Use the sum of residues to find the unknown residue in the following expansion. Then find the

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Use the sum of residues to find the unknown residue in the following expansion. Then find the inverse transform of the completed expansion. Finally, validate your answer using MATLAB.

\[
F(s)=\frac{5000(s+1000)}{(s+500)(s+5000)}=\frac{\frac{5000}{9}}{s+500}+\frac{k}{s+5000}
\]

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