Triangle Definition and 1000 Threads

Let $$ABC$$ be a triangle such that $$\frac{BC}{AB-BC}=\frac{AB+BC}{AC}$$. Determine the ratio $$\frac{\angle A}{\angle C}$$.

Homework Statement There are three point masses. 1 is fixed in space with the 2nd point mass directly below it on the ground. The 3rd point mass is an unknown distance to the right of mass number 2. These 3 point masses for a rt triangle with point 2 at the 90 degree angle. The vertical...

Homework Statement Hello I'm learning Fourier transforms via the Stanford lecture series on Youtube. In the 6th lecture, the professor claims that the FT of a triangle function is the square of the sinc function. I'm trying to derive this, but I can't get my math to work out. Could someone...

Homework Statement B=magnetic flux density . A is the vector potential of magnetic field. How to get the formula B=∇A Homework Equations http://en.wikipedia.org/wiki/Magnetic_moment The Attempt at a Solution B=magnetic flux density . A is the vector potential of magnetic field...

Homework Statement Consider the points A(1,2) B(-2,-1) and C(3,-2) on the Cartesian plane. 1. Find the length of the segments AB and BC 2. Find the angle of the triangle at the vertex B Homework Equations Cosθ=(AB*BC)/|AB| |BC| ? The Attempt at a Solution The length of the...

1. ∫1/(x2 + 36)dx 2. I started by trying a trig substitution. The normal form, "a2 + x2, x=(a)tan(θ)," I thought could be reversed here: x2 + 62 x = 6tan(θ) dx= 6sec2θdθ ∫1/[(6tanθ)2 + 36] = ∫1/[36(tan2θ + 1)]*6sec2θdθ = ∫1/[36sec2θ]*6sec2θdθ = ∫1/6dθ = (1/6)θ + C...

Homework Statement prove that sin^2(a)=sin^2(b)+sin^2(c) if and only if ABC is a right triangle in A i worked really hard on this one I'm really confused why i didn' get the answer Homework Equations The Attempt at a Solution a+b+c=pi tried turning everythng to cos 2x didn't helpi...

http://https://www.physicsforums.com/attachment.php?attachmentid=56297&stc=1&d=1362318192 problem:- The situation is shown in attachment. the right angled frame of rods (in stationary ) is moving at speed v perpendicular to its hypotenuse. according to length contraction the corresponding...

Hello. I have an example for you. I'm curious how. Yesterday I was on the mathematical competition. One example I can not solve. I want to know how. Can you help me, please? Consider a convex polygon of 1415 sides, which circumference is 2001 cm. Prove that between its peaks, there are 3 such...

Let a, b, c be the lengths of the sides of a triangle. Prove that: $\sqrt{a+b-c}$+$\sqrt{b+c-a}$+$\sqrt{c+a-b}\leq\sqrt{a}+\sqrt{b}+\sqrt{c}$

Homework Statement Suppose that the magnitude of the net electrostatic force exerted on the point charge q2 in the figure is 0.65 N . (Figure 1) http://imgur.com/4lZliPq Find the distance D. q1 = 2.1 micro C q2 = 6.3 micro C q3 = -.89 micro C Homework Equations F = k |q1|...

Homework Statement Let pascal(n,i) be the value of the ith element of the nth row of Pascal's triangle. Using induction show that the number of unique paths from entry {0,0} to entry {n,i} in Pascal's triangle is equal to pascal(n,i). The Attempt at a Solution The base case n=1 seems easy...

Homework Statement The first problem is as follows And the second one is Homework Equations For the first question, I do not really know what equations to use. I tried writing it out in the form Z1 = a + ib, Z2 = c + id, etc, but that got me nowhere. The second question has been...

Homework Statement What is the area of a right triangle whose inscribed circle has radius 3 and whose circumscribed circle has a radius 8? Homework Equations The diameter must be the hypotenuse of the circle The Attempt at a Solution The answer is 57, but I do not know the...

[FONT=arial]Problem: Let A, B, C be three non-collinear points. Let D, E, F be points on the respective interiors of segments BC, AC and AB. Let θ, φ and ψ be the measures of the respective angles ∠BFC, ∠CDA and ∠AEB. Prove IAS(ABC) < θ +φ + ψ < 540 - IAS(ABC).(IAS means internal angle sum). Now...

Find the electric potential at point P in the figure. http://i.imgur.com/8FNSoML.png V = kq / r So what I did was calculated the electric potential each force gives on the point P. Vp1 = (8.99e^9) (2.75e^-6) / .625 Vp2 = (8.99e^9)(-1.72e^6) / .625 Vp3 = (8.99e^9) (7.45e^6) /...

Is it possible that a triangle with angles totaling over 180 degrees could exist without being embedded in a 3rd dimension?

Hi, I'm still practicing how to find volume. 1. My problem is this: "Find the volume of the solid described below: The base of the solid is the disk x^2 + y^2 ≤ 4. The cross-sections by planes perpendicular to the y-axis between y=-2 and y=2 are isosceles right triangles with one leg in the...

Homework Statement Find a formula for the sum of the elements of the nth row of Pascal's Triangle Homework Equations C(n,r) = [C(n-1,r-1) + C(n-1,r)] C(n,0) = C(n,n) = 1 The Attempt at a Solution I started with the summation of the elements in the rows n \sum^{n}_{r=0} C(n,r)...

EDIT: My guess to the below question is that no you can't triangulate a triangle because a legitimate triangulation each edge can only be linked up to exactly two distinct faces, so if you just have one triangle, each edge would be linked up to one face (the face of the triangle) I'm really...

Hello, I have been given a homework problem and I don't want any help on solving the problem, (I'm not even going to post the problem - I want to figure it out myself), I only want to understand what the problem is asking. (That's why I've posted in this section rather than the homework...

Okay, I tried to draw a picture of the graph the word problem is talking about. This is a bad picture, but it was the best my computer could take! :/ 1. Les triangles dangereux is an 80-minute movie showing nothing but a slowly growing triangle. It got a strong reception at Cannes...

Hey guys, I hope someone can give me some pointers with this because it should be really easy but I am just not getting it! I want to show that for a triangle inscribedin a circle an equilateral traingle gives the maximal perimeter. I've tried a few things and just get bogged down in algebra...

Hi, I should Show the following: D is subset of R^2 with the triangle (0,0),(1,0),(0,1). g is steady. Integral_D g(x+y) dL^2(x,y)=Integral_0^1 g(t)*t*dt my ansatz: Integral_0^1(Integral_0^(1-x) g(x+y) dy) dx With Substitution t=x+y Integral_0^1(Integral_x^1 g(t) dt) dx...

Suppose we have 3 points in the plane given by: $\displaystyle (x_1,y_1),\,(x_2,y_2),\,(x_3,y_3)$ and we wish to find the area of the triangle whose vertices are at these points. We may let the base b of the triangle be the line segment between the first two points, and the altitude h of the...

Homework Statement hi i have a photo with some given information. I need to find the length of all three sides of that triangle and also the area of the triangle I have already found them but i get 2 different results Homework Equations I have used both cosinus and pythagoras...

Homework Statement let ABC be a triangle where I divides angle BAC(angle A) => BAI=IAC Prove that I is the centroid of (B,AC)and (C,AB) Homework Equations i think phitagors wil come in handy but don't know how to use it The Attempt at a Solution let ac = a and AB = b aIB+bIC=0 (vectors)...

I have this triangle and I know just the two sides indicated there. How can I find angle theta? I tried decomposing the triangle in two right triangles and using trigonometry find one side, but I can't figure how to do that using just the hypotenuse

Good day, while reading up on an elementary math study book, i have encountered that a proof is build upon the following (see attachment for the figure). Are the Areas CDE and BED really the same? I tried to calculate this from abstraction, not sure where I could have made a mistake.. g1 is the...

Homework Statement Three positive charges, A, B and C, of 3 × 10-6, 2 × 10-6, and 3 × 10-6 Coulombs respectively, are located at the corners of an equilateral triangle of side 0.2 meters. Find the magnitude in Newtons/Coulomb of the electric field at the center of the triangle...

a, b, and c are unit vectors and a+b+c=0. This is the first part of a question and the solution involves the fact that a, b, and c form a triangle. I am having a really hard time how these vectors form a triangle. Can you pleases be as thorough as possible in your answer. Thank you so much for...

Homework Statement Let C be the oriented triangle lying in the plane 2x+y+z=4. Evaluate ∫ _{C} F*dr where F(x,y,z)=y2i + z - xk. Homework Equations I will be using ∫C∫curl F \bullet \vec{n} to solve this problem. But when I'm trying to find \vec{n} using -gxi - gyj + k, I get Using...

Homework Statement area of triangle with a base of: 2 & 3/4 and a height of 4/9 Homework Equations 1/2 * (b*h) The Attempt at a Solution i used: 1/2*(11/4 * 4/9) = 44/72 = 22/36 = 11/18

Homework Statement Deepa’s house is five blocks west and four blocks south of a bus stop. A store is three blocks west and one block south of the bus stop. How many ways can Deepa walk home if she wishes to stop on her way home by walking only west and south? Homework Equations...

Hello, I'm a little confused as to how I can go about solving this problem.. Any help is appreciated. Homework Statement Draw and copy the following checkerboard. Then, on the board, show all of the paths that the checker piece can take to reach the bottom square marked with an “X,”...

a function for a line in a square (or a triangle or a pentagon etc) I don't have one off the top of my head (my maths is very rusty) but I think that ,starting from a cartesian point it is possible to create a function that allows one to draw a polygon in 2 or 3(?) dimensions. This...

Prove that the rᵗʰ term in the nᵗʰ row of Pascal's triangle is nCr. nCr formula: n!/r!(n-r)! I've tried everything I can but I don't know how to approach this question.

In square ABCD need to show $cos a = \frac{1}{12}$

I'm doing some trigonometry, and right now I'm given this equilateral triangle, http://i.imgur.com/WOPCk.png So how would I go about to find side AP, AQ, and PQ? I think I have a grasp of what it is, but not sure how to execute. I know you have 60 degree angle for ABC and all sides are 3, but...

Homework Statement Using the generalized triangle inequality, prove |d(x,y) - d(z,w)| ≤ d(x,z) + d(y,w) Homework Equations d(x,y) is a metric triangle inequality: d(x,y) ≤ d(x,z) + d(z,y) The Attempt at a Solution I know that this needs to be proved with cases: a) d(x,y) - d(z,w)...

Homework Statement Determine which row of pascals triangle contains 3 consecutive entries that are in the ratio 1:2:3. Homework Equations (n, k ) = n!/k!(n-k)! The Attempt at a Solution (n,k):(n,k+1):(n,k+2) 1 : 2: : 3 What I did was cross multiply. 2 times (n,k) =...

Homework Statement In the figure F1= 27.9KN, F2= 39.8KN, F3= 61.8KN What distance d is required for the net couple moment on the triangle to be 1140 counterclockwise? Express your answer to three significant figures and include the appropriate units. link to image http://imgur.com/cBnLJ...

Homework Statement I have a program which will sort out three inputted variables into order from lowest to highest. I now must get the program to work out if these 3 values could be the sides of a right angled triangle. Homework Equations I am going to use a^2+b^2=c^2 to solve...

Homework Statement The original question is from AP French's Classical Mechanics. It's about a boat trying to catch up with a ship. I've interpreted the question as follows: which is to express tan θ as a function of u and v. I tried working with vectors, where v is actually -v in...

I am not getting anywhere with this problem. Prove the Schwarz's and the triangle inequalities for infinite sequences: If $$ \sum_{n = -\infty}^{\infty}|a_n|^2 < \infty\quad\text{and}\quad \sum_{n = -\infty}^{\infty}|b_n|^2 < \infty $$ then $\displaystyle\left(\sum_{n = -\infty}^{\infty}|a_n +...

Homework Statement Prove the following inequality for any triangle that has sides a, b, and c. -1<\frac{a}{b}+\frac{b}{c}+\frac{c}{a}-\frac{b}{a}-\frac{a}{c}-\frac{c}{b}<1 Homework Equations The Attempt at a Solution I think we have to use sine or cosine at a certain point because...

Homework Statement Consider the points P(1,0) and Q(0,1) on the unit circle. For which point R(cos(theta),sin(theta)) on the unit circle, is the area of the triangle PQR maximal? Homework Equations Hint - It might be easier to use vectors to calculate the area of the triangle. The...

Homework Statement Prove the following inequality for any triangle that has sides a, b, and c. -1<\frac{a}{b}+\frac{b}{c}+\frac{c}{a}-\frac{b}{a}-\frac{a}{c}-\frac{c}{b}<1 Homework Equations The Attempt at a Solution I think we have to use sine or cosine at a certain point because...

Homework Statement From the inequality |a.b| <= |a||b| prove the triangle inequality: |a+b| <= |a| + |b| Homework Equations a.b = |a|b| cos theta The Attempt at a Solution Making a triangle where side c = a+b. Don't know how to approach the question. Thanks.

Homework Statement Where exactly is the center of mass of a triangle ? the file attached shows a diagram of a triangle which is equilateral, and the blue spots are the mid-points of each side. Homework Equations a distance = 2/3 from the vertex (along the median) The Attempt...