I'm not quite sure how you would figure that, seeing as how, in order to find K, you need a value for R. The value of R is dependent on K. Wouldn't that make this set of equations recursive? Or, should I have replaced every R in the first equation with the expression in the second equation...
I have, but everything I've found talks about eigenvalues, pivoting, and vectors. I have absolutely no idea what any of those are. Please take into account that I am a sophomore in high school, currently enrolled in an Algebra II class that covered determinants only for use in Cramer's Rule.
A tool that I use and love is GraphCalc, a sort-of open-source program. It's quite similar to a TI-85.
Note: If you don't use Windows, you're SOL. The source code is uploaded, but it's incredibly incomplete. If you're running OS X/Unix, and you really want to use GraphCalc, you can use WINE...
Well, after a couple of hours of work, I figured out how to get K explicit in the first equation. I came up with the following:
K = (-R[1-e^([W*pi]/[D*ln([1+R]/[1-R])])])/(1+3^[(W*pi)/(D*ln[(1+R)/(1-R)])])
It should be fairly easy to subsititute the second equation in for R, and then...
Ok, so I understand the method of finding a determinant of any order by expansion of minors. I was recently challenged by my teacher to find the determinant of a 10th order determinant she gave me. I succeeded, and felt quite proud of myself, after working for 3 months and filling up 300 pages...