18) R=sqrt((p_(m)-q)/(q+c m)) make m the subject of the formula.

To make $m$ the subject of the formula $R=\sqrt{\frac{p_{m}-q}{q+c m}}$, we need to isolate $m$ on one side of the equation. Here are the steps:

1. Square both sides of the equation to eliminate the square root:
$$R^2 = \frac{p_m - q}{q + cm}$$

2. Multiply both sides by $q + cm$ to get rid of the denominator on the right side:
$$R^2 (q + cm) = p_m - q$$

3. Distribute $R^2$ on the left side:
$$R^2 q + R^2 cm = p_m - q$$

4. Move $R^2 q$ to the right side to isolate the term with $m$:
$$R^2 cm = p_m - q - R^2 q$$

5. Divide both sides by $R^2$ to isolate $cm$:
$$cm = \frac{p_m - q - R^2 q}{R^2}$$

6. Finally, divide both sides by $c$ to solve for $m$:
$$m = \frac{p_m - q - R^2 q}{R^2 c}$$

So, the formula for $m$ in terms of $p_m$, $q$, $R$, and $c$ is:
$$m = \frac{p_m - q - R^2 q}{R^2 c}$$