A rain gutter is formed by bending up the sides of a 52-in.-wide rectangular metal sheet as shown in the figure. width (a) Find a function that models the cross-sectional area of the gutter in terms of x. A(x) = %3D (b) Find the value of x that maximizes the cross-sectional area of the gutter. X = in (c) What is the maximum cross-sectional area for the gutter? in?

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter3: Polynomial And Rational Functions
Section3.1: Quadratic Functions And Models
Problem 64E
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A rain gutter is formed by bending up the sides of a 52-in.-wide rectangular metal sheet as shown in the figure.
width
(a) Find a function that models the cross-sectional area of the gutter in terms of x.
A(x) =
%3D
(b) Find the value of x that maximizes the cross-sectional area of the gutter.
X =
in
(c) What is the maximum cross-sectional area for the gutter?
in?
Transcribed Image Text:A rain gutter is formed by bending up the sides of a 52-in.-wide rectangular metal sheet as shown in the figure. width (a) Find a function that models the cross-sectional area of the gutter in terms of x. A(x) = %3D (b) Find the value of x that maximizes the cross-sectional area of the gutter. X = in (c) What is the maximum cross-sectional area for the gutter? in?
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