If a=c(1-s2) how do you express S in terms of A and C

Question

asked Dec 10, 2023 126k views

1 Answer

Mosheb · Answer 1 · 2023-12-13T15:26:24+0000

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

$\begin{gathered} (A)/(C)=(C(1-S^2))/(C) \\ \\ (A)/(C)=1-S^2 \\ \\ \end{gathered}$

- Substract 1 in both sides of the equation:

$\begin{gathered} (A)/(C)-1=1-1-S^2 \\ \\ (A)/(C)-1=-S^2 \end{gathered}$

-Multiply both sides of the equation by -1:

$\begin{gathered} (-1)((A)/(C)-1)=(-1)(-S^2) \\ -(A)/(C)+1=S^2 \end{gathered}$

-Take square root of both sides of the equation:

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

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

$S=\sqrt[]{-(A)/(C)+1}$