Your approach is correct, but there is a slight error in your calculation. Let's go through the process step by step to find the correct function representing the area of the rectangle in terms of x.
We know that the rectangle is inscribed in a circle of radius 2, so the lengths of the rectangle's sides will be the diameter of the circle, which is 4. Let's call the length of one side of the rectangle x, and the length of the other side y.
Using the Pythagorean theorem, we can relate x, y, and the radius of the circle:
(x/2)^2 + (y/2)^2 = 2^2
x^2/4 + y^2/4 = 4
x^2 + y^2 = 16
Now let's solve this equation for y^2:
y^2 = 16 - x^2
Taking the square root of both sides, we get:
y = sqrt(16 - x^2)
The area of the rectangle is given by the formula A = xy. Plugging in the value of y, we have:
A = x * sqrt(16 - x^2)
So the correct function representing the area of the rectangle in terms of x is:
A(x) = x * sqrt(16 - x^2)
Therefore, your final expression for the area of the rectangle should be:
A = 2x * sqrt(4 - x^2)