Recent content by foo_daemon

Hm, I still had problems finding the solution. I 'cheated' and used WolframAlpha to solve that last formula for theta. Wolfram uses substitution and gives: \theta = tan^{-1} \left ( \frac{ -V_i^2 \pm \sqrt{-g^2 x^2 + 2 g H V_i^2 + V_i^4}}{gx} \right ) WolframAlpha then states that...

Aha... yes, I didn't really want to solve for t, I just didn't see a way around it. Your approach is simple, and I'm dumbfounded I didn't realize it first ;) However, it still seems to be an involved problem. Now we have: t = \frac{x}{V_0} Plugging this t into the formula for V_y, I...

Hi, I've been muddling over this problem for a few days. I thought there would be a simple approach, but I'm having trouble reaching a solution. Here is the rundown: We have a 2D projectile launcher. It hurls an object from the origin (0,0) at some initial velocity with magnitude V_i at angle...

Wow, was just testing around and it appears the exact same recursive formula satisfies the second part of the equation as well (the 'conjugate' square, I guess you could call it?). You just need to use the different set of initial values: n_i = 1, 5, 65, 901, 12545... m_i = 0, 8, 112...

RamaWolf: Haha, nice! Yep, you identified where this problem stems from (I was sort of partitioning it up): http://projecteuler.net/index.php?section=problems&id=94 To find integer areas of the isosceles triangle \left( n, n, n-1 \right) one must solve (expanded from Heron's formula):Area =...

Hi, I have a problem that I'm a bit stuck on, and need some direction: I need to find \forall_n within a certain domain that can satisfy this equation: \left( 3n-1 \right) \left( n+1 \right) = m^{2} where m,n \in \mathbb{Z} Or, to put it in a different context, I'm looking for...

Homework Statement Prove the \lim_{n\to +\infty}{\sqrt[n]{ n! }} \equiv \infty Homework Equations uses well-known operations The Attempt at a Solution I think the best (easiest) approach is to find some f(n) \leq n! , and express it as some g(n)^{n} . This will then get rid of the...

Hi, I need to solve the following integral from 0 to \infty : Please note that my professor has defined log(x) = ln(x) , i.e. 10 is not the default base. \int { e^{\frac{-log(x)^2}{2} } dx } Through 'simplification' ( e^{log(x)} = x ), I have translated the function to: \int { x^{...