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3. Show that the area of the optimal rectangle inscribed inside a semi- circle of radius 2 (found in the video "Optimization Examples") is indeed a maximum, using either the first or second derivative rule. 4. You have 20 ft of wire that you want to cut and fold into two different shapes, a circle and a square. You must use all of the wire in your construction. Consider the following scenarios:

3. Show that the area of the optimal rectangle inscribed inside a semi- circle of radius 2 (found in the video "Optimization Examples") is indeed a maximum, using either the first or second derivative rule. 4. You have 20 ft of wire that you want to cut and fold into two different shapes, a circle and a square. You must use all of the wire in your construction. Consider the following scenarios:

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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3. Show that the area of the optimal rectangle inscribed inside a semi- circle of radius 2 (found in the video "Optimization Examples") is indeed a maximum, using either the first or second derivative rule. 4. You have 20 ft of wire that you want to cut and fold into two different shapes, a circle and a square. You must use all of the wire in your construction. Consider the following scenarios: (a) How would you cut the wire if you want to have the minimal area possible enclosed by your two shapes? How much of the wire would be used for the circle/square? (b) How would you cut the wire if you want to have the maximal area possible enclosed by your two shapes? How much of the wire would be used for the circle/square?
Transcribed Image Text:3. Show that the area of the optimal rectangle inscribed inside a semi- circle of radius 2 (found in the video "Optimization Examples") is indeed a maximum, using either the first or second derivative rule. 4. You have 20 ft of wire that you want to cut and fold into two different shapes, a circle and a square. You must use all of the wire in your construction. Consider the following scenarios: (a) How would you cut the wire if you want to have the minimal area possible enclosed by your two shapes? How much of the wire would be used for the circle/square? (b) How would you cut the wire if you want to have the maximal area possible enclosed by your two shapes? How much of the wire would be used for the circle/square?
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