MathGroup Archive 1998

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RE: weird eqns

Hi Troy,
Like so many problems in Mathematica, you often need to manipulate a bit
 to get the answer you want, rather than simply blindly plugging
things  in.  And even if you can get an answer by blindly plugging
things in, if  you haven't played around with the equations with
pencil and paper you  will likely get blindsided with an unexpected
(ie wrong) answer.   Playing around with your equations it is clear
that they have such large  exponents that it makes them rather
unstable to a direct numerical  attack unless you have some idea in
advance where you are looking. If  you label your constants as: alpha
 38530, beta 6, gamma  .987*2.303, delta 3000, and
epsilon 167 then you are really  interested in the region where
the exponent of 10 is close to zero.  You  can find this using:
NSolve[ -(alpha + delta) + (beta + epsilon) t Ð0, t] Which
gives the solution t-> 27.9301 If you rearrange your equations you can
use FindRoot to get the more  exact answer: t->27.8973
Then you easily find that the rest of the solutions are (essentially,
rounded to close rational):
b /3; c  (actually c .12 x 10^(-294)); o /3

Hope that helps.

-----Original Message-----
From: []
Sent:	Friday, January 30, 1998 3:25 AM To:
Subject:	[mg10698] weird eqns

I have four equations ond would like mathematica to solve them using
NSolve. everytime i try this it returns with a transcendental function
error. I would  like to solve thiese equations without have to
manipulate them by hand. anybody with any ideas would be welcomed,
Please email me as my newserver is spotty at best.

eone og[10, c] Ð(-38530+ 36*t)/(1.987*2.303*t); etwo Log[10, b] +
0.5*Log[10, o] - Log[10, c] Ð(-23000+2167*t)/(1.987*2.303*t);
ethree  + c + o Ð1;
efour /o Ð0.5;

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