You are blowing air into a spherical balloon at a rate of cubic inches per second. (The reason for this strange looking rate is that it will

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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You are blowing air into a spherical balloon at a rate of cubic inches per second. (The reason for this strange looking rate is that it will
Transcribed Image Text:You are blowing air into a spherical balloon at a rate of cubic inches per second. (The reason for this strange looking rate is that it will
simplify your algebra a little.) Assume the radius of your balloon is zero at time zero. Let r(t), A(t), and V(t) denote the radius, the surface area,
and the volume of your balloon at time t, respectively. (Assume the thickness of the skin is zero.) All of your answers below are expressions in t:
r'(t) =
inches per second,
A'(t) =
square inches per second, and
V'(t) =
cubic inches per second.
Hint: The surface area A and the volume V of a sphere of radius r are given by
4tr3
V =
3
A = 4r2
and
Transcribed Image Text:simplify your algebra a little.) Assume the radius of your balloon is zero at time zero. Let r(t), A(t), and V(t) denote the radius, the surface area, and the volume of your balloon at time t, respectively. (Assume the thickness of the skin is zero.) All of your answers below are expressions in t: r'(t) = inches per second, A'(t) = square inches per second, and V'(t) = cubic inches per second. Hint: The surface area A and the volume V of a sphere of radius r are given by 4tr3 V = 3 A = 4r2 and
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