens and ones digits are the same I am a odd number what am I ? Answered by Penny Nom. 





Counterclockwise 
20010914 

From Rolanda: When Descartes invented the coordinate system he decided to number them counterclockwise. Why? Answered by Chris Fisher. 





Earthquake warning 
20010903 

From Dillon: In the city of Skangai there are 6 million people.Each person has to tell 2 more people that theres going to be an earthquake. After they do they leave the city. There will be no duplications.It takes 3 minutes to tell each person. How long will it take for the whole city to know about the earthquake? Answered by Penny Nom. 





Integration by parts 
20010409 

From A student: how do you integrate x tan^{1}x dx, i know it can be done by integration by parts maybe, but i'm not sure.... Answered by Claude Tardif and Harley Weston. 





Two integrals 
20010403 

From Jim: I'm having trouble with these integrals. Can you help me out? 1)the integral of:
x^{5} arctan x dx 2)the integral of:
2x^{5} + 9x^{4} + 19x^{3} + 13x^{2}  5x  25  dx x^{4} + 4x^{3} + 5x^{2} Answered by Claude Tardif. 





A quartic equation 
20010215 

From George: Let P(x) = x^{4} + ax^{3} + bx^{2} + cx + d. The graph of y = P(x) is symmetric with respect to the yaxis, has a relative max. at (0,1) and has an absolute min. at (q, 3) a) determine the values for a, b c, and d using these values, write an equation for P(x) b) find all possible values for q. Answered by Harley Weston. 





Part of a part 
20010211 

From Katie: Hello! I was looking at your Fraction questions and since i am pursuing to be an elementry school teacher i feel i don't understand one of your responses. How would you explain this to an elem, midd, and high school student. Even me myselfin college really does not understand. The question was: When you multiply two positive fractions less than 1, how does the answer compare to the size of the fraction? Why? Answered by Penny Nom. 





Place value chart 
20010111 

From Charles: Can you send me a pictorial example of a place value chart? Answered by Harley Weston. 





A dollar, quarter, dime, nickle and penny 
20010107 

From Sarah: Arnold has a dollar coin, one dime, one quarter, one nickel, and a penny. The number of different sums of money that can be formed using three coins is... Answered by Penny Nom. 





A quartercircle and two semicircles 
20001231 

From Christopher: Inside the quartercircle are two semicircles with the same radius, (r). Which has a greater area, G or L? Answered by Penny Nom. 





A cycloid in Cartesian form 
20000920 

From Billy: The parametric equation of cycloid is given: x=r(tsint) y=r(1cost) How to eliminate t? Answered by Harley Weston. 





Buying art supplies 
20000918 

From Travis: An art teacher buys exactly 100 items at this sale, and the total cost before tax is $100. She buys at least one of each item. How many of each item does she buy? Markers $0.50 Sketch Pads $3.00 Paint Sets $10.00 Answered by Denis Hanson. 





Uniting algebra and geometry 
20000416 

From Beth: Who is the mathmatician that united algebra and geometry??? Answered by Claude Tardif. 





All the roots of x^6  64 
20000415 

From Dakota: Find ALL zeros of P(x) = x^{ 6}  64 Answered by Walter Whiteley. 





Congruent parts of congruent figures 
20000310 

From Erica: Yesterday, I recieved a test problem asking to prove two line segments equal. Here is the problem as I was given it: Given: paralleogram ABCD AE is perpendicular to DB CF is perpendicular to DB Prove: AE is equal to CF I answered the problem as follows: . . . Answered by Walter Whiteley. 





Party favors 
20000222 

From Krystina Fernandez: Luanne was making party favors for her little sister's birthday party. Each party favor was in the shape of a cube. Luanne had pink and purple paint to paint the cubes and she could paint each face only solid pink or solid purple (no dots,stripes,ect.).For example, one cube may be all purple, another may have two purple faces and four pink faces. Her little sister wanted to have a different cube for each guest.(A cube is not considered different if it can be turned so that all it's sides match the corresponding sides of another cube.)How many different cubes was it possible for Luanne to make? Answered by Claude Tardif. 





A valentines project 
20000221 

From Courtney Dohoney: I was assigned a valentines project. Our job is to make a valentines card that has a math theme. On my valentines card I would like to include the set of equations that when graphed look like a heart. If you can figure out a set of equations and get it back to me I would be very happy. Answered by Harley Weston. 





Mass of the earth 
20000221 

From Terry Broughton: My name is terry i am 15 my question is how much does our planet earth weigh ? Answered by Chris Fisher and Harley Weston. 





How wide is the well? 
19991124 

From Chris Baranski: There is a well and in the well there are 2 sticks one is 2 meters long the other is 3 meters long and they are opposite to each other. They are leaning against the wall of the well. The place where they touch is 1 meter of the bottom of the well. How wide is the well? Answered by Chris Fisher. 





Rolling Circles 
19990912 

From Craig Ellis: We have a circle of radius 3. inside the circle and tangent to the circle of radius 3 at one point is a circleof radius 1. The question is if we could roll the smaller circle around the inside of the larger circle how many revolutions would it take to get around to where we started. Answered by Chris Fisher and Walter Whiteley. 





A ladder problem 
19990422 

From Michael Blade: There is a cube box 3feet x 3feet x 3ft resting against a vertical wall on level ground. Resting against the outside corner of the box is a ladder 10 feet tall, this ladder is of course resting on the ground but also against the outside corner of the box and rests on the wall. The question the ladder is divided into two unequal section bounded by the box to the ground and the box to the wall. what are those dimensions? Answered by Penny Nom. 





Calculus problems 
19980713 

From Lorraine: I'm stuck again. Can you help? This involves integration using the method of partial fractions the integral of: 7x(to the 5th)  2x(cubed) + 3 dx  x(to the fourth)  81 Do I have to do long division to reduce the numerator to the fourth power? the integral of: 4 16x +21x(squared) + 6x(cubed)  3x(fourth) dx  x(cubed)(x  2)(squared) Lorraine Answered by Harley Weston. 





Curvature of the Earth 
19980316 

From Robert Dyck: How can I find the curvature per mile of the earths surface? What is it? Answered by Harley Weston. 





The Earth's Arc 
19980206 

From Robert Dyck: How do I find the arc/mile of the earths surface? What is the arc? Answered by Harley Weston. 





Cos(x) Cos(2x) Cos(4x)=1/8 
19970924 

From Tan Wang: How many distinct acute angles x are there for which cosx cos2x cos4x=1/8? Answered by Chris Fisher Harley Weston and Haragauri Gupta. 





Les dérivées partielles 
20120516 

From Haddouche: Bonjour,
Je vous demande de bien vouloir m'éclaircir comment on calcule les dérivées partielles généralement étudiées dans les modèles de la concurrence fiscale à titre d'exemple celui de Wildasin ""NASH EQUILIBRIA IN MODELS OF TAX COMPETITION "", dont j'ai essayé toutes les méthodes et aucune d'elle n'est arrivée à trouver le résultat des dérivées de ce dérnier papier, à cet effet, je vous serais reconnaissant de m'éclaicir la méthode afin de résoudre ce problème qui pour moi un vrai mistère à percer.
Je vous remercie infiniment à l'avance.
Et comptant sur votre compréhension, mes salutations les meilleures.
HA Answered by Claude Tardif. 





le prix de départ 
20060910 

From un élève: Une jupe coûte 36 euros après une démarque de 20% quel est le prix de départ moi j'ai trouvé 45 euros mais je n'ai pas la formule de calcul exacte Answered by Claude Tardif. 





Partages inégaux 
20050929 

From Un eleve: Alex et julie ont ensemble 4728 . euro Si Alex donne 538. euro à Julie, ce dernier aurait alors le triple de Julie. Quelle est la somme possédée de chacun? Answered by Claude Tardif. 





Marie achète un croissant et une tartelette 
20040201 

From M. et Mme Simoneton: Marie achète un croissant et une tartelette. Elle paie 1,64 €
Isabelle achète un croissant et un pain au chocolat. Elle paie 1,51 €
Marc achète un poain au chocolat et une tartelette. Elle paie 1,77 €
Trouver le prix d'un croissant, d'une tartelette et d'un pain au chocolat.
Answered by Claude Tardif. 





l'équation d'une rotation dans un graphique cartésien 
20011114 

From Ghaith: je d6sir que vous me rafraichissez un peu la mémoire s.v.p. j'aimerai savoir l'équation d'une rotation dans un graphique cartésien merci Answered by Claude Tardif. 





Point de partage 
20000221 

From Sebastian Murciano: J'aurais besoin de savoir où je peux trouver de l'informations, ou estce que vous pouvez me donner de l'information sur : Point de partage d'un segment étudié en Secondaire 4. Answered by Claude Tardif. 





Derivées partielle 
19991019 

From Arnaud Flandin: Quel est la definition des derivées partielle Answered by Claude Tardif. 

