Explanation
We must solve for n the following equation:
[tex]E=Z_c*\frac{\sigma}{\sqrt{n}}.[/tex]
1) First, we assume n ≠ 0 and multiply both sides by √n, we get:
[tex]\begin{gathered} E*\sqrt{n}=Z_c*\frac{\sigma}{\sqrt{n}}*\sqrt{n}, \\ E*\sqrt{n}=Z_c*\sigma. \end{gathered}[/tex]
2) Now, we divide both sides by E:
[tex]\begin{gathered} \frac{E*\sqrt{n}}{E}=\frac{Z_c*\sigma}{E}, \\ \sqrt{n}=\frac{Z_c*\sigma}{E}. \end{gathered}[/tex]
3) Finally, taking the square on both sides, we get:
[tex]\begin{gathered} (\sqrt{n})^2=(\frac{Z_c*\sigma}{E})^2, \\ n=(\frac{Z_c\cdot\sigma}{E})^2. \end{gathered}[/tex]Answer[tex]n=(\frac{Z_{c}\sigma}{E})^{2}[/tex]
