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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: π === (a) (b) r(t) = 5t²+2, 0(t) = t 6 4 Recall that the area of a sector in a circle is given by the formula 3²0 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?

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: π === (a) (b) r(t) = 5t²+2, 0(t) = t 6 4 Recall that the area of a sector in a circle is given by the formula 3²0 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?

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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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) = (a) (b) π 7 ==- 6 4 Recall that the area of a sector in a circle is given by the formular²0 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) = (a) (b) π 7 ==- 6 4 Recall that the area of a sector in a circle is given by the formular²0 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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