SOLUTION: A Norman window is constructed by adjoining a semicircle to the top of ab ordinary rectangular window. The perimeter of the window is 12 feet. The diameter of a circle and the leng
Algebra.Com
Question 1134762: A Norman window is constructed by adjoining a semicircle to the top of ab ordinary rectangular window. The perimeter of the window is 12 feet. The diameter of a circle and the length of a rectangle are x， the width is y.
1) Write the area A of the window as a function of x.
2) What dimensions will produce a window of maximum area?
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
given:
The perimeter of the window is feet. The diameter of a circle and the length of a rectangle are the width is .
1) Write the area of the window as a function of .
The perimeter is ft.
.......given .
.....solve for
We find an equation for maximum area.
......
Substitute in for . Now
->the area of the window as a function of
2) What dimensions will produce a window of maximum area?
Next compute . Set it equal to zero and solve for .
set =.
≈
then
Next find .
≈
dimensions that will produce a window of maximum area are:
≈
≈
≈
check the perimeter first then see what would be maximum area
-> true
now find maximum area
≈
RELATED QUESTIONS
A Norman window is constructed by adjoining a semicircle to the top of an ordinary... (answered by ikleyn)
A Norman window has the shape of a rectangle surmounted by a semicircle, as shown in the... (answered by josgarithmetic,ikleyn)
A norman window is one that consists of a rectangle with a curved top to it. the curved... (answered by ankor@dixie-net.com)
A norman window consist of a rectangle surmounted by a semicircle. For the window shown... (answered by josgarithmetic)
A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter (answered by Theo)
A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter (answered by ankor@dixie-net.com)
A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter (answered by greenestamps)
A Norman window has the shape of a rectangle surmounted by a semicircle, as shown in the... (answered by math_tutor2020,josgarithmetic,ikleyn)
A Norman window consists of a rectangular shape surmounted by a semicircle. The length of (answered by timofer)