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The given problem asks to write an equation that expresses the relationship:

"**w varies directly with the square of u**" and using **k** as the constant of proportionality.

### Direct Variation
In a direct variation, one quantity is directly proportional to another. If we say that \( w \) varies directly with the square of \( u \), this means:

\[
w = k u^2
\]

where:
- \( w \) is the variable that depends on \( u \),
- \( u^2 \) is the square of \( u \),
- \( k \) is the constant of proportionality.

Thus, the equation expressing the relationship is:

\[
w = k u^2
\]

Would you like further details or clarifications?

### Here are 5 related questions to explore further:
1. How does changing the value of \( k \) affect the relationship between \( w \) and \( u \)?
2. If \( u = 3 \) and \( k = 2 \), what is the value of \( w \)?
3. What would happen if \( w \) varied inversely with the square of \( u \)?
4. Can you find the value of \( k \) if \( w = 36 \) and \( u = 4 \)?
5. What would the equation look like if \( w \) varied directly with the cube of \( u \)?

### Tip:
Remember, in any direct variation problem, the constant \( k \) can be found by dividing the dependent variable by the square (or cube, etc.) of the independent variable, once a specific point is known.

Write an equation that expresses the following relationship: w varies directly with the square of u. In your equation, use k as the constant of proportionality.

Learn how to write an equation where w varies directly with the square of u using k as the constant of proportionality. This problem explores direct variation and proportional relationships, suitable for students in Grades 8-10.

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