I need some help with my Calculus Review

A rectangle is inscribed in a circle as shown. The diameter of the circle and the diagonal of the rectangle are both 8 meters.

Express the length of the side y (The long side) of the rectangle as a function of the side labeled x (The short side).

Write an expression to represent the area of the rectangle, A(x).'

Determine the domain of A(x).

In your own words, interpret the meaning of the function graph of A(x).

I'm not lazy, I just need help with this review. I don't understand the steps I have to take. I have tried asking for help with my family, but they don't know. Detailed answers please. I do not earn any grade or points for this.

any angle inscribed in a semi-circle is a right angle

thus, the diameter of the circle / diagonal of the rectangle is also the hypotenuse of a right triangle with legs x and y

using Pythagoras, we know that x^2 + y^2 = 8^2 = 64

or, solving for y:
y = sqrt(64 - x^2)

Area of the rectangle is xy = x(sqrt(64 - x^2)

A(x) = x sqrt(64 - x^2)

the domain of this function is [-8 , 8]
however, as a model for the drawing, the sides can't be negative, so the domain will be (0 , 8), or
0 < x < 8

once you plot this graph, you can interpret it...

(see linked graph: http://www.wolframalpha.com/input/?i=y+%… )

by the pythagorean theorem,
x² + y² = 8²

y² = 64 - x²
y = √(64 - x²)

A(x) = xy
= x√(64 - x²)
domain 0
-

.