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The problem is asking for a formula that describes the direct proportionality between the diameter \( d \) and the circumference \( C \) of a circle, using \( k \) as the constant of proportionality.

### Solution:
The formula for the circumference \( C \) of a circle is:

\[
C = \pi d
\]

This means that the circumference is directly proportional to the diameter, with \( \pi \) being the constant of proportionality. However, the problem specifies that \( k \) should represent the constant of proportionality.

Therefore, using \( k \) as the constant, we get:

\[
C = k d
\]

But we know that \( k = \pi \), so:

\[
d = \frac{C}{k}
\]

Thus, the formula for \( d \) in terms of \( C \) and \( k \) is:

\[
d = \frac{C}{k}
\]

Would you like any further clarification on this concept?

### Related Questions:
1. What is the exact value of \( k \) in the context of a circle's circumference?
2. How can we derive the relationship between radius and circumference?
3. What happens to the value of \( d \) if \( k \) is a constant other than \( \pi \)?
4. Can you express the radius \( r \) in terms of the circumference \( C \)?
5. How would the formula change if the circle was an ellipse?

### Tip:
Remember, in the case of circles, the constant \( k \) is always \( \pi \), but for other geometric shapes, the constant may vary.

Write a formula to describe the following: The diameter, d, of a circle is directly proportional to the circumference, C. NOTE: Use k to denote the constant of proportionality.

Learn how to express the diameter, d, of a circle in terms of its circumference, C, using direct proportionality. The constant of proportionality, k, represents a key geometric relationship. Suitable for Grades 6-8.

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