A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window (see figure). Consider the following Norman windo Let P represent the total perimeter of the window, measured in feet. Write an equation for P in terms of x and y, each measured in feet. P = Let A represent the area of the window, measured in square feet. The total perimeter of the given Norman window is known to be 20 feet. Use this inform A(x) = Find A'(x) and A"(x). A'(x) A"(x) Find the dimensions of a Norman window of maximum area if the total perimeter is 20 feet. X = y =

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter11: Rational And Irrational Numbers
Section11.6: The Pythagorean Theorem
Problem 11P
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A Norman window is constructed by adjoining a semicircle to the top of
ordinary rectangular window (see figure). Consider the following Norman window.
Let P represent the total perimeter of the window, measured in feet. Write an equation for P in terms of x and y, each measured in feet.
P =
Let A represent the area of the window, measured in square feet. The total perimeter of the given Norman window is known to be 20 feet. Use this information to write an equation for A in terms of x.
A(x) =
Find A'(x) and A"(x).
A'(x) =
A"(x) =
Find the dimensions of a Norman window of maximum area if the total perimeter is 20 feet.
Transcribed Image Text:A Norman window is constructed by adjoining a semicircle to the top of ordinary rectangular window (see figure). Consider the following Norman window. Let P represent the total perimeter of the window, measured in feet. Write an equation for P in terms of x and y, each measured in feet. P = Let A represent the area of the window, measured in square feet. The total perimeter of the given Norman window is known to be 20 feet. Use this information to write an equation for A in terms of x. A(x) = Find A'(x) and A"(x). A'(x) = A"(x) = Find the dimensions of a Norman window of maximum area if the total perimeter is 20 feet.
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