Recent content by Jadehaan

Homework Statement This is the question followed my my attempt at the solution: Just wondering if this looks right? Thanks for any and all feedback, Jim

Thanks for the help snipez90 and Dick. I redid the problem. This is my original: And this is my new proof:

Homework Statement Let a, b, and c be lengths of sides of triangle T, where a ≤ b ≤ c. Prove that if T is a right triangle, then (abc)2=(c6-a6-b6)/3 Homework Equations If T is a right triangle, then Pythagorean’s Theorem states: The sum of the squares of the lengths of the...

Right, I misdefined the unit ball in my last two posts. Now the unit ball should be defined by x^{2}_{1}+x^{2}_{2}+x^{2}_{3}=1 Using the result for y_{1} if x_{1} is on the surface of the ball, x_{1}=1 and the other x's must equal 0. This implies that y_{1}=c. And if x_{1} grows large, the...

Got it, thanks!

y_{1}=\frac{cx_1}{x_1^2+x_2^2+x_3^2} If x is on the unit ball, x=\sqrt{1-y^2} How do x_1, x_2, x_3 play a part?

Homework Statement The problem is as follows: Let T be the triangle with vertices (0,1), (1,0), (0,0). Compute the integral \int\int\frac{sin^{2}(x+y)}{(x+y)} dxdy by making an appropriate change of variables. (Hint: check #24 Section 15.9) Homework Equations Problem 24 in 15.9 of...

Yep, thanks so much Dick.

I see. I was using the wrong distance formula. So using the formula for the distance between a point (m,n) and a line Ax+By+c=0 the distance is r= |Am+Bn+C|/ sqrt(A2+B2) Using the point (x,y) and the line x-y=0 I calculated the distance r=|x-y|/sqrt(2) Does this sound correct?

Homework Statement Let B be the outside of the unit ball centered at the origin, and let c be a non-zero constant. Consider the mapping where k=1,2,3. Find the image of the set B under the mapping. (Hint: consider the norm of (y1, y2, y3)) Homework Equations The unit ball would be 2...

Thanks for your help. You were right, I mistyped the formula for the moment about the x axis. Using points (x,y) and (y,x) I calculated r2=2x2-4xy+2y2 So the formula would be the integral of this multiplied by rho dA.

Homework Statement Let \Omega represent a two dimensional material region who density is given by \rho(x,y). Establish an integral formula for the moment of inertia of the material region about the line y=x. Homework Equations The moment of inertia about the x axis...

Homework Statement Justify if the limit of the following function exists as (x,y) approaches (0,0). If it exists find the limit using the squeezing technique. f(x,y)=(exy-1)/(x2+y2) Homework Equations The Attempt at a Solution I found the limit of f(x,0) to approach 0 I found...

Homework Statement Find the range of the parameter d for which the intersection of the sphere x2+y2+z2=1 and the plane x+y+z=d is non-empty. Homework Equations Cartesian coordinates of a sphere: x=rcos\thetasin\phi y=rsin\thetasin\phi z=rcos\phi r=1 The Attempt at a Solution...

Ok I see now that there is only 1 photon energy from 6 to 1. Since the Thomson model did not take this into account does that mean there are 0 photon energies for that model?