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MathGroup Archive 2004

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Re: Re: Re: Solve given that a variable is between 0 and 1

  • To: mathgroup at smc.vnet.net
  • Subject: [mg52683] Re: [mg52659] Re: [mg52636] Re: Solve given that a variable is between 0 and 1
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Thu, 9 Dec 2004 20:22:37 -0500 (EST)
  • References: <200412070909.EAA09210@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

This is indeed the kind of problem that is not very suitable for a 
computer algebra program. But with a little human help Matheamtica can
manage it (well, sort of )


eq1 = w - k^(1 - b)*r*((-((a*k^b - OverBar[y])/a))^(1/b))^
       (-1 + b) == 0

rule = (a*k^b - OverBar[y])/a -> d



Solve[PowerExpand[Eliminate[{Equal @@ rule, eq1 /. rule},
     d]], k]

.....
various messages
......

{{k -> ((a*(w^(b/(b - 1))/r^(b/(b - 1)) + 1))/OverBar[y])^
      (-b^(-1))}}

Of course in general you can't expect to get in this way the complete 
solution nor indeed that what you do get is a solution at all. This has 
to be verified by hand.

Andrzej Kozlowski

On 7 Dec 2004, at 18:09, yehuda ben-shimol wrote:

>
> The problem at hand is easily solved by hand in about 60 seconds.
> Yehuda
>
> -----Original Message-----
> From: Steve Luttrell 
To: mathgroup at smc.vnet.net
> [mailto:steve_usenet at _removemefirst_luttrell.org.uk]
> To: mathgroup at smc.vnet.net
> Subject: [mg52683] [mg52659] [mg52636] Re: Solve given that a variable is 
> between 0 and 1
>
> 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
>>
>
>
>


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