Author Topic: Need some professional math help  (Read 3416 times)

Offline Botsareus

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Need some professional math help
« on: April 01, 2010, 11:35:21 AM »
Need some professional math help:

Solve the following equation for q in terms of Globex and Globey and get rid of X:
(ScaleWidth is a constant)

(X - Globex) ^ 2 + ((X ^ q / ScaleWidth ^ (q - 1)) - Globey) ^ 2 = 0

I have tried to break it down, I've got:
 
 (X ^ (q*2) / ScaleWidth ^ (q *2- 2))  -   (X ^ q / ScaleWidth ^ (q - 1))  * Globey    *2 + Globey   ^2  =    -(X^2) + Globex*X*2 - Globex^2

I have no idea what to do next...

Just to clarify the ans. must be:

 q = blabla Globex blabla Globey //without X

or similar

P.S.

I stopped work on my main project nick named “The ultimate F1 First Bot evolver” version of DB for about a month while I tackle smaller projects that should benefit the big one. I hope to resume work soon.
« Last Edit: April 01, 2010, 11:58:53 AM by Botsareus »

Offline abyaly

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Need some professional math help
« Reply #1 on: April 01, 2010, 12:26:54 PM »
[img class=\"tex\" src=\"http://www.forkosh.dreamhost.com/mathtex.cgi?\left( x - G_x \right) ^2 + \left( \dfrac{x^q}{s^{q-1}} - G_y \right) ^2 = 0\" alt=\"LaTeX: \left( x - G_x \right) ^2 + \left( \dfrac{x^q}{s^{q-1}} - G_y \right) ^2 = 0\" /]

Assuming we're in the reals, squaring gives positive numbers. Adding two positive numbers to get 0 means both of them are 0. So..

[img class=\"tex\" src=\"http://www.forkosh.dreamhost.com/mathtex.cgi?\left( x - G_x \right) ^2 = 0 \" alt=\"LaTeX: \left( x - G_x \right) ^2 = 0 \" /]
and
[img class=\"tex\" src=\"http://www.forkosh.dreamhost.com/mathtex.cgi?\left( \dfrac{x^q}{s^{q-1}} - G_y \right) ^2 = 0\" alt=\"LaTeX: \left( \dfrac{x^q}{s^{q-1}} - G_y \right) ^2 = 0\" /]

But the only thing that squares to give 0 is 0. We can quickly get these:

[img class=\"tex\" src=\"http://www.forkosh.dreamhost.com/mathtex.cgi?x = G_x\" alt=\"LaTeX: x = G_x\" /]

[img class=\"tex\" src=\"http://www.forkosh.dreamhost.com/mathtex.cgi?\dfrac{x^q}{s^{q-1}} = G_y\" alt=\"LaTeX: \dfrac{x^q}{s^{q-1}} = G_y\" /]

Substitute it in

[img class=\"tex\" src=\"http://www.forkosh.dreamhost.com/mathtex.cgi?\dfrac{{G_x}^q}{s^{q-1}} = G_y\" alt=\"LaTeX: \dfrac{{G_x}^q}{s^{q-1}} = G_y\" /]

Then take it apart with logs.

[img class=\"tex\" src=\"http://www.forkosh.dreamhost.com/mathtex.cgi? q \ln G_x  - (q-1) \ln s = \ln G_y \" alt=\"LaTeX:  q \ln G_x  - (q-1) \ln s = \ln G_y \" /]

And from here just solve for q in the usual way.

[img class=\"tex\" src=\"http://www.forkosh.dreamhost.com/mathtex.cgi? q \ln G_x  - q \ln s + \ln s = \ln G_y \" alt=\"LaTeX:  q \ln G_x  - q \ln s + \ln s = \ln G_y \" /]

[img class=\"tex\" src=\"http://www.forkosh.dreamhost.com/mathtex.cgi? q \left( \ln G_x  -  \ln s  \right) = \ln G_y - \ln s \" alt=\"LaTeX:  q \left( \ln G_x  -  \ln s  \right) = \ln G_y - \ln s \" /]

[img class=\"tex\" src=\"http://www.forkosh.dreamhost.com/mathtex.cgi? q  = \dfrac {\ln G_y - \ln s} { \ln G_x  -  \ln s } \" alt=\"LaTeX:  q  = \dfrac {\ln G_y - \ln s} { \ln G_x  -  \ln s } \" /]

Which you can then compress into a single log if you want.
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the time and handed on the fight to their descendants.
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Offline Botsareus

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Need some professional math help
« Reply #2 on: April 02, 2010, 10:30:43 AM »
Well Thank You. I will go home and punch it in as soon as I can. I will let you know if it worked.

Offline Botsareus

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« Reply #3 on: April 04, 2010, 07:25:14 PM »
Totally worked. TY.