Triangle Definition and 1000 Threads

Hello everyone, I have here one important abstract question which makes up some perplexity to my understanding. Attached to this post is one pic of F and two new introduced axes ( u and v ) . Let us for instance not consider them as perpendicular to each other. Now, if I...

Three charged particles are placed at the corners of an equilateral triangle of side L = 1.74 m. The charges are q1 = 3.63 µC, q2 = −8.05 µC, and q3 = −6.31 µC. Calculate the magnitude and direction (counterclockwise from the positive x axis) of the net force on q1 due to the other two...

I solved this many years ago, but after revisiting Trig in order to tutor my daughter, I revisited this to stimulate myself but am hitting a brick wall. Problem: A 4 inch square sits in a corner(picture x,y origin). A 12 inch ruler or line leans against the wall at an angle such that there are...

Show that the curve $x^3+3xy+y^3=1$ has only one set of three distinct points, $P$, $Q$, and $R$ which are the vertices of an equilateral triangle, and find its area.

I understand that S = P + jQ however I am confused how they got from that to the yellow box. Also, how did they get from the yellow box to the pink box and from the pink box to the blue box? Thanks

2 particles of charge q are placed at 2 vertices of an equilateral triangle of side a. An electric dipole is placed at the third vertex with its dipole moment orientated parallel to the opposite side of the triangle. a) Determine the magnitude of the torque on the dipole due to the electric...

A triangle hypotenuse given rectangle is rotated around one of their legs to generate a right circular cone? find the cone of greater volume. resp V= (2Sqrt(3)pi L^3)/27 It says hypotenuse given but it has no value According to the answer you can name it L

Inside a triangle $ABC$, there is a point P satisfies $\angle PAB=\angle PBC=\angle PCA=\lambda$. If the angles of the triangle are denoted by $\alpha$, $\beta$ and $\gamma$, prove that $\dfrac{1}{\sin^2 \lambda}=\dfrac{1}{\sin^2 \alpha}+\dfrac{1}{\sin^2 \beta}+\dfrac{1}{\sin^2 \gamma}$

Homework Statement Part (a): Find the intensity as function of ##\theta## and sketch it. Part (b): Find the intensity as function of ##\theta## and sketch it. Comment on first minima. Homework Equations The Attempt at a Solution Part(a) Convolution Method V_b = \frac{1}{2a}, 0 \leq...

Homework Statement Prove that the medians to the equal sides of an isosceles triangle divide each other into respectively equal parts Homework Equations The Attempt at a Solution suppose we have a triangle ABC where AB = AC. Let D be the point on AB in which the median intersects...

So hi, there's one little thing which I'm not understanding in the proof. After the inequality Spivak considers the two expressions to be equal. Why?!? I just don't see why we can't continue with the inequality and when we have factorized the identity to (|a|+|b|)^2 we can just replace...

Homework Statement If in any triangle r=r1-r2-r3, then which type of triangle is it? r1,r2,r3 denotes ex-radii. The Attempt at a Solution 4R = r1+r2+r3-r r2+r3 = 2R I can't figure out what to do next.

Homework Statement If in a ΔABC , \left( 1-\dfrac{r_1}{r_2} \right) \left( 1-\dfrac{r_1}{r_3} \right) = 2 then which triangle is it? r1, r2, r3 denotes ex-radii. The Attempt at a Solution I get this condition a^2+2b^2+2c^2+3bc=3ac+3ab Also \sum tan \frac{A}{2} tan \frac{B}{2} = tan^2...

Given a triangle $ABC$ such that $\angle BAC=103^{\circ}$ and $\angle ABC=51^{\circ}$. Let $M$ be a point inside triangle $ABC$ such that $\angle MAC=30^{\circ}$, $\angle MCA=13^{\circ}$. Find $\angle MBC$ with proof.

This is just a curiosity from my part: Has anyone know the proof of "Intersection of one internal angle bisector and two external angle bisectors of triangle is the center of an excircle."? I tried some things, but no luck.

Hi I have a problem understanding a figure in my lecture notes. The figure is the following one It shows the deformation of a triangular element from time t to time t+dt: So at t it is a isosceles triangle and at t+dt it is deformed. According to my lecture notes (page 16, eq. 28), the...

My daughter was given this problem in an exam. She could not do it and was never given the solution. I can do the problem using trig but she has not been taught trig yet. She says that it can be done without trig using a more simple method that she doesn't know. Could somebody please explain...

Homework Statement A rectangle is to be inscribed in a right triangle having sides 3 cm, 4 cm and 5 cm, as shown on the diagram. Find the dimensions of the rectangle with greatest possible area. Homework Equations 1. x^{2}+y^{2}=w^{2} in terms of w=\sqrt{x^{2}+y^{2}} 2...

The number of degrees in one acute angle of a right-angled triangle is equal to the number of grades in the other; express both the angles in degrees. So I have found the following answers : 810/17=47,05... degrees and 810/17=47,05... grades which gives 42,35... degrees Now, the real answer...

Homework Statement Lets say I have an equilateral triangle, and you are asked to calculate the net force on the top of the triangle Homework Equations Coulombs Law The Attempt at a Solution I know to use Coulombs law to find the forces acting on the top of the triangle, then since...

Here is the question: I have posted a link there to this thread so the OP can view my work.

Triangle ABC with side lengths a,b,c please prove : $ \sqrt {ab}+\sqrt {bc}+\sqrt {ca}\leq a+b+c<2\sqrt {ab}+2\sqrt {bc}+2\sqrt {ca}$

1. A plane flies horizontally at an altitude of 5 km and passes directly over a tracking telescope on the ground. When the angle of elevation is \frac{\pi}{3}, this angle is decreasing at a rate of -\frac{\pi}{3} rad/min. How fast is the plane traveling at that time? Homework Equations...

Homework Statement The .274 and .88 was found using the equation of electrostatic force . Homework Equations K=q1q2/d^2 The Attempt at a Solution Would I just tan inverse of .274N and .88N which would be 17 degrees. However my question is: how to determine the reference pt: would...

Homework Statement There is the moment of inertia about an x and a y-axis named, I_{x}, I_{y}. Then there is the moment of inertia about the centroidal x and y-axis named, \overline{I}_{x}, \overline{I}_{y}. Often we can look up these values in a table (like the figure included) and apply...

Here is the question: I have posted a link there to this thread so the OP can view my work.

Hello all! New to the forums, and I have a question for you. In my classes, we have been dealing a lot with proofs lately, so when I was working on an assignment, I figured I would try and find my own proof for something, just for the hell of it. I decided to tacle the area of a right angled...

Homework Statement Find the maximum area of a triangle with sides a\in (0,1] ,b\in [1,2], c\in [2,3]. Homework Equations The Attempt at a Solution I tried to make the area as a function of a single variable so that by differentiating I can get the answer. But it was...

A line divides an equilateral triangle into two parts with the same perimeter and having areas $A_1$ and $A_2$ respectively. Prove that $\dfrac{7}{9} \le \dfrac{A_1}{A_2} \le \dfrac{9}{7}$.

Homework Statement In triangle ABC with A as obtuse angle, AD and AE are median and altitude respectively. If BAD = DAE=EAC, then sin^3(A/3)cos(A/3) equals Homework Equations The Attempt at a Solution CE = a/2. Let DE = x. Then BD = a/2 - x. Let AE = p, AD = q. For ΔADB \cos...

Homework Statement Solving for base angles in a congruent triangle One of the base angles in a congruent triangle is 3x+5 The other base angle is unknown The remaining angle is x+16. Homework Equations See attached PDF The Attempt at a Solution Because two base angles in a...

I'm stuck on one aspect of the proof on page 105 of the 2nd edition. Equation 6.13 is necessary for the inequality to be an equality as it says but they never seem to account for inequality 6.11. Specifically, I don't see how this satisfies 2 Re<u,v> = 2 |<u,v>| Thanks for any guidance.

Homework Statement A molecule consists of three identical atoms located at the vertices of a 45 degree right triangle. Each pair of atoms interacts by an effective spring potential, with all spring constants equal to k. Consider only planar motion of this molecule. What are 6 normal modes and...

Hamming distance satisfies the triangle inequity that is for all x, y, u in c such that d(x,y) <= d(x,u) + d(u,y) where c is a code. Also when does the equality hold? My approach is Turning x to u by changing at most d(x,u) letters and turning u to y by changing at most d(u,y) letters. So...

Homework Statement I know the area of a right angled triangle, I also know the ratio of the two non-hypotenuse sides. Is there anyway of finding the lengths? Thanks! Homework Equations I don't think there are any like Area = 1/2abSinC The Attempt at a Solution I obviously...

Hello,, I'm reading about beams in mechanics of matrials. But I'm a bit stuck because of one thing that I either don't understand or just don't comply with! So, here's a picture from the book: picture 003 It says that the center of mass should be at 2/3 of the length.. I tried to...

Homework Statement In a triangle ABC, with usual notation, if ##a^2b^2c^2 (\sin 2A + \sin 2B + \sin 2C) = λ(∆)^x## where ∆ is the area of the triangle and x ##\in## Q, find (λx). Homework Equations The Attempt at a Solution The usual notation is: a,b,c are three sides of the...

9 A Ladder 13ft long is leaning against the side of a building. If the foot of the ladder is pulled away from the building at a constant rate of 8in per second how fast is the area of triangle formed by the ladder, the building and the ground changing (in feet squared per second) at the instant...

Prove |x|+|y| ≤ |x+y| + |x-y| for all real numbers x and y. Some ideas I have is let a = x+y and b = x-y and apply triangle inequity Could anyone give me some direction? Thanks

The following inequality can easily be proved on ##ℝ## : ## ||x|-|y|| \leq |x-y| ## I was wondering if it extends to arbitrary normed linear spaces, since I can't seem to prove it using the axioms for linear spaces. (I can however, prove it using the definition of the norm on ##ℝ## by using...

Homework Statement Use vectors to demonstrate that on a circle any two diametrically opposed points along with an arbitrary third point(on the circle) form a right triangle Homework Equations Hint: assume without a loss of generality that the circle is centered at the origin and let v...

Homework Statement Three vectors A, B, C point from the origin O to the three corners of a triangle. Show that the area of the triangle is given by area = \frac{1}{2}|(B\timesC) + (C\timesA) + (A\timesC)| Homework Equations area of triangle with sides a, b, c = \frac{1}{2}|a\timesc|...

Suppose A1, A2 and A3 are closed convex sets, and let Δ be a triangle with edges F1, F2 and F3 such that A_1 \cup A_2 \cup A_3 = \Delta and F_i \cap A_i = \emptyset \text{ for } i=1,2,3 Prove there exists some point x\in \Delta such that x\in A_1 \cap A_2 \cap A_3 Figurative bonus...

Homework Statement Three rods each of uniform charge Q and length a are formed into an equilateral triangle. Given[Q,a,q] determine: 1. The voltage at the center of the triangle. 2. If a charge -q is placed at the center of the triangle determine potential energy. 3. Determine the initial...

Homework Statement Hey guys. Basically I have a wavefunction that looks like this http://imageshack.com/a/img843/3691/22r3.jpg I have to find: (a) The normalization constant N, of course by normalizing it (b) Find <x> and <x^2> and use this to find Δx. Homework Equations I'm just...

okay so I know that the area of the triangle is half the area of the parallelogram, ill try using pictures because this is a bit confusing to describe only with words: for example we have this http://farside.ph.utexas.edu/teaching/301/lectures/img243.png and then if we use the cross product of...

Here is the question: I have posted a link there to this topic so the OP can see my work.

Homework Statement If I have a triangle that has the hypo as √(u^2 +1) adj as 1 and oppo as u I did an integral with trig sub. So I used Homework Equations u = tan(θ) The Attempt at a Solution At the end of my integral I ended up with an expression (1/4)sin(2θ) When I...

The two shortest sides of a right-angled triangle, $a$ and $b$ satisfy the inequality $$\sqrt{a^2-6a\sqrt{2}+19}+\sqrt{b^2-4b\sqrt{3}+16}\le3$$. Find the perimeter of this triangle.

Homework Statement I got an answer as you can see in both pictures, but apparently it is wrong. What did I do? Homework Equations The Attempt at a Solution In this picture I found the y components of the electric field at C. Since the bottom 2 are the same i just doubled one of...