Recent content by HmBe

You're a hero, I have mental problems. Thank you so much.

Homework Statement Find the surface area of the Earth (as a fraction of the total surface of the earth) that lies above 50 degrees latitude North. Homework Equations $$A = \int_R\sqrt{|\det(g)|}d\theta d\phi$$ The Attempt at a Solution Hence I get $$\int_0^{360}...

Homework Statement Homework Equations The Attempt at a Solution I'm fine with the second part (n = 6). But the first part is eluding me, I've been told it's quite simple. I feel like it's something to do with the fact that for each prime factor of C_n, p1, p2, p3, we have...

Ah right yeah I thought they were too separate inequalities which really messed me up. Quite simple now. Got down to this.. (b-b')^2 + 2(a-a')^2 = pk for some integer k. I'm having a little struggle getting rid of the k (so to speak). a, b, a', b' are all < sqrt(p) so...

Yeah I'm happy with the pigeon hole principle, although I can't quite see how it applies as a can be any natural number or 0, so surely the size of set A is infinite?

Homework Statement The Attempt at a Solution Don't have a clue how to even start this one, sorry.

Anyone?

Homework Statement Homework Equations The Attempt at a Solution For the acceleration I got du/dt=0, and the rest ends up equalling (-3x)i + (-3y)j, so this is the acceleration. A mate of mine got something slightly different, but I'm pretty sure mine is right - can anyone...

Yeah, that's what I got. Except I got N(N-1) rather then (N-1)(N-2). Thanks a lot for the help.

Thanks. I've kinda got another question though. I thought I understood the matrix for part ii, but thinking about it it doesn't really make much sense. Can anyone help me understand it? Cheers.

Homework Statement The Attempt at a Solution For part ii) I wrote it out as a matrix, getting \begin{array}{ccccccc} 0 & 0 & 0 & 0 & ... & 0 \\ 0 & 0 & 2 & 0 & ... & 0 \\ 0 & 0 & 0 & 6 & ... & 0 \\ . & . & . & . & . & . \\ 0 & 0 & 0 & 0 & ... & N(N-2) \end{array} So...

Your 4yz term is not correct. EDIT: Yep, beat me to it.

When you said, y = 3^(st), did you mean y = e^(st)?

Oh yes, just realized I made a pretty big mistake when I plotted the function, and that it's not continuous, so applying IVT would be very tricky.

I was pretty sure the definition of a repeated root was that if there is a root at x=a, that is f(a)=0, and f'(a)=0, then the root is repeated. Thinking about it, it seems to make sense, but I couldn't find anything on the internet to verify this.