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The problem asks to write an equation where \( w \) varies jointly with the square of \( u \) and the cube of \( d \), with \( k \) as the constant of proportionality.

In this case, "varies jointly" means \( w \) is proportional to the product of the square of \( u \) and the cube of \( d \). The equation can be written as:

\[
w = k \cdot u^2 \cdot d^3
\]

Here, \( k \) is the constant of proportionality, \( u^2 \) represents the square of \( u \), and \( d^3 \) represents the cube of \( d \).

Let me know if you'd like more details or have any questions!

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### Related Questions:
1. What does "joint variation" mean in mathematics?
2. How do you find the constant of proportionality in a joint variation problem?
3. How does this equation change if \( w \) varies inversely with another variable?
4. Can a variable vary jointly and inversely in the same equation? If so, how?
5. What are other real-world applications of joint variation equations?

**Tip:** In joint variation problems, always remember to multiply the terms involving each variable and include the constant of proportionality!

w varies jointly with the square of u and the cube of d. In your equation, use k as the constant of proportionality.

Learn how to express an equation where w varies jointly with the square of u and the cube of d, using k as the constant of proportionality. This problem is suitable for high school students studying algebra and joint variation concepts.

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