







4sin(2x)cos(2x)+1=0 
20200702 

From Sheila: 4sin(2x)cos(2x)+1=0 Answered by Penny Nom. 





cos (3pi/2 x) 
20191120 

From sam: 1. express the following as a trigonometric function of angle x for cos (3pi/2 x)
the answer in the textbook is sin x but i am unsure of the process to get the answer. Answered by Penny Nom. 





The area of a triangle in acres 
20190623 

From Karen: if I have a triangle that measures 78 ft x 54 ft x 50 ft, how do I figure out what part of an acre that is?? Answered by Harley Weston. 





Loan payment formula 
20190224 

From Kenneth:
I have a question regarding the loan payment formula shown below.
Calculating the Payment Amount per Period
The formula for calculating the payment amount is shown below.
Simple Amortization Calculation Formula
A = P X r(1 + r)n over (1 + r)n  1
where
A = payment Amount per period
P = initial Principal (loan amount)
r = interest rate per period
n = total number of payments or periods
Is this formula/calculation a condensed version of a longer calculation? I am curious to know how the (1 +r)n  1 was developed from the longer calculation. For example, r(1 + r)n may have been (r + rn)n. The n's are exponents.
I thank you for whatever helpful explanation that may be provided.
Kenneth Answered by Harley Weston. 





cos(2x) = sin(x) 
20181218 

From Liz: Determine all values of x in [0,2pi] that solve the equation Cos(2x)=sinx Answered by Penny Nom. 





Simplify 1/2^i 
20180128 

From Deepak: How do I simplify this complex equation:
z=1/(2^i) Answered by Penny Nom. 





Euler's polyhedron formula 
20160520 

From Antonia: why does not cylinders follow Euler's polyhedron formula ( VE+F=2) ??
if a cylinder has 3 faces, 2 edges and 0 vertices it doesn't follow Euler's formula??? Answered by Penny Nom. 





sin 2x  sin x = 0 
20160424 

From lilly: sin 2x  sin x = 0 0 Answered by Penny Nom. 





Solve for theta 
20140425 

From ALASTAIR: Hi, The question asks Solve for 'theta' cos2theta=sintheta x costheta.
Substituting for cos2th either 12sin^2th or 2cos^2th does not give an equation in either sine or cosine alone how do I solve this please? Answered by Penny Nom. 





Compound interest 
20130510 

From Kyla: I am doing correspondents and cannot figure out how to explain the solution to this question, I do not understand how they came to this answer and need it explained step by step so I can complete the following questions in this unit, please help!!!
Calculating compound Interest
Johnny invest $800 that pays 8% compounded quarterly for 5 years. How much is the investment worth at the end of the 5th year? Answered by Penny Nom. 





How do i reverse this formula? 
20130420 

From MK: I have 22,000,000 worth of gold and wants to want to resell the gold back with a profit.
Each transaction of gold will have a transaction fee of 15%, so if i resell the gold back at 22,000,000, I will only get back 18,700,000 after 15% transaction cut.
The current formula is X15%X = Y where X = 22,000,000 and Y = 18,700,000
Will u be able to come up with a new formula if we don't know the value of X but we know the value of Y
Something like this X15%X = 22,000,000.
How do i reverse this formula to find the value of X
Thanks Answered by Penny Nom. 





A trig identity 
20130104 

From Tehmas: Prove sinC+sinD=2sin(C+D/2)cos(CD/2) Answered by Harley Weston. 





The quadratic formula 
20130103 

From itsel: Find the discriminant ans use it to determine the use the quadratic formula to solve the equasion 2x^2+3x+2=0 Answered by Penny Nom. 





The area of a quadrilateral 
20120421 

From Rajat: calculate the area ABCD in which AB is 48'1'',BC is 98'4'',CD is 61'4'',DA is 102'10'',AC is 110'3'',BD is 116'9''. Answered by Penny Nom. 





Three sides of a triangle 
20111224 

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





A mythical soccer ball 
20111027 

From Joel: We've been working on this problem diligently and can't seem to come up with the answer book's answer. We think it may be wrong, yet want to check it with an expert. Here goes.
The school's new soccer balls are covered with 64 regular hexagonal panels. Each hexagon measures 2 inches between opposite corners and 1.5 inches between opposite sides. What is the total surface area of the soccer ball? Answered by Robert Dawson and Lorraine Dame. 





Solve x(x3) = 5 (x+4) 
20110419 

From Ashley: I have to solve using the quadratic formula. And my answer should be in simplest exact form. And I can't approximate.
I really need help to prepare for a test ....
x(x3) = 5 (x+4) Answered by Penny Nom. 





If 25 items are evenly spread over 7 days 
20110323 

From michael: What is the formula to calculate:
If 25 items are evenly spread over 7 days, but one day has 3 items less than the other days, what is the number if items for each of the remaining 6 days? Answered by Penny Nom. 





Vertices and sides of a polygon 
20110304 

From RINA: My questions is : would a vertices and sides of a polygon be the same number. For example, a octagon it has 8 points and 8 sides. Am i correct? Answered by Robert Dawson. 





Can determine if it is scalene, isosceles, or equilateral 
20101201 

From Jessie: find the measures of the sides of triangle KPL and classify each triangle by its sides. my first problem would be K(3,2) P(2,1) L(2,3) ...The three points they give you are the vertices of the triangle and you need to match them up. Draw the triangle and write in the vertices and the related point with the vertex. You will then do the distance formula three times to find the distance of all three sides. Once you have the three sides you can determine if it is scalene, isosceles, or equilateral...using the distance formula how do i solve this? Answered by Penny Nom. 





Two girls agree to mow a lawn 
20101123 

From Milorad: Two girls agree to mow a lawn 60m by 80m so that the first girl cuts one half by
cutting a uniform strip around the lawn. How wide a strip should the first girl cut?
I've been struggling with the question above, mainly with the equation and I have
set it up as 2400=(602x)(802x), if this is incorrect I would like to know where I've
gone wrong and also would like a full answer to see it properly done. I need an algebraic
answer and not one with a diagram. Answered by Penny Nom. 





i^i 
20101121 

From trale: Can we use e^ix=cosx+isinx for finding i^i like that: x= pi/2 =>
e^(ipi/2)=0+i then [e^(ipi/2)]^i=i^i.then we find i^i= 0,207879576....
is it true? can we give value for x for free?thank you. Answered by Harley Weston. 





Compound interest 
20100601 

From Kenneth: Hello:
I have a question regarding the following compound interest and future value
calculation.
Year 1 P + rP equals balance after the first year.
Year 2 (P + rP) + r(P + rP) equals balance after the second year.
Year 3 ? equals balance after the third year.
This question is in two parts.
1. What would follow for year three?
2. I know that a pattern will develop. What will it be so that I can determine
the extended pattern for following years ? Answered by Penny Nom. 





A trig equation 
20100428 

From Steve: 2cos^2(X)2sin^2(x)+1=0 Answered by Harley Weston. 





cos(x) = sin(x  1) 
20100428 

From alex: In the equation cos x = sin x1 for pi/2
A: solve for x graphically
B: solve algebraically and prove the solution is correct.
Alex Answered by Penny Nom. 





If (x, 4) is equidistant from (5, 2) and (3, 4), find x. 
20100421 

From abeth: If (x, 4) is equidistant from (5, 2) and (3, 4), find x.
Find the point on the y  axis that is equidistant from (4, 2) and (3, 1). Answered by Penny Nom. 





A model for the population of a Canadian city 
20100407 

From jess: Let t^2 represent tsquared. The population of a Canadian City is modelled by: f(t) = 12t^2 + 800t + 40,000, where t is the time in years. When t= 0, the year is 2007.
a) According to the model, what will the population be in 2010?
B) In what year is the population predicted to be 300,000? Answered by Penny Nom. 





Trigonometry and picture hanging 
20100113 

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





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. 





Completing the square 
20090427 

From Daniel: I tried following an example of yours but I still couldn't figure it out.
Here is my question,
2x^2  6x + 1 = 0.
Any help would be greatly appreciated. Answered by Stephen La Rocque. 





2sinB=3tanA 
20090410 

From Xanathax: ABC is a rightangled triangle. 2sinB=3tanA.
Calculate the measure of angle A. Answered by Penny Nom. 





Winding paper after a break 
20090410 

From Olen: Question from Olen:
I work in a paper mill and have been handed the task to search for a formula to determine how much paper needs to be added to a parent roll to make up the difference at the winder. (Ex. The spool diameter at the reel is 18.25" we measure roughly 33.5" to make two 58" rolls in the winder. If the is a paper break and the roll diameter in the winder is 30" how much do I add to a single parent roll (22" roughly) to make one 58 " and the 28" needed at the winder. I would appreciate any help to complete this task. I would like to be able to build a chart that operators can refer to based on what is needed. Thank you. Answered by Harley Weston. 





Time in a Swing 
20090222 

From Barb: I looked at the questions concerning a pendulum as I know I need to use this formula but I am stiil not able to figure this problem out. Can you help?
If a child is on a swing with a 10 foot chain, then how long des it take to complete one cycle of the swing?
I know I am suppose to use the formula 8T^2 = pi^2 L but I do not understand how to do this.
Thanks Answered by Janice Cotcher. 





The height of a triangle 
20090214 

From GARIMA: IF THE SIDES OF TRIANGLE ARE GIVEN . HOW WE WILL
CALCULATE THE HEIGHT OF TRIANGLE. Answered by Penny Nom. 





Faces, edges and vertices 
20090204 

From sheila: what is the relationship between the number of faces and the number of edges of a triangular pyramid ? Answered by Penny Nom. 





Archimedes' formula for parabolic arches 
20090123 

From La: Use calculus to verify Archimedes' formula for y=9x^2. Prove Archimedes' formula for a general parabolic arch. Answered by Harley Weston. 





Gravity's Effect at a Distance 
20081206 

From ROHAN: AT WHAT HEIGHT FROM THE SURFACE OF EARTH,THE WEIGHT OF THE BODY BECOMES HALF? (RADIUS OF THE EARTH = 6400) Answered by Stephen La Rocque. 





The height of an equilateral triangle 
20081106 

From touqeer: My question is that how can we find the height of an equilateral triangle without using pythagoras theorem? Answered by Penny Nom. 





I have 6 vertices and 10 edges 
20081020 

From Jacquelin: I have 6 vertices and 10 edges. One of my faces is a regular polygon. Answered by Chris Fisher. 





3,6,10,15,and 21 
20080928 

From jarred: i am currently stumped on a math project that requires me to find out the recursive formula for a sequence of numbers. the numbers in the sequence are 3,6,10,15,and 21. Thank you for your time. Answered by Walter Whiteley. 





A Falling Rock 
20080711 

From Rita: This question has 3 parts.
If a rock falls from a height of 20 meters on the planet Jupiter, its height H
(in meters) after x seconds is about H(x) = 20  13x^2
(a) What is the height of the rock when x = 1.2 seconds?
(b) When is the height of the rock 15 meters?
(c) When does the rock strike the ground?
Thank you Answered by Janice Cotcher. 





A recursive formula for 9, 18, 36, 27, ... 
20080605 

From Rita: I am having trouble understanding how to write formulas (I should say create formulas) from a given sequence.
It does not matter what sort of sequence it is. The confusion remains.
I have not found a textbook or easy math book that explains this process for the average Joe to grasp.
Here are the two questions:
(1) Write a recursive formula for the sequence
9, 18, 36, 72, ...
(2) Write a recursive formula for the sequence
3, 3(sqrt{3}), 9, 9(sqrt{3}) Answered by Penny Nom. 





A shape 
20080403 

From Joshua: what shape has 4 faces, 4 corners and 9 edges. Answered by Penny Nom. 





The area of a piece of property 
20080105 

From Greg: I need to know the area of a six sided piece of property. I sent a map by regular mail. Answered by Harley Weston. 





Shooting an arrow over a wall 
20071211 

From Amy: The path of a large arrow fired from a non
torsion catapult can be modeled by y=0.0044x^2 + 1.68x, where x is the distance the
arrow travelled (in yards) and y is the height of the arrow (in yards). Given the height of
a castle wall, find the safest distance from the wall to launch an arrow over a 120 yardhigh wall. Answered by Victoria West and Stephen La Rocque. 





Area of a 17sided lot 
20071121 

From Lynda: My uncle is wanting to buy this piece of land [a 17sided polygon] but we are questioning the acerage total. the measurements are [on the attached diagram]. Answered by Stephen La Rocque. 





The height of a triangle 
20071103 

From William: I need to find the height of a triangle if the base is 15, one side is 14 and the other side is 13. Answered by Stephen La Rocque and 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. 





Area of a triangle formed by three points on a graph 
20071026 

From Betty: My question is 'find the are of a triangle whose vertices have
coordinates (3,5),(6,5), and (4,10) Answered by Stephen La Rocque. 





A triangular lot 
20071017 

From Brian: Seeking the square footage of a triangular property lot, dimensions are: 620 X 620X 720. Answered by Penny Nom and Melanie Tyrer. 





Four triangles in a square 
20071015 

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





Triangle perimeter and area 
20071005 

From divakar: The sides of the triangle are integers. The perimeter is 8. What is the area? Answered by Stephen La Rocque. 





Can you solve this by factoring? 10r^2  35r = 10 
20070812 

From Aranxa: how do u solve this equation by factoring:
10r^2  35r = 10 Answered by Stephen La Rocque. 





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

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





Using Heron's Formula to help maximize the area of a triangle 
20070627 

From Claire: Given one side of a triangle is 4 cm and the ratio 1:3 for the other 2 sides. What is the largest area of the triangle? Answered by Stephen La Rocque and Harley Weston. 





Circumscribing a golden cuboid with a sphere: surface areas 
20070614 

From Ainslie: A golden cuboid is defined as a rectangular prism whose length, width and height are in the ratio of phi : 1 : 1/phi.
Prove that the ratio of the Surface Areas of the golden cuboid to that of the sphere that circumscribes it is Phi : Pi. Answered by Stephen La Rocque. 





Angles of depression 
20070613 

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





Solving a quadratic equation using the Quadratic Formula 
20070605 

From Stuart: Solve the following quadratic equation:
3xsquared5x4=0 Answered by Stephen La Rocque. 





Finding the area of a lot without knowing the angles 
20070605 

From Cristin: I have a landlocked piece of land. I need to know the square
footage in order to determine the acreage. My deed only gives the lengths of its five sides. Answered by Stephen La Rocque. 





The area of a parcel of land 
20070403 

From Ricky: I need the attached land parcel (#0436) converted to acreage.
This would be of great help to me.
Thanks,
Ricky Answered by Penny Nom. 





The area of an irregular pentagon 
20070326 

From grace: hi I am doing graphics and need to find the area of the section given to us (it is just drawn). the sides measure 15m, 35.4m, 5m, 17.8m, 35.7m. the angle between the 15m side and the 35.4m side is 17degrees, the angle between the 35.4m side and the 5m side is 73degrees. the angle between the 5m side and the 17.8m side is 151degrees, the angle between the 17.8m side and the 35.7m side is 90degrees and the angle between the 35.7m side and the 15m side is 95degrees. if you could tell me the area i would be extremely grateful. thanks very much. Answered by Penny Nom. 





Triple angle tangent formula 
20070315 

From sam: Hi I am trying to derive a triple angle formulae for tan. I know i need to use compound and double angle formulae but am finding it difficult to "clean" up my fraction to get the triple angle formulae can you show me a worked derivation?! thanks Answered by Penny Nom. 





The area of a property 
20070314 

From Greg: Hi my name is Greg. I have a piece of property I am trying to buy,
but need to find out the square feet of it first.
The four sides are unequal lengths and none at a right angle or
parallel. Here are the measurement in feet.
The base of the square is 29.12 feet in width.
The right side of the square is 44.33 feet high.
The top of the square is 28.80 feet in width.
The left side of the square is 46.20 feet high.
I have not done this math in ages and really need your help. Answered by Harley Weston. 





Finding the xintercept 
20070302 

From Ash: Y = 1/100X^2 =27/10X +0 = 0 THE Y INTERCEPT IS 50 HOW DO I FIND THE X INTERCEPT Answered by Gabriel Potter. 





sin(3a), cos(3a) and tan(3a) 
20070228 

From mailene: hi, i...indeed,to..need..your..help how..cn..i..prove..this,formula??? sin3a=3sina4sin^3a cos3a=4cos^33cosa tan3a=3tantan^3a /13tan^2a the..symbol...^is..the..expOnent Answered by Haley Ess and Penny Nom. 





Find the area of the triangle 
20070220 

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





What constitutes a face for a geometric solid? 
20070214 

From Erica: What constitutes a face for a geometric solid? We have been getting conflicting answers from different textbooks. Some teachers are saying that cylinders and cones do not have faces. I'm thinking that cylinders have 2 and cones have 1. Please enlighten me. Thanks! Answered by Walter Whiteley. 





Irregular multi sided polygon 
20070120 

From Graham: I have an irregular polygon. I know the length of all the sides and know approximately all the internal angles. Is there a formula or table that can calculate the area for me? Answered by Steve La Rocque, Chris Fisher and Penny Nom. 





The area of an irregular octagon 
20060823 

From Billy: How do you figure the area of an irregular octagon? Measurements are 4 equal sides of =BD", and 4 equal sides of =BE". It measures 1 1/2" = from flat to flat. Answered by Penny Nom. 





The area of a triangle 
20060521 

From A student: how do you find the area of a triangle? Answered by Penny Nom. 





A hallway in an old house 
20060506 

From Sabrina: I am trying to determine how many square feet is in a room that is not square or rectangular. It has basically 5 walls of different lengths, it is acutely considered a hallway in an old house, how can I figure out the footage, the Length times Width requires to much wasted materials Answered by Penny Nom. 





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. 





cos(3X) 
20060329 

From Joshua: I'm having trouble proving that cos(3X)=cos^{3}X (cosX)(sin^{2} X) 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. 





The quadratic formula 
20060303 

From Miriam: Please show work and indicate "answer", using the quadratic formula 
(x+2) (2x+3) = 6 Answered by penny Nom. 





Is there a solid shape with 5 faces, 8 edges, and 4 vertices? 
20060211 

From Annie: Is there a solid shape with 5 faces, 8 edges, and 4 vertices? Answered by Penny Nom. 





Area of a lot 
20051203 

From Ben:
How do you calculate the area of the following Lot?
I figured the following angles from the deed, which read:
N 86 degrees, 45 minutes E, for 322 feet.
S 10 degrees, 30 minutes W for 113 feet.
N 84 degrees, 30 minutes W for 368 feet.
N 50 degrees, 42 minutes E for 76 feet.
N 40 degrees, 40 minutes E for 15 feet.
There is a discrepancy between two surveyors and I'd like to figure out how to calculate the Area of such a shape. Answered by Harley Weston. 





I = PRT 
20051116 

From Ryan: Use the formula to find the value of the variable that is not given:
I=PRT;I=$2880, R=0.08, P=$12,000 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. 





The area of a lot 
20050717 

From John: A plot of land has the following dimensions: 391 ft. x 757 ft. x 208 ft. x 788 ft. Q: How many acres is this? Answered by Harley Weston. 





sin x + sin 2x + sin 3x + sin 4x = 0 
20050510 

From Elia: I tried many times, but can't get to solve the following question:
sin x + sin 2x + sin 3x + sin 4x = 0 Answered by Chris Fisher. 





Some triangle problems 
20050506 

From A student: 1.use the
heron's formula to find area of triangle ABC to nerest tenth
A.a=21 b=28 c=11
B.a=23 b=28 c=12
2.Find the nearest tenth the altitude of the longest side if a=3 b=3 c=5
3.the length of each side of a rhombus is 10 cm the length of one diagonal
is 12 cm find the area to the nearest square centermeter 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. 





The area of a quadrilateral 
20050227 

From Jonathan: I want to know how to find the area of a quadrilateral. Answered by Penny Nom. 





Finding the missing side of a triangle 
20050120 

From Jason: I found a geometry problem that reads as follows:In triangle ABC, Answered by Penny Nom. 





The area of a triangle 
20041230 

From Perry: What is the area of a triangle with dimensions 3"X5"X7"? Could you provide the formula? Answered by Penny Nom. 





sin(3A) 
20041020 

From A student: Express sin3A in terms of sinA and cosA. Answered by Penny Nom. 





Finding the height of a triangle 
20040914 

From A student: I have to calculate the height of a triangle.
The base is 6 (units)say ab
One of the top sides is 4 (units)say ca
The other side is 2 (units) say cb
I don't know the angles.
How to find the height? Answered by Chris Fisher and Penny Nom. 





The distance formula 
20040904 

From Joe: Why do we use square roots and squares in the distance formula Wholdnt they cancel each other out? Answered by Claude Tardif. 





Some trig expressions 
20040523 

From A student: Prove:
sin A + sin B = 2sin(A+B/2)cos(AB/2)
cos A  cos B = 2sin(A+B/2)sin(AB/2)
cos A + cos B = 2cos(A+B/2)cos(AB/2)
sin A  sin B = 2cos(A+B/2)sin(A+B/2) Answered by Penny Nom. 





The area of a plot of land 
20031219 

From David: I have a plot of land that I cannot find the square footage of. Actually my home sits on a large lot. Local building codes require that a home is seated on no less than 7500 square feet of land and have no less than 50ft of road frontage (the rear of the lot has 65ft of frontage on another road). I need to know if I have enough square footage to build a second home on the rear lot. The lot has five sides. Only one angle is a 90 deg. angle. The others I cannot determine. Of the 4 remaining angles, all 4 angles are obtuse, or greater than 90 deg. The dementions are 89.19' x 130' x 118.52' x 65' x 170.94'. The two legs that make the 90 deg angle are 89.19' and 170.94'. The measurements fall in order using the 90 deg angle as the point of origin and proceeding clockwise, 89.19', 130', 118.52', 65', 170.94'. I have used all the skill I can muster, however, it has been a long time since school and regretably I cannot find an answer. Answered by Penny Nom. 





The area of a triangle 
20031201 

From A student: Find the Area of Triangle ABC
A(3,2)
B(4,0)
C(0,8) Answered by Penny Nom. 





The volume of an irregular tetrahedron 
20031124 

From Peter: How do I calculate the volume of an irregular shaped tetrahedron where: side a = 1.4 m side b = 1.4 m side c = 1.2 m and height = 0.75 m at the junction of sides a and b. Answered by Penny Nom. 





The quadratic formula 
20030831 

From Alex: I am using Houghton Mifflin's Precalculus with Limits book, 2nd edition. However, the first chapter encompasses Algebra review, and I am stuck on a problem. All that's required is to solve the following and verify using a calculator: 3y2+6y+2=0 I have solved the problem using the quadratic formula, but from what I remember, the quadratic formula is used in the case of equations following the AX2+BX+C=0 pattern. As the problem I am attempting uses a yvariable, can I still use the quadratic formula? Since I am not sure what route to take in solving this problem, I am hoping you can assist me. Answered by Harley Weston. 





A rule with a variable 
20030824 

From Crystal: what is a rule with a variable Answered by Penny Nom. 





Write sin(3x) in terms of sin(x) 
20030505 

From A student: Write sin 2x in terms of sin x Answered by Penny Nom. 





Formulating equtions 
20020914 

From Theresa: Hello. In math class we have to formulate equations for certin questions for extra credit. We are allowed to ask anyone and anyone can do it for us and explain it to us. Could you please do that? Here are the questions  Jordan has 3 times as much money as Reva. Together they have $44. How much money does each have?
 The Tigers played 48 games. They won twice as many as they lost. How many did they win?
 There are 900 students in Sewickley Academy. There are 20 more girls than boys. How many girls are there?
 A board 400 cm long is cut into 2 pieces. One piece is 66 cm longer than the other. Find the lenght of the shorter piece.
Answered by Penny Nom. 





The quadratic formula 
20020911 

From Kathleen: im having a problem trying to understand quadratic formulas can u please help me i have problems like 3x^{2}  4x  11 = 0 how do i work out that problem? i have the formula written down but it doesnt seem to register for me. Answered by Penny Nom. 





The area of a triangle 
20020907 

From Phill: How do you find the area of a equilateral and other triangles? Answered by Penny Nom. 





Distance in 3space 
20020816 

From David: The question is: how do I figure out the distance of one object in 3D space to another object in 3D space? I have an object at say x = 5.872, y = 2.876, and z = 7.290; and the other object is at x = 1.129, y = 8.213, and z = 11.127. I have been suggested to use the pythagorean theory on this, but since there are three variables, I don't understand how. Answered by Penny Nom. 





The area of a circle 
20020603 

From Jessica: I am doing a maths assigment for university, which is aimed towrds primary school students(k6). I was wondering if you could give me some information as to how I could describe to students the rule for finding the area of circle, using a circle cut up into equal sectors (like a pizza). I know it has something to do with the fact that you can make these shapes into a parallelogram, but I am a bit uncertain as to how I can express this idea clearly and articulately to students. Answered by Penny Nom. 





A triangular prism 
20020428 

From A student: Need the formula for the surface area of a triangular prisim? Answered by Penny Nom. 





Area of a triangle 
20020407 

From Puzzled: What is the surface area of a triangle 13 ft x 13 ft x 18 ft? Answered by Penny Nom. 





sin 2x = cos 3x 
20020225 

From Allan: solve: sin 2x = cos 3x Primary question: how do you handle the cos 3x? Answered by Paul Betts and Chris Fisher. 





Rewriting and evaluating formulas 
20011119 

From A conserned mother: Due to the wide range of temperatures experienced in Canada, engineers who construct roads must allow for expansion and contraction of the road surface. The following formula is used to calculate the amount of expansion E to allow for: E= kL(Tt), where k is the constant of expansion for the road surface. L is the length of the section of highway in metres. T is the temperature of the air in degrees Celsius. t is the temperature, in degress Celsius, at which the section of the highway was constructed. Answered by Walter Whiteley. 





Faces 
20010221 

From Sandy: How many faces are there on a sphere? What are the faces of a cone? What is the definition of a "face" of a 3D object? Answered by Walter Whiteley. 





An irregular polygon 
20010209 

From Jason: I have a 5 sided irregular polygon I am trying to figure out the area of. There are no right angles in the polygon as far as I can tell. I do not know any angles. Answered by Chris Fisher. 





A problem with distance 
20010116 

From A student: For what values of a is the distance between P(a, 3) and Q(5, 2a) greater than the square root of 26. Answered by Penny Nom. 





Euler's Formula 
20001111 

From Denise Roberts: I'm trying to design a unit (possibly involving a Webquest) on Polyhedra and I cannot find a formula I once used. The formula involved the number of vertices (V), edges (E), and faces (F) of the polyhedra. Answered by Walter Whiteley. 





Triple angle formula 
20000223 

From Sara: Can one derive a triple angle formula for sine and cosine? If so, how? Answered by Chris Fisher. 





Derive the quadratic equation 
20000101 

From Thuy: My teacher asked us this question in which i can't understand when she asked to derive the quadratic equation. What does this mean? Answered by Penny Nom. 





A Trigonometry Question 
19990828 

From Diane Simms: My question is can the following be factored. I am a teacher who needs the factors to this right away. 2 Sin^{2}X + 2 SinX CosX  1= 0 Answered by Harley Weston. 





The Quadratic Formula 
19990122 

From Eric Morgan: Hi my name is Eric Morgan and I m in 8th Grade honors math (middle) and I'd like to know how to prove the quadratic formula b±sqrt of b(a)(c)over 2(a) Answered by Penny Nom. 





Complex numbers and the quadratic formula 
19981225 

From Richard Peter: My age is 16, and my name is Richard. My question relates to the topic complex numbers & the quadratic formula. I would like to know how to solve quadratic equations in which the discriminant is less than 0 (i.e. we get two complex solutions to the quadratic) 3x^{2}+2x+5 = 0 and how mathematicians like euler contributed to this field. If it would be possible I would also like to know how this type of quadratic equations can be graphed? Answered by Harley Weston. 





The bricklayers formula 
19981124 

From Rachel Kaplan: I have to do a report on the bricklayers formula N = 7LH. Can you give me any information on this. Answered by Harley Weston. 





Area of a triangle. 
19980201 

From Jodi Blucher: Is there a formula for the area of an equilateral triangle knowing the length of the sides? Answered by Chris Fisher and Harley Weston. 





Equivalent Expressions 
19970226 

From Karyn Jones: Josie says that s=n/(n+1) and s/(1s)=n are two ways to write the same formula. Describe whether or not you agree with Joise. Explain how you made your decision. Answered by Walter Whiteley and Penny Nom. 





Deriving the Quadratic Formula 
19970204 

From James: How do you derive the quadratic formula? I know what it is, but the textbook doesn't say how to derive it. Answered by Penny Nom. 





problème de trigonométrie 
20051101 

From Manon: Soit un triangle ABC, de cotes a , b et c, avec A=45° et B=60°.
Apres avoir demontre que 3a²2b²=0 (que jai fais en utilisant la regle du sinus) et a²2c²+2ac=0 (que jai fait en utilisant la regle du cosinus), vous montrerez que laire du triangle ABC peut sexprimer: { [ 3 + racine carre 3 ] / 12 } b² unites.
Je ne sais pas comment arriver a cette expression de laire. Je narrive pas a exprimer c² et ac en fonction de b².. et je pense que ca pourrait vraiment aider..
puisque je suis arrive a letape:
ac[(racine carre 3) / 4]
avec ac = a² + c²  b²
et a² = 2/3 b²
ms c²= 1/3 b² + ac Answered by Claude Tardif. 

