Triangle Definition and 1000 Threads

Homework Statement In a right triangle ABC, AD is a Median to BC (see drawing) Given: AB+BC = 4 A) Mark BD with an x, and express the lengths of the adjacent and opposite through x. B) Find the x for which the length AD is minimal http://img641.imageshack.us/img641/6798/abctriangle.jpg The...

Does anyone know how one could calculate the maximum number of whole rectangles that can fit into a triangle. Say you know the length of the sides of the triangle (t1,t2,t3) and the of the sides of the rectangle (r1,r2). Thanks.

Homework Statement Show that the system of forces represented by the lines joining any point to the angular points of a triangle is equivalent to the system represented by straight lines drawn from the same point to the middle points of the sides of the triangle Homework Equations...

Hi folks. Since people have already discussed tetrahedral and triangular numbers from the Pascal Triangle in nuclear physics, in peer-reviewed journals, this isn't a new idea. In the electronic system one can also find these numbers instantiated. In the left-step periodic table by Charles Janet...

Trig right triangle solving question How do you know if you should pick tan, cot, etc for the last part? if b = 2 , A =40 , find a,c, and B I found all of them except for c , how do you get c There's a part almost at the end that goes like tan40 degrees = a/2 and Cos 40 degrees = 2/c Why do you...

Hello, As I believe is normal policy, please don't give me the answer to the problem :) I would, however, greatly appreciate a bump in the right direction. Homework Statement Triangle abc: side a=12, side b=15, angle C is increasing at 2 degress/minute. How fast is the length of side...

Two blocks are connected by a string-one on an incline, the rope draped over a pulley, and one hanging from the string. The smooth inclined surface makes an angle of 35 with the horizontal, and the block on the incline has a mass of 5.7 kg. The mass of the hanging block is 3.2kg. Find the...

Can someone help me understand why this is the case? I tried forming a cartesian equation for the two circles but there were too many variables that it would be too messy to compute. Otherwise I am rather stuck on how to do it. I would appreciate it if someone can explain how to prove this...

Homework Statement Given that: OA = 5s OB = 10 t P is on the middle of OA and AQ = 3 QB Find λ if BG = λ BP Homework Equations basic vector The Attempt at a Solution I have found AB, BQ, OQ, BP; all in terms of s and t. How to find λ? I've tried but always came back to...

Homework Statement Find the area of the largest rectangle that can be inscribed in a right triangle with legs adjacent to the right angle of lengths 5cm and 12cm. the two sides of the rectangle lie along the legs. Homework Equations N/a The Attempt at a Solution

Homework Statement an isosceles triangle with mass m and constant density is placed on an xy plane with base on the y axis. its height ranges from (0,-b/2) to (0,b/2) and its height is (a,0) Find its center of mass. I know that its density is equal 2m/ab. The Attempt at a Solution...

1. I am an architecture student and the assignment is to design a truss, set up the problem and solve it using graphic statics. I think I did it correctly using the graphical method but I am interested in solving it mathematically. Did I set the problem up correctly in my diagram and if so...

Homework Statement Prove the Triangle Inequality Theorum using the coordinate system. Homework Equations The corners of the triangles will be at (x1,y1), (x2, y2), (x3,y3) The Attempt at a Solution The proof that I know is proving that |x+y|<=|x|+|y|: -|x|<x<|x|, and...

So i have the points A=(1,0,1) and B=(1,-1,0) and the third corner lies on the line L:(x,y,z) = (t,t,t) and i need to find a triangle with the minimum area possible. My initial approach was to calculate the vector BA and BC and then apply both vectors in the area triangle formula...

Dear all, right now, I am doing my IGCSE and this question is in my coursebook. I can't think of any way to calculate it... It's part of the section circumference and area of circles. So must be some how solved using this. The semi-circle and the isosceles triangle have the same base AB and...

Homework Statement A right triangle ABCD is formed from four jointed links. The joint D at the midpoint of the hypotenuse is pushed until it lies on the leg AB. Homework Equations Find the height x when a = 50 mm The Attempt at a Solution give me a hint please cause I'm lost :mad:

I have the following question on metric spaces Let (X,d) be a metric space and x1,x2,...,xn ∈ X. Show that d(x1, xn) ≤ d(x1, x2) + · · · + d(xn−1, xn2 ), and d(x1, x3) ≥ |d(x1, x2) − d(x2, x3)|. So the first part is simply a statement of the triangle inequality. However, the metric...

[b]1. Homework Statement [ what is the distance from one corner of an equilateral triangle of sides a to the circumcentre? I can figure out the length from one corner to the opposite side to be sqrt3*a/2 but that's about it. I just can't see how to do this. thanks

Homework Statement How much work is needed to arrange three charges, Q, into an equilateral triangle? The particles are initially infinitely far apart. Take 'a' to be the length of each side of the triangle. Homework Equations U = {(kqq)/L} The Attempt at a Solution I was under...

Homework Statement I need help once again with this question below: Thanks, aeromat The Attempt at a Solution This is what I have so far: GP = GQ + QP GQ = GP + PQ GR = GP + PR GP + GQ + GR = GQ + QP[-] + PQ[+] + GP + PR + GP GP + GQ + GR = GQ + 2GP + PR I am stuck...

I am trying to get a different orientation on this triangle; specifically I want this output: ********** ********* ******** ******* ****** ***** **** *** ** * Here is the code that I have #include <iostream> using namespace std; int main () { int lines=10; int start =...

Homework Statement Here is a drawing with all the needed variables: http://i.imgur.com/192GI.jpgHomework Equations The Attempt at a Solution I have been trying to figure out how this approximation is derived for some time now and have no progress to show for it. Any help in figuring out the...

Homework Statement When the sun is 74° above the horizontal a vertical flag pole casts an 8.5m shadow on the horizontal. Find the shadow cast when the sun lowers to 62° above the horizontal. Homework Equations The Attempt at a Solution I drew the following diagram...

I'm having a hard time figuring out what to do here and it feels as though it involves converting the function into polar coordinates but I'm not a hundred percent sure. Essentially, I have a triangle in which two sides are straight and one side is a curved function. Knowing only the length...

Homework Statement Hi I am really stuck on this problem. It reads as such: A uniform triangular lamina is isocceles and has the line y= 4 as its axis of symmetry. One of the vertices of the triangle is the point (2,1). Given that the x-co-ordinate of the centre of mass of the lamina is -3...

Homework Statement The circle x2 + y2 - 4x - 4y + 4 = 0 is inscribed in a triangle, which has two of its sides along the coordinate axes. If the locus of the circumcentre is of the form x + y - xy + k(x2 + y2)1/2= 0. Find k.The Attempt at a Solution The centre of the given circle is (2,2) and...

Homework Statement Prove that ||a|-|b||\leq |a-b| for all a,b in the reals Homework Equations I know we have to use the triangle inequality, which states: |a+b|\leq |a|+|b|. Also, we proved in another problem that |b|\leq a iff -a\leqb\leqa The Attempt at a Solution Using the...

Homework Statement How many different paths will spell the word BINOMIAL in the following arrangement(moving diagonally downwards to the left or right)? ...B ...I I ..N N N O O O O .M M M ...I I ...A ...L L Homework Equations The Attempt at a Solution Starting from B using Pascal's Triangle...

Homework Statement What is the moment of inertia WRT to the x-axis (Ix) of a right triangle with base b and height h where the legs of the triangle coincide with the x and y axis? It would be helpful to know both the single integral and double integral method. Homework Equations Ix=int(y^2 dA)...

Homework Statement Problem: Find the force on one face of a right triangle of sides 4 meters and altitude of 3 meters. The altitude is submerged vertically with the 4 meter side in the surface. The selections by the way are a. 58.86 kNewton b. 53.22 kNewton c. 62.64 kNewton d...

Homework Statement How can I find the center of mass of a right triangle, of height h, length a, and mass m, without using calculus? Homework Equations The Attempt at a Solution I just need a hint on how to start please

Homework Statement Without parameterizing the path, determine what the value of the line integral (integral of F dot dr) is, if C is the closed, oriented path that travels around the triangle with vertices (0,0) (5,2), and (-3,6) and F=yi + xj Homework Equations Curl possiblY? The...

Homework Statement O is any point inside the triangle ABC. AO, BO, CO are joined and produced to meet the opposite sides BC, CA, and AB at D,E and F respectively. Prove that AO/AD+BO/BE+CO/CF=2 Homework Equations The Attempt at a Solution Obviously, O is meant to be the...

Homework Statement Let ABC be a triangle in which angle A = 600. Let BE and CF be the bisectors of the angles B and C, with E on AC and F on AB. Let M be the reflection of A in the line EF. Prove that M lies on BC. http://img135.imageshack.us/img135/606/sumu.png The Attempt at a Solution I...

Homework Statement You're given a hoop with mass m and radius R balanced on top of a knife blade. (The diagram looks like a triangle with a circle balanced on the tip.) Find the period of small oscillations. (Yes, that is all the problem says.) Homework Equations Moment of inertia of a...

Homework Statement a line passes through the point (1,1/8) and intersects the positive x-axis at the point A and the positive y-axis at the point B. What is the shortest possible distance between A and B? Homework Equations i came up with three slopes for this line m1=-b/a...

How would I find the maximum area of a triangle given a fixed perimeter? I assume that it would be an equilateral triangle, but I'm finding it very hard proving it. I started by drawing a triangle of side lengths a, b and P -(a+b) with angles of alpha, beta and gamma. I then used the...

Prove that in any triangle ABC with a sharp angle at the peak C apply inequality:(a^2+b^2)cos(α-β)<=2ab Determine when equality occurs. I tried to solve this problem... I proved that (a^2+b^2+c^2)^2/3 >= (4S(ABC))^2, S(ABC) - area but I don't know prove that (a^2+b^2)cos(α-β)<=2ab :(...

Homework Statement what is the resultant vector of an isosceles triangle? Homework Equations R^2=a^2+b^2-4abcos(theta) The Attempt at a Solution The books answer R=2acos(theta/2) Using the formula above, and knowing that a=b in a isosceles triangle I am getting...

A triangle has sides of length 10 and 14 units respectively, and one of the non-included angles is 30 degrees. Find the possible lengths of the third side. The answers is the product of these lengths.

Is it true in general that: |\int f(x)dx| < \int |f(x)|dx Not sure if "Triangle Inequality" is the right word for that, but that seems to be what's involved.

The problem Can anyone explain me a step given in my book? This is actually the derivation of the distance between orthocentre and circumcentre of a triangle using vectors. ABC is a triangle. S is the circumcentre and H is the orthocentre. \vec{SA} + \vec{SB} + \vec{SC} = \vec{SA} +...

Homework Statement I know traditionally the center of mass of a triangle is 2/3 the way down its height, but i believe it varies here due to the uneven mass distribution. Here i have to find the center of mass distance from Q http://img508.imageshack.us/f/scn0001p.jpg/ Here is an image...

Homework Statement [PLAIN]http://img59.imageshack.us/img59/9484/fp5.gif to find the moment of inertia through point A Homework Equations I = \int{r^2dm}The Attempt at a Solution Used a double integral from point A: \displaystyle\int_{0}^{h}\displaystyle\int_{-L/2}^{L/2}\rho(x^2+y^2)dxdy =...

Homework Statement Two point particles of mass m are attached to two vertices of an equilateral triangle made of three massless rigid rods of length l. The third vertex is pivoted to a fxed point, so that the triangle can swing in a vertical plane under the effect of gravity. The system...

Homework Statement I need to calculate center of mass of this isosceles triangle using integration: the density is constant. Homework Equations Rcm = integral(xdm) / integral(dm) The Attempt at a Solution I know how to begin: dm = density * dx * dy; x = double-integral(x*dx*dy)...

Homework Statement Three uniform spheres are located at the corners of an equilateral triangle. Each side of the triangle has a length of 1.23 m. Two of the spheres have a mass of 2.84 kg each. The third sphere (mass unknown) is released from rest. Considering only the gravitational forces...

The "Tetraktysal Kissing Triangle" (TK_n) & Lower Bounds of Kissing Numbers to D=10 The Tetraktysal Kissing Triangle (TK_n) Nickname: "The TetraKiss Triangle" A Fibonacci, Lucas, Tetrahedral Convolution Construction for Lower Bounds of Sphere Packings to Dimension 10 Based Upon the Pythagorean...

Homework Statement Two sides of a triangle of fixed length measure 12m and 15m. The angle between these two sides increases at a rate of 2 degrees per minute. When the angle between these two sides is 60 degrees, at what rate is the third side increasing? Homework Equations That's the...

Homework Statement d(x,y)=(a|x_1-y_1|^2+b|x_1-y_1||x_2-y_2|+c|x_2-y_2|^2)^{1/2} where a>0, b>0, c>0 and 4ac-b^2<0 Show whether d(x,y) exhibits Triangle inequality? Homework Equations (M4) d(x,y) \leq d(x,z)+d(z,y) (for all x,y and z in X) The Attempt at a Solution I...