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Answer :

[tex]A=C(1-S^2)[/tex]

The given equation express A in function of C and S. To express the equation as S in terms of A and C​ you need to solve the variable S:

-Divide both sides of the equation into C

[tex]\begin{gathered} \frac{A}{C}=\frac{C(1-S^2)}{C} \\ \\ \frac{A}{C}=1-S^2 \\ \\ \end{gathered}[/tex]

- Substract 1 in both sides of the equation:

[tex]\begin{gathered} \frac{A}{C}-1=1-1-S^2 \\ \\ \frac{A}{C}-1=-S^2 \end{gathered}[/tex]

-Multiply both sides of the equation by -1:

[tex]\begin{gathered} (-1)(\frac{A}{C}-1)=(-1)(-S^2) \\ -\frac{A}{C}+1=S^2 \end{gathered}[/tex]

-Take square root of both sides of the equation:

[tex]\begin{gathered} \sqrt[]{(-\frac{A}{C}+1)}=\sqrt[]{S^2} \\ \\ \sqrt[]{-\frac{A}{C}+1}=S \end{gathered}[/tex]

Then, the equation that express S in terms of A and C​ is:

[tex]S=\sqrt[]{-\frac{A}{C}+1}[/tex]