







An analytic proof that a quadrilateral is a parallelogram 
20201026 

From Apollo: Prove analytically that if ABCD is a parallelogram in which points P and Q trisects the diagonal AC, then BPDQ is a parallelogram. Answered by Penny Nom. 





A barn roof 
20160529 

From Joe: Is it possible to build a barn roof (irregular pentagon?) with a 12' base and the other 4 sides 4' each? Thanks. Answered by Penny Nom. 





Proof that an erroneous algebraic statement is false 
20151214 

From Berteanu: I need help with this proposition:
"It exists x a real number that for every y real number 5*x2*y*y=1
This is false.
Let x be from R.
And I need an y real number that 5*x2*y*y!=1
Please,could you help me? Answered by Penny Nom. 





The area of a domed roof 
20151113 

From Brandon: I have a tank with a 13' radius that has a domed roof of 3.5' tall How do I figure out the area in SQFT? Answered by Penny Nom. 





Roof Square footage 
20151111 

From Todd:
Question from Todd:
Good Day.
I have to figure out the square footage of a quonset style roof that's not playing by the rules The building dimensions (rectangular) are 63'x135' the height of the roof is 9.25'. It not an entire Quonset, It's that style of roof,(curved). There are concrete block walls 10' up to the metal roof.
Thank you!
Todd Answered by Harley Weston. 





Prove that you cannot factor x squared + 5 
20150528 

From lily: the question is: prove that you cannot factor x squared + 5 Answered by Robert Dawson. 





We can't write sinx and cosx as a finite polynomial. 
20130331 

From rimoshika: prove that we can't write sinx and cosx as a finite polynomial. Answered by Walter Whiteley. 





A shed roof 
20130112 

From christine: A roof on a shed is 7.3 ft wide has an incline of 20 degrees what is the height? Answered by Penny Nom. 





If n is odd, then n^2  3 is even 
20121211 

From Tracy: Prove the statement:
For all integers n, if n is odd, then n2  3 is even. Answered by Penny Nom. 





A storage box with a slanted roof 
20120213 

From Sophia: Hi!
I have another problem.
The diagram shows a side view of a box which is used to store small logs of
wood for burning in a fire place. The slopping lid has an overhand of 15cm.
a) Calculate the total length of the slopping lid to the nearest cm.
b) When the lid is open above ground will the end of the lid be?
P.S. Please see attached. Answered by Penny Nom. 





1 + 3 + 3^2 ...+3^(n1) = 3^n  1/2 
20120127 

From Vicki: I am trying to find out how to do show how this proof was worked.
Here is the end result 1 + 3 + 3^2 ...+3^(n1) = 3^n  1/2
This equation was used to find the number of white triangles in the Sierpinski Triangle Answered by Walter Whiteley. 





Prove sin x = sin (pi  x) 
20110215 

From Janet: Prove sin x = sin (pi  x) Answered by Penny Nom. 





If ac = bc ... 
20110104 

From jamielle: if ac=bc, then a is not equal to b, c is not equal to zero Answered by Penny Nom. 





Modelling the roof of a house 
20100323 

From Sandi: This question has been haunting my dreams at night. It states the cross section of the roof of a house is modelled by the function y= 5\12x12+5, where y>0 or y. Now I'm suppose to graph the function. b) Find the slope, height, length of sides, and base of the isosceles triangle. c)Explain what transformation must be applied to the graph of y=x to obtain the graph of y= 5\12x12+5, where y>0 or y=0. 1st I put the equation into my calculator and graphed it. I got 10 for the height. We have had 2 sub teachers this past week. The first one told me the height should be 12 the other one told me 5. So I'm really confused. If I use my 10 units as height and the Pythagorean Theorem I get my sides to be 26 units the base 48 and my slope I calc to be 5/12. Both teachers are pretty sure I'm wrong and they are right but we all have different answers. Please help put this problem to rest so I can rest soundly at night. Thank you for your time. Answered by Penny Nom. 





Prove A intersect B =X iff A = X and B = X 
20100306 

From Gloria: how would you prove A intersect B =X iff A = X and B = X Answered by Tyler Wood. 





The height of a roof 
20100131 

From carl: Width of my roof I am building is 5M at baseline, and the pitch is 40%.
What will the height be, and how can I work this out in the future. Answered by Penny Nom. 





A proof by induction 
20100112 

From Bhavya: Prove by induction that if Xi >= 0 for all i, then
(Summation Xi from 1 to n)^2 >= Summation Xi^2 from 1 to n Answered by Penny Nom. 





A proof involving real numbers 
20100111 

From Amper: Let a,b is an element of real numbers, and suppose that for every x>0 we have a is lesser than or equal to b+x.
(a) Show that a is lesser than or equal to b.
(b) Show that it does not follow that a is lesser than b.
i'm feeling bad of having no idea with this, hope i you can help me. GRACIAS!! Answered by Penny Nom. 





Proof that the root of 27 is irrational 
20091018 

From Scarlet: How do you prove that the square root of 27 is irrational? Answered by Victoria West. 





Prove by induction 
20091002 

From Anonymous: How can you prove the following by induction:
Any fraction (A / B), where 0 < (A / B) < 1, can be expressed as a finite sum
(1 / c(1)) + (1 / c(2)) + (1 / c(3)) + ... + (1 / c(k)),
where c(1), c(2), ..., c(k) are natural numbers greater than 0.
[ex. (20 / 99) = (1 / 9) + (1 / 11)] Answered by Claude Tardif. 





Highest Common Factor of Two Polynomials 
20090728 

From Nazrul: If x+a be the h.c.f. of x^2+px+q and x^2+mx+n, how can I prove that (pm)a=qn. Answered by Robert J. Dawson & Janice Cotcher. 





Inequalities Proof 
20090724 

From ABOU: good morning.......a b c are real positive no zero......proof that
sq root(2a/(a+b))+sq root(2b/(b+c))+sq root(2c/(c+a))inferior or equal 3
thank you Answered by Janice Cotcher. 





Properties of Natural Numbers 
20090724 

From nazrul: If m,n,k are natural number how can I prove that (m+n)k=mk+nk. In the proof the properties of natural number should be used. Answered by Janice Cotcher. 





Proof of a Unique Solution 
20090724 

From muele: Find matrix A such that A is not invertible, and
b such that Ax=b has a unique solution Answered by Robert J. Dawson. 





Prove that the set of all positive odd integers is an infinite set 
20090620 

From Nazrul: How can I prove that the set of all positive odd integers is an infinite set.
Thank you in advance. Answered by Victoria West. 





The product of gradients between 2 perpendiculars lines 
20090611 

From Alister: how do i prove that the product of gradients between 2 perpendiculars lines equal to 1.... Answered by Penny Nom. 





The sides of a parallelogram 
20090317 

From Sami: If ABCD is a parallelogram, prove that line AB is congruent to line CD. Clearly state your reasons and conjectures. Answered by Penny Nom. 





The midpoints of two sides of a triangle 
20090317 

From Manis: Prove that the line joining the midpoint of two sides of a triangle is parallel to the third and half of it. Answered by Robert Dawson. 





Mathematical induction 
20080905 

From James: I need to prove a problem by induction regarding the Triangle Inequality. The problem is
abs(a1 + a2 +...+an) <= abs(a1) + abs(a2) +...+ abs(an). Answered by Victoria West. 





A roof angle 
20080830 

From carla: Use vectors to find the angle in the attached diagram Answered by Chris Fisher and Stephen La Rocque. 





Proofs 
20080726 

From Taylor: when doing a proof, how do i figure out the steps in which i find the statements? i find the reasons pretty easily but i do not understand how to get the proving part. that would be great if you can help me! Thanks Answered by Victoria West. 





Four Positive Integers 
20080720 

From william: let a, b, c and n be positive integers. If a+b+c=(19)(97) and a+n=bn=c/n, compute the value of a. Answered by Janice Cotcher. 





A proof in geometry 
20080227 

From Kimberly: I'm trying to write a proof for the following: If all altitudes are equal in an equilateral triangle then all sides are equal. Answered by Stephen La Rocque and Penny Nom. 





A parallelogram and a rhombus 
20080122 

From miguel: i have a problem proving a parallelogram a rhombus.. if a diagonal of a parallelogram bisects an angle
of the parallelogram , then its a rhombus
prove Answered by Stephen La Rocque and Walter Whiteley. 





A geometric proof 
20071116 

From Julie: Prove that tangents to a circle at the endpoints of a diameter are parallel. State what is given, what is to be proved, and your plan of proof. Then write a twocolumn proof. Answered by Walter Whiteley. 





The area of a roof 
20070927 

From RANDY: I have an area of roof. It's in a sort of triangle.
it's 25' across the top
30' at each edge
86' across the bottom Answered by Stephen La Rocque. 





Prove that any two consecutive integers are relativley prime. 
20070918 

From Michael: Im not very good at proofs and I was wandering if you would be able to help me with the following question:
Prove that any two consecutive integers is relativley prime.
Thanks a million. Answered by Penny Nom. 





Twocolumn proof for a circle geometry problem 
20070824 

From Kendra: i have to prove that tangents to a circle at the endpoints of a diatmeter are parallel by stating whats given, whats to prove and a plane, then write a two column proof i dont understand this Answered by Stephen La Rocque. 





Induction  divisibility 
20070804 

From Jerry: How would you prove that for any positive integer n, the value of the expression 3^(2n+2)  8n 9 is divisible by 64. Answered by Chris Fisher and Penny Nom. 





Proving a quadrilateral is a rectangle 
20070714 

From Sonja: I was having this discussion with another teacher and we need a third opinion. When you are trying to prove a quadrilateral is a rectangle which method should you use:
 Prove the shape is a parallelogram by doing slope 4 times by stating that parallel lines have equal slopes. Then proving a right angle by stating that perpendicular lines have negative reciprocal slopes.
 Doing the slope 4 times and stating that the shape is a rectangle because opposite sides are parallel because of equal slopes and it contains a right angle because of negative reciprocal slopes.
I guess the real question is do you have to first state that the shape is a parallelogram? Answered by Stephen La Rocque. 





Grams of vodka 
20070710 

From Andrew: milliliters to grams..vodka 80 proof? Answered by Stephen La Rocque. 





Proof that any side of a triangle is less than half the perimeter. 
20070707 

From Omkar: Any side of a triangle is smaller than half of its perimeter, prove this in short ? Answered by Stephen La Rocque. 





Area of an isosceles triangle 
20070601 

From Josh: In a previous question answered by Sue regarding the area of a regular polygon you gave a formula for the area of an isosceles. My question is how did you get this formula? Can you please explain to mean the process that you used to get that formula?
Thanks Answered by Stephen La Rocque. 





Are proofs important in geometry? 
20070507 

From BJ: Are proofs very important to know how to do?
My daughter has been in Geometry & the teacher skipped proofs. Answered by Penny Nom. 





An even positive integer cubed minus four times the number 
20070207 

From Rachael: I can't figure out the proof or the method to get the proof for this question: any even positive integer cubed minus four times the number is divisible by 48 Answered by Haley Ess and Penny Nom. 





cos(n)pi = (1)^n 
20061214 

From Idrees: How can I prove the following: cos(n)pi = (1)^n Answered by Steve La Rocque. 





A proof by induction 
20061002 

From Zamira: i'm studying induction but i don't get how to proof that 1+2+2^2+2^3+...+2^(n1) = (2^n)  1. Answered by Penny Nom. 





Prove that 2nCn is less than 4n, for all positive integers n? 
20061001 

From Anna: How can I prove that 2nCn is less than 4n, for all positive integers n? Answered by Penny Nom. 





Proof by induction 
20060424 

From Meshaal: Find an expression for:
13+5  7 + 9  11 + ... + (1)^(n1) * (2n1)
and prove that it is correct.
Answered by Stephen La Rocque. 





Geometry proof 
20060423 

From Jade: From a point P outside a circle with centre O, tangents are drawn to meet the circle at A and B.
a) Prove that PO is the right bisector of the chord AB.
b) Prove that Answered by Stephen La Rocque. 





Proving a summation formula by induction 
20060419 

From Sharon: Prove by induction that the sum of all values 2^i from i=1 to n equals 2^(n+1)  2 for n > 1. Answered by Stephen La Rocque. 





A proof by induction 
20060409 

From Sharon: prove by induction: For every n>1, show that
2 + 7 + 12 + ...+ (5n3) = n(5n1)/2 Answered by Penny Nom. 





given that p is a prime and pa^n, prove that p^na^n 
20060324 

From Janna: given that p is a prime and pa^{n}, prove that p^{n}a^{n} Answered by Stephen La Rocque. 





A proof by contraposition 
20060316 

From Eban:
1)by mathematical induction prove that 1^{2} + 3^{2 }+ 5^{2 }+ ...... + (2k1)^{2} = (1/3)k(2k1)(2k+1) for all positive integers k.
2)show that the contrapositive of the following statement is true. if 1 + M^{7} is even, then M is odd.
Answered by Stephen La Rocque. 





Proof by induction 
20060210 

From Victoria:
how do i prove by induction on n that
n
Σ 1/i(i+1) = n/(n+1)
i=1
for all positive integers n
Answered by Penny Nom. 





Prove that p^n >= (p!)/(pn)! 
20060202 

From Rhydian:
PROVE:
p^{n} >= (p!)/(pn)!
Answered by Penny Nom. 





The sum of the angels in a triangle 
20051125 

From Rachel: how do you prove, without knowing any of the measurements or degrees, that the three angles of a triangle equal 180? what are the steps for proving that? Answered by Penny Nom. 





An isosceles triangle 
20051114 

From Chris: PX and QY are attitudes of acute triangle PQR, and Z is the midpoint of PQ. Can you write a proof that triangle XYZ is isosceles? Answered by Chri Fisher. 





Prove that a rhombus' diagonals are perpendicular 
20051002 

From Tania: How do you prove that a rhombus' diagonals are perpendicular using the 2 column proof method? Answered by Walter Whiteley. 





Proof by induction? 
20050810 

From Peter:
I am a lecturer and am having a problem with the following Proof by
Induction.
If
(N x N x N x N) + (4 x N x N x N) + (3 x N x N) + (N) = 4000
Prove that N is even!
Answered by Chris Fisher and Penny Nom. 





A flaw in a problem 
20050415 

From Bryce:
Question:
(x^{2}x^{2}) = (x^{2}x^{2})
x(xx) = (x+x)(xx) [divide both sides by (xx)]
x = x + x
x = 2x [divide both sides by x]
2 = x/x = 1
Where is the flaw in this problem?
Answered by Paul Betts. 





Dimensions of a roof 
20050318 

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





An isosceles triangle 
20050103 

From Abraham: The question is,"Triangle ABC is not isosceles.Prove that if altitude BD were drawn, it would not bisect AC."My question is If an altitude is drawn wouldn\'t that mean automatically its isosceles because, In a triangle the sides opposite congruent angles(in this case the right angles)are congruent? What am I thinking wrong? Answered by Harley Weston. 





A geometric proof 
20041211 

From Hanna: Given: ABCD is a quadrilateral;
Prove: ABCD is a parallelogram Answered by Penny Nom. 





Proof by induction 
20041120 

From Vic: Problem: Find the first 4 terms and the nth term of the infinite sequence defined recursively as follows:
a(1) = 3 and a(k+1) = 2a(k) for k > 1.
Note: Quantities in brackets are subscripts
> means 'equal to or greater than'.
Using the recursive formula, the first 4 terms are;
a(1) = 3, a(2) = 6, a(3) = 12, a(4) = 24
The nth term a(n) = 2n1 x 3 (equation 1)
Equation 1 must be proven using mathematical induction. This is where I am having a problem. Answered by Penny Nom. 





A theorem involving a trapezoid 
20040929 

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





A proof in geometry 
20040716 

From An: Im taking a geometry course for the summer , and we just started to learn about proofs for about one week. Today in class, we started to do this one proof but didnt finish it because class ended. the problem is as follows. Answered by Penny Nom. 





n! > n^2 
20040330 

From Jose: How can you prove by mathematical induction that:
n! > n2. Answered by Penny Nom. 





Proof by induction 
20040302 

From Chris: I need some help of how to solve the problem
"use the principle of mathematical induction to prove that the following are true for all positive integers"
cos(n x pi + X) = (1)^n cosX
any help would be appreciated Answered by Penny Nom. 





Three proffs of a trig identity 
20030318 

From Nadene: Prove the identity. cos [x + (ypi/2)] = sin (x+y)
A hint was also provided which is: "Apply cos (alpha + beta) first then within that apply cose (alphabeta)" Answered by Penny Nom. 





Proof by induction 
20020926 

From Pooh: Use induction to show that
1^{ 2} + 2^{ 2} + .....+n^{ 2} = (n^{ 3})/3 + (n^{ 2})/2 + n/6 Answered by Paul Betts. 





Proof by induction 
20020831 

From Tabius: Use mathematical induction to prove that the following formulae are true for all positive integers: a) 1 + 3 + 5+...+(2n  1) = n^{ 2} b) 2^{ n} > n. Answered by Penny Nom. 





Proof by induction 
20020220 

From Tamaswati: How do I prove the assertion that "the determinant of an upper triangular matrix is the product of the diagonal entries" by mathematical induction? (Before I check this assertion for a few values of n how do I rephrase the assertion slightly so that n appears explicitly in the assertion?) Answered by Penny Nom. 





Proof by induction 
20011016 

From John: Can you help me with any of these?  For any natural number n > 1, prove that
(4^{n}) / (n + 1) < [(2n)!] / [(n!)^{2}].
 For any natural number n > 1, prove that
1/sqrt(1) + 1/sqrt(2) + 1/sqrt(3) + ... + 1/sqrt(n) > sqrt(n).
 For any natural number n and any x > 0, prove that
x^{n} + x^{n  2} + x^{n  4} + ... + x^{n} >= n + 1. Answered by Penny Nom. 





Proof by induction 
20010930 

From Kyle: I'm trying to learn induction and I need to see how this done please help with this problem... 2^{0} + 2^{1} + 2^{2} +... + 2^{n} = 2^{n+1} 1 is true whenever n is a positive integer. Answered by Penny Nom. 





e^pi > pi^e 
20010727 

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





Harmonic numbers 
20010523 

From Leslie: The harmonic numbers H_{k}, k = 1,2,3.....are defined by H_{k} = 1 + 1/2 + 1/3....1/k I am trying to prove by mathematical induction: H_{2n} >= 1 + n/2 , whenever n is a nonnegative integer. H_{8} = H_{23} >= 1 + 3/2 Can you help? Answered by Harley Weston. 





A sequence of even terms 
20010429 

From A student: A sequence c is defined recursively as follows: c0 = 2 c1 = 4 c2 = 6 ck= 5ck3 for all integers Prove that cn is even for all integers. Answered by Leeanne Boehm and Penny Nom. 





A geometry proof 
20010418 

From Melissa: Extend the bisectors of angle A, angle B, and angle C of triangle ABC to meet the circumcircle at points X, Y, and Z respectively. Show that I is the orthocenter of triangle XYZ. Answered by Chris Fisher. 





How can you prove a quadrilateral to be a parallelogram? 
20010316 

From Joy: How can you prove a quadrilateral to be a parallelogram? Answered by Walter Whiteley. 





Mr. Moser's roof 
20010221 

From Michelle: Mr. Moser is planning to replace the roof of his home. He needs to order a pack of shingles. Each pack covers 100 sq. ft. of roof. Without a ladder, Mr. Moser can not climb to the roof to measure it. Instead, he measures his attic and finds it to be 40 ft. long, 24 ft. wide, and 5 ft. high at the peak of the roof which is in the center of the house. Although the roof is even with the side walls, he estimates the roof line continues 1.5 ft. beyond the front and back walls. How many full packs of shingles should Mr. Moser order to cover his roof? Answered by Penny Nom. 





1 + 1 = 1 
20010123 

From Stephanie: My friend has this as a bonus question the other day and I want to figure it out. I don't know how 1+1 in any form could equal 1. Please let me know how you come about geting that. Answered by Claude Tardif. 





A proof that 1=2 
20000919 

From sporky: Why does the proof for 1=2 not work? x = 1 x^{2} = 1 x = x^{2} 1 = 2x (derivitive) 1 = 2(1) 1 = 2 ??? please tell me where the false logic is. Answered by Walter Whiteley. 





Induction 
20000907 

From Joe Peterson: How do I prove by the principal of mathematical induction? 1.n+2.(n1)+3.(n2)+.....+(n2).3+(n1).2+n.1=(n(n+1)(n+2))/6 Answered by Paul Betts. 





Parallel tangents 
20000630 

From Ebony Indalecio: I need to prove the theroem: Tangents to a circle at the end points of a diameter are parallel. Answered by Walter Whiteley. 





The square root of 3 
20000404 

From Mr. William: Prove that root 3 is irrational Answered by Harley Weston. 





Induction 
20000316 

From William Tsang: I am trying to prove a induction question Sigam r=1 n (2r 1)cube = n square (2 n square  1) Answered by Harley Weston. 





The quotient rule 
20000221 

From Charlene Anderson: Question: I came across a question in our book that states: Let Q(x) = N(x) / D(x) Then rewrite Q(x) in a form that can utilize the Power and Product Rules. Use this rearranged form to derive the Quotient Rule. The Quotient Rule can be derived from the Power Rule and the Product Rule. One must also use the chain rule too, right? Answered by Harley Weston. 





2 = 1 
20000216 

From Chuck Kennedy: Question:  Assume a=b
 Multiply both sides by a, a^{2}=ab
 Subtract b^{2}, a^{2}b^{2}=abb^{2}
 Factor (ab)(a+b)=b(ab)
 Cancel like factors a+b=b
 Substitue b for a b+b=b
 Then 2b=b
 Therefore 2=1
Question; Were is the mistake? Answered by Claude Tardif. 





Two algebra problems 
19991217 

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





An Invalid Argument 
19990531 

From Rod Redding: Can an invalid argument have a true conclusion? If yes then why? Answered by Walter Whiteley. 





A 
19990502 

From Leah: a=b a^2=ab a^2+b^2=abb^2 (ab)(a+b)=b(ab) a+b=b b 2=1 why is this proof wrong? Answered by Penny Nom. 





Root 17 is Irrational 
19990121 

From John Murdock: If you could help me out with this I would appreciate it. Prove that the square root of 17 is irrational. Answered by Harley Weston. 





Proofs 
19970413 

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





A Presidential Proof 
19970318 

From Greg Smith: Which US president developed a proof for the Pythagorean Theorem? Where can a copy of the proof be located? Answered by Chris Fisher and Harley Weston. 





A/B = C/D 
20020306 

From Un eleve: Démontrer que si A sur B et = à C sur D, alors AxD et = à BxC. Answered by Claude tardin. 

