The given problem states:

• $d$ varies directly with the square of $w$
• $d$ varies inversely with $p$
• $k$ is the constant of proportionality

Using these conditions, the mathematical expression can be written as:

$d = k \cdot \frac{w^2}{p}$

This equation reflects the direct relationship of $d$ with $w^2$ and the inverse relationship with $p$, with $k$ as the constant of proportionality.

Do you want more details or have any questions?

Here are 5 related questions:

1. What happens to $d$ when $w$ is doubled, keeping $p$ constant?
2. How does $d$ change if $p$ is halved, but $w$ remains the same?
3. Can you derive the constant $k$ if values for $d$, $w$, and $p$ are provided?
4. What are examples of real-life scenarios where direct and inverse variation occur together?
5. How would the equation change if $d$ varied directly with $w$ (not $w^2$)?

Tip: Direct variation means multiplying the independent variable, while inverse variation means dividing by the independent variable.