Write an equation that expresses the relationship. Then solve the equation for $\mathrm{f}$.
$b$ varies directly as the cube of $q$ and inversely as $f$.
Answer
Solving the equation for $f$ gives us \(\boxed{f = k \cdot \frac{q^3}{b}}\).
Step 1 ：Write an equation that expresses the relationship. The relationship is described as $b$ varies directly as the cube of $q$ and inversely as $f$. This means that $b$ is proportional to $q^3$ and inversely proportional to $f$. We can express this relationship as an equation of the form \(b = k \cdot \frac{q^3}{f}\), where $k$ is the constant of proportionality.
Step 2 ：Solve this equation for $f$. To do this, we can multiply both sides of the equation by $f$ and then divide both sides by $b$ to isolate $f$.
Step 3 ：Solving the equation for $f$ gives us \(\boxed{f = k \cdot \frac{q^3}{b}}\).
