Topic: theorem list of topics
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	The length of a line at 45 degrees		2022-04-09
		From Aiden: Let's say one line is diagonal and one line is vertical. If they eventually meet at a 45 Degree angle, How long will the diagonal line be compared to the vertical line? (For Example: If The Vertical Line is Exactly 1 Inch. Answered by penny Nom.
	Scale drawing		2021-02-10
		From Elias: a football field is 160m long and 120m wide . Find the distance between its opposite corner flag posts . use the scale of 1cm:20m Answered by Penny Nom.
	The height of a building		2019-04-05
		From Hayley: A young man is 36 meters away from a building and looking at a bird sitting on top of the building. The man knows he is 85 meters away from the bird. How tall is the building? Answered by Penny Nom.
	The Polynomial Remainder Theorem		2019-02-23
		From pasandi: f(x) is a quadratic polynomial. when f(x) is divided by (x-1),(x-2) & (x+2) the remainders respectively are -1, 4 and 2 how to find the f(x) in a question like this? Answered by Penny Nom.
	(2018^2019)-(2019^2018)		2019-01-23
		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		2019-01-14
		From herm: what is the length of each side of a hexagonal tray, with the height of each side 0.75 inch, to hold seven spheres, each with a diameter of 3.00 inches? The spheres are placed such that each side of the hexagon is touched by one sphere at its midpoint (and the seventh sphere is place in the center of the "ring" of the other six spheres. Answered by Harley Weston.
	A binomial expansion		2019-01-05
		From shifali: if the binomial expansion of (m-nx)^3 is 1+9x+-- find the values of m & n Answered by Penny Nom.
	A rope fom a dock to a boat		2018-03-14
		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		2018-01-30
		From Grayson: f(x)=x^6-x^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?		2016-10-06
		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		2016-10-04
		From A student: need help with this f(x)=4x^4-15x^2-4; x-2 using the remainder theorem to find the remainder Answered by Harley Weston.
	Lisa went for a run		2016-07-14
		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		2016-05-13
		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		2016-04-11
		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		2016-03-27
		From Pratyasha: A quadratic polynomial when divide by x+2 leaves a remainder of 1 and when divided by x-1 leaves a remainder of 4. What will be the remainder if it is divided by (x+2)(x-1)? Answered by Penny Nom.
	A limit of a rational function		2016-01-16
		From selvamani: F (x) = x^3+3x^2-9x-2 / x^3-x-6 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		2015-05-17
		From Ari: In a 45-45-90 triangle find the ratio of a leg to the hypotenuse Answered by Penny Nom.
	The Pythagorean Theorem		2014-03-30
		From brenae: The Pythagorean Theorem, what is it? Answered by Penny Nom.
	A scalene triangle		2014-01-07
		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		2013-12-21
		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		2013-01-23
		From Dakota: My problem has multiple steps and I have done everything but the last one. 8The original problem is f(x)=x^4-5x^3+7x^2+3x-10 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^3-3x^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		2012-12-26
		From Tehmas: Determine the values of m and n so that the polynomials 2x^3+mx^2+nx-3 and x^3-3mx^2+2nx+4 are both divisible by x-2. Answered by Penny Nom.
	The height of a triangle		2012-10-17
		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		2012-06-08
		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		2012-03-25
		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		2012-03-25
		From Victoria: When k^2 + 3kx + 13k +k^2x - 3x^2 is divided by (x-4) the remainder is 22. Find the value(s) of K. Answered by Penny Nom.
	A circle and a chord		2012-02-11
		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		2011-09-07
		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		2011-04-27
		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		2011-04-22
		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?		2011-04-11
		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		2011-04-08
		From Ataa: I am doing a assignment on Pythagorean Theorem and i am stuck on the sub-question 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		2011-03-29
		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		2011-02-05
		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)		2011-01-19
		From Alexa: Find all points having a x-coordinate of 2 whose distance from the point (-2, -1) is 5. Answered by Penny Nom.
	Semicircles and the Pythagorean Theorem		2011-01-09
		From Jas: Okay well, in math we are learning about the pythagorean theorem and we have to do a math journal on the question: ****Can you replace the squares (that are put on the sides of a right triangle) with semicircles and still get the same answer?? I do not understand because i tried doing an example and comparing it with a normal way of doing it and I didnt get the same answer! Answered by Penny Nom.
	A polynomial remainder		2010-12-25
		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		2010-12-02
		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		2010-11-25
		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		2010-10-20
		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) co-ordinates 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 m-gon and genrealizations		2010-10-16
		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		2010-08-26
		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		2010-08-04
		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		2010-07-17
		From GARY: WHAT NUMBER DIVIDED BY 11 LEAVES 1, DIVIDED BY 13 LEAVES 8, AND DIVIDED BY 17 LEAVES 3. Answered by Chris Fisher.
	The equation of a circle		2010-06-23
		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		2010-06-21
		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		2010-05-25
		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		2010-05-22
		From linda: find the length of the hypotenuse of a triangle with legs of 12in. and 17in. round to the nearest hundredth Answered by Tyler Wood.
	How far is the runner from the starting point?		2010-05-22
		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?		2010-05-18
		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		2010-04-14
		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		2010-03-25
		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		2010-02-27
		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		2010-02-27
		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		2010-02-16
		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		2010-01-21
		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		2010-01-20
		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?		2010-01-19
		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		2010-01-12
		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^3-3x^2+px+30		2010-01-09
		From Ruby: (x+3) is a factor of 2x^3-3x^2+px+30. Determine the value of p Answered by Penny Nom.
	A quilt square		2010-01-07
		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 right-angled triangle		2009-10-02
		From Hunter: The three sides of a right-angled triangle measure x-1, 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		2009-09-08
		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		2009-08-13
		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.		2009-07-06
		From Mukulu: What is the value of a if 2x2-x-6 ,3x2-8x+4 and ax3-10x-4 have a common factor. Answered by Janice Cotcher.
	A diagonal of a rectangle		2009-07-01
		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		2009-06-24
		From supreet: What are some real-world 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		2009-06-15
		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		2009-05-14
		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		2009-04-20
		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		2009-03-07
		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		2009-03-01
		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		2009-02-14
		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?		2009-01-17
		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		2008-12-18
		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		2008-11-18
		From Scott: A homeowner wishes to insulate her attic with fiberglass insulation to conserve energy. The insulation comes in 40-cm-wide 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		2008-09-25
		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		2008-09-24
		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		2008-09-16
		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		2008-09-11
		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		2008-08-20
		From kelvin: find the are and perimeter of a square with diagonal of 200 meters? Answered by Penny Nom.
	Limit as it Approaches Infinity		2008-07-29
		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 x-cosx/x x->oo Answered by Harley Weston.
	The length of a side of a square		2008-07-27
		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		2008-07-26
		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?		2008-06-13
		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		2008-05-28
		From paul: 4x^3 - 6x + 2 = 0 Answered by Janice Cotcher.
	What is the length of the 3rd side?		2008-05-23
		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		2008-05-16
		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		2008-05-06
		From Nomaan: factorise x³-2x²-x+2 using factor theorem Answered by Penny Nom.
	The Pythagorean theorem with triangles rather than squares		2008-04-29
		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		2008-04-24
		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 30-60-90 triangle		2008-04-16
		From Ron: 30-60-90 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		2008-04-02
		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?		2008-03-30
		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?		2008-03-22
		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		2008-03-19
		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		2008-02-21
		From tim: is there a formula for finding the diagonal of a rectangle? Answered by Penny Nom.
	A triangle and a rectangle		2007-12-14
		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		2007-10-31
		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		2007-10-27
		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		2007-10-04
		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		2007-09-29
		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		2007-08-20
		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 mid-point 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		2007-08-07
		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		2007-08-03
		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		2007-08-01
		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		2007-07-29
		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		2007-07-20
		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		2007-07-19
		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		2007-06-23
		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		2007-06-18
		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		2007-05-31
		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		2007-05-28
		From arun: a semi circle is drawn with ab as diameter from p a point on ab a line perpendicular to ab is drawn meeting circumference of semi circle at c, ac = 2cm, cd = 6cm find area of the semi circle? Answered by Penny Nom.
	The area of a pyramid		2007-04-28
		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		2007-04-14
		From Rajendra: Find the remainder when x3+3x+1 is divided by x+pi Answered by Penny Nom.
	How far apart are the cars?		2007-04-07
		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		2007-04-04
		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^2-14x+24. Find the value of b?		2007-03-11
		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^2-14x+24. Find the value of b? Answered by Penny Nom.
	Finding the vertical height of a roof		2007-03-05
		From Zainab: The question is: If the vertical height if a triangle is half the width of the base and the slant length is 6 metres, find the exact vertical height of this part of the roof. I'm actually confused about finding out the height of an equilateral triangle if you're only given the length or slant height. Please help! O.o Answered by Stephen La Rocque.
	The factor theorem		2007-03-04
		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) (x-2) are both factors of x^3+Ax^2+Bx-12 and find the values of A, B, and C so that (x-3) (x+1)and (x-2) 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		2007-03-04
		From Colburn: 27 feet long base 14 feet height what is the diagonal Answered by Stephen La Rocque.
	Line segments on dot paper		2007-01-21
		From Khaori: The three line segments below are drawn on centimeter dot paper. a. Find the length of each segment to the nearest ten-thousandth of a centimeter. b. Could these line segments be arranged to form a triangle? If no, explain why or why not. If yes, answer this question: could they form a right triangle? Explain why or why not. Answered by Penny Nom.
	A rhombus		2006-12-26
		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		2006-12-12
		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		2006-12-07
		From Erika: If f(x) = (x^2)(square root of [3-x]) 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 (x-2) the remainder is 3		2006-11-09
		From Brianna: For the dividend, find the value of k if the remainder is 3. (kx^2+3x+1) divided by (x-2) Answered by Penny Nom.
	The height of a triangle as a function		2006-10-19
		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		2006-10-02
		From Ashley: How do you find the hypotenuse of a right triangle? I don't understand how to find c. Answered by Stephen La Rocque.
	X^1/3-X^1/9=60		2006-09-26
		From Harini: I need the answer for The value of X in X^1/3-X^1/9=60. Answered by Penny Nom.
	I need to cut an octagon		2006-09-23
		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		2006-09-15
		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		2006-09-11
		From Sydney: (√x + 5)4 expanded using the binomial theorem Answered by Penny Nom.
	What are the 3rd and 4th terms of (2x-y)^7?		2006-06-18
		From April: What are the 3rd and 4th terms of this sequence: (2x-y)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		2006-06-08
		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		2006-05-18
		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		2006-05-09
		From Vicky: How do you the Pythagorean relation to find the length of the hypotenuse x to one decimal place? x2 = 3.62+ 5.32 My teacher, Mr. Mutrie, wants to know what this means? SOH CAH TOA Answered by Harley Weston.
	Cutting an octagon from a square		2006-05-07
		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		2006-04-26
		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		2006-04-20
		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+2x-3 is a factor f(x)=x^4+2x^3-7x^2+ax+b		2006-04-06
		From Maha: Given that x2+2x-3 is a factor f(x)=x4+2x3-7x2+ax+b, find a and b and hence factor f(x) completely. Answered by Penny Nom.
	The area of a block of land		2006-03-26
		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.		2006-03-24
		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.		2006-03-13
		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		2006-03-08
		From Skye: Show that (x+2) is a factor of f(x) where: f(x) = px3 + (4p+2)x2 + (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		2006-02-09
		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		2006-01-20
		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		2006-01-16
		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		2006-01-03
		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		2005-12-22
		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)=3x2 + 2x +5 [-1, 1] Answered by Penny Nom.
	Folding a sheet of paper		2005-12-15
		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		2005-11-02
		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		2005-10-19
		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		2005-10-18
		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		2005-10-07
		From Ron: If f(x) is divided by (x-3), 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 (x-3)(x+1). Answered by Chris Fisher.
	City A is 30 miles directly north of City C		2005-10-04
		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		2005-09-22
		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		2005-08-29
		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		2005-08-09
		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		2005-06-22
		From Raymond: Given that 4x3 - kx is divisible by 2x+1, find the remainder when the expression is divided by 4 - x2. Answered by Penny Nom.
	arccos(5/13)		2005-05-31
		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		2005-05-21
		From Jeremy: i need to find the area of an octagon with each side measuring 1 foot Answered by Penny Nom.
	A right triangle		2005-05-18
		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		2005-04-03
		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		2005-03-18
		From A roofer?: A right triangle (roof of a house) has a base of 7 feet and a 22 degree angle. What is the height of the roof and what is the hypothenus of the triangle. Answered by Penny Nom.
	A diagonal in a cube		2005-03-06
		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		2005-01-17
		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		2004-11-24
		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		2004-10-24
		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		2004-10-13
		From Tiffany: I was wondering if you have any real-life uses of the pythagorean theorem that you use in your everyday life. Answered by Penny Nom.
	A theorem involving a trapezoid		2004-09-29
		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		2004-09-29
		From Deb: I am trying to figure out how many square feet are in a piece of property. Start at Point A-then go 140 feet north-then 100 feet due east-then 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		2004-09-17
		From Florita: My daughhter, who is a 9th grader is attempting to cut a piece of wood after determining the length of the cut for the hypotenuse. These are the measures: a=4squared, b=6squared. She determined that c should equal 52. But when she measured the actual piece to be cut, c measured 39.5 inches! Can you offer any insight as to what she is doing wrong? I have suggested that she may be working with an Acute rather than a Right angle . But she insists that it is a Right angle after using a "framing square". Answered by Claude Tardif.
	A cube is inscribed inside a sphere		2004-08-18
		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		2004-07-13
		From Levi: I'm building an octagon playhouse for my son that is 8 feet wide. what would be the measurements of each of the eight sides. Answered by Harley Weston.
	How far apart are they?		2004-05-23
		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		2004-03-29
		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		2004-03-17
		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		2004-03-08
		From LisaMarie: Hi, I have a career link question from gr.12 advanced functions and intro. calculus. The equations is: R(t) = 5(t4 - 4t3 + 19/4 t2 - 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		2004-02-27
		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		2004-01-24
		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		2003-11-22
		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		2003-10-29
		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		2003-09-11
		From Jaidev: Is there any general equation for a sphere? Answered by Penny Nom.
	A 16 foot ladder		2003-09-04
		From Kelly: Two buildings are separated by a three-foot 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		2003-08-30
		From William: According to page 126 of Murtha & Willard's "Statistics and Calculus" (Prentice-Hall, 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		2003-07-09
		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		2003-04-06
		From Rosa: If Each side of an equilateral triangle is 10 m. What is the height? Answered by Penny Nom.
	Friends and enemies		2003-03-24
		From Becky: Consider a room that contains six people. Any two people are either friends of each other, or they are enemies. A. Argue why there are three people, all who are friends, or there are at least three people, all who are enemies B. Rephrase the situation using graph terminology, using all of these terms correctly: vertex, edge, graph, complement, clique, independent set, and bipartite. Answered by Penny Nom.
	A triangle and a circle		2003-03-21
		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		2003-02-04
		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'4-12x'3-44x'2+24x c)x'4-21x'2-100 Answered by Penny Nom.
	Factoring a cubic		2002-12-05
		From Dorota: I got a problem with factorise the expression 2x3+11x2-5x-50. Answered by Penny Nom.
	The height of a triangle		2002-11-29
		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		2002-10-27
		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		2002-10-14
		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		2002-09-10
		From Yael: Prove (x - a - b) is a factor of x3 - a3 - b3 - 3ab (a + b) Answered by Penny Nom.
	A limit		2002-09-03
		From Circe: Lim 3x 3+ax+a+3 /(x 2+x-2), X->-2 Answered by Penny Nom.
	Overlapping circles		2002-05-29
		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		2002-05-22
		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 octagon-shaped deck		2002-02-20
		From An instructor: How can you solve for finding the side measurements of an octagon-shaped deck that is 10 feet long and 10 feet wide. Answered by Penny Nom.
	A degree 5 polynomial		2002-02-17
		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		2002-01-20
		From Tony: When rolling 2 dice, what is the probability of rolling 5 sevens before rolling a six or an eight? Answered by Andrei Volodin and Penny Nom.
	Multinomial theorem		2001-11-28
		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		2001-11-15
		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		2001-10-09
		From Tania: How could I demonstrate: nCp is congruent to floor(n/p) (modulo p)? where rCk is a binomial coefficient, rCk = r(r-1)...(r-k+1)/k(k-1)...1, and p is a prime number Answered by Richard McIntosh.
	The Mean Value Theorem		2001-07-23
		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) = |x2-25| on the interval [-10,0] Answered by Harley Weston.
	Dots on squared paper		2001-03-30
		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		2001-01-22
		From Phillipe: How do you find the hypotenuse of a right triangle? Answered by Penny Nom.
	The Pythagorean Theorem		2001-01-08
		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		2001-01-06
		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		2000-09-09
		From Becky: What are all the real values of x that are solutions for the inequality [x-2] < 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		2000-06-26
		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		2000-06-02
		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		2000-05-22
		From William Wright: I am a Calculus Teacher, and me and my class ran into these two problems without solutions in my manual, we got answers, but are unable to check them. If anyone gets this email and can respond to this with the solutions it be greatly appreciated. . . . Answered by Harley Weston.
	The pythagorean theorem		2000-05-19
		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		2000-03-23
		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		2000-02-24
		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		2000-01-11
		From Dylan Kirkwood: How can you factor a quadratic equation by graphing it? Answered by Penny Nom.
	Solving a cubic equation		1999-12-30
		From Natalia: How can I solve: 2 x3 - x2 + x - 2 = 0 ??? Answered by Penny Nom.
	The area of a garden		1999-12-17
		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		1999-12-17
		From Michael Standfest: If x+4 is a factor of 2x4+kx3-3kx2+6x-40, find k and Prove that n2-n is even for all n, using the proof of contradiction Answered by Penny Nom.
	Advanced Calculus		1999-12-07
		From Kay: Hi, my name is Kay. Please help---these 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		1999-07-11
		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		1999-04-15
		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		1999-03-30
		From Maggie Stephens: I don't know anything about factoring would you plese help me. 3x4 - 48 54x6 + 16y3 125-8x3 12x2 - 36x + 27 9 - 81x2 a3 + b3c3 I would greatly appreciate any help you can give me thanks. Answered by Jack LeSage.
	Factoring polynomials		1999-03-29
		From Karen: I have been unable to factorise a polynomial equation and was wondering if you could please help. It is level (10-12) maths. The polynomial is x3 + x2 - 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		1998-12-31
		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		1998-10-01
		From Tom Barker: My eighth grade niece called with the following homework problem: A teacher wanted to divide her class into equally numbered groups. She tried to divide the class into groups of two, but was one student short. She tried to divide the class into groups of five, but was one student short. She tried to divide the class into groups of seven and was successful. What is the least number of students that were in her class? I know the answer is 49, but don't know how to prove it. I must be getting old if I can't solve eighth grade math problems. Your assistance would be appreciated. Answered by Penny Nom.
	The Factor Theorem		1998-01-18
		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		1997-08-28
		From Faye Tan: I am a trainee teacher. I would appreciate it very much if you could help me solve the following two problems which I think are meant for students at middle grade. 1. If a hen and a half lays an egg and a half in a day and a half, how many hens are needed to lay a dozen eggs in one day? 2. There are fewer than 200 passengers on a train. If they get off in pairs, one passenger will be without a partner. If they get off in groups of 3 or 4, there will still be one passenger left by himself. However, if they get off in groups of 5, no one will be left by themselves. How many passengers are there on the train? Answered by Penny Nom.
	A Monte Carlo Procedure		1997-04-23
		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		1997-04-21
		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		1997-04-13
		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.		1997-03-21
		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.		1997-02-23
		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		1996-04-09
		From Mike: 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		2006-06-06
		From Jean-Claude: 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.

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