If A is the area of a circle with radius r and the circle expands as time passes, find dA dt dA dt dr dt in terms of dr dt Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 2 m/s, exactly how fast (in m²/s) is the area of the spill increasing when the radius is 33 m? m²/s

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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Q1. Please answer all the parts to this question

(a) If A is the area of a circle with radius r and the circle expands as time passes, find
dA
dt
dA
dt
=
dr
dt
in terms of
dr
dt
(b) Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 2 m/s, exactly how fast (in m²/s) is the area of the spill increasing when the radius is 33 m?
m²/s
Transcribed Image Text:(a) If A is the area of a circle with radius r and the circle expands as time passes, find dA dt dA dt = dr dt in terms of dr dt (b) Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 2 m/s, exactly how fast (in m²/s) is the area of the spill increasing when the radius is 33 m? m²/s
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