Triangle Definition and 1000 Threads

Homework Statement Given an isosceles triangle - Length = L - Uniform Density = ρ - Width Varies from 0 at x = 0 to a at x = L I attached a picture of it. Homework Equations Have to show the width at position x is given by (a/L)x The Attempt at a Solution Now it is...

1. Homework Statement Sin(sec^-1(sqrt(x^2+16)/4)) 2. Homework Equations 3. The Attempt at a Solution I did the math and ended up getting x^2-1 as the opposite, but the answers on the back of the book say other wise.

Homework Statement Cos(Tan^-1(x)) Homework Equations The Attempt at a Solution Dont know how drawing a right triangle would do anything, don't know what to plug in.

I meet with a triangle integral where x+y≤1, and function is dependant only on x*y. I am wondering if there any possibility to relate ∫∫dxdyf(x*y)=∫d(x*y)f(x*y)g(x*y) or something similar? Or maybe there are some assumptions needed to relate like this?

Homework Statement http://img221.imageshack.us/img221/4861/figure1h.png Mod note: Fixed the image link.[/color] Consider the rigid object shown in this image. Four masses lie at the points shown on a rigid isosceles right triangle with hypotenuse length 4a. The mass at the right angle...

Geometry Triangle Congruence - **Edited to include diagram** Homework Statement Hi! The three simple geometry problems are in the attached photo. Sorry if they're difficult to read. I haven't seen this information in so long, and could use some help. :D Can you use the given information...

Prove that, if (c - b).a = 0 and (c - a).b = 0, then (b - a).c = 0. Show that this can be used to prove the following geometric results: a. The lines through the vertices of a triangle ABC perpendicular to the opposite sides meet in a point. b. If the tetrahedron OABC has two pairs of...

Prove that, if (c - b).a = 0 and (c - a).b = 0, then (b - a).c = 0. Show that this can be used to prove the following geometric results: a. The lines through the vertices of a triangle ABC perpendicular to the opposite sides meet in a point. b. If the tetrahedron OABC has two pairs of...

Homework Statement If the height of a triangle is five centimeters less than the length of its base and if the area of the triangle is 52 cm^2, find the base and the height.Homework Equations N/A The Attempt at a Solution height = h-5 base = h A=(bh)/2 52=(h(h-5)/2 52=(h^2-5h)/2 104=h^2-5h...

Homework Statement A point charge q = +2.0 µC is placed at each corner of an equilateral triangle with sides 0.23 m in length. What is the magnitude of the electric field at the midpoint of any of the three sides of the triangle? 3. I want to know if I did this correctly, or totally...

Vector A and vector B are expressed in component form. A = [2.32,-5.16,7.88] B = [-1.12,3.45,-12.8] The standard arrow representation of these vectors and that of can be arranged to form a triangle in a plane that represents the geometric equivalent of the subtraction operation. The...

Homework Statement Prove the triangle inequality for the following metric d d\big((x_1, x_2), (y_1, y_2)\big) = \begin{cases} |x_2| + |y_2| + |x_1 - y_1| & \text{if } x_1 \neq y_1 \\ |x_2 - y_2| & \text{if } x_1 = y_1 \end{cases}, where x_1, x_2, y_1, y_2 \in \mathbb{R}...

A FAQ is why the spacetime interval has a minus sign. A geometrical answer is that the interval is always the shortest path (the straight line) between two points. If we talk about spatial points, that interval is the hypotenuse of a right angle triangle, whose sides are the projections of...

Homework Statement Let a, x, and y be real numbers and let E > 0. Suppose that |x-a|< E and |y-a|< E. Use the Triangle Inequality to find an estimate for the magnitude |x-y|. Homework Equations The Triangle Inequality states that |a+b| <= |a| + |b| is valid for all real numbers a and...

If you have a triangle circumscribed around a circle, how do you find the area of that circle? Say that the triangle is an equilateral triangle with side length of 8 cm. I found the area of the triangle using Heron's formula: 16√3 cm^2. Apparently the answer is 16π/3 cm^2. I'm just confused...

Given an equilateral triangle ABC, P is any point inside it where PA = 3, PB = 4 and PC = 5. Find area of the triangle using the Law of Sines or Law of Cosines.

Homework Statement If A, B, and C are the vertices of a triangle, find the following. (A→B) + (B→C) + (C→A) The answer has to be given like this: _____ i + _____ j 2. Homework Equations (I think?) a+b=b+a a+(b+c)=(a+b)+c a+0=a a+(-a)=0 c(a+b)=ca+cb (c+d)a=ca+da (cd)a=c(da)...

Homework Statement The length of the sides of the acute angled triangle ABC are x-1, x and x+1. BD is perpendicular to AC. Then CD-DA equals? Homework Equations cosine law The Attempt at a Solution

Homework Statement An Isosceles triangle has two equal sides of length 10cm. Let x be the angle between the two equal sides. a. Express the area A of the triangle as a function of x in radians. b. Suppose that x is increasing at the rate of 10 degrees per minute. How fast is A changing...

Homework Statement Anyone mind checking my answer for me? The area of a right triangle with hypotenuse H is A=1/4H^2sin(2x) x is one of the acute angles. Use differentials to estimate the relative errors of the area if H = 4cm exactly and x is measured to be 30degrees with an error of...

I am wondering is there any general analytic solutions to the following integrals First moment of area Integral(xdxdy) Integral(ydxdy) Second moment of area) Integral(x^2dxdy) Integral(y^2dxdy) Integral(xydxdy) Over the triangle (x1,y1) (x2,y2) (x3,y3) thanks Wei

Well another op-amp thread, while the other one is being cooked. http://pokit.org/get/a09120280ee2f6b6e3de7a99989b8bd9.jpg To speed you up, this is a triangle wave op amp generator. It generates a triangle wave at U2. In general I understand how the circuit works, but from the engineering...

Similar to my other thread https://www.physicsforums.com/showthread.php?t=557750 I think in this case I need to use triple integrals But what is the integrand and limits? Can someone please help me set it up? Here's all I know ∫∫∫dydx Please help I have my final next wednesday.

I am stuck on the job; I need to find the angles. It’s not an angle or side based triangle, just a right triangle. The lengths are known, A-B-C. What I need to know is the angles, a-b-c. So, a=90*, what formula could I use to find b, and c? Sorry, please make it easy enough for me to work it...

Homework Statement I have attached the problem. I am confused about how they got x(θ) and h(θ). From the diagram it looks like they made it with reference to the triangular support beam. Why? Homework Equations The Attempt at a Solution

Homework Statement The hypotenuse of a right triangle has length of 10cm. Determine its maximum possible area. c= 10cm Homework Equations a^2 + b^2 = c^2 ? b*h*(1/2) The Attempt at a Solution just drew out the triangle so far, confused as to where to go from here i assume ill...

Homework Statement Please see below... Homework Equations Please see below... The Attempt at a Solution Hi. This question is on geometry with circle and triangle. I am stuck only on 2 parts of the solution and not the whole solution... Thank you...

Homework Statement Find the center of mass of a triangle with two equal sides of length a. The triangle's third side is length b and it has a uniform mass of M. Homework Equations R = \frac{1}{M} \int dm \vec{r} dm = \frac{M}{A} A = \frac{1}{2}base*height The Attempt at a Solution...

Homework Statement Explorers in the jungle find an ancient monument in the shape of a large isosceles triangle. The monument is made from tens of thousands of small stone blocks of density 3 800 kg/m3. The monument is 15.7 m high and 64.8 m wide at its base and is everywhere 3.60 m thick...

I am not sure how the configuration would look like if we add a voltage across these points. I have drawn out what I think it would look like after a potential is applied across Vab. My question is, is this drawing correct?? What about Vbc and Vac? This is question 26.5. And here is my...

Homework Statement F=<xy, x-y> and C is the triangle joining (1,0), (0,1) and (-1,0) in the clockwise direction. Homework Equations How do I have the second part of this curve? The Attempt at a Solution Apparently, there should only be a sum of two integrals. So I got that curve...

Find the x and y coordinates of the center of mass of a flat triangular plate of a height H =17.3cm and a base B = 10 Cm Homework Equations Area = A = 1/2bh x = 1/A ∫ x(f(x)) y = 1/A ∫ 1/2((f(x)^2) The Attempt at a Solution Area = 1/2(10)(17.3) = 86.5 f(x) = 17.3-1.73x or...

Homework Statement Based on my understanding of the question the diagram should be like this ABC is an equilateral triangle with side 2a.Two circle are are drawn , with one of them crossing the points A,B and C.another circle crossess B and C with A as centre Prove that the area enclosed by...

Hi, I have an equilateral triangle and I put another equilateral triangle within it. The inner triangle has exactly half of the area of the outer triangle. As well, the inner triangle is placed in the centre of the outer triangle i.e. they both have the same central point. I want to...

1. Homework Statement A rope of 5m is fastened to two hooks 4m apart on a horizontal ceiling. To the rope is attached 10kg mass so that the segment of the rope are 3m and 2m.Compute the tension in the string 2. Homework Equations Sine rule, cosine rule 3. The Attempt at a Solution...

if we toss 4 coins and we want to know the probability of having 3 heads we can easily calculate that using pascal triangle . I want to know if we have an Urn that contain 3 balls : 1 black , 1 red, 1 yellow. and we want to draw 3 balls , but when we draw the first ball we put it back in the...

Homework Statement A body of mass 700g hangs from the end of a long wire fixed to a high tree. A horizontal string attached to the body pulls it until the wire is at 30 degrees to the vertical.Find the tensions in the both the string and the wire Homework Equations Sine rule The...

Homework Statement What I want to show is this: ∫|x+y| ≤ ∫|x| + ∫|y| Homework Equations |x+y| ≤ |x| + |y| The Attempt at a Solution So I thought if I used the triangle inequality I could get to something along the lines of: Lets g belong to the real numbers ∫|x+y| =...

I'm a little confused about this problem. I attached the pic. The solution manual states " capacitors C1 and C3 are in series with each other and in parallel with capacitor C2." I don't understand why it has to be C1 and C3 in series which is parallel with C2. Can't it also be C2&C3 in...

Homework Statement A metal bar of length l in the figure below has one end attached at a point P to a circle ofradius a < l. Point Q at the other end can slide back and forth along the x–axis. (a) Find x as a function of θ (θ=angle POQ). (b) Assume the lengths are in centimeters and the...

Homework Statement I have the side lengths of a triangle. The base is 190 ft long, side A is 182 ft long and side B is 363 ft long. That's all I know. Homework Equations The Attempt at a Solution I know these side lengths are related somehow.

Hello all! I just had a question about combining elements of matrices. In the MATLAB documentation, there was a function called triu and tril that extracts the upper and lower components of a matrix, respectively. I was wondering if there was a way to copy the elements of the upper triangle...

Homework Statement Find the implicit equation of the curve that goes through the point (3, 1) and whose tangent and normal lines always form with the x-axis a triangle whose area is equal to the slope of the tangent line. Assume y` > 0 and y > 0. Homework Equations Hint: ∫( √(a^2 -...

Homework Statement Three triangles are placed into a circle; The vertices of the triangle are tangential to each circle. How do you find the ratio of the area of the circles to that of the triangle? Homework Equations pi r^2, 1/2(b)(h), sqrt3/4 * a^2 (2r^2). The Attempt at a...

Homework Statement Consider a large triangle, the tip is located at the origo x=0, it is sloped at an angle θ and -θ relative to the x-axis, relative to the x-axis, its dimensions in x can be considered infinite. A large stripe/strip/band is placed on top of the triangle but perpendicular to...

Homework Statement A car travels 20.0 km due north and then 35.0 km in a direction 60.0° west of north. Using a graph, find the magnitude and direction of a single vector that gives the net effect of the car's trip. This vector is called the car's resultant displacement. I am...

Let's recall the Euclidean Rule for Pythagorean Triangles: Let (m,n) be co-prime natural numbers (m<n), then h := n^{2} + m^{2} e := 2 m n d := n^{2} - m^{2} = (n - m) * (n + m) form the hypothenuse, the even and the odd leg of a primitive Pythagorean triangle (PPT) If we...

Homework Statement [PLAIN]http://img832.imageshack.us/img832/5249/unledhbk.png The Attempt at a Solution Alright PF just erased all my work so here is my work without LaTex because I am too frustrated to do this all again Basically I found the vectors QP = <7,8,0> |QP|...

Moment of inertia of a "music triangle" Homework Statement Find the moment of inertia about an axis thru the centre of mass, perpendicular to the plane of an equilateral triangle consisting of identical rods of length 'l' and mass 'm' connected at their ends. Homework Equations...

Homework Statement > a[1], a[2], a[3], .. , a[n] are arbitrary real numbers, prove that; abs(sum(a[i], i = 1 .. n)) <= sum(abs(a[i]), i = 1 .. n) Homework Equations The Attempt at a Solution I have uploaded my attempt as a pdf file, since I'm not too familiar with the...