Triangle Definition and 1000 Threads

Homework Statement Hello, so I'm going to be a freshman physics major next year, and over the summer I'm trying to improve my problem solving skills. I've started going through Irodov's problems in general physics, and I have a question about two different solutions to one of the problems...

Hey guys, This is NOT homework. I remember solving this question many years ago (at least 10 years ago). I am trying to recall the solution again and am just not able to. The question is - In a triangle ABC, AD is the angle bisector of angle BAC. AB = CD. Prove that angle BAC = 72 degrees...

Homework Statement Triangle A has three points a(2,3)b(0,0)c(2,0) and its center is (2/3,1). Find the other three points of Triangle B with a center of (4/3,3). Homework Equations Center of a triangle: x = ax+bx+cx /3 y = ay+by+cy / 3 Magnitude = <a,b> , √(a^2+b^2) The Attempt at...

Homework Statement The area is bounded by the equation y=x^2, x-axis and the line x=3 and is perpendicular to the x axis Homework Equations A=1/2bh Height=Base The Attempt at a Solution A=1/2B^2 V=1/2B^2 from 0 to 3 V=1/2 B^3/3 from 0 to 3 V=B^3/6 from 0 to 3 V=27/6 please...

Homework Statement the formula of a triangle is b2/2, so the integral should be b3/6, right? Well, that can't be right. Because if the base of the triangle is 4, it's area will not add up to 8. What am I doing wrong?

Homework Statement see attachment Homework Equations The Attempt at a Solution No idea how to do this. Tried extending the 10 thus getting a big triangle of (10+x)^2+y^2=400. But then again no idea what x and y is. This is wrong. Any help would be appreciated.

Hi all ! I got stuck in establising an method to Convert a Quadrangle mesh to a Triangle mesh (CFD). I have a mesh file (.dat) which have information: Number of Element - Node 1 - Node 2 - Node 3 - Node 4 1 1 2...

What is Bermuda Triangle? Is gravitational Forces exist there or not?

This might seem easy, but I am sort of rusty on the math since i haven't taken a math course in a while. Homework Statement A 2 meter long bar lies in the xy plane with one end at the origin. find position at the xy plane of the other? end point of the bar if the angle the bar makes with...

I'm pretty shaky with my understanding of much beyond simple tree-level calculations. When people talk about triangle diagrams, they sometimes say one will get a 'supression factor' of xxx. For example, in the consider the triangle diagram for H\rightarrow\gamma\gamma with Ws running around...

Homework Statement A inverted isosceles triangle gate with height a=3ft and base b=2ft is 6ft under the water (top of the inverted triangle). Find the Force on the gate and hp (the depth of the) center of pressure. Homework Equations hc= depth to gate + depth to centroid= 6+(1/3)•3= 6+1 =...

Hello everybody, I've been trying to understand the CHSH proof as it is listed on Wikipedia: http://en.wikipedia.org/wiki/CHSH_inequality I got to this without any problem: E(a, b) - E(a, b^\prime) = \int \underline {A}(a, \lambda)\underline {B}(b, \lambda)[1 \pm \underline {A}(a^\prime...

B 15 A 9 M 11 N 5 C Triangle ABC, BC = 15, AC = 25. M and N on AC, such that AM = 9, MN = 11 and CN = 5. Angle ABM = angle CBN. Calculate side AB.

I have tried but still cannot get it. Simple geometry question. Tangents to the inscribed circle of triangle PQR are parallel to [QR], [RP] and [PQ] respectively and they touch the circle at A, B and C. Prove that [PA], [QB] and [RC] are concurrent relevant formula: Ceva's theorm (Any...

Homework Statement A triangle has sides of length (n2+n+1), (2n+1) and (n2-1), where n > 1. (a) Explain why the side (n2+n+1) must be the longest side of the triangle (b) Show that the largest angle, θ , of the triangle is 120º. Homework Equations In a triangle of sides a, b...

[FONT=Verdana]Points (6,0) and (O,8) are the endpoints of the hypotenuse of a [FONT=Verdana]right-angled triangle, whose other vertex is at (x,y). What equation relates x [FONT=Verdana]and y?[FONT=Verdana]Attempt at solution: [FONT=Verdana]So What I am thinking is that the line will be...

Points (6,0) and (O,8) are the endpoints of the hypotenuse of a right-angled triangle, whose other vertex is at (x,y). What equation relates x and y?Attempt at solution: So What I am thinking is that the line will be perpendicular to the line with end points 6,0 and 0,8. So The gradient of...

Homework Statement I am having trouble with right triangles. I understand how to use the formulas, however I don't know which angle is appropriate when using the formulas. For example, in this picture: http://imgur.com/C2lxg . There was a problem in my book that had a triangle like this. The...

1. The streets of a city are laid out in a rectangular gird, as shown below a) Use combinations to find the number of routes through the grid that lead from point A to point B by only traveling north or east. Show your calculations b) How many of these routes pass through intersections...

Hello .. This is a question with answer , From where " 1 " in the solution ? http://store1.up-00.com/Mar12/yd170715.jpg

The problem is to find the moment of inertia for a solid equilateral triangle about an axis at the triangle's vertex which is perpendicular to the plane of the triangle. Mass is given as M. I was wanting to treat it like 3 point masses at each vertex with 1/3 mass. Then I could use the sum...

The base of a solid is the region bounded by the parabola x2 = 8y and the line y = 4 and each plane section perpendicular to the y-axis is an equilateral triangle. What is the volume of the solid?(Barron's Problem) so I solved for x since y must be used because the cross section is...

Homework Statement I have a triangle with given vertices ABC. Given a vector that starts from A and intersects side BC, how can I find the point of intersection, p? Thanks Homework Equations The Attempt at a Solution

Homework Statement http://img23.imageshack.us/img23/9427/imageyakj.jpg AC+CB=24 The bisector = 8. Find angle DCB, i.e. x. Homework Equations The Law of sines, I think.The Attempt at a Solution

Homework Statement I think this must be really easy but I am not getting a visual for this triangle description. Let ABC be a triangle with \UparrowOA=a and /UparrowOB=b and /UparrowOC = c Where O is the origin . Homework Equations The Attempt at a Solution How can I...

My answer to this question seems close to that of the book but I have only solved for +1/2 and not the -1/2. Can anyone help? Many thanks. Homework Statement Q. The area of a triangle is \frac{-4m^2 + 4m - 1}{m}. Find the value of m via differentiation. Homework Equations The...

Homework Statement Triangle ABC has A (−1, 3,−3), B (2, 4, 6) and C (3, 0,−5). Use the scalar product to find the angle ACB. No pictures are given The Attempt at a Solution I have attempted the question by naming the triangle ABC with each angle opposite the line with the same...

Homework Statement Charges Q, Q, and q lie on the corners of an equilateral triangle with sides of length a. Charge q lies on the top corner with Q and Q on the left and right corners. (a) What is the force on the charge q? (b) What must q be for E to be zero half-way up the altitudeat...

Homework Statement Three point charges are located at the corners of an equilateral triangle as in the figure below. calculate the net electric force on the 7-nc charge. Each sides are .5 m. (q1=7μc) (q2=2 μc) (q3= -4 μc) ___1 __/__\ 2/____\3 Homework...

In the book by Keith Devlin on the Millenium Problems - in Chapter 6 on the Birch and Swinnerton-Dyer Conjecture we find the following text: "It is a fairly straightforward piece of algebraic reasoning to show that there is a right triangle with rational sides having an area d if and only if...

Homework Statement Consider a triangle ABC, where angle A = 60o. Let O be the inscribed circle of triangle ABC, as shown in the figure. Let D, E and F be the points at which circle O is tangent to the sides AB, BC and CA. And let G be the point of intersection of the line segment AE and the...

Homework Statement Find the area of triangle with vertices (-2,-2,2,2), (0,0,1,-1), (-1,-2,1,1) Homework Equations The Attempt at a Solution The only way I know how to find the area of a triangle is by finding half the parallelogram. I.e. A = (1/2)||u x v|| But this requires cross...

Each of ten segments has integer length and each one's length is greater than 1cm and less than 55cm. Prove that you can select three sides of a triangle among the segments.

I have attached a file with all needed information including the function and path of integration. My work seems right to me, but the correct answer is a^2. Will someone please take a look and show me where my misstep is.

Hey Guys, My question involves finding all of the forces acting upon each member. It is known that each side of the triangle has a length of l. It is also known that the force is acting at the very top of the triangle in the x direction (to the right) labelled as F. Attempt: I found moments...

Proving the "triangle inequality" property of the distance between sets Here's the problem and how far I've gotten on it: If you are unfamiliar with that notation, S(A, B) = (A \ B) U (B \ A), which is the symmetric difference. And D(A, B) = m^*(S(A, B)), which is the outer measure of...

Hi, I am trying to find the last vertex coordinates of a triangle given that Vertex 1 = (2,10) Vertex 2 = (3,6) Angle at Vertex 1 = 75.9638 degrees Angle at Vertex 2 = 70.3462 degrees. I have tried using the equations based on the length of each side, as well as using the cos dot...

find the area of the triangle with vertices (-1 2 -1 2) (-1 2 -1 1) and (2 -1 2 2) its 4 d Im confused thanks in advance

Given this seemingly simple problem of maximising the area of an isosceles triangle with perimeter equal to 1. What is the best approach and how will I find a result easiest (I know how to get the answer but I need to be able to do these problems fast, so please help me look for a quick method...

Homework Statement "At a given instant the legs of a right triangle are 8in. and 6in., respectively. The first leg decreases at 1in/min and the second increases at 2in/min. At what rate is the area increasing after 2 minutes?"Homework Equations A=\frac{1}{2}bh \frac{db}{dt}=-1...

In a triangle ABC, prove that $1<cosA+cosB+cosC \leq \frac{3}{2} $. One can easily prove that $cosA+cosB+cosC \leq 3/2 $, i.e. it can be proven to be true by 1. Using only the method of completing the square with no involvement of any inequality formula like Jensen's, AM-GM, etc. 2. By...

Let ABC be a triangle. Prove that $sin^2\frac{A}{2}+sin^2\frac{B}{2}+sin^2\frac{C}{2}+2sin\frac{A}{2}sin\frac{B}{2}sin\frac{C}{2}=1$. Conversely, prove that if x, y and z are positive real numbers such that $x^2y^2+z^2+2xyz=1$, then there is a triangle ABC such that $x=sin\frac{A}{2}...

Homework Statement The Attempt at a Solution I can't figure out how thales found the measurement of the length of this triangle without trigonometry since the sine and cosine ratios were not worked out until the 14th century I think. In any case, they certainly weren't known in...

Homework Statement Please see picture attached. Homework Equations The Attempt at a Solution If I use the pythagoras formula with the ratio I get the height as 3 yet it is longer than the side that is 4. Am I doing something wrong? Thanks.

I am trying to show $|(n+z)^2|\leq (n -|z|)^2$ where is complex $|(n+z)^2| = |n^2 + 2nz + z^2| \leq n^2 + 2n|z| + |z|^2$ But I can't figure out the connection for the final piece.

Homework Statement Write down the condition for the numbers p, q, r to form an arithmetic sequence. Homework Equations The Attempt at a Solution Have no idea, but I looked at the answer and they have assigned each letter with a given value (number). How is this possible?

Homework Statement In isosceles triangle RST, RS = RT. Which side of the triangle is the base? Which angle is the vertex angle? Homework Equations The Attempt at a Solution I believe the base is RT, and the vertex angle is S. I don't know the proper notation to name the line...

Homework Statement Show that if z_1,z_2 \in \mathbb{C} then |z_1+z_2| \leq |z_1| + |z_2| Homework Equations Above. The Attempt at a Solution I tried by explicit calculation, with obvious notation for a,b and c: my frist claim is not that the triangle inequality holds, just that...

Homework Statement The measure of the sides of an isosceles triangle are represented by x + 5, 3x +13, and 4x + 11. What are the measures of the sides? Two answers are possible. Homework Equations The Attempt at a Solution Well, I set up three different triangles, to account for the...

Three points are randomly chosen on a circle. Then they are connected together to make a triangle. What's the probability to see a 1. Right triangle 2. Triangle with all angles less than 90 degrees 3. Triangle with an angle bigger than 90 degrees I'm pretty sure to solve one of them...