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To express the relationship where \( p \) varies directly with \( d \) and inversely with \( u \), you can use the following equation:

\[
p = k \frac{d}{u}
\]

Here, \( k \) is the constant of proportionality. This equation means that \( p \) increases as \( d \) increases and decreases as \( u \) increases, with \( k \) scaling the relationship.

If you have further questions or need more details on how this relationship works, feel free to ask!

Here are some related questions you might consider:
1. How would the equation change if \( p \) also varies directly with another variable, say \( v \)?
2. What happens to \( p \) if \( d \) is doubled while \( u \) remains constant?
3. How can you determine the value of \( k \) given specific values for \( p \), \( d \), and \( u \)?
4. Can you provide a real-life scenario where such a relationship might be applicable?
5. What is the graphical representation of this relationship when \( d \) and \( u \) take on various values?

**Tip:** When dealing with direct and inverse variations, remember that the constant of proportionality \( k \) holds the key to how the variables influence each other. Always check units and dimensional consistency in practical applications.

p varies directly with d and inversely with u. Write an equation expressing this relationship. Use k as the constant of proportionality.

Learn how to express the relationship where p varies directly with d and inversely with u using the equation p = k(d/u), with k being the constant of proportionality. This explanation covers key concepts in algebra and variation, suitable for students in Grades 8-10.

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