Triangle Definition and 1000 Threads

[Homework Statement 1.) Three charges are placed 25 cm apart in an equilateral triangle. Q1 has a charge of -6.0 nC, q2 has a charge of 4.0 nC and q3 has a charge of 4.0 nC. what is the force on q2? q1 is the top point, q2 is the bottom left leaving q3 on the bottom right Homework...

I'm interested in thing that are norms except for the fact that they satisfy the reverse triangle inequality ||x+y|| \geq ||x|| + ||y||. The obvious example is taking p-norms for 0<p<1. Does anyone know of others or if there's any theory developed on this topic?

Hi all I have a question concerning Euler's triangle formula, where the distance (d) between the incenter and circumcenter of a triangle is given as d2 = R(R-2r), with R being the circumradius and r the inradius. I suck at algebra and I need to know how to solve this if I only know the...

Homework Statement Let (X,\theta) be a metric space. Take K > 0 and define. \theta : X \cross X \rightarrow \real_{0}^{+}, (x,y)\rightarrow \frac{K\phi(x,y)}{1+K\phi(x,y)} Show that (X,\theta) is a metric space. Homework Equations can someone please check my triangle...

Homework Statement I'm attempting Q 3 from ch 16.4 of Stewart (p 1060). We are required to find the line integral where C is the triangle with vertices (0,0), (1,0) and (1,2). The line integral is Int xy dx + x^2*y^3 dy Homework Equations The Attempt at a Solution...

I am trying to transform a triangle in 3 space with the constraint that z = 1-x-y. At this point I have the following transformation matrix A, and three vector equations: | a1 a2 a3 | A = | a4 a5 a6 | | a7 a8 a9 | A*x1 = k1*y1...

i am trying to write a code that calculates the hypotenuse of a triangle... when i try to run it, i get a run time error. I'm not exactly sure what the problem is. #include <iostream> #include <cmath> using namespace std; void hypotenuse(double side1, double side2...

Homework Statement I had this exam question for a final exam and I was wondering if I got it right or not. There are three point charges +4q equally spaced apart at the tips of an equilateral triangle with distance .11m apart from each other. What is the magnitude of the electric field at the...

MY ATTEMPT: gPE to KE - Water in waterfall KE to gPE - Climbing mountain Strain to KE - Firing an arrow KE to Strain - Trebuchet being wound back Strain to gPE - ? gPE to Strain - ? It is the last 2 for which I really cannot think of instances in life - PLEASE help me out!

Given triangle ABC. And given that it’s a common 3-4-5 right triangle. (this still qualifies as a scalene) So AB = 4 BC = 3 AC = 5 is the hypotenuse If Angle A was bisected, do the two newly formed triangles have the same area? And would the bisecting line hit the midpoint of...

Homework Statement Point charges Q, -2Q and 3Q are situated at the corners A, B and C respectively of an eqilateral triangle of side l, and another point charge q, of the same sign as Q, is placed at the centre of this triangle. What is the force acting on the charge q, and what is the angle...

Right triangle problem,please check! Homework Statement In the figure,TN=NK, ST=12 and SN=\sqrt{69}.Find the length of TK. [PLAIN]http://img695.imageshack.us/img695/633/50042657.png Homework Equations Pythagorean Theorem The Attempt at a Solution Segment SN is the median of the...

Homework Statement Consider an isosceles triangles with height x and a fixed incircle of radius R. Show that the minimum area of such triangle occurs when x = 3R Homework Equations None. The Attempt at a Solution Well, I know that have to express the area of the triangle in terms...

Homework Statement Here's the problem: refer to question no. 6 http://img1.uploadscreenshot.com/images/orig/5/12314183569-orig.jpg" Homework Equations I am not sure :S The Attempt at a Solution This, honestly, is a question which I have no clue how to go about... Thanks...

Homework Statement If the base b of a triangle is increasing at a rate of 3 inches per minute while its height h is decreasing at a rate of 3 inches per minute, which of the following must be true about the area A of the triangle? a. A is always increasing b. A is always decreasing c. A...

I have not had any luck in finding out how much is known about the actual positions of quarks in protons and neutrons. I am confused by the brief snippets of information I have managed to find. First by the fact that an electron is fired at a nucleon and that its path can reveal the prescence...

Homework Statement Triangle ABC formed by two vectors a = ( 2, 10, 25 ) and b = ( 5, 4, -2 ) attached at a point A. The area of the triangle is (81 root 5) / 2 And I need to find the length of the height AM (AM perpendicular to BC and the point M belongs to the line BC). Don't know where to...

Homework Statement I have a triangle ABC formed by vectors a = ( 2, 10, 25 ) and b = ( 5, 4, -2 ) attached at a point P. And I have to calculate the area of the triangle ABC. Homework Equations I'm pretty certain that I need to find the area of the parellogram and then half it. So I...

Homework Statement Given triangle ABC with vertices A(4, 1, 7), B(-2, 1, 1) and C(-3, 5, -6)..is ABC a Right triangle Homework Equations The Attempt at a Solution I took the dot product of vertices A(4, 1, 7).B(-2, 1, 1), and it gives 0..but however I am a little confused, as...

Homework Statement integrate f(x,y) = sqrt(x^2+y^2) over triangle with vertices (0,0) (0,sqrt2) (sqrt 2, sqrt 2) Homework Equations x= rcosO, y = rsinO x^2+y^2=r^2 The Attempt at a Solution im supposed to use a double integral converted to polar coordinates, so i used...

On my school days it was very simple because I used to take whatever I've and keep solving and by some or other ways I get succeed answering it but now as we are bounded by very less time (nearly a minute) so now I'm facing very hard time. How you know in which direction you need to go. I can't...

Homework Statement Let ABC be a piece of a parabola. The point B is chosen such that the tangent to the parabola at B is parallel to the line AC. Archimedes proved the Area of parabola inside ABC is 4/3 times the triangle ABC. Prove this using calculus Homework Equations The integral...

This is the first time I've ever been to this forum, so I'm hoping this is an appropriate place to post this. It's been a good amount of time since my college level physics courses and this rock climbing phenomenon has me stumped. There is a rock climbing anchor arrangement called the...

Hi. I need some help for a test tomoorow on thi sone kind of problem: Homework Statement Set up and evaluate an intergral to find the olume of a cone of height 12 m and radius 3 m at teh open end. A fast replay would be really helpful.

In an equilateral triangle a positive point charge +q is located at each of the vertices. If a 4th charge is added at the midpoint between one of the sides could this charge be such that the force on it would be zero?

Homework Statement how can i find the length of an oblique triangle given the 3 altitudes (the line drawn perpendicular from a point of the triangle to the opposite side). I have no idea on how to solve it. Homework Equations The Attempt at a Solution

Homework Statement A trough is 9 ft long and its ends have the shape of isosceles triangles that are 5 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 14 ft3/min, how fast is the water level rising when the water is 8 inches deep...

Homework Statement Prove: If the limit inf as k goes to infinity of abs(ak+1 / ak) > 1 then the sum from 1 to infinity of ak diverges Homework Equations The Attempt at a Solution So far I have this: Suppose lim inf abs(ak+1/ak) >1 then, there exists an r such that lim inf...

Homework Statement Prove: If the limit inf as k goes to infinity of abs(ak+1 / ak) > 1 then the sum from 1 to infinity of ak diverges Homework Equations The Attempt at a Solution So far I have this: Suppose lim inf abs(ak+1/ak) >1 then, there exists an r such that lim inf...

Homework Statement What is the electric potential at the point indicated with the dot in the figure? The dot is in the center of an equilateral triangle with sides of 3 cm. The top point is a +2 uC charge and the bottom points are both -1 uC charges. Homework Equations V= kq/r The...

I often read on books that linear triangles do not have membrane locking for large deformations of plates/shells. I completely don't understand how this is possible. If one uses the well-known CST, stretching is measured as the increase in length of each edge of the triangle. Then, in the limit...

Homework Statement Prove that a scalene triangle exists Homework Equations The Attempt at a Solution I really don't know how to approach this proof... should I do a direct proof or maybe by contradiction? Any help would be great...

Hi Guy's I was wondering If anyone new of a good link about the P-adic metric Strong triangle inequality. I am trying to constuct a proof to show that the p-adic is a metric space. Must the proof use the Strong triangle inequality ie d(a,c)\leq max{d(a,b),d(b,c)} or can it use the...

The vertices of a triangle are A(4;2) ; B(11;6) ; C(-3;-1) What is the equation of the perpendicular bisector of side a? (i think -7x+14y=7) What is the equation of the altitude of side c? (i think -4x+7y=5) What is the intersection of the previous lines? i have no idea about this,please...

Homework Statement Take an Isosceles triangle with a height of 10 and draw a line parallel to the base. How far from the top of the triangle does the drawn line have to be for the top half's area to equal the bottom half's area. Homework Equations The area of a triangle...

I was wondering if anyone knew of a text or website that has a very indepth explanation of the triangle inequality and its variations really just how to apply it with limit proofs. I mean i understand it in terms of a triangle as no one side can be longer than the sum of the two other sides...

Volume by cross-section: ellipse and equilateral triangle cross sections?? Homework Statement The base of a solid is the region bounded by the ellipse 4x^2+9y^2=36. Find the volume of the solid given that cross sections perpendicular to the x-axis are: a) equilateral triangles b) squares...

Homework Statement A particle moves from rest and has impressed a uniform velocity of 10 meters per second parallel to one side of an equilateral triangle, and a uniform acceleration of 10 meters/sec2 parallel to an adjacent side of the triangle. Find the distance of the particle from its...

Homework Statement Show that the area of a triangle with sides of lengths a and b with included angle theta is... A = 1/2 a*b*sin(theta) I am not sure what this question is really asking. Any help? Homework Equations The Attempt at a Solution

Homework Statement A particle moves from rest and has impressed a uniform velocity of 10 meters per second parallel to one side of an equilateral triangle, and a uniform acceleration of 10 meters/sec2 parallel to an adjacent side of the triangle. Find the distance of the particle from its...

Homework Statement A point charge q = 4.9 \mu C is placed at each corner of an equilateral triangle with sides 0.20 m in length. Is the magnitude of the electric field at the center of the triangle greater than, less than, or the same as the magnitude at the midpoint of a side? Explain...

Homework Statement Airplane flies over route in shape of triangle ABCD. Time(t1, t2, t3) of flying over sections AB, BC, CA are known. Lenght of sections is also known. During fly wind is present. velocity of wind is constant, and speed of airplane relative to wind is also constant. Find...

Hey folks, can someone quickly check my algebra? Given: d(x,A) \leq d(x,y) + d(y,A) To show: \left|d(x,A) - d(y,A) \right| \leq d(x,y) Proof: from given, d(x,A) - d(yA) \leq d(x,y); and -d(x,A) + d(y,A) \geq -d(x,y); \Rightarrow d(y,A) - d(x,A) \geq -d(x,y)...

1. The base of the yellow triangle has length 8 inches; its height is 10 inches. Each of the circles is tangent to each edge and each other circle that it touches. There are infinitely many circles. The radius of the largest of them is __________ and the total area of all the circles is...

Homework Statement A proton and an electron form two corners of an equilateral triangle of side length 5.3 x 10-6 m. What is the magnitude of the net electric field these particles produce at the third corner? Homework Equations E=kQ/r^2 The Attempt at a Solution I drew a triangle...

Homework Statement A = (7,6,8) B = (2,3,-1) C = (2, -7, 9) Find the area of the triangle these 3 points make I'm getting slightly different results for different combinations I use if I take CA = a - c = (5 , 13 , -1) CB = b - c = (0, 10, -10) Taking another combination AB = b - a = (-5...

Homework Statement http://folk.uio.no/robinbj/gg/ggstart.pdf" I am supposed to find the area of the triangle PQD. The numbers given are the areas of the other triangles.Homework Equations A= \frac{1}{2} a b \sin{C} As well as Heron's formula, possibly? A= \sqrt{s(s-a)(s-b)(s-c)} where s =...

Homework Statement Find the area of the triangle with vertices at the points with coordinates (1,2,3), (4,-3,2) and (8,1,1)Homework Equations The Attempt at a Solution well area of a triangle is 0.5 x base x height . We can get the length of each side by taking the modulus of each vector, but...

I'm trying to calculate the RMS for square, triangle and sine waves. I can easily do the integrtion for sine waves and for square waves by looking at the graphic and getting the areas. It doesn't seem as easy for triangle waves since its squared form looks much more complicated and I'm not...

Looks like \triangleq. I first came across it on the wikipedia article for Lie derivative. http://en.wikipedia.org/wiki/Lie_derivative#The_Lie_derivative_of_a_function