The image you uploaded contains the following mathematical problem:

4. Express the length of the radius of a circle as a function of the circumference.

To solve this, let's break it down:

Step 1: Recall the formula for the circumference of a circle.

The circumference $C$ of a circle is related to its radius $r$ by the formula: $C = 2\pi r$

Step 2: Express the radius as a function of the circumference.

We want to express $r$ as a function of $C$. Rearranging the formula above to solve for $r$: $r = \frac{C}{2\pi}$

So, the radius $r$ of a circle can be expressed as a function of the circumference $C$ by: $r(C) = \frac{C}{2\pi}$

Would you like more details or have any questions about this solution?

Here are five questions that expand on this concept:

1. What is the relationship between the area of a circle and its radius?
2. How would you express the diameter of a circle as a function of its radius?
3. How does the circumference of a circle change if the radius is doubled?
4. Can you derive the area of a circle using the relationship between circumference and radius?
5. How would you calculate the circumference if you are only given the area of the circle?

Tip: When working with circle-related problems, always remember the basic formulas for circumference and area, as they form the foundation for solving various geometric questions.