Question

The radius r of a circle can be written as a function of the area A with the following equation: r=square root A over pie What is the domain of this function? Explain why it makes sense in this context.

Answer 1

The domain of the function relating the radius of a circle to its area is all non-negative real numbers.

Step-by-step explanation:

The domain of the function, which relates the radius r of a circle to its area A using the equation r = sqrt(A/π), is all non-negative real numbers. In other words, any non-negative real number can be a valid input for the area of the circle. This makes sense in the context of the problem because the area of a circle can never be negative, and any value greater than or equal to zero is valid.

Answer 2

The formula of the radius is

`r= \sqrt{ (A)/( \pi )`

In this context, it makes sense as the radius cannot have a negative value.
Thus, the domain of the function is [0,∞)
This means that the Area can have any positive value starting from zero.