Recent content by ocohen

Hello, I am currently reading about electromagnetic fields: In one of the examples in the textbook we calculate the electric field of a hydrogen proton. We then compute the electric force acting on the orbiting electron to be 8.2 \times 10^{-8} N So I thought I could get the...

yeah this is what I got. Thanks for the reply, I just wanted to see if I was doing something wrong since I haven't typically had to use the cubic formula for textbook questions

hi, I have tried both lagrange multiplier and basic derivative minimization for this but keep ending with an ugly polynomial. Any ideas would be appreciated: find the shortest distance between the curve <t, t^2> and (2,2)

A_n = a_0 + a_1 + ... + a_n B_n = b_0 + b_1 + ... + b_n (A_n)(B_n) = (a_0 + a_1 + ... + a_n) (b_0 + b_1 + ... + b_n) = sum of i=0 to n (inner sum of j = 0 to n) a_i b_j Sorry I don't know how to use latex on this forum. Does that help with multiplying the sequences? so for example...

I get cot(x) as well, though you can skip quite a few steps in the simplification. Graphing confirms these are equivalent.

Having a hard time understanding this example from a book: The function f(x) = 1/x is locally bounded at each point x in the set E = (0,1). Let x \in (0,1). Take \delta_x = x/2, M_x = 2/x. Then f(t) = 1/t <= 2/x = M_x if x/2 = x-\delta_x < t < x + \delta_x This argument is false since...

10k/31 does not need to be a positive integer. Consider 9^(1/2)

If we are simply trying to satisfy the equation for the smallest k, just solve it like this m^(31/10) = p^k => m^(31/10k) = p So if k = 6, we just need some m such that its 60th root is a whole number. So let m = 2^60 or anything like that. we have that n = m^(21/10) so n is also a whole number...

I would suspect that 10k/31 must be an integer so that p^(10k/31) is also an integer. I don't have any proof for this, but someone else might. As such it means that 10k must be a multiple of 31. Does that make sense? EDIT: sorry this is incorrect.

you now get m = p^(10k/31) which means p^(10k/31) must be a whole number > 1. So what does that mean for (10k/31)?

try to get n in terms of m. Then see what k has to be such that p^k = nm

Your proof is false because you are dividing by b. This is incorrect since b could be 0.

no this is not true.

http://wally.cs.iupui.edu/n351/3D/matrix.html hope it helps

sorry no. I'm not sure. It has nice roots though so that suggests there should be a nice solution