- #1

slayer16

- 10

- 0

## Homework Statement

A rectangle is bounded by the x-axis and the semicircle y=√(36-x^2) (see figure). Write the area A of the rectangle as a function of x.

I will try to explain the figure as best as possible. The figure is basically a semicircle on the Cartesian plane with a domain of [-6,6]. There is a point on the semicircle of (X,Y) where y is the height of the rectangle and x is the maximum width of the rectangle. The value of x is around five on the graph, while the value for y is around 3.5 on the graph (note: they are just estimates to help visualize the figure better).

## Homework Equations

A=(w)(h)

## The Attempt at a Solution

I substitute the (x,y) for (w,h). I then realized that the height stays constant, therefore I can write the height as √(36-w^2), where w is a constant. Now, I do not know how to write the width because the x has a limited domain.