(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant 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 dont know and I cannot use derivatives or calculus, which is why im having

trouble here.

3. 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]x^{2}

hence A= 15x - 1/2x^{2}- 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 isnt looking right.

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# Homework Help: Norman Window - maximum light

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