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Differentiate
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Homework Statement
A decorative window has the form of a rectangle surmounted by a semicircle whose diameter is equal to the top of the rectangle. If the TOTAL perimeter of the window 16+pi, then what is the maximum area?
A. 25.653
B. 32.148
C. 15.923
D. 38.047
E. 30.018
Correct answer is A: 25.653, but explain step by step please.
2. The attempt at a solution
I completely started off on the wrong foot here.
What I did was made the radius = x/2 where x is the total width/diameter of the rectangle/circle. Then I made the equations:
P=2∏(x/2)+2x+2y=16+pi
A=∏(x/2)^2+xy=z
I seem to not be getting the answer after I plug everything in, so I know I am starting off wrong.
Please explain by a step-step process.
Thanks in advance.
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