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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. Use calculus to find an exact answer. When the base length is zero, the area of the window will be zero. There is also a limb on how large x can her when x 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?

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. Use calculus to find an exact answer. When the base length is zero, the area of the window will be zero. There is also a limb on how large x can her when x 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?

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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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. Use calculus to find an exact answer. When the base length is zero, the area of the window will be zero. There is also a limb on how large x can her when x 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? 

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. Use calculus to find an exact answer. When the base length is zero, the area of the window will be zero. There is also a limit on how large x can be: when a is large enough, the rectangular portion of the window shrinks down to zero height. What is the exact largest value ofx when this occurs? largest æ: cm, Determine a function A(x) which gives the area of the window in terms of the parameter a (this is the function plotted above): A(x) = cm?. Now find the exact base length x which maximizes this area: cm.
Transcribed Image Text: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. Use calculus to find an exact answer. When the base length is zero, the area of the window will be zero. There is also a limit on how large x can be: when a is large enough, the rectangular portion of the window shrinks down to zero height. What is the exact largest value ofx when this occurs? largest æ: cm, Determine a function A(x) which gives the area of the window in terms of the parameter a (this is the function plotted above): A(x) = cm?. Now find the exact base length x which maximizes this area: cm.
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