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.

The equation that expresses the relationship "d varies jointly with w and p and inversely with u" is:

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

Here:
- \( k \) is the constant of proportionality,
- \( d \) varies directly with \( w \) and \( p \),
- \( d \) varies inversely with \( u \).

Would you like more details or have any questions?

Here are some related questions:

1. How does the value of \( d \) change if \( u \) is doubled?
2. What happens to \( d \) if both \( w \) and \( p \) are halved?
3. How can you solve for \( k \) if \( d \), \( w \), \( p \), and \( u \) are known?
4. What is the effect on \( d \) if only \( w \) increases while \( p \) and \( u \) remain constant?
5. How would the equation change if \( d \) varied directly with the square of \( w \) instead?

**Tip:** Remember, when dealing with joint variation, multiple factors directly influence the dependent variable, while inverse variation reduces the influence of other factors.

Explore the concept of joint and inverse variation in mathematics with an equation example. Learn how variables 'd', 'w', 'p', and 'u' interact using the constant of proportionality 'k'. Suitable for Grades 10-12 students.

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