Recent content by Kb1jij

Wow, never mind that recursion relation is wrong. Silly me. If anyone feels like it they are still welcome to find an expression for that sequence

I just finished a final in my differential equations class. One of the problems had me solve a second order homogeneous differential equation using series. I boiled it down to this recursion relation: a_{n+2}=\frac{(n+3)a_{n}}{2(n+2)(n+1)} I found that the even coefficients work out...

Ah, got it now. Thank you. I don't like these induction problems...

Homework Statement Use Mathematical Induction to prove that 12^n + 2(5^{n-1}) is divisible by 7 for all n \in Z^+ Homework Equations The Attempt at a Solution First, show that it works for n = 1: 12^1 + 2 \cdot 5^0 = 14 , 14/7 = 2 Next assume: 12^k + 2(5^{k-1}) = 7A Then, prove for...

Well I'm really big into fishing, but from what I hear its good... Are you from around here?

I figured it out. The square root simplifies to 2e^(-2t), I just drop a sign. Nevermind!

I'm having trouble with the following: The problem is to find the arc length of the following parametric function: x=(e^-t)(cos t), y=(e^-t)(sin t) from 0 to \pi I found that \frac{\partial y}{\partial t} = e^{-t}(\cos{t}-\sin{t}) , \frac{\partial x}{\partial t} =...

suicide defeats Hitler

Of course this wall served a different purpose. It was made to keep out hostile invaders and not needy peasants and laborers

Wow, great. That does work out very nicely. That is a pretty tricky problem, but that's what I would expect from this competition. Thanks! Tom

I don't have a serious moral objection to the issue, but I think that spending a lot of time and money building such a wall would create a bad image of our nation (well, not that its is a good one now). America is supposted to be the land of opportunity, so I don't think walling people out is a...

Do you mean an ellipse? This is a specific type of an "oval" and is like a streched out circle. It follows the formula: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 Unfortunately, there is not a simple exact formula for the perimeter of an ellipse. You might want to check out this website for...

I don't understand how I can factor a 3^2 out. 3^2(3^x+3^-x) is equal to (3^x)(3^2)+(3^-x)(3^2) or 3^(x+2)+3^(-x+2). Also, 3^(2x)/3^2 would just become 3^(2x-2).

Ok, I got the second one, it's 4. I was avoiding using the sum formulas because I thought that I would just get a large mess of sines and cosines, but if you use integral's approach, the sums up being the difference of two squares, and it isn't really that complicated. How can I factor...

Yesterday in a math competition, I came across two problems that I couldn't (and still can't) figure out how to solve under the competion conditions (in under three minutes, without using a calculator). The first one involved expential functions. When I try to do it I just get a huge mess of...