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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.

d varies directly with the square of w and inversely with p. Use k as the constant of proportionality.

Learn how to express a relationship where d varies directly with the square of w and inversely with p, using k as the constant of proportionality. This concept involves direct and inverse variation principles and is suitable for Grades 8-10.

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