Answer: A(C) = C^2 / (4π)
Explanation:
The area A of a circle can be written as a function of its circumference C by using the formula for the circumference of a circle and the formula for the area of a circle.
The formula for the circumference of a circle is:
C = 2πr
where r is the radius of the circle, and π is the mathematical constant pi (approximately equal to 3.14159).
Solving the formula for r, we get:
r = C / (2π)
The formula for the area of a circle is:
A = πr^2
Substituting the expression for r from above into the formula for the area, we get:
A = π(C/(2π))^2
Simplifying, we get:
A = C^2 / (4π)
Therefore, the area A of a circle can be written as a function of its circumference C as:
A(C) = C^2 / (4π)