A Norman window has the shape of a rectangle surmounted by a semicircle. Suppose the outer perimeter of such a window must be 600 cm. In this problem you will find the base length x which will maximize the area of such a window. The applet above shows a plot of the area function. Use the slider to visualize how the area changes for different values for a, and use the corresponding graph to estimate the optimal radius. Then use calculus to find an exact answer. (Correction: In the figure "r" should be "x"). When the base length is zero, the area of the window will be zero. There is also a limit on how large a can be: when a is large enough, the rectangular portion of the window shrinks down to zero height. What is the exact largest value of a when this occurs? largest r: cm.
A Norman window has the shape of a rectangle surmounted by a semicircle. Suppose the outer perimeter of such a window must be 600 cm. In this problem you will find the base length x which will maximize the area of such a window. The applet above shows a plot of the area function. Use the slider to visualize how the area changes for different values for a, and use the corresponding graph to estimate the optimal radius. Then use calculus to find an exact answer. (Correction: In the figure "r" should be "x"). When the base length is zero, the area of the window will be zero. There is also a limit on how large a can be: when a is large enough, the rectangular portion of the window shrinks down to zero height. What is the exact largest value of a when this occurs? largest r: cm.
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter59: Areas Of Rectangles, Parallelograms, And Trapezoids
Section: Chapter Questions
Problem 79A
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Transcribed Image Text:A Norman window has the shape of a rectangle surmounted by
semicircle. Suppose the outer perimeter of such a window must be
600 cm. In this problem you will find the base length x which will
maximize the area of such a window. The applet above shows a plot
of the area function. Use the slider to visualize how the area changes
for different values for a, and use the corresponding graph to
estimate the optimal radius. Then use calculus to find an exact
answer. (Correction: In the figure "r" should be "x").
When the base length is zero, the area of the window will be zero.
There is also a limit on how large a can be: when z is large enough,
the rectangular portion of the window shrinks down to zero height.
What is the exact largest value of x when this occurs?
largest æ:
cm.
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