Recent content by Kitty Kat

Homework Statement Prove that there are infinitely many primes using Mersenne Primes, or show that it cannot be proven with Mersenne Primes. Homework Equations A Mersenne prime has the form: M = 2k - 1 The Attempt at a Solution Lemma: If k is a prime, then M = 2k - 1 is a prime. Proof of...

Homework Statement So basically for n ∈ {1, ... , 16} Find the lowest t to satisfy nt ≡ 1 (mod 17) Homework Equations Euler's Theorem tells us that the order, t, must be a divisor of φ(17), which is Euler's Phi Function. φ(17) = 16 t ∈ {1, 2, 4, 8, 16} The Attempt at a Solution n = 1 11 ≡ 1...

umm that's weird, let me mirror it.. Try https://gyazo.com/875b7ec82e66e0333e383a73e63a077c

Not quite exactly. Here's a picture of my notes since I don't know how to type it here with proper notation. Link: https://dl.pushbulletusercontent.com/wwTIGu5Cjgt9OlhFWP6geOc1nuuUgJJX/20151024_164749.jpg

Homework Statement f(x,y) = (xy) / (x2 + y4), when (x, y) ≠ (0,0) 0, when (x,y) = (0,0) Homework Equations Explicitly show that f(x,y) does not satisfy lim h -> 0 [ E(v,h) / ||h|| ] = 0 when v = 0 (h, v, and 0 are all vectors; I'm not sure how to put a hat on them) The Attempt at a Solution I...

Oops, I haven't been on for a while and am readjusting to the forums new style, my bad! I'll make sure to post in the correct sections next time! Thanks.

The problem: Relevant Equations: A = l * w So I drew a rectangle like this: And I'm not really sure how to proceed from this point.. I always have a hard time setting up the problems for optimization :/ Any tips to the right direction would be greatly appreciated! Just to clarify, this is...

Wow, thankyou again HakImPhilo, that diagram really helped! Am I still doing problem 1 incorrectly? I seem to get different points of intersection when I graph sin^2x + sinx = 0 compared to sinx + 1 = cosx sinx + 1 = cosx (sinx + 1)^2 = 1 - sin^2x sin^2x + 2sinx + 1 = 1 - sin^2x...

Mmm, so just to double check my answers... Question 1: sinx + 1 = cosx (sinx + 1)^2 = 1 - sin^2x sin^2x + 2sinx + 1 = 1 - sin^2x 2sin^2x + 2sinx = 0 sin^2x + sinx = 0 x = 0, pi, 2pi, 3pi, 4pi (And for the record, how would I input sin^2x into my calculator anyways? I think it's...

Thank you Sammy for clearing that up! I thought it had to satisfy both equations, since I was finding the point of intersection, but I guess it only needs to satisfy one or the other. And thanks again HakImPhilo for the in depth explanation, it really helped clear my understanding.

Mmm, I think I'm still a little slow on the uptake. I still don't really understand why [π, 3π] work, because the cos values of [π, 3π] are both -1, and if cosx = 1, then that doesn't make the equation true, since -1 doesn't equal 1. I think I'm really missing some fundamental basic idea here...

Thanks a lot HakimPhilo, you really cleared it up for me, but I still don't understand question 2 though. I thought that the only time cosx = 1 was when x = 1 (Likewise for sinx = 0 being y = 1).

So I have several problems that ask me to find all points of intersection algebraically, but I haven't been able to make much headway on most of them. [SIZE="3"]The first problem Homework Statement Find all the points of intersection algebraically of the graphs of ... on the interval [0...