Triangle Definition and 1000 Threads

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...

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

Hello! I'm trying to understand how this formula: 1/2 magnitude of v × w (area of triangle) yields the same value no matter which 2 adjacent sides are chosen. How would you prove mathematically that this is the case?

Let's say you have a triangle like: 1 2 3 4 5 6 7 8 9 10 The children of each element in the triangle are those directly adjacent on the next row. For example the children of 4 are 7 and 8. The children of 5 are 8 and 9. Now let's say we flatten it to...

Homework Statement We place three charges in the corners of the equilateral triangle; the size of the sides is 1 m. Charges are of sizes: e1, e2 = −2e1, and e3 = 3e1, where e1 = 10 ^-6 As. What is the force on the first (second, third) charge and in which direction are they showing...

easy question :) If you have a simple sierpinski's triangle (3 up 1 down). Does the line intersecting the two midpoints of the triangles "legs" also intersect the mid-point of the height? (if it is a equilateral triangle)

I need some help with spherical triangles. I am looking for the lengths of the sides of a spherical triangle given that all the angles. One being 90 degrees and the other 2 angles being 50 and 70 degrees. I don't even know how to go about solving this. I know there are 4 formulas for solving...

Homework Statement In Triangle ABC, tan A=3/4, tan B=1, and a=10. Find what b equals. Homework Equations You can use sina/A=sinb/B The Attempt at a Solution This problem is really easy using inv tangent functions and what not, but my teacher said we should be able to get it without...

Homework Statement Three positive particles of charges +7.0 uC are located at the corners of an equilateral triangle of side 20 cm. Calculate the magnitude and direction of the net force on each particle. Answer: 19.0 N [AWAY FROM THE CENTRE] Homework Equations F = (kQ1Q2)/(r^2)...

This is an mensurational problem of triangles. Homework Statement In triangle ABC, anngle B=90degrees and D is the mid point of AC .If AB=20 cm and Bd=14.5cm,find the area and perimeter of the triangle ABC. My book says that BD=AD=DC=> AC=2BD=29 and so on But i can't get how could they...

Homework Statement C is triangle (0,0), (4,0), (0,3). R is the enclosed region. Compute the following integral, where n is the outward pointing normal: \int_{C} \left(4x-y^{2}\right)n^{1}ds where n^{1} = \widehat{i} \cdot \widehat{n} Homework Equations The Attempt at a...

Homework Statement Which of these two triangles have a higher altitude (height)? NOTE: BOTH TRIANGLES ARE EQUILATERAL! Triangle 1 (all of the legnths going to the center are 665) Triangle 2 (lengths of each line going to center writen) Homework Equations none The Attempt...

Homework Statement the attachment is a drawing of what was given/what i have already found the mass and weight are the only things i have to find and i can't find any equations that will help me figure this out

Homework Statement In triangle ABC, the point P bisects the side BC, the point Q is the point on side AB for which |AQ| = 2|QB|, and the point R is the point of intersection between AP and CQ. Designate vectors a=AB and b=AC. Describe vector AR in terms of vectors a and b. Homework...

Homework Statement 3 equal point charges on the vertices of a triangle. If the each of the charges are doubled, why is the resulting force on each charge quadrupled? Homework Equations F= Fx +Fy F= kqk2/r^2 The Attempt at a Solution I got doubled

My lecturer keeps simplifying trigonometric integrals in one line such as \int^{2\pi}_{0}sin^{4}(t)dt=\frac{3\pi}{4} and writes pascals triangle next to it. Just wondering what's the link between them? I'm sure it's obvious and easy, I'd just like to have an fast way of dealing with these

A=(1,-1,-6), B=(4,4,2) and C=(-2,2,-4) are the vertices of a triangle. a) ||AB||^2 + ||BC||^2 = ||AC||^2 b) ||AB||^2 + ||BC||^2 - ||CA||^2 = 152 c) ||AB||^2 + ||BC||^2 + ||CA||^2 = 196 d) The triangle has a right angle at A e) The triangle is a right triangle a) T b) F, should be...

Homework Statement What is the electric potential at point P, the center of an equilateral triangle with side length of 2a and total charge of Q? Use infinity as the reference point. Homework Equations ∆v = -∫E∙ds v(r)= kq/r The Attempt at a Solution I already have the...

Homework Statement An equilateral triangle is formed with 3 rods, each with a length of 10cm. Two of them carry a charge of +63nC and 1 carries a charge of -63nC. The charge is uniformly distributed along each rod. What is the magnitude of the electric field at the center of the triangle...

If I know the length of all three sides of a triangle and the coordinates of two of those points, how can I find the coordinates of the third point (in a scalene non-right triangle)? Thanks

Homework Statement Consider a closed triangular box resting within a horizontal electric field of magnitude E = 7.80 & 104 N/C as shown in Figure P24.4. Calculate the electric flux through (a) the vertical rectangular surface, (b) the slanted surface, and (c) the entire surface of the box...

Suppose that I have three 3d vectors, pq, pr, and v, where v is the cross product of pq and pr. I want to fill the triangle formed by these three vectors, as shown in the picture. But I'm having difficulties finding the right command doing so, I've tried the polygonplot and apparently it...

Homework Statement i have a triangle with 2 legs of 96 inches. the angle between them is 104.5 degrees. how do i get the length of the 3rd leg? Homework Equationswish i knew. The Attempt at a Solution tried Cos, Sin, and Tan of 104.5 * length of a leg

What is the orientation of the largest equilateral triangle contained within a square?

Homework Statement Use Schwarz inequality on \bar{v} \bullet \bar{w} to prove: ||\bar{v} + \bar{w}||^2 \leq (||\bar{v}|| + ||\bar{w}||)^2 Homework Equations Schwarz inequality: |\bar{v} \bullet \bar{w}| \leq ||\bar{v}|| ||\bar{w}|| The Attempt at a Solution The way I...

To calculate the centroid of a cone, it seems that you have to use calculus. It comes out to be h/4, where h is the height from the base of the cone. But intuitively I thought that the centroid would have been h/3 because that's a triangle's centroid, and the cone can be obtained by rotating a...

Need some help with this one. Please be detailed and methodic in your understandable explanations because I find this very difficult. http://a.imagehost.org/0288/n_5.jpg