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4. The area of a semicircle is given by A = 0.5r, where r is the radius in inches. The semicircle, %3D displayed on a computer screen, is increasing in size, and its dimensions are measured over a period of t seconds. a) If the radius is increasing at the rate of 0.25 inch per second, at what rate is the area changing when the area is 67 square inches?

4. The area of a semicircle is given by A = 0.5r, where r is the radius in inches. The semicircle, %3D displayed on a computer screen, is increasing in size, and its dimensions are measured over a period of t seconds. a) If the radius is increasing at the rate of 0.25 inch per second, at what rate is the area changing when the area is 67 square inches?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 74E
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Solve part a, b, and c. 

4. The area of a semicircle is given by A = 0.5ar, where r is the radius in inches. The semicircle, displayed on a computer screen, is increasing in size, and its dimensions are measured over a period of t seconds. a) If the radius is increasing at the rate of 0.25 inch per second, at what rate is the area changing when the area is 67 square inches? b) If the area of the semicircle is increasing at a constant rate of 8 square inches per second, is the radius of the semicircle increasing more rapidly when the radius is 2 inches or when the radius is 3 inches? c) Suppose that the area of the semicircle is increasing at a constant rate. At 5 seconds, the semicircle has an area of 47T square inches. At 7 seconds it has an area of 5 square inches. In terms of r, at what rate is the radius changing?
Transcribed Image Text:4. The area of a semicircle is given by A = 0.5ar, where r is the radius in inches. The semicircle, displayed on a computer screen, is increasing in size, and its dimensions are measured over a period of t seconds. a) If the radius is increasing at the rate of 0.25 inch per second, at what rate is the area changing when the area is 67 square inches? b) If the area of the semicircle is increasing at a constant rate of 8 square inches per second, is the radius of the semicircle increasing more rapidly when the radius is 2 inches or when the radius is 3 inches? c) Suppose that the area of the semicircle is increasing at a constant rate. At 5 seconds, the semicircle has an area of 47T square inches. At 7 seconds it has an area of 5 square inches. In terms of r, at what rate is the radius changing?
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