Question

A window has the shape of a semi-circle placed on top of a rectangle, as shown. a. Express the area ( A ) of the window in terms of the width ( w ) and height ( h ) of the rectangle. [ A(h, w)= ] b. If the area is 7 , express the height in terms of the width. [ h(w)= ]

          A window has the shape of a semi-circle placed on top of a rectangle, as shown.
a. Express the area ( A ) of the window in terms of the width ( w ) and height ( h ) of the rectangle.
[
A(h, w)=
]
b. If the area is 7 , express the height in terms of the width.
[
h(w)=
]

A window has the shape of a semi-circle placed on top of a rectangle, as shown.
a. Express the area ( A ) of the window in terms of the width ( w ) and height ( h ) of the rectangle.
[
A(h, w)=
]
b. If the area is 7 , express the height in terms of the width.
[
h(w)=
]

Added by Zoey O.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Oswaldo Jiménez

10/20/2023

Step 1

The area of the rectangle is \(wh\). The area of the semi-circle is \(\frac{1}{2} \pi r^2\), where \(r\) is the radius of the semi-circle. Since the width of the rectangle is the same as the diameter of the semi-circle, we have \(r = \frac{w}{2}\). So, the area of Show more…

Show all steps