# Help please to solve equation

hotvette
Homework Helper
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 substitute that entire thing into the third equation.

Sorry for the sloppy text, LaTeX really doesn't like me. I'll attach a picture to make it easier to read.

What value of K do you get when W= 5, D=5 & B=10? Does it match what I got via numerical methods?

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?

EDIT: Tried doing it that way, now I have an even bigger recursive mess.

$$\frac{W}{B}=\frac{1}{\pi}*[ln(\frac{1+\sqrt{K^{2}B^{2}-K^{3}BD-KBD+K^{3}D}}{1-\sqrt{K^{2}B^{2}-K^{3}BD-KBD+K^{3}D}})*\frac{D}{B}*ln(\frac{K+\sqrt{K^{2}B^{2}-K^{3}BD-KBD+K^{3}D}}{K-\sqrt{K^{2}B^{2}-K^{3}BD-KBD+K^{3}D}})]$$

If anyone can figure out how to get K explicit in that one, I'll get you a Nobel Prize.

Last edited: