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 p³ / 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 = k₁ p³, where k₁ is the constant of proportionality.

Now, u varies inversely with d.

So, u = k₂/d, where k₂ is the constant of proportionality.

Now, we can combine the above two formulas as u = k p³ / d, where k is the constant of proportionality.

Thus, the formula is u = k p³ / d, where k is the constant of proportionality.