







(2018^2019)(2019^2018) 
20190123 

From Nazrul: Find the remainder when (2018^2019)(2019^2018) is divided by 4? Please show me the process. Answered by Harley Weston. 





7 spheres on a hexagonal tray 
20190114 

From herm: what is the length of each side of a hexagonal tray, with the height of each side 0.75 inch, to hold seven spheres, each with a diameter of 3.00 inches? The spheres are placed such that each side of the hexagon is touched by one sphere at its midpoint (and the seventh sphere is place in the center of the "ring" of the other six spheres. Answered by Harley Weston. 





A binomial expansion 
20190105 

From shifali: if the binomial expansion of (mnx)^3 is 1+9x+ find the values of m & n Answered by Penny Nom. 





A rope fom a dock to a boat 
20180314 

From Tracey: A boat is tied with a rope to a dock that is 16 feet tall. Along, the water, the water the boat is 17 feet from the dock. How long is the rope connecting the boat to the dock? Let c represent the length of the rope.? Answered by Penny Nom. 





Positive and negative values of a function 
20180130 

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





How far is the boat from the harbour? 
20161006 

From Karabo: a boat sails 30 km due east from a harbour. Then it sails 40 km due north. How far is it from the harbour? Answered by Penny Nom. 





The remainder theorem 
20161004 

From A student: need help with this
f(x)=4x^415x^24; x2
using the remainder theorem to find the remainder Answered by Harley Weston. 





Lisa went for a run 
20160714 

From Olive: Lisa ran 3km north and then 4 km east what was her total distance Answered by Penny Nom. 





A puzzle embedded in a table top 
20160513 

From Aaron: I want to make a table with a puzzle embedded in it. The table top would be a
36" circle and the puzzle is 20"x27" I'm thinking that it's not going to fit,
but not sure. Any help would be appreciated.
Thanks,
Aaron Answered by Penny Nom. 





The diagonal of a 10 acre square 
20160411 

From Derrick: I own 100 acre square of land. I want to run from farthest corner of property to farthest corner, Diagonally. How many miles would I have traveled? Answered by Penny Nom. 





The remainder theorem 
20160327 

From Pratyasha: A quadratic polynomial when divide by x+2 leaves a remainder of 1 and when divided by x1 leaves a remainder of 4. What will be the remainder if it is divided by (x+2)(x1)? Answered by Penny Nom. 





A limit of a rational function 
20160116 

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





An isosceles right triangle 
20150517 

From Ari: In a 454590 triangle find the ratio of a leg to the hypotenuse Answered by Penny Nom. 





The Pythagorean Theorem 
20140330 

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





A scalene triangle 
20140107 

From cherry: Hi
I have been given a scalene triangle of sides 
8m, 6m, and 10m ..
Please help me to find out the area and help me to find out the height .. Answered by Penny Nom. 





The area of a quadrilateral 
20131221 

From khushboo: Find the area of quadrilateral pqrs in which
angle QPS=90°,PQ=12cm, PS=9cm, QR=8cm and SR=17cm.
(Hint: PQRS has two parts) 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. 





Two polynomials are divisible by x  2 
20121226 

From Tehmas: Determine the values of m and n so that the polynomials 2x^3+mx^2+nx3 and x^33mx^2+2nx+4 are both divisible by x2. Answered by Penny Nom. 





The height of a triangle 
20121017 

From Brian: the base of my triangle is 12 metres and the two sides are 8.45 metres
can you help me find the height of the triangle Answered by Penny Nom. 





A multinomial theorem 
20120608 

From Anuj: if (1+x+xsquare) whole raise to 20 is a0 + a1x + ........ + a20xraise to 40, then find a0 + a2 + a4 + .......... + a38.
How do you solve this??????? Answered by Robert Dawson. 





A cubic inequality 
20120325 

From Victoria: The flight path of a bumblebee above the ground can be modelled by the function f(x)= 2x^3 17x^2+ 11x + 130. Where x is the time in seconds and f(x) represents the height in inches above the ground. The entrance to the bee's hive is located 100 inches above the ground. Determine when the bumblebee's height is greater than 100 inches. The bee's height was monitored from 0 to 25 seconds inclusive. (over the domain 0 Answered by Penny Nom. 





The remainder theorem 
20120325 

From Victoria: When k^2 + 3kx + 13k +k^2x  3x^2 is divided by (x4) the remainder is 22. Find the value(s) of K. Answered by Penny Nom. 





A circle and a chord 
20120211 

From Sophia: The diagram shows a circle with a chord that is 10cm long. The middle of the chord is 12cm from the centre of the circle. Calculate the radius.
Chord length is 10cm.
The distance from the centre to chord is 12 cm. 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. 





The perimeter of a figure 
20110427 

From syed: Hello I'm Syed from Bangladesh.
Please help me out! It is killing me.
The question is=2C find the perimeter of the figure. I can't find the perimeter.
I am enclosing the figure as an attachment. Answered by Penny Nom. 





A right angled triangle 
20110422 

From jeremy: Solve the right triangle with the given sides and angles. a=3.0 cm and b=1.6 cm Answered by Penny Nom. 





How far is it from the control tower? 
20110411 

From Varun: An aircraft is vertically above a point which is 10 kms west and 5 kms north of a control tower. if the aircraft is 4000 mts above the ground,how far is it from the control tower? Answered by Penny Nom. 





The development of the Pythagorean theorem 
20110408 

From Ataa: I am doing a assignment on Pythagorean Theorem and i am stuck on the subquestion
development of the Pythagorean theorem and i really need help can u give me accurate info
for this because i am not finding anything!!!thanks in advance.
Yours truly
AUMAKHAN Answered by Chris Fisher. 





A circle in a square in a circle in a square 
20110329 

From George: A circle within a square which is inside
a larger circle which is also within a square.
(a circle in a square inside a circle in a square)
Equation of the smaller circle is: x ^ 2 x y ^ 2 = 25.
What are the dimensions of the larger square?
Been 40 years, trying to help my son. Answered by Penny Nom. 





Calibrating a conical tank 
20110205 

From Bill: Hi, I have a round tank with tapered sides where I know the diameter at the top and bottom. Is there a formula I can use to calculate the volume by measuring from the bottom up the side (at the angle of the side) to any given point? Thanks, Bill Answered by Stephen La Rocque and Penny Nom. 





Points with distance 5 from the point (2, 1) 
20110119 

From Alexa: Find all points having a xcoordinate of 2 whose distance from the point (2, 1) is 5. Answered by Penny Nom. 





Semicircles and the Pythagorean Theorem 
20110109 

From Jas: Okay well, in math we are learning about the pythagorean theorem and we have to do a math journal on the question:
****Can you replace the squares (that are put on the sides of a right triangle) with semicircles and still get the same answer??
I do not understand because i tried doing an example and comparing it with a normal way of doing it and I didnt get the same answer! Answered by Penny Nom. 





A polynomial remainder 
20101225 

From Asterdine: When a polynomial f(x) is divided by x+1 and x+2, the remainders are 3 and 7 respectively. Find the remainder when f(x) is divided by (x+2)(x+1). Answered by Penny Nom. 





Two chords in a circle 
20101202 

From girma: one chord of a circle is 8cm long and it's distance from the center is 4cm long.what will be the length of another chord, of the same circle ,which is 2cm from the center Answered by Penny Nom. 





A man made circular lake 
20101125 

From ailish: A man made circular lake has a diameter of 338 m. A bridge is to be constructed across the lake in such a way that it is 119 m away from the center of the lake. How long is the bridge? Answered by Penny Nom. 





The equation of a circle 
20101020 

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





The 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. 





A truck goes south and then east 
20100826 

From MARK: A truck starts at point A and drives South 3 miles. Then it turns left at Point B and drives east four miles to point C. How many miles is the truck at point C from point A if it were to drive directly from point A to Point C.My book says the answer is 5 miles. How did they come up with the answer? Answered by Robert Dawson. 





Two overlapping circles 
20100804 

From Husen: two circles of radius 5 cm intersect each other .the distance between their centers is 5root 2.find the area of the portion common to the two circles Answered by Penny Nom. 





Remainders 
20100717 

From GARY: WHAT NUMBER DIVIDED BY 11 LEAVES 1, DIVIDED BY 13 LEAVES 8, AND DIVIDED BY 17 LEAVES 3. Answered by Chris Fisher. 





The equation of a circle 
20100623 

From Michelle: Write and equation for the circle with a center, (0,0) and a diameter of 12 Answered by Penny Nom. 





The height of a triangle 
20100621 

From Taylor: how do i find the height of a triangle with a base of 3 and a side of 5 the book says 4 but i cant get that Answered by Penny Nom. 





A square inscribed in a circle 
20100525 

From Middle: what is the perimeter of a square inscribed in a circle of radius 5.0 inches? Answered by Penny Nom. 





The hypotenuse of a triangle 
20100522 

From linda: find the length of the hypotenuse of a triangle with legs of 12in. and 17in. round to the nearest hundredth Answered by Tyler Wood. 





How far is the runner from the starting point? 
20100522 

From Richard: A marathon runner runs 6 miles south and then 8 miles east. How far is the runner from the starting point? Answered by Tyler Wood. 





How far am I from the starting point? 
20100518 

From jilayna: if i walk 5 miles north, 7 miles east, and 3 miles north again.to the nearest tenth of a mile ,how far,in a straight line, am i from my starting point Answered by Penny Nom. 





Rational root theorem 
20100414 

From deciree: How could i get the value of x with this equation:
1/13x^3+12x/13=1/2
Thank you! Answered by Harley Weston. 





A ladder against a wall 
20100325 

From amber: the distance from the bottom of the ladder to the building is18 foot less than the length of the ladder.How high up the building is the top of the ladder if that distance is 1 ft less than the length of the ladder? Answered by Penny Nom. 





The hypotenuse 
20100227 

From Dannielle: how do you find the hypotenuse if a=8 and b=6? Answered by Penny Nom. 





A 25 foot ladder reaches a window 20 feet high 
20100227 

From Tanner: a 25 foot ladder reaches a window 20 feet high. how far is the ladder from the building? how far must the foot of the ladder be moved to lower the top of the ladder by four feet? Answered by Tyler Wood. 





The center of a rectangular room 
20100216 

From Diana: Consider a rectangular room, 15 feet wide, 30 feet long and 12 feet high. What is the exact distance from any of the 8 corners of the room and its geometric center? Can you write a generic formula for such a distance? And if we keep the same proportions on all dimensions, can you write an expression for the same distance as a function of the floor perimeter? Answered by Penny Nom. 





The binomial theorem 
20100121 

From Laura: Using the fact that (1 + x)^4 * (1 + x)^9 = (1 + x)^13 show (4C0 * 9C4 + 4C1*9C3 + 4C2*9C2 + 4C3*9C1 + 4C4*9C0) = 13C4 Answered by Harley Weston. 





Loading a headboard in a uhaul 
20100120 

From gina: I have a uhaul 9'10" long 4"9"wide 4'7"height I have a headboard 74 inches in height would it fit the box diagonally Answered by Penny Nom. 





How high up the building does the ladder reach? 
20100119 

From rosenda: A 10 meter ladder is 6 meter from the base of a building. How high up the building does the ladder reach? Answered by Robert Dawson. 





Related Rates Problem 
20100112 

From Neven: A woman raises a bucket of cement to a platform 40 ft
above her head by means of a rope 80 ft long that passes
over a pulley on the platform. If she holds her end of
the rope firmly at head level and walks away at 5ft/s,
how fast is the bucket rising when she is 30 ft away
from the spot directly below the pulley?
(G. F. Simmons, Calculus with Analytic Geometry, pg.142) Answered by Penny Nom. 





(x+3) is a factor of 2x^33x^2+px+30 
20100109 

From Ruby: (x+3) is a factor of 2x^33x^2+px+30.
Determine the value of p Answered by Penny Nom. 





A quilt square 
20100107 

From Kimi: A quilt square is stitched along each diagonal to make 4 right triangles.
Each diagonal is 12 inches long. ( 1 foot)
How many quilt squares can be cut from a piece of fabric that is 8 feet
long and 2 feet wide?? Answered by Penny Nom. 





A rightangled triangle 
20091002 

From Hunter: The three sides of a rightangled triangle measure x1, x+6, and 2x+1 in length.
What are the possible lengths of the hypotenuse? Answered by Penny Nom and Melanie Tyrer. 





A ladder leaning against a wall 
20090908 

From Mackenzie: A 7 foot long ladder is leaning against the building. The foot of the ladder is 2 feet from the base of the building. How far up the wall is the top of the ladder? Answered by Stephen La Rocque. 





An antiderivative problem 
20090813 

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





Using the Remainder Theorem to Find an Unknown Coefficient. 
20090706 

From Mukulu: What is the value of a if 2x2x6 ,3x28x+4 and ax310x4 have a common factor. Answered by Janice Cotcher. 





A diagonal of a rectangle 
20090701 

From Ruben: Please assist me with the following problem: A rectangle has a diagonal that is 3.6 feet longer than the length and 7.1 feet longer than the width. What are the dimensions of the rectangle? Thanks Answered by Harley Weston. 





The Pythagorean theorem 
20090624 

From supreet: What are some realworld applications of the Pythagorean theorem?
and
How are the Pythagorean theorem and the distance formula related? Answered by Harley Weston. 





nC0 + nC1 + nC2 + ... + nCn = 2^n 
20090615 

From Chinonyerem: For n >= 1, derive the identity
nC0 + nC1 + nC2 + ... + nCn = 2^n
[Hint: Let a = b = 1 in the binomial theorem] Answered by Penny Nom. 





Ladder Leaning on a Wall 
20090514 

From clinton: a ladder rests against a wall 24m high.the foot of the ladder is 7m from the foot of the wall. How do you calculate the length of the ladder Answered by Robert Dawson. 





The shadow of a tree 
20090420 

From Lindsey: James found that a 30 ft. tree that cast a shadow of 40 ft. A wire from the top of the tree to the beginning of its shadow must be how long? Answered by Penny Nom. 





A walkway through a park 
20090307 

From felicia: a diagonal walkway through a park is 18 meters long. If the park is a square, how long is one of its sides to the nearest tenth of a meter? 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. 





The floor area in a spherical space station 
20090214 

From Ed: I am writing a science fiction novel that involves a spherical space station with a
radius of 800 meters. Inside, artificial gravity allows parallel floors set 4 meters
apart. If you count the floor that has a radius of 800 meters as Floor 0, then the
next floor up (Floor +1) would by 4 meters above the surface of Floor 0. There
would then be Floor 1 4 meters down from Floor 0. This would continue until
you reach the top or bottom floor, where there is at least 4 meters but less than
8 meters to the top or bottom of the sphere. Obviously the top and bottom
floors would have the (same) smallest area, while Floor 0 would have about 2
million square feet.
My problem is figuring out the total area of all of the floors, or for that
matter, any particular floors or the total number of floors (the total of all the
+ floors, the  floors (these numbers will be the same) plus Floor 0.
Ed Answered by Penny Nom. 





How far is the airplane from the control tower? 
20090117 

From Murtaza: An aircraft is vertically above a point which is 10 km west and 15 km north of a control tower. The aircraft is 4000 m above the ground, how far is it from the control tower? Answered by Penny Nom. 





The 2 rightmost digits 
20081218 

From Peter: Is there a pattern for the 2 rightmost digits of a power? For example, one problem for a math competition was what are the 2 rightmost digits of 3^1993? Answered by Robert Dawson and Victoria West. 





Insulation in an attic 
20081118 

From Scott: A homeowner wishes to insulate her attic with fiberglass insulation to
conserve energy. The insulation comes in 40cmwide rolls that are cut
to fit between the rafters in the attic. If the roof is 6 m from peak to eave
and the attic space is 2 m high at the peak, how long does each of the
pieces of insulation need to be? Round to the nearest tenth. Answered by Harley Weston. 





A right triangle 
20080925 

From john: a right triangle has hypotenuse wich measures 20cm and a perimeter 47cm. find the measure of the remaining two sides Answered by Harley Weston. 





Consecutive Even Integer Sides of a Triangle 
20080924 

From Brad: I am having a problem coming up with a formula for my son's eighth grade math problem.
We have found the answer by guess and check but have a mental block on the equation.
Any help would be appreciated.
The problem is: A right triangle has sides whose lengths in feet are consecutive even intergers. Determine the length of each side.
Thanks Answered by Janice Cotcher. 





The Intermediate Value Theorem 
20080916 

From A.: When dealing with the intermediate value theorem you have the function x^2. It bounces on the axis so you can't tell if lies on the interval [a,b]. So is the ivt proven false or does the ivt not tell you all the roots for sure. Answered by Harley Weston. 





The perimeter of an equilateral triangle 
20080911 

From Gerry: How can I find the perimeter (length of side) of an equilateral triangle if the only information I have is the altitude? Answered by Penny Nom. 





A square with diagonal 200 metres 
20080820 

From kelvin: find the are and perimeter of a square with diagonal of 200 meters? Answered by Penny Nom. 





Limit as it Approaches Infinity 
20080729 

From mary: i was trying to find the limit of this problem
the limit as x approches infinity of x minus cosx divided by x
lim xcosx/x
x>oo Answered by Harley Weston. 





The length of a side of a square 
20080727 

From FRANK: WHAT IS THE LENGTH OF ONE SIDE OF A SQUARE WITH A DIAGONAL OF LENGTH 2 TO THE HALF POWER Answered by Stephen La Rocque. 





The product of the digits of a four digit number 
20080726 

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





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. 





4x^3  6x + 2 = 0 
20080528 

From paul: 4x^3  6x + 2 = 0 Answered by Janice Cotcher. 





What is the length of the 3rd side? 
20080523 

From lee: If you have a triangle 12ft across the bottom then on the right is a 90 degree
angle and that side is 18ft tall. What is the length of the 3rd side? Answered by Penny Nom. 





A right angled triangle 
20080516 

From bryan: The sides of a right angled triangle are x, x+1, x+2 cm. Find the perimeter. Answered by Penny Nom. 





The factor theorem 
20080506 

From Nomaan: factorise
x³2x²x+2
using factor theorem Answered by Penny Nom. 





The Pythagorean theorem with triangles rather than squares 
20080429 

From Zachary: I need to figure out how to prove the pythagorean theoorem using equilateral triangles
instead of using square. I know that A^2+B^2=C^2, but how do you get that by using equilateral
triangles. I know the area of a triangle is BH1/2=Area. So what i need to know is how to derieve the
formula of a triangle to get the pythagorean theorem Answered by Penny Nom. 





Find the length and the width of the rectangle 
20080424 

From Vickie: A rectangle is 2 times longer than it is wide. It has a diagonal length of 50 centimeters. Find the length and the width of the rectangle. Round your answers to the nearest tenth. Show your work. Answered by Penny Nom. 





A 306090 triangle 
20080416 

From Ron: 306090 triangle. Base is 2.75 how do I find the length of the other two sides? Answered by Penny Nom. 





Factor 2x^3 + 3x^2  32x + 15 
20080402 

From sarah: I have a course review I'm working on and I'm not sure how I'm supposed to factor the following
2x^3 + 3x^2  32x + 15. Answered by Penny Nom. 





How far is she from her starting point? 
20080330 

From Nancy: A child runs due east for 23.5m and then she runs 10.5m due south. How far is she from her starting point? Answered by Stephen La Rocque. 





How would I factor 2x^3 + 11x^2  7x  6? 
20080322 

From Sean: How would I factor this polynomial?
2x^3 + 11x^2  7x  6 Answered by Stephen La Rocque. 





The area of a right triangle 
20080319 

From Tate: I need to find the area of a right triangle. I already know that the formula would be a squared + b squared = c squared. However, I only have the length of the hypotenuse and the base. Answered by Victoria West. 





The diagonal of a rectangle 
20080221 

From tim: is there a formula for finding the diagonal of a rectangle? Answered by Penny Nom. 





A triangle and a rectangle 
20071214 

From Someone: A certain triangle has sides that are, respectively, 6inches,
8inches, and 10 inches. A rectangle with a n area equal to that of the triangle
has a width of 3 inches. What is the perimeter of the rectangle, in inches. Answered by Penny Nom. 





A wiffleball field 
20071031 

From Svitlana: The Adam's family has set up a wiffleball field in their backyard. The bases are arranged like a typical baseball diamond, where the distance between consecutive bases is the same. First base is opposite of third base, and second base is opposite of home plate. The distance between consecutive bases is 50 feet. Now, the pitcher stands 25 feet from home plate and lies on the line between home plate and second base. How far is the pitcher from first base? Round your answer down to the nearest inch. Answered by Penny Nom. 





How to solve related rates problems 
20071027 

From David: Can you plz explain how and where you come up with an equation to solve this?
Find the rate of change of the distance between the origin and a moving point on the graph of y = sin x if dx/dt = 2 centimeters per second. Answered by Stephen La Rocque. 





Finding radius given chord length and distance to center 
20071004 

From Venus: a chord of 48mm long is 7mm from the center of the circle. What is the radius of the circle? Answered by Stephen La Rocque. 





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 geometry problem 
20070820 

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





Diameter of an octagon 
20070807 

From Bree: I am trying to find the diameter of a octagon with 20' sides . What formula do I use? Answered by Stephen La Rocque. 





Find the area of a regular pentagon inscribed in a circle 
20070803 

From Tracy: Can you please help me with finding the area of a regular pentagon inscribed in a circle using the Pythagorean theorem. The radius of the circle is 5 cm and each side AB = BC = CD = DE = EA = 6 cm. Answered by Stephen La Rocque, Leeanne Boehm and Chris Fisher. 





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. 





Building a garage 
20070729 

From charles: I want to build a garage that is 24 feet 4 inches wide by 50 feet long.
can you please tell me what the length of one corner is to the other? Answered by Penny Nom. 





Some trig problems 
20070720 

From Jocelyn: I wasn't able to solve this equation:
only find the function using Pythagorean theorem
Please help me....
sinA = 3/4 find secB
tanA = 3/4 find cosA
sinB = 4/5 find tan A
cosA = 5 find csc A
b =5; a= 12 find sin A
c =25; a = 24 find cot A
a = 6; c =10 find b?
Find B when c = 25; a = 24
Find A when a = 5 and b = 12
csc = 1/2 find cos Answered by Penny Nom. 





An oblique triangle 
20070719 

From fhay: In an oblique triangle, If side a=95, side b=102 and side c = 150 find the missing angles solved by right angles...Thank's a lot...... Answered by Penny Nom. 





The volume of a cube 
20070623 

From Leah: I am having trouble finding the equation for this problem.:
What is the volume of a cube with diagonals of length 6 sqrt(3) cm?
answer: (BLANK) cm3 Answered by Penny Nom. 





Using the Pythagorean Theorem 
20070618 

From cynthia: Hi,
If I have a question with a right triangle and it asks....
If ABC is say 400 miles. How much shorter will the miles be if I travel
from BC?
I don't exactly remember the question but, I would I solve a problem
similiar to this one? Answered by Stephen La Rocque. 





A circle inside a square 
20070531 

From Mer: there is a circle inside a square... there is a shaded rectangle that measures 5mm X 10mm and they want to know what the radius is. The edge of the shaded rectangle touches a point on the circle. Answered by Penny Nom. 





A point on a semicircle 
20070528 

From arun: a semi circle is drawn with ab as diameter from p a point on ab a line perpendicular to ab is drawn meeting circumference of semi circle at c, ac = 2cm, cd = 6cm find area of the semi circle? Answered by Penny Nom. 





The area of a pyramid 
20070428 

From Alexander: Total area of the plate required to fabricate a vessel(pyramid) the base is 0.6mx0.6m and height of 1.0m. Answered by Stephen La Rocque. 





Division of polynomials 
20070414 

From Rajendra: Find the remainder when x3+3x+1 is divided by x+pi Answered by Penny Nom. 





How far apart are the cars? 
20070407 

From ian: 2 cars set off in opposite directions and travel for 6 miles,
they both take a left turn, and travel for a further 8 miles...........
how far apart are the cars???
a) 10 miles
b) 22 miles
c) 20 miles
d) 18 miles Answered by Penny Nom. 





The Pythagorean theorem 
20070404 

From Cassandra: how do u find a and/or b using the Pythagorean theorem of a right triangle? Answered by Leeanne Boehm. 





(x+2) is a factor of x^3+bx^214x+24. Find the value of b? 
20070311 

From victoria: hi my names victoria and i have been stuck on this question for ages can you please help me! (x+2) is a factor of x^3+bx^214x+24. Find the value of b? Answered by Penny Nom. 





Finding the vertical height of a roof 
20070305 

From Zainab: The question is: If the vertical height if a triangle is half the width of the base and the slant length is 6 metres, find the exact vertical height of this part of the roof. I'm actually confused about finding out the height of an equilateral triangle if you're only given the length or slant height. Please help! O.o Answered by Stephen La Rocque. 





The factor theorem 
20070304 

From Sophia: hi this is sophia, 10th grade from the philippines. im really having a hard time in factor theorem im just asking if you could help me solve these problems because i really dont have an idea on how to do solve these.. please
find the values of A and B so that (x+3) (x2) are both factors of x^3+Ax^2+Bx12
and
find the values of A, B, and C so that (x3) (x+1)and (x2) factors of P(x)=x^4+Ax^3+Bx^2+Cx+12
please help me.. i really do not understand these problems Answered by Penny Nom. 





a^2 + b^2 = c^2 
20070304 

From Colburn: 27 feet long base 14 feet height what is the diagonal Answered by Stephen La Rocque. 





Line segments on dot paper 
20070121 

From Khaori: The three line segments below are drawn on centimeter dot paper.
a. Find the length of each segment to the nearest tenthousandth of a centimeter. b. Could these line segments be arranged to form a triangle? If no, explain why or why not. If yes, answer this question: could they form a right triangle? Explain why or why not. Answered by Penny Nom. 





A rhombus 
20061226 

From Jose: show mathematically that a quadrilateral whose vertices are A(2,1),B(6,2) C(10,1),and D(6,4) is a rhombus Answered by Penny Nom. 





The Pythagorean theorem 
20061212 

From Beth: In a pythagorean theorem can the sides of a right triangle be three consecutive odd integers Answered by Stephen La Rocque. 





Rolle's Theorem 
20061207 

From Erika: If f(x) = (x^2)(square root of [3x]) on the interval [0,3] is given, Does Rolle's Theorem apply? If yes, find any values of c such that f '(c)=0 Answered by Penny Nom. 





When kx^2+3x+1 divided by (x2) the remainder is 3 
20061109 

From Brianna: For the dividend, find the value of k if the remainder is 3. (kx^2+3x+1) divided by (x2) Answered by Penny Nom. 





The height of a triangle as a function 
20061019 

From Ryan: Let 2s denote the length of the side of an equilateral triangle. Express the height of the triangle as a function of s Answered by Penny Nom. 





The hypotenuse 
20061002 

From Ashley: How do you find the hypotenuse of a right triangle? I don't understand how to find c. Answered by Stephen La Rocque. 





X^1/3X^1/9=60 
20060926 

From Harini: I need the answer for
The value of X in X^1/3X^1/9=60. Answered by Penny Nom. 





I need to cut an octagon 
20060923 

From Freddie: I have a 48 inch square piece of wood that I need to cut into an octagon, help. What's an easy way to just measure and cut it. Answered by Penny Nom. 





The length of 2 sides of a triangle 
20060915 

From Lonnie: I need to know how to figure the length of 2 sides of a triangle, as the following example:
The length of the bottom is 12' and the angles are 45, 45 I need to know how long the other 2 sides must be to get an angle of 90 at the top. Answered by Stephen La Rocque. 





Square roots in a binomial expansion 
20060911 

From Sydney: (√x + 5)^{4} expanded using the binomial theorem Answered by Penny Nom. 





What are the 3rd and 4th terms of (2xy)^7? 
20060618 

From April: What are the 3rd and 4th terms of this sequence: (2xy)^{7}?
I'm having an issue with this...is there any easier way to get it without completely factoring the whoooole thing out? 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. 





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. 





The Pythagorean relation 
20060509 

From Vicky:
How do you the Pythagorean relation to find the length of the hypotenuse x to one decimal place?
x^{2} = 3.6^{2}+ 5.3^{2}
My teacher, Mr. Mutrie, wants to know what this means?
SOH CAH TOA
Answered by Harley Weston. 





Cutting an octagon from a square 
20060507 

From Veronica: 1.A regular octagon is to be cut out of a square piece of metal which has sides of 1 metre. What will be the length of the sides of the octagon?
2.What will be the area of the octagon? Answered by Penny Nom. 





Pythagorus and cone dimensions 
20060426 

From Glynnis: How do you find the measure of a side that is not the hypotenuse using the Pythagorean Theorem? Also, how do you figure the surface area and volume of a cone when the radius is 5 yards and the height is 8 yards? Answered by Stephen La Rocque. 





The perimeter of a regular octagon 
20060420 

From Martin: I would like to make an octagon out of 2x4 lumber. I know that the lumber needs to be cut at 67.5 degree angles, but how do I determine the length of each piece if I want to make, say, a 2.5 ft diameter octagon? Answered by Stephen La Rocque. 





x^2+2x3 is a factor f(x)=x^4+2x^37x^2+ax+b 
20060406 

From Maha: Given that x^{2}+2x3 is a factor f(x)=x^{4}+2x^{3}7x^{2}+ax+b, find a and b and hence factor f(x) completely. Answered by Penny Nom. 





The area of a block of land 
20060326 

From Ronald:
I have a building block of land with four unequal sides and only one right angle. I want to know the total area (in metres) and how the calculations were carried out.
The four sides are: Rear of property: 9.14 metres
left side: 36.9 metres
Right side: 32.61 Metres
front to street: 27.43 Metres
The front to street and right side constitute a right angle. but there are no others. Answered by Penny Nom. 





A 25 foot ladder is leaning against a building. 
20060324 

From Ali: A 25 foot ladder is leaning against a building. The base of the ladder is 7 feet from the building. How high up the building does the ladder reach? Answered by Stephen La Rocque. 





f(x) is a polynomial of degree 3. 
20060313 

From Meadow: f(x) is a polynomial of degree 3. It leaves a remainder of 10 and 4 when divided by
x + 1 and x  2 respectively. Given also that f(1) = f(2) = 0, find the remainder when
f(x) is divided by x  3. Answered by Penny Nom. 





Factors of a cubic 
20060308 

From Skye: Show that (x+2) is a factor of f(x) where:
f(x) = px^{3} + (4p+2)x^{2} + (5p+4)x + 2p
Find the range of values for which the equation f(x) = 0 has 3 distinct real roots Answered by Penny Nom. 





The third side of a triangle 
20060209 

From Clayton: How do I find the length of the third side of a triangle if a=30m, b=30m and I need to find c? Answered by Steve La Rocque and Penny Nom. 





An irregular octagon 
20060120 

From Robert: I am building a poker table which is in the shape of an irregular octagon. I know the table measures 72 inches long and 48 inches wide with two parallel straight sides of equal length and six smaller sides of equal length ( three at each end of the table), what I don't know are the lengths of the any of the sides. Answered by Harley Weston. 





The height of a triangle from the lengths of the sides 
20060116 

From A student: How do you figure out the height of a triangle when all you have is the length of the sides of the triangle? Answered by Claude Tardif. 





The area of an octagon 
20060103 

From Nikki: I want to figure out the square footage of an octagon. i have 8 panels that are 24" wide. Its for my dogs and i wanna know how much room they'll have. Answered by Penny Nom. 





The Mean Value Theorem 
20051222 

From Candace: Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given interval. Find all numbers "c" that satisfy the Mean Value Theorem. 11. f(x)=3x^{2} + 2x +5 [1, 1] Answered by Penny Nom. 





Folding a sheet of paper 
20051215 

From Victoria: The current problem is to take a normal 8 1/2 x 11 sheet of paper, take a corner and fold it to meet the opposite corner, and (without actually measuring) produce a formula to describe the result fold/crease. Answered by Penny Nom. 





The sides of an octagon 
20051102 

From Royce: I understand there is a simple calculation to determine the sides of an octagon when you know the distance across the parallel flats. something like .447 . can you help? Answered by Penny Nom. 





A cube in a sphere 
20051019 

From Damian: A sphere passes through the eight corners of a cube side 10cm. Find the volume of the sphere. Answered by Penny Nom. 





A line that intersects a circle 
20051018 

From Bruce: I would like to solve the following problem illustrated below. How do you calculate the length of a line that intersects a circle. Answered by Penny Nom. 





The remainder theorem 
20051007 

From Ron: If f(x) is divided by (x3), the remainder is 5, and if it is divided by (x+1), the remainder is 3. Find the remainder when f(x)is divided by (x3)(x+1). Answered by Chris Fisher. 





City A is 30 miles directly north of City C 
20051004 

From A student: City A is 30 miles directly north of City C, and City B is 40 miles directly east of City C. Cities A and B are connected by a straight road. Find the length of the shortest path from City C to the road that connects A and B. Answered by Penny Nom. 





The length of the side of an octagon 
20050922 

From Billy: How can you find the length of the side of an octagon when all that you know are the long sides of one of the eight perfect isc. triangles inside the octagon that share the same center point? Answered by Penny Nom. 





The area of a lot 
20050829 

From Richard: My wife and I are interested in buying property in Idaho but the owner can't give us a square footage of the lot. The dimensions are as follows:
121.0 on the left side
157.0 on the right side
135.0 on the bottom
162.0 on the top
The bottom right corner of the lot is a true right angle, the rest are not. Answered by Penny Nom. 





Constructing a fence 
20050809 

From Andres: I was constructing my fence and was having some problems trying to do a perfect (or as close as possible) arch. If i know a section of a fence is for example 85 inches wide and I want a 4 inch rise from the top rail how do i figure out the radius? Answered by Penny Nom. 





An algebraic remainder 
20050622 

From Raymond: Given that 4x^{3}  kx is divisible by 2x+1, find the remainder when the expression is divided by 4  x^{2}. Answered by Penny Nom. 





arccos(5/13) 
20050531 

From Kyle: I would like to know how to evaluate the problem of: Arccos 5/13. Answered by Penny Nom. 





The area of an octagon 
20050521 

From Jeremy: i need to find the area of an octagon with each side measuring 1 foot Answered by Penny Nom. 





A right triangle 
20050518 

From Bill: If I know the base and the slanted side of a right triangle, how do I figure out the height? Answered by Penny Nom. 





Bayes Theorem 
20050403 

From wei:
In the January 11,1988,issue of the Oil&Gas Journal, R.A.Baker
describes how the Bayesian approach can be used to revise probabilities
that a prospect field will produce oil. In one case he describes,
geological assessment indicates a 25% chance the field will produce
oil. Further,there is an 80% chance that a particular well will strike
oil given that oil is present on the prospect field.
 Suppose that one well is drilled on the field and
it comes up dry. What is the probability the prospect field will
produce oil?
 If two wells come up dry, what is the probability
the field will produce oil?
 The oil company would like to keep looking as long
as the chances of finding oil are greater than 1%. How many dry wells
must be drilled before the field will be abandoned
 If the first well produces oil,what is the chance
the field will produce oil?
Answered by Andrei Volodin and Penny Nom. 





Dimensions of a roof 
20050318 

From A roofer?: A right triangle (roof of a house) has a base of 7 feet and a 22 degree angle. What is the height of the roof and what is the hypothenus of the triangle. Answered by Penny Nom. 





A diagonal in a cube 
20050306 

From Brett: A cube has a volume of 64 cubic inches. What is the length of segment AB? Segment AB is a straight line from the top left corner of the cube to the lower right bottom corner Answered by Penny Nom. 





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. 





A right triangle 
20041124 

From Bruce: In triangle ABC.
Angle ABC is 90 degrees.
Side AB measures 34.
Side BC measures 31.
What does side AC measure? Answered by Penny Nom. 





Practical applications: parabolas and Pythagoras 
20041024 

From Connie: Provide two examples of real life objects that incorporate parabolic shapes. Explain the reason why the parabolic shape was used in each object.
I need at least one practical application of the Pythagorean Theorem. Answered by Penny Nom. 





Pythagoras in everyday life 
20041013 

From Tiffany: I was wondering if you have any reallife uses of the pythagorean theorem that you use in your everyday life. Answered by Penny Nom. 





A theorem involving a trapezoid 
20040929 

From Abraham: Given:Trapezoid ROSE with diagonals RS and EO intersecting at point M
Prove:Diagonals RS and EO do not bisect each other. Answered by Harley Weston. 





The area of a lot 
20040929 

From Deb: I am trying to figure out how many square feet are in a piece of property. Start at Point Athen go 140 feet norththen 100 feet due eastthen 300 feet at an angle southeast so that connecting to point A would be a straight line (right angle to first line north.) Answered by Penny Nom. 





The length of a cut 
20040917 

From Florita: My daughhter, who is a 9th grader is attempting to cut a piece of wood after determining the length of the cut for the hypotenuse. These are the measures:
a=4squared, b=6squared.
She determined that c should equal 52. But when she measured the actual piece to be cut, c measured 39.5 inches! Can you offer any insight as to what she is doing wrong? I have suggested that she may be working with an Acute rather than a Right angle . But she insists that it is a Right angle after using a "framing square". Answered by Claude Tardif. 





A cube is inscribed inside a sphere 
20040818 

From A student: A cube is inscribed inside a sphere with radius sqrt8cm. Find the
(a) length of the cube
(b) volume of the space inside the sphere but outside the cube. Answered by Penny Nom. 





An Octagonal playhouse 
20040713 

From Levi: I'm building an octagon playhouse for my son that is 8 feet wide.
what would be the measurements of each of the eight sides. Answered by Harley Weston. 





How far apart are they? 
20040523 

From A student: 2 cars start at same loc. drive opposite direction for 6 miles then they each turn left and travel for 8 miles how far apart are they? Answered by Penny Nom. 





A stained glass window 
20040329 

From Kay: I'm doing a stain glass project and it's on a 4 foot across octagonal window...and I'm trying to set up the pattern and I don't know how long the sides are! Answered by Penny Nom. 





A water lily 
20040317 

From Inba: A water lily with a rigid stem extends one foot above the surface of the water. When pulled over, it disappears beneath the water at a distance 3 feet from where the stem originally entered the water. How deep is the pond? Answered by Penny Nom. 





The factor theorem 
20040308 

From LisaMarie:
Hi, I have a career link question from gr.12 advanced functions
and intro. calculus. The equations is:
R(t) = 5(t^{4}  4t^{3} +
19/4 t^{2}  3/2 t)
The question is to apply the factor theorem
and quadratic formula to determine the times it crosses the t axis. The
only method i know of for using the factor theorem is when the last number
does not have a variable beside it so i'm not sure how you would even
use the factor theorem for this? We haven't dealt with any that have 0 as
the last number with no variable so i'm a little confused! please help!
Thank you
Answered by Penny Nom. 





Napoleon's theorem 
20040227 

From David: How do i prove this : For any triangle, if you make 3 equillateral triangles
using the sides of the the original triangle, the central points of the 3
tringles another triangle that is equillateral.z Answered by Chris Fisher and Penny Nom. 





Bundles of asphalt shingles 
20040124 

From Larry: According to my study material 4:12 multiplying factor for shingles is 1.054. The question reads as follows: A building with a floor plan of 3350 sq. ft. and a roof slope of 4:12 will require _______ bundles of standard asphalt shingles. Answered by Harley Weston. 





The volume of a cube 
20031122 

From A student: i have a cube, and the line that cuts threough the middle of the cube across to the other side is 4 radical6. what is the volume of the cube? Answered by Penny Nom. 





A rectangle on a disk 
20031029 

From Arthur: How do I go about solving the following problem: What is the width of the largest rectangle with a length of 16 inches you can cut from a circular piece of cardboard having a 10 inch radius? Answered by Penny Nom. 





The general equation for a sphere 
20030911 

From Jaidev: Is there any general equation for a sphere? Answered by Penny Nom. 





A 16 foot ladder 
20030904 

From Kelly: Two buildings are separated by a threefoot alleyway. Fatima wants to use a 16 foot ladder to reach a window in the wall of one of these buildings. If she places the foot of the ladder against the base of the other building, how far up the wall will the top of the ladder reach?? Answered by Penny Nom. 





Newton's binomial theorem 
20030830 

From William: According to page 126 of Murtha & Willard's "Statistics and Calculus" (PrenticeHall, 1973), Newton's binomial theorem can proved inductively. I suppose that was his method, which I would like to see. Answered by Penny Nom. 





Two cars 
20030709 

From Nicole: Two cars start off at the same point on a striaght highway facing opposite directions. Each car drives 6 miles, talkes a left turn, and drives for 8 miles. How far apart are the two cars. Answered by Penny Nom. 





The height of an equilateral triangle 
20030406 

From Rosa: If Each side of an equilateral triangle is 10 m. What is the height? 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. 





A triangle and a circle 
20030321 

From Jynks: We need a formula that we can use to figure this out for work. We aren't math wiz's or students. Basically we know 3 points in space of a triangle, we know the length of each side and the length of the line from apex to base line. Each point of the base line ends upon the circumference of a circle. IS three a way to work out the radius of that circle. Answered by Penny Nom. 





Factoring 
20030204 

From Marcin: I am having a really hard time with the factor theorem. Can you please help me with the following? (a'3 means a to the exponent 3)
a)8a'3+64b'3c'6 b)8x'412x'344x'2+24x c)x'421x'2100
Answered by Penny Nom. 





Factoring a cubic 
20021205 

From Dorota: I got a problem with factorise the expression 2x^{3}+11x^{2}5x50. Answered by Penny Nom. 





The height of a triangle 
20021129 

From Dean: Could you please tell me the formular for me to calculate the height of a triangle. I have the angles and side lengths. I am trying to calculate the height of an isosceles triangle, does this make a difference from a normal triangle or is the formular the same. Answered by Penny Nom. 





The four colour theorem 
20021027 

From Rhonda: is there an actual equation for the four colour map theorem??? i cannot find it anywhere!! if so can you give a breif description on how it works!! Answered by Penny Nom. 





Pythagoras in three dimensions 
20021014 

From Miki: A room is 6m long, 5m wide and 3 m high. Find the distance from the corner of the floor to the opposite corner of the celing. Answered by Peny Nom. 





The factor theorem 
20020910 

From Yael: Prove (x  a  b) is a factor of x^{3}  a^{3}  b^{3}  3ab (a + b) Answered by Penny Nom. 





A limit 
20020903 

From Circe:
Lim 3x^{ 3}+ax+a+3 /(x^{ 2}+x2), X>2 Answered by Penny Nom. 





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. 





Bob swam across a river 
20020522 

From Torri: Bob swam across a river 420 ft wide. A strong current carried him 580ft downstream as he swam. Find x, the distance bob actually swam. Answered by Penny Nom. 





An octagonshaped deck 
20020220 

From An instructor: How can you solve for finding the side measurements of an octagonshaped deck that is 10 feet long and 10 feet wide. Answered by Penny Nom. 





A degree 5 polynomial 
20020217 

From Carla: Write an equation for a polynomial of degree 5 given the following zeros: 7+3i, 2+sqrt(13), 6 Answered by Penny Nom. 





Rolling 5 sevens before rolling a six or an eight 
20020120 

From Tony: When rolling 2 dice, what is the probability of rolling 5 sevens before rolling a six or an eight? Answered by Andrei Volodin and Penny Nom. 





Multinomial theorem 
20011128 

From Murray: Could you please state and explain the multinomial theorem (I already know the binomial theorem etc, to give you an idea of where i am) Answered by Harley Weston. 





A clap of thunder 
20011115 

From Frustrated Mom: While getting a recipe for the Thanksgiving feast. The teacher was talking on the phone with a friend who lives four miles north of her. She saw a flash of lightning through the window: fifteen seconds later, she heard a clap of thunder. Ten seconds after that she heard the thunder over the phone. Where did the lightning strike in relation to the teacher's house. (There are two possible answers. Sound travels about 1/5 mile per second. Some people say it's not good to be on the phone in a thunderstorm). Answered by Claude Tardif and Penny Nom. 





Lucas' theorem 
20011009 

From Tania: How could I demonstrate: nCp is congruent to floor(n/p) (modulo p)? where rCk is a binomial coefficient, rCk = r(r1)...(rk+1)/k(k1)...1, and p is a prime number Answered by Richard McIntosh. 





The Mean Value Theorem 
20010723 

From Corrie: I need to find if the mean value theorem exists. and if so, find all values c guaranteed by the theorem. f(x) = x^{2}25 on the interval [10,0] Answered by Harley Weston. 





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. 





The hypotenuse of a right triangle 
20010122 

From Phillipe: How do you find the hypotenuse of a right triangle? Answered by Penny Nom. 





The Pythagorean Theorem 
20010108 

From Megan: Why the Pythagorean Theorem so important in our lives and what is it's history? Answered by Penny Nom. 





The pythagorean theorem in everyday life 
20010106 

From Josh: What are some ways that we use the pythagorean theorem in jobs, or even in everyday life? Answered by Claude tardif. 





Two geometry problems 
20000909 

From Becky: What are all the real values of x that are solutions for the inequality [x2] < 6? ( it's less than or equal to) What is the distance between the points with (x,y) coordinates (3,2) and (3,1)? Answered by Peny Nom. 





Central Limit Theorem and Law of Large Numbers 
20000626 

From Jonathan Yam: The Central limit Theorem states that when sample size tends to infinity, the sample mean will be normally distributed. The Law of Large Number states that when sample size tends to infinity, the sample mean equals to population mean. Is the two statements contradictory? Answered by Paul Betts and Harley Weston. 





4 Color map Theorem 
20000602 

From Rick Slen: I am challenging my students to find a map that can not be coloured using only 4 colours. I know that it is not possible, but one boy drew a map with a "country" totally surrounding all the others so of course it touched all other colours. How do I explain that this type of map is not permissable? Answered by Denis Hanson. 





Calculus Research Questions 
20000522 

From William Wright: I am a Calculus Teacher, and me and my class ran into these two problems without solutions in my manual, we got answers, but are unable to check them. If anyone gets this email and can respond to this with the solutions it be greatly appreciated. . . . Answered by Harley Weston. 





The pythagorean theorem 
20000519 

From Lauren Fitzgerald: how do you find the length of th hipotnuse( or however you spell that word). i understand you have to add the two sides. but when i do add i always end up with this way off answer. i donot understand at all. Answered by Paul Betts. 





Sylvester's Problem 
20000323 

From Sheryl Webb: I am trying to find a proof of the theorem: Given n points in a plane, there is a line that contains exactly two points. Answered by Chris Fisher. 





The isoperimetric theorem 
20000224 

From Raj Bobal: How can you prove Mathematically that the maximum area enclosed by a given length is a circle? Answered by Chris Fisher. 





Factoring by graphing 
20000111 

From Dylan Kirkwood: How can you factor a quadratic equation by graphing it? Answered by Penny Nom. 





Solving a cubic equation 
19991230 

From Natalia: How can I solve: 2 x^{3}  x^{2} + x  2 = 0 ??? Answered by Penny Nom. 





The area of a garden 
19991217 

From Jessica Wells: Hi My name is Jessica Wells and I am 10 years old. I was hoping you could help me out wityh a question my dad gave me. It is if aq graden is 32cm in diameter and I want to know the area of it what process do I use? He's a math wiz so I need o show him that I'm smart too Answered by Penny Nom. 





Two algebra problems 
19991217 

From Michael Standfest: If x+4 is a factor of 2x^{4}+kx^{3}3kx^{2}+6x40, find k and Prove that n^{2}n is even for all n, using the proof of contradiction Answered by Penny Nom. 





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. 





Standard Deviation 
19990711 

From Anthony Fama: I have seen several answers to this question: If one standard deviation represents 68% of the population, what does two, three, four and five sigma [std deviation] represent? As stated, I have seen several different answers and thus, the impetus for my question. Answered by Harley Weston. 





The Binomial Theorem for rational exponents 
19990415 

From Angela Evans: The full question is this: Isaac Newton generalized the Binomial Theorem to rational exponents. That is, he derived series of expansions for such expressions as (x+y)^{3} (x+y)^{2/3} (x+y)^{5/6} What did Newton find? What are the first four terms of the series expansions of binomials above? How can this extended Binomial Thrm. be used to aid in calculations? Answered by Penny Nom. 





Factoring 
19990330 

From Maggie Stephens: I don't know anything about factoring would you plese help me. 3x^{4}  48 54x^{6} + 16y^{3} 1258x^{3} 12x^{2}  36x + 27 9  81x^{2} a^{3} + b^{3}c^{3} I would greatly appreciate any help you can give me thanks. Answered by Jack LeSage. 





Factoring polynomials 
19990329 

From Karen: I have been unable to factorise a polynomial equation and was wondering if you could please help. It is level (1012) maths. The polynomial is x^{3} + x^{2}  24x + 36 I have tried a few factorisation methods such as foctorisation by grouping but it won't work this polynomial. Please help. Answered by Jeff Walters and Jack LeSage. 





Pythagorean theorem research project 
19981231 

From Mohammed Hasan: Hi my name is Mohammed Hasan. I am a math honors student in 8th grade. I have to do a research project in math. The only problem is that I have to do the research project at a 10th grade level. I am having trouble raising the project at a tenth grade level. Would you please kindly take your time to give me some tips and web sites that will help me raise the Pythagorean theorem to a 10th grade level. Answered by Jack LeSage and Walter Whiteley. 





Dividing a Class 
19981001 

From Tom Barker: My eighth grade niece called with the following homework problem: A teacher wanted to divide her class into equally numbered groups. She tried to divide the class into groups of two, but was one student short. She tried to divide the class into groups of five, but was one student short. She tried to divide the class into groups of seven and was successful. What is the least number of students that were in her class? I know the answer is 49, but don't know how to prove it. I must be getting old if I can't solve eighth grade math problems. Your assistance would be appreciated. Answered by Penny Nom. 





The Factor Theorem 
19980118 

From Dhruv Bansal: Hi, I'm a ninth grade student doing a math project for school. I'm trying to learn about various ways of solving 3rd and 4th degree polynomial equations using the remainder theorem, the factor theorem, and synthetic division. The books I have all mention x  r, which I know nothing about, not even how to get it. I would really appreciate any information on this. Thanks. Dhruv Bansal Answered by Penny Nom. 





Two Questions 
19970828 

From Faye Tan: I am a trainee teacher. I would appreciate it very much if you could help me solve the following two problems which I think are meant for students at middle grade. 1. If a hen and a half lays an egg and a half in a day and a half, how many hens are needed to lay a dozen eggs in one day? 2. There are fewer than 200 passengers on a train. If they get off in pairs, one passenger will be without a partner. If they get off in groups of 3 or 4, there will still be one passenger left by himself. However, if they get off in groups of 5, no one will be left by themselves. How many passengers are there on the train? Answered by Penny Nom. 





A Monte Carlo Procedure 
19970423 

From Donna Hall: A irregularly shaped object of unknown area A is located in the unit square 0<=x<=1. Consider a random point uniformly distributed over the square. Let X = 1 if the point lies inside the object and X = 0 otherwise. Show that E(X) = A. How could A be estimated from a sequence of n independent points uniformly distributed over the square? How would you use the central limit theorem to gauge the probable size of the error of the estimate. Answered by Harley Weston. 





The Central Limit Theorem 
19970421 

From Donna Hall: A skeptic gives the following argument to show that there must be a flaw in the central limit theorem: We know that the sum of independent Poisson random variables follows a Poisson distribution with aparameter that is the sum of the parameters of the summands. In particular, if n independentPoisson random variables, each with parameter 1/n, are summed, the sum has a Poisson distributionwith parameter 1. The central limit theoren says the sum tends to a normal distribution, butPoisson distribution with parameter 1 is not normal. What do you think of this argument? Answered by Neal Madras. 





Proofs 
19970413 

From Daniel: I'm having trouble understanding proofs. I don't know how to come up the answers on my own. I search through the book looking for the answer. I understand what they are doing, but I don't know how to do it. Answered by Walter Whiteley. 





The normal distribution. 
19970321 

From Donna D.Hall: I am looking for a proof for the normal distribution. I suppose "proof" was not a good choice of words. What I am looking for is a way to "derive" the normal distribution in simple terms so that the most average teenager can see the logic. Can you help me? Answered by Harley Weston. 





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. 





An application of Pythagoras' theorem 
19960409 

From Mike Jones: We'd like to know what practical applications there may be for the Pythagorean theorem. Answered by Penny Nom and Maxine Stinka. 





Dernier théorème de Fermat 
20060606 

From JeanClaude: Bonjour, je suis étudiant au baccalauréat en mathématique et j'aimerais savoir où et comment je peux me procurer la démonstration du dernier théorème de Fermat écrite par Wiles. Answered by Claude Tardif. 

