Write an equation that expresses the following relationship, P varies directly with D and inversely with U in your equation use K as a constant of proportionality

To express the relationship where \( P \) varies directly with \( D \) and inversely with \( U \), we use the constant of proportionality \( K \). The equation can be written as:

\[ P = K \frac{D}{U} \]

In this equation:
- \( P \) is directly proportional to \( D \), meaning as \( D \) increases, \( P \) increases.
- \( P \) is inversely proportional to \( U \), meaning as \( U \) increases, \( P \) decreases.
- \( K \) is the constant of proportionality that relates \( P \), \( D \), and \( U \).

Would you like more details or have any questions?

Here are 5 related questions to further explore this topic:
1. How would you solve for \( K \) if \( P \), \( D \), and \( U \) are known?
2. How does the value of \( K \) affect the relationship between \( P \), \( D \), and \( U \)?
3. What happens to \( P \) if both \( D \) and \( U \) are doubled?
4. Can you give a real-life example where this type of relationship might occur?
5. How would you graph the relationship between \( P \) and \( D \) for a fixed value of \( U \)?

**Tip:** When dealing with direct and inverse variations, always keep in mind how changes in one variable affect the others to understand the overall relationship fully.

Explore how to write an equation expressing direct and inverse variation with a constant of proportionality. Learn about the relationship between variables like P, D, and U. Includes practical examples and step-by-step explanations.

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