Re: Solve given that a variable is between 0 and 1
- To: mathgroup at smc.vnet.net
- Subject: [mg52700] Re: Solve given that a variable is between 0 and 1
- From: "Jason Roth" <jsr123 at gmail.com>
- Date: Thu, 9 Dec 2004 20:23:18 -0500 (EST)
- References: <cos13d$dl2$1@smc.vnet.net><coudkj$qdt$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
OK, so you need to substitute numerical values...I see...thank you Steve! :-) Steve Luttrell wrote: > To solve algebraically you need to give a numerical value to b, and then > only certain values lead to simple closed-form solution. Otherwise, you have > to solve numerically. > > Algebraic example: > > b = 1/2; > Solve[w - k^(1 - b)*r*((-((a*k^b - OverBar[y])/a))^ > (1/b))^(-1 + b) == 0, k] > > gives > > {{k -> (w^2*OverBar[y]^2)/(a^2*(-r + w)^2)}, > {k -> (w^2*OverBar[y]^2)/(a^2*(r + w)^2)}} > > Numerical example: > > b = 0.4; > w = 1; > a = 1; > r = 1; > OverBar[y] = 1; > NSolve[w - k^(1 - b)*r*((-((a*k^b - OverBar[y])/a))^ > (1/b))^(-1 + b) == 0, k] > > gives > > {{k -> 0.17677669529663688110021109052621}} > > Steve Luttrell > > "Jason" <jsr123 at gmail.com> wrote in message > news:cos13d$dl2$1 at smc.vnet.net... > > Hi all, > > > > I need some help with solving the following: > > > > \!\(Solve[ > > w - k\^\(1 - b\)\ r\ \((\((\(-\(\(a\ k\^b - > > y\&_\)\/a\)\))\)\^\(1\/b\))\)\ > > \^\(\(-1\) + b\) \[Equal] 0, k]\) > > > > given that a>0 and 0<b<1. > > > > How do I do this? > > > > Thanks MUCH!!---jason > >