A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. Find the area of the largest possible Norman window with a perimeter of 44 feet. Round your answer to one place after the decimal.

A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. Find the area of the largest possible Norman window with a perimeter of 44 feet. Round your answer to one place after the decimal.

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter61: Areas Of Circles, Sectors, And Segments

Section: Chapter Questions

Problem 38A: Three pieces, each in the shape of a sector, are cut from the rectangular sheet of steel shown. How...

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Question

A Norman window has the shape of a semicircle atop a
rectangle so that the diameter of the semicircle is equal to
the width of the rectangle.
Find the area of the largest possible Norman window with a
perimeter of 44 feet. Round your answer to one place after
the decimal.
square feet

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Step 1: Define the problem

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Step 2: Calculate the perimeter of window and area of window

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Step 3: Calculate the derivative of fA(x)

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Step 4: Calculate the critical values

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Step 5: Calculate the second derivative of A(x)

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Step 6: Calculate the maximum area

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