A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window (see figure). Consider the following Norman window.A window is constructed from a semicircle fit above a rectangle.The horizontal width of the rectangle is labeled x.The height of the rectangle is labeled y.The flat edge of the semicircle fits perfectly along the upper horizontal edge of the rectangle.A horizontal line labeled x⁄2 is drawn from the middle of the rectangle to the edge.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 14 feet. Use this information to write an equation for A in terms of x.A(x) = FindA'(x)andA''(x). Find the dimensions of a Norman window of maximum area if the total perimeter is 14 feet.x= y=

Width of the Norman window is x feet Height of the window is y feet Since the semi-circle of the…

Answered: A Norman window is constructed by…

Elementary Geometry for College Students

6th Edition

ISBN:9781285195698

Author:Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:Daniel C. Alexander, Geralyn M. Koeberlein

Chapter6: Circles

Section6.3: Line And Segment Relationships In The Circle

Problem 39E: The center of a circle of radius 2 inches is at a distance of 10 inches from the center of a circle...

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A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window (see figure). Consider the following Norman window.

A window is constructed from a semicircle fit above a rectangle.

The horizontal width of the rectangle is labeled x.
The height of the rectangle is labeled y.
The flat edge of the semicircle fits perfectly along the upper horizontal edge of the rectangle.
A horizontal line labeled x⁄2 is drawn from the middle of the rectangle to the edge.

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 14 feet. Use this information to write an equation for A in terms of x.

A(x) =

Find

A'(x)

and

A''(x).

Find the dimensions of a Norman window of maximum area if the total perimeter is 14 feet.

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