Triangle Definition and 1000 Threads

Homework Statement What is the flux of the uniform electric field E=8 N/C through an equilateral triangle with the side a=1m, if the normal vector makes 60 degrees to the direction of the electric field. Homework Equations \phi=EAcosøThe Attempt at a Solution E=8 N/C A= √3/4 m^2 Is the ø in...

Homework Statement Three particles with masses m1=2.5kg, m2=1.2kg and unknown mass m3 are placed at the corners of an equilateral triangle of side 30.0cm. If the resultant force in x-direction acting on m1 is zero, find the net force acting on m1. Homework Equations F=(Gm1m2)/R^2...

Homework Statement Find the flux through the equilateral triangle with corners at the points (1m,0,0), (0,1m,0), and (0,0,1m) in x,y,z space (measured in meters) for an electric field with magnitude E=6N/C pointing (a) in the z direction, (b) parallel to the line y = x. Homework...

http://en.wikipedia.org/wiki/CHSH_inequality#Bell.27s_1971_derivation The last step of the CHSH inequality derivation is to apply the triangle inequality. I see there are relative polarization angles, but I don't see any sides have defined length to make up a triangle. Where is the triangle?

Homework Statement Find a nonzero vector orthogonal to the plane through the point P, Q,and R. (b) also find the area of triangle PQR P(1,0,1) , Q(-2,1,3) , R(4,2,5) Homework Equations -Cross product -Finding the Angle -Area formula The Attempt at a Solution My steps: 1. i found the...

Homework Statement Write a recursive function void recurTriangle ( int n, char ch ) which prints out an upside-down triangle. The parameter ch is the character to be used for drawing the triangle, and n is the number of characters on the first row. For example, if n is 7 and ch is ’+’...

Prove that if the sides of a triangle are prime numbers its area cannot be whole number.

Let $PQR$ be a triangle with $\angle P=90^{\circ}$ and $PQ=PR$. Let $A$ and $B$ be points on the segment $QR$ such that $QA:AB:BR=3:5:4$. Find $\angle APB$.

I am trying to solve the 'ant and honey problem on a spherical bowl' to find the shortest route between two points on a sphere when the path is constrained by not being allowed to pass higher than a certain latitude (so interrupting some great circles connecting the two points). I intuitively...

Hi, i am trying to model a triangle in a square cell based on its dimension. However, i have some problem with parts of the code, i think it might be the logic behind my programming or over definition with the code itself. i have attached the code. the problem lies with the second half of...

Homework Statement For the vectors in a Triangle, with a = 16, b = 12, and c = 20 what are (a) the magnitude and (b) the direction of A x B (c) the magnitude and (d) the direction of A x C (e) the magnitude and (f) the direction B x C this is Vector Multiplication. Homework Equations...

If $Q$ is a point on the altitude $AM$ of triangle $ABC$, and that $\angle QBA=20^{\circ}$, $\angle QBC=40^{\circ}$ and $\angle QCB=30^{\circ}$, find $\angle QCA$.

Hey! I just started study landsurveying and got a task i don't figure out how to get the right answer. My goal is to find the length of one of the sides in a triangle, but i can not use pytagoras formula. Here is the formula i am supposed to use (dont care about the text, its norwegian)...

Find the smallest possible area of an isosceles triangle that has a circle of radius $r$ inside it. I cannot seem to find the relationship between the circle and triangle. Any hints? I'm thinking similar triangles, but I want to know if they're any other approaches before I try that.

Homework Statement Side ##a=4 cm##, altitude to side a is 3 cm , angle ##\alpha =60 °##. How can I draw that? Step by step Homework Equations The Attempt at a Solution

Homework Statement How to find area of an n-dimensional triangle using vectors? Homework Equations The Attempt at a Solution

Let $ABC$ be an equilateral triangle, and let $K$ be a point in its interior. Let the line $AK,\,BK,\,CK$ meet the sides of $BC,\,CA,\,AB$ in the points $A',\,B',\,C'$ respectively. Prove that $A'B'\cdot B'C'\cdot C'A' \ge A'B\cdot B'C\cdot C'A$.

On this triangle: Show a formula for finding co-ordinates of B. You know: - the co-ordinates of A and C; - Angle B = 90 degrees Is this possible? If not, is it possible if you know all 3 angles?

Prove that $p^4+q^4+r^4-2p^2q^2-2q^2r^2-2r^2p^2<0$ for $p,\,q,\,r$ are the sides of a triangle.

Homework Statement 3 rods each of length 1 meter form an equilateral triangle. Two rods have a uniform charge distribution of 8\times 10^{-6} C and the third of -8\times 10^{-6} C. What is the electric field strength at the center of an equilateral triangle Homework Equations \vec{E} =...

Let $x,\,y,\,z$ be the sides of a triangle. Prove that $x^3+y^3+3xyz>z^3$.

Consider an equilateral triangle of side 15.6 cm. A charge of +2.0uc is placed at one vertex and charges of -4.0C uc each are placed at the other two, as shown in the diagram to the right. Determine the electric field at the centre of the triangle ANgle= 60 sides--> d1= d2=d3=0.156m...

Consider an equilateral triangle of side 15.6 cm. A charge of +2.0uc is placed at one vertex and charges of -4.0C uc each are placed at the other two, as shown in the diagram to the right. Determine the electric field at the centre of the triangle ANgle= 60 sides--> d1= d2=d3=0.156m...

Definition/Summary Vectors (such as velocity or force or momentum) obey the Vector Law of Addition. That means in particular that combination of two vectors \vec{V}_1 and \vec{V}_2 is a vector \vec{V}_3 only if three directed lines (lines with arrows) \vec{L}_{AB} \vec{L}_{BC} and...

Hi friends, I have been trying to calculate the centroid of triangle (show in attachment) . I have got centroidal Y= h/3 Not able to get centroidal X = (1/3)*(a+b) Could anyone help on this stuff? Thanks..

Homework Statement Three charges, +Q, +Q, and -Q are placed at the vertices of an equilateral triangle of length "s" on a side. Find the magnitude and direction of the force on one of the +Q charges. Homework Equations ForceElectric=(K*q1*q2/d2) The Attempt at a Solution I've set...

Homework Statement Is it possible to determine all the angles in a triangle, if we only know the length of two sides?Homework Equations The Attempt at a Solution I was thinking for quite some time and I don't think it is possible. It probably is, if two sides are peprendicular but if not, I...

Homework Statement Youtube: Lec 2 | MIT 18.02 Multivariable Calculus, Fall 2007 (Video time frame: between 11:00 minutes and 12:30 minutes) Find the area of a triangle. Area = \frac{1}{2}(base)(height) = \frac{1}{2}|a||b|sinθ The lecturer says to first find cosine of the angle using dot...

I have a 30-60-90 triangle with the length of 8 for the long leg. I am trying to find the lengths of the other two legs. I believe the short leg is x, and hypotenuse is 2x, and the long leg is x times the \sqrt{3}. I put x times \sqrt{3}=8 although I am not sure how to do this formula to...

Homework Statement An ideal gas adiabatic coefficient γ is submitted to the ABCA cycle of fig, where AB is a line segment.. a) Calculate the income. b) Show that it is smaller than the yield of a Carnot cycle operating between the same temperature extremes. this is my attempt...

Homework Statement This is a general question about Statics. I was not able to find a specific question that includes this situation. I have a right triangle ABC with two (or three) members. Member AC is diagonal with a pin support (prevents translation) at C. Member AB is horizontal with...

$\triangle ABC, \,\, AB=AC$,point $D$ is the midpoint of $AC$ if $BD=m$,and $n$=area of $\triangle ABC$ please find $max(n)$ and corresponding $\angle A$

Can anyone refer me to a paper where the "plus sign in triangle", "minus sign in triangle", and/or "multiplication sign in triangle" are used? I'm reading a paper from the 80's where these symbols act on an image ("internal law" and "external law"); however, I'd like to see the symbols applied...

Is the Sierpinski triangle composed of equilateral or isosceles triangles? I've seen references for both but I have a student asking which one it is... any help is here greatly appreciated. Isosceles example...

Let A(1, 2), B (3,4), C( x, y) be points such that (x- 1) (x-3) +(y-2) (y-4)=0. Area of triangle ABC=1. maximum number of positions of C in the xy plane is (a) 2 (b) 4 (c) 8 (d) None of these I have tried using the staircase formula which gives me something like x-y=2. Therefore I see only...

For example: if it was given that two right triangles are similar triangles and that the hypotenuse of one is twice as long than the other how would you find the area of the triangle with the twice as long hypotenuse given the area of the other? Similar right triangles means they are the same...

WARNING: THIS IS NOT HOMEWORK~! Okay, so the problem goes like this: "Find a,b,c of a triangle; If a+b+c = 10 ; Area = 10" I know it sounds totally vague (I think so too). So I tried using the Pythagorean theorem; c2 = a2+b2 then the given equation; 10 - a - b = c; then the...

Show that for all $a>1$, there is a triangle with sides $a^4-1$, $a^4+a^3+2a^2+a+1$, and $2a^3+a^2+2a+1$.

I'm participating in research this summer and it's has to do with the Fourier Series. My professor wanted to give me practice problems before I actually started on the research. He gave me a square wave and I solved that one without many problems, but this triangle wave is another story. I've...

Homework Statement Find the area of triangle formed by the points ##A(5,2)## , ##B(4,7)## , ##C(7,-4)## Homework Equations Nah The Attempt at a Solution Is there any better way than finding the angle between lines and their lengths and then the area?

Homework Statement In an equilateral triangle with sides u, v, w, where they are all unit vectors, find u dot w. Homework Equations u dot w = |u||w|cosθ The Attempt at a Solution The answer is ##\frac {-1} {2} ## cos(120) = -1/2 Elsewhere, I read the statement that since these are...

$QB$ and $RA$ are angle bisectors of the triangle $PQR$. Given that $\angle QBA=24^{\circ}$ and $\angle RAD=18^{\circ}$. Find the measure of each angles $P,\,Q$ and $R$.

Homework Statement Let A, B, C be the vertices of a triangle in the plane and let a, b, c be respectively, the midpoints of the opposite sides. Show that Aa+ Bb+ Cc = 0 (all of them have vector signs on the left). Homework Equations definition of plane The Attempt at a Solution...

Homework Statement A triangle has verticies A(-2,1,3), B(7,8,-4), and C(5,0,2). Determine the area of the triange ABC. The correct answer is 35.9 square units. Homework Equations Has to be done by using dot product and/or cross product. Dot product: a(dot) b= |a||b|cos(theta) Cross...

Given a triangle $PQR$ where $QR=m$, $PQ=PR=n$ and $\angle P=\dfrac{\pi}{7}$. Show that $m^4-3m^2n^2-mn^3+n^4=0$.

In triangle $PQR$, $\tan P,\,\tan Q,\,\tan R$ are integers, find their values.

In a triangle $ABC$, it's given that $AB=AC$, point $D$ is on $BC$ whereas point $E$ is on $AD$ such that $\angle BED=2 \angle CED=\angle BAC$. Prove that $BD=2CD$. Note: This problem is actually posted by Albert at another math forum about 2 years ago and for all information, I have gained...

An ellipse has some model standard form values, a, b, and c which are easily enough to identify from the graph and parts of the graph related to the ellipse's graph. Seeing the right triangle relating a, b, and c, is easy enough. The Pythagorean Theorem is used to relate these three values...

Given that $PA,\,QB,\,RC$ are the altitudes of the acute triangle $PQR$ such that $9\vec{PA}+4\vec{QB}+7\vec{RC}=0$. Show that one of the angles of triangle $PQR$ is $60^{\circ}$.