[Date Index]
[Thread Index]
[Author Index]
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
>>
>
>
>
Prev by Date:
**Re: Re: Complex Analysis using Mathematica**
Next by Date:
**Re: Re: A problem of numerical precision**
Previous by thread:
**Re: Re: Solve given that a variable is between 0 and 1**
Next by thread:
**Re: Solve given that a variable is between 0 and 1**
| |