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
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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F64e22453-08e9-4901-b6d4-29904b54e3b3%2F93d17164-a4ab-491a-bffc-18880e66aa07%2Fxnaft0b_processed.png&w=3840&q=75)
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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