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# Simple Substituting and Rearranging watch

1. Hi there.

In a scientific paper I have the following equation

q=aq^3+b [eq1]

eq1 is approximated with q=a^-0.5 + delta [eq2]

delta=-b/2

Where does this approximation come from and why is delta=-b/2?

Thank you very much.
2. I have updated the first message, since there is some progress.
3. (Original post by Caccioppoli)
I have updated the first message, since there is some progress.
Do you have a link to the paper?
4. I haven't a link for the paper which is
"Application of the Higuchi model for drug release from dispersed
matrices to particles of general shape" by M. Regina Brophy and P.B. Deasy , 1987

I've found the solution !!

we have two equations, basically:

and with a small δ

Writing those two equations in a system, we have that the δ that satisfy both equations is a δ that satisfy this 3rd order equation:

ignoring third order and second order terms in δ we have simply

so the result

5. (Original post by Caccioppoli)
I've found the solution !!
Thanks for posting it.

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Updated: April 23, 2013
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