Recent content by PinkCrayon

Sorry to revive a somewhat dead thread, but I thought about this and we can just complete the square. I spent like half an hour typing out the itex of the full solution and to my dismay, somehow hit the back button on my browser. So I'll just post the hard part. I thought I should post my...

2^{2} = 2 + 2 3^{2} = 3 + 3 + 3 4^{2} = 4 + 4 + 4 + 4 Generalizing... x^{2} = x + ... + x (x times) Take the derivative of both sides. \frac{\delta}{\delta x} x^{2} = \frac{\delta}{\delta x}[ x + ... + x] (x times) 2x = 1 + ... + 1 (x times) = x !? Surely, there must be something...

Sorry, I can't seem to find an edit button. By "best" method, I mean that this is a question that would typically appear on an exam and it seems like applying the principal axis theorem, making two change of variables and then taking two integrals is at least 30 minutes of work. On an exam that...

What would be the best method of finding the principal axes?

Homework Statement Evaluate. ∫∫D x2 dAxy, bounded by 5x2 + 4xy + y2 = 1 Homework Equations ∫∫D H(x,y) dAxy = ∫∫D H(u,v)\frac{\delta(x,y)}{\delta(u,v)}dAuv The Attempt at a Solution So I understand I'm supposed to find a change of variables to transform the ellipse into a circle...

Thanks! Amazing stuff :D

I think she means inverse sine.

Homework Statement For each positive integer n, let T(n) be the number of triangles with integer side lengths, positive area, and perimeter n. For example, T(6) = 1 since the only such triangle with a perimeter of 6 has side lengths 2, 2 and 2. (a) Determine the values of T(10), T(11) and...

Hey there, I'm not sure if I'm qualified to help you, but I'll try my best. It seems you are trying to equate the potential elastic energy of the bungee cord when it is fully stretched with Sam's potential gravitational energy from when he is at the top of the tower with respect to when the...