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[nycmath]

Precalculus
Michael Sullivan
Edition 10
Chapter 3, Section 3.4

[Eigenvalue]

Let x be the length of the rectangle
1500=2([tex]\frac{1}{2}[/tex]*2πr)+2x
2x=1500-2πr
x=750-πr

The area of the rectangle can be denoted as A(r)
A(r)=r(750-πr)=-πr²+750π

To find the maximum area of the rectangle, find the values for the vertex:

r=[tex]\frac{-b}{2a}[/tex]=[tex]\frac{-750}{-2π}[/tex]=[tex]\frac{375}{π}[/tex]

A([tex]\frac{375}{π}[/tex])=750-π([tex]\frac{375}{π}[/tex])=750-375=375