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A woman at a point A on the shore of a circular lake with radius R kilometer wants to arrive at the point B diametrically opposite on the other side of the lake in the shortest possible time (see the figure). She can walk at the rate of 5 kilometer per hour and row a boat at 3 kilometer per hour. 1- Find the total distance she must travel if she rows from A to C and walks from C to B. 2- How should she proceed to arrive at B in the shortest possible time? 3- In a half page explain why this is an Extreme Value Theorem problem. Explain also, why the answer cannot happen at a critical point. C B A

A woman at a point A on the shore of a circular lake with radius R kilometer wants to arrive at the point B diametrically opposite on the other side of the lake in the shortest possible time (see the figure). She can walk at the rate of 5 kilometer per hour and row a boat at 3 kilometer per hour. 1- Find the total distance she must travel if she rows from A to C and walks from C to B. 2- How should she proceed to arrive at B in the shortest possible time? 3- In a half page explain why this is an Extreme Value Theorem problem. Explain also, why the answer cannot happen at a critical point. C B A

Mathematics For Machine Technology
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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A woman at a point A on the shore of a circular lake with radius R kilometer wants to arrive at the point B diametrically opposite on the other side of the lake in the shortest possible time (see the figure). She can walk at the rate of 5 kilometer per hour and row a boat at 3 kilometer per hour. 1- Find the total distance she must travel if she rows from A to C and walks from C to B. 2- How should she proceed to arrive at B in the shortest possible time? 3- In a half page explain why this is an Extreme Value Theorem problem. Explain also, why the answer cannot happen at a critical point. C. B A.
Transcribed Image Text:A woman at a point A on the shore of a circular lake with radius R kilometer wants to arrive at the point B diametrically opposite on the other side of the lake in the shortest possible time (see the figure). She can walk at the rate of 5 kilometer per hour and row a boat at 3 kilometer per hour. 1- Find the total distance she must travel if she rows from A to C and walks from C to B. 2- How should she proceed to arrive at B in the shortest possible time? 3- In a half page explain why this is an Extreme Value Theorem problem. Explain also, why the answer cannot happen at a critical point. C. B A.
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