Triangle Definition and 1000 Threads

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...

[SIZE="4"]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}...

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 $60^{\circ}$.

Homework Statement So I'm doing a physics problem, and I think I'd get the right answer if I solved this triangle. I don't know any angles. The base is 56 meters long, its height is 500 meters, and the difference between the other two sides is 4 meters. Can I figure out the sides based on this...

Homework Statement Homework Equations x^2 + y^2 = 9 A = 0.5xy x ≠ y The Attempt at a Solution x^2 + y^2 = 9 A = xy/2 (x + y)^2 = x^2 + 2xy + y^2 = 9 + 2xy = 9 + 4A A = ((x+y)^2 - 9)/4 Then I am lost. I need to find the area.

Consider a pole of 1 light second long in the ##y## direction (the vertical line(s) in the enclosed figure). It is moving in the ##-x## direction. According SR, the pole's length is not contracted because its length is not parallel to the propagation direction. However, given the time of flight...

Problem: Let $0<a<b$ i)Show that amongst the triangles with base $a$ and perimeter $a+b$, the maximum area is obtained when the other two sides have equal length $b/2$. ii)Using the result (i) or otherwise show that amongst the quadrilateral of given perimeter, the square has maximum area...

I know the Double Angle for Sine is: $$\sin(2x) = 2\sin(x) \cos(x)$$ but from the triangle given, how do I figure it out? We did this in class, but the teacher just told a small amount of things, and then let us talk amongst each other to solve it. Nearly all the students were glossy eyed and...

Triangle $PQR$ is an isosceles triangle with $PQ=PR$. Given that the angle bisector at $Q$ meets $PR$ at $A$ and that $QR=QA+PA$. Find angle $P$.

Problem: If A is the area and 2s the sum of three sides of a triangle, then: A)$A\leq \frac{s^2}{3\sqrt{3}}$ B)$A=\frac{s^2}{2}$ C)$A>\frac{s^2}{\sqrt{3}}$ D)None Attempt: From heron's formula: $$A=\sqrt{s(s-a)(s-b)(s-c)}$$ From AM-GM: $$\frac{s+(s-a)+(s-b)+(s-c)}{4}\geq...

in what point of the circumference: x2 + y2 = 1 the tangent to this, (to yhe circunference) form with the coordinate axes the triangle of smaller area?. answer ( +/-(sqrt2/2), +/-(sqrt2/2) ) Ok y2= 1-x2 Now I don't know in what point must i get the tangent?? I don't think it is in 0,0 I...

Gents, Thanks for all the guidance in the past with my work and brothers too. Can anyone help with these , see file attached

Hi, I am working on some MATLAB for my engineering classes and I need help with understanding a given diagram. In the attached diagram, I need help understanding how we determined the equations For example, I would like to know the equations for a triangle with the peak at 2/3L I know...

Homework Statement Consider the triangle of charges diagrammed below, for which d = 5 cm, q = 2 nC, and the +x-axis points to the right. What is the force Fvec on the 1 nC charge? Give your answer as a magnitude and a direction.Homework Equations F=K(q)(Q)/r^2 The Attempt at a Solution I...

Homework Statement Find the fluid force of a triangle with base of 6 ft and height of 4 ft submerged vertically into a body of water,vertex down, to a depth of 3 feet. Homework Equations from c to d W [SIZE="6"]∫ h(y) L(y) The Attempt at a Solution I set up the triangle on...

Homework Statement Two charges of opposite sign and equal magnitude Q = 0.82 C are held 2.0 m apart as shown in the figure. Picture: http://gyazo.com/a78a049ce0a24ad464fd7bb99dffd665 A) Determine the magnitude of the electric field at the point P. B) Determine the electric potential...

Problem: Given that $a,b$ and $c$ are the sides of $\Delta ABC$ such that $$z=\log_{2^a+2^{-a}} \left(4(ab+bc+ca)-(a+b+c)^2\right)$$ then $z$ has a real value if and only if A)a=b=2c B)3a=2b=c C)a-b=3c D)None of these Attempt: I am not sure where to start with this kind of problem. I wrote the...

Suppose we have a quantity which can take discrete equally spaced values. Iteratively, we can increase or decrease this quantity by one quantum, splitting into two new worlds each time. After multiple iterations we have some indistinguishable worlds, as described by Pascal's triangle. As the...

Why do trigonometric ratios have to be related to the angle between the base and hypotenuse of a right angle triangle? I am trying to understand why I can't use these ratios to any angle of a right angle triangle. I try to do that in the attached document. It seems to work for all ratios...