 |
|---|
| PAGE: 258 | SET: Exercises | PROBLEM: 32 |
A norman window has the shape of the rectangle surmounted by a semicircle.
Observe the figure.
be the radius of the semicircle.
and 
are the length and width of the rectangle.
Therefore the perimeter of the norman window is 
.
But perimeter of the window is 
ft.
The area of the window is the area of rectangle and area of semicircle.
Therefore the area of the window is 
.
Apply derivative on each side with respect to 
.
The area of the rectangle is maximum when its first derivative becomes zero.
Equate 
to zero.
Therefore the radius of the semicircle is 
.
Substitute 
in 
.
Therefore the length of the rectangle is 
.
Therefore the width of the rectangle is 
.
The radius of the semicircle is .
The length of the rectangle is .
The width of the rectangle is 
.
|
"I want to tell you that our students did well on the math exam and showed a marked improvement that, in my estimation, reflected the professional development the faculty received from you. THANK YOU!!!" June Barnett |
|
"Your site is amazing! It helped me get through Algebra." Charles |
|
"My daughter uses it to supplement her Algebra 1 school work. She finds it very helpful." Dan Pease |
Simply chose a support option
  
|