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
Related questions
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 18 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage