# Write an equation that expresses the following relationship: u varies directly with the cube of p and inversely with d. In your equation, use k as the constant of proportionality.

The proportion helps us to find how one quantity varies with the other.

## Answer: The formula is u = k p^{3} / d, where k is the constant of proportionality.

We will use the definition of direct proportional and indirect proportion to answer this.

**Explanation:**

Here, u varies directly with the cube of p.

So, u = k_{1} p^{3}, where k_{1} is the constant of proportionality.

Now, u varies inversely with d.

So, u = k_{2}/d, where k_{2} is the constant of proportionality.

Now, we can combine the above two formulas as u = k p^{3} / d, where k is the constant of proportionality.