- #1
nikita33
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Homework Statement
a norman window has the shape of a rectangle surmounted by a semicircle. A norman window with the perimeter 30 ft. is to be constructed.
a.) find a function that models the area of the window.
b.) find the dimensions of the window that admit the greatest amount of light
Homework Equations
part a.) area= LW (this problem, it will be xy, with x as the width)
semicircle circumference= 1/2[tex]\Pi[/tex]x s
part b.) i don't know and I cannot use derivatives or calculus, which is why I am having
trouble here.
The Attempt at a Solution
a.)
P= x + 2y + 1/2[tex]\Pi[/tex]x = 30
2y = 30 - 1/2[tex]\Pi[/tex]x - x
y = 15 - 1/2x - 1/4[tex]\Pi[/tex]x
A= (x)(15 - 1/2x - 1/4[tex]\Pi[/tex]x) + 1/2[tex]\Pi[/tex](1/2x)2
(x)(15 - 1/2x - 1/4[tex]\Pi[/tex]x) + 1/8[tex]\Pi[/tex]x2
hence A= 15x - 1/2x2 - 1/8[tex]\Pi[/tex]2
b.)
i know the area equation is correct. I have no idea as to how to begin to figure out the max dimensions for the light. i would appreciate any clues. and sorry if the pi isn't looking right.