Write an equation that expresses the following relationship.
"d" varies jointly with "w" and "p" and inversely with "u"
In your equation, use "k" as the constant of proportionality, do not use multiplication.

The relationship described is that \( d \) varies jointly with \( w \) and \( p \) and inversely with \( u \). 

This means that:

- \( d \) is directly proportional to both \( w \) and \( p \).
- \( d \) is inversely proportional to \( u \).

The equation that expresses this relationship, using \( k \) as the constant of proportionality, is:

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

Would you like more details or have any questions?

### Related Questions:

1. How do you solve for \( k \) in this equation if given specific values for \( d \), \( w \), \( p \), and \( u \)?
2. How does changing \( u \) affect \( d \) when \( w \) and \( p \) are held constant?
3. What does it mean for a variable to vary jointly with others?
4. Can you provide an example problem using this equation with specific values?
5. How does this equation change if \( d \) were only directly proportional to \( w \) and \( p \) without the inverse relationship?

**Tip:** In problems involving proportional relationships, identifying whether the variables are directly or inversely related is key to forming the correct equation.

Understand how to express a relationship where a variable varies jointly with two others and inversely with a third using constants of proportionality. Learn the formula and its application with detailed examples and problem-solving tips. Suitable for Grades 9-12 students and anyone studying proportional relationships in mathematics.

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