To solve the given formula [tex]\( v^2 = \frac{3P}{mn} \)[/tex] for [tex]\( m \)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[
v^2 = \frac{3P}{mn}
\][/tex]
2. To isolate [tex]\( m \)[/tex], first get rid of the fraction by multiplying both sides of the equation by [tex]\( mn \)[/tex]:
[tex]\[
v^2 \cdot mn = 3P
\][/tex]
3. Next, to solve for [tex]\( m \)[/tex], divide both sides of the equation by [tex]\( v^2 n \)[/tex]:
[tex]\[
m = \frac{3P}{v^2 n}
\][/tex]
Thus, the correct solution is:
[tex]\[
m = \frac{3P}{v^2 n}
\][/tex]
Therefore, the correct option is:
C. [tex]\( m = \frac{3 P}{v^2 n} \)[/tex]
