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A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle, labeled x.) If the perimeter of the window is 20 feet, find the exact value of x (in ft) so that the greatest possible amount of light is admitted.

A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle, labeled x.) If the perimeter of the window is 20 feet, find the exact value of x (in ft) so that the greatest possible amount of light is admitted.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Tutorial Exercise A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle, labeled x.) If the perimeter of the window is 20 feet, find the exact value of x (in ft) so that the greatest possible amount of light is admitted. Step 1 X Let x be the width (in ft) and y be the height (in ft) of the window. Thus, the semi-circle has radius We must maximize the 2 area of the window, A = xy + - y = Submit - X π 2 플(슬)? 2 2 y TTX . The perimeter of the window is 20 = 2y + x + π T(\-), 2 Skip (you cannot come back) and so
Transcribed Image Text:Tutorial Exercise A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle, labeled x.) If the perimeter of the window is 20 feet, find the exact value of x (in ft) so that the greatest possible amount of light is admitted. Step 1 X Let x be the width (in ft) and y be the height (in ft) of the window. Thus, the semi-circle has radius We must maximize the 2 area of the window, A = xy + - y = Submit - X π 2 플(슬)? 2 2 y TTX . The perimeter of the window is 20 = 2y + x + π T(\-), 2 Skip (you cannot come back) and so
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