(a) If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in terms of dr/dt. dA dr dt 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 1 m/s, how is the area of the spill increasing when the radius is 20 m? m²/s

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 18EQ
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(a) If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in terms of dr/dt.
dA
dr
dt
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 1 m/s, how fast
is the area of the spill increasing when the radius is 20 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 in terms of dr/dt. dA dr dt 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 1 m/s, how fast is the area of the spill increasing when the radius is 20 m? m²/s
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