A rectangle is bounded by the x-axis and the semicircle in the positive y-region (see figure). Find the dimensions of the largest rectangle that can be inscribed in a semicircle of radius r. (smaller value) (larger value) (x, y)

A rectangle is bounded by the x-axis and the semicircle in the positive y-region (see figure). Find the dimensions of the largest rectangle that can be inscribed in a semicircle of radius r. (smaller value) (larger value) (x, y)

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter1: Equations, Inequalities, And Mathematical Modeling

Section: Chapter Questions

Problem 110RE

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A rectangle is bounded by the x-axis and the semicircle in the positive y-region (see figure). Find the dimensions of the largest rectangle that can be inscribed in a semicircle of radius r.
(smaller value)
(larger value)
R(x, y)

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A soda can is made from 40 square inches of aluminum. Let x denote the radius of the top of the can, and let h denote the height, both in inches. a. Express the total surface area S of the can, using x and h. Note: The total surface area is the area of the top plus the area of the bottom plus the area of the cylinder. b. Using the fact that the total area is 40 square inches, express h in terms of x. c. Express the volume V of the can in terms of x.

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