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Use optimization techniques to answer the questions in Exercises 25-30. 25. Find two real numbers x and y whose sum is 36 and whose product is as large as possible. 26. Find two real numbers x and y whose sum is 36 and whose product is as small as possible. 27. Find real numbers a and b whose sum is 100 and for which the sum of the squares of a and b is as small as possible. 28. Find the area of the largest rectangle that fits inside a circle of radius 4. 29. Find the area of the largest rectangle that fits inside a circle of radius 10. 30. Find the volume of the largest cylinder that fits inside a sphere of radius 10.

Use optimization techniques to answer the questions in Exercises 25-30. 25. Find two real numbers x and y whose sum is 36 and whose product is as large as possible. 26. Find two real numbers x and y whose sum is 36 and whose product is as small as possible. 27. Find real numbers a and b whose sum is 100 and for which the sum of the squares of a and b is as small as possible. 28. Find the area of the largest rectangle that fits inside a circle of radius 4. 29. Find the area of the largest rectangle that fits inside a circle of radius 10. 30. Find the volume of the largest cylinder that fits inside a sphere of radius 10.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.6: Inequalities
Problem 77E
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Use optimization techniques to answer the questions in Exercises 25-30. 25. Find two real numbers x and y whose sum is 36 and whose product is as large as possible. 26. Find two real numbers x and y whose sum is 36 and whose product is as small as possible. 27. Find real numbers a and b whose sum is 100 and for which the sum of the squares of a and b is as small as possible. 28. Find the area of the largest rectangle that fits inside a circle of radius 4. 29. Find the area of the largest rectangle that fits inside a circle of radius 10. 30. Find the volume of the largest cylinder that fits inside a sphere of radius 10.
Transcribed Image Text:Use optimization techniques to answer the questions in Exercises 25-30. 25. Find two real numbers x and y whose sum is 36 and whose product is as large as possible. 26. Find two real numbers x and y whose sum is 36 and whose product is as small as possible. 27. Find real numbers a and b whose sum is 100 and for which the sum of the squares of a and b is as small as possible. 28. Find the area of the largest rectangle that fits inside a circle of radius 4. 29. Find the area of the largest rectangle that fits inside a circle of radius 10. 30. Find the volume of the largest cylinder that fits inside a sphere of radius 10.
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