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Find the dimensions of the rectangle of maximum area that can be drawn within a semicircle of radius 3, if one side of the rectangle lies along the diameter of the semicircle. (Suggestion: draw your semicircle on the ry-plane as the top half of the circle 22 +y? = 9.) Solution

Find the dimensions of the rectangle of maximum area that can be drawn within a semicircle of radius 3, if one side of the rectangle lies along the diameter of the semicircle. (Suggestion: draw your semicircle on the ry-plane as the top half of the circle 22 +y? = 9.) Solution

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Yet another (fictional) student submitted the following solution to an optimization problem. This time the solution is technically correct, but it is still insufficient there isn't nearly enough detail/explanation to receive full credit. Rewrite the solution below, adding all details (including a diagram) that are necessary to produce a complete solution worthy of full marks. (To be clear: the final answer is correct. What we want to see are the necessary explanations to make it clear where each step is coming from.) Problem: Find the dimensions of the rectangle of maximum area that can be drawn within a semicircle of radius 3, if one side of the rectangle lies along the diameter of the semicircle. (Suggestion: draw your semicircle on the ry-plane as the top half of the circle ? + y? = 9.) Solution: A = 2ry = 2r9-a A' = 2/9-2 272 2(9 - 22?) V9-2 2x = 9 so r Dimensions: 2x = 3/2 and y =
Transcribed Image Text:Yet another (fictional) student submitted the following solution to an optimization problem. This time the solution is technically correct, but it is still insufficient there isn't nearly enough detail/explanation to receive full credit. Rewrite the solution below, adding all details (including a diagram) that are necessary to produce a complete solution worthy of full marks. (To be clear: the final answer is correct. What we want to see are the necessary explanations to make it clear where each step is coming from.) Problem: Find the dimensions of the rectangle of maximum area that can be drawn within a semicircle of radius 3, if one side of the rectangle lies along the diameter of the semicircle. (Suggestion: draw your semicircle on the ry-plane as the top half of the circle ? + y? = 9.) Solution: A = 2ry = 2r9-a A' = 2/9-2 272 2(9 - 22?) V9-2 2x = 9 so r Dimensions: 2x = 3/2 and y =
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