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There is a circle whose radius r is changing with time t. We are interested in the area A of a sector of this circle whose central angle ◊ is also changing with time t. Here are the formulae by which r and are changing: r(t) = 5t² + 2, 0(t) (a) (b) = π 6 4 π t Recall that the area of a sector in a circle is given by the formula 1r²0 where the central angle is measured in radians. What is the initial area of this sector? That is, what is A when t = 0? How fast is the area A changing at t = 1?

There is a circle whose radius r is changing with time t. We are interested in the area A of a sector of this circle whose central angle ◊ is also changing with time t. Here are the formulae by which r and are changing: r(t) = 5t² + 2, 0(t) (a) (b) = π 6 4 π t Recall that the area of a sector in a circle is given by the formula 1r²0 where the central angle is measured in radians. What is the initial area of this sector? That is, what is A when t = 0? How fast is the area A changing at t = 1?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.1: Angles
Problem 38E
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2. There is a circle whose radius r is changing with time t. We are interested in the area A of a sector of this circle whose central angle is also changing with time t. Here are the formulae by which r and are changing: r(t) = 5t² + 2, 0(t) ㅠ π (a) (b) -t 6 4 Recall that the area of a sector in a circle is given by the formula r²0 where the central angle is measured in radians. What is the initial area of this sector? That is, what is A when t = 0? How fast is the area A changing at t = 1?
Transcribed Image Text:2. There is a circle whose radius r is changing with time t. We are interested in the area A of a sector of this circle whose central angle is also changing with time t. Here are the formulae by which r and are changing: r(t) = 5t² + 2, 0(t) ㅠ π (a) (b) -t 6 4 Recall that the area of a sector in a circle is given by the formula r²0 where the central angle is measured in radians. What is the initial area of this sector? That is, what is A when t = 0? How fast is the area A changing at t = 1?
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