X 3.11.19 ft3 How fast is the balloon's radius increasing at the instant the radius is 3 ft? A spherical balloon is inflating with helium at a rate of 72n min Write an equation relating the volume of a sphere, V, and the radius of the sphere, r. 4 V=Tr° (Type an exact answer, using a as needed.) Differentiate both sides of the equation with respect to t. dV dr 4xr2 dt dt (Type an exact answer, using n as needed. Type an expression using r as the variable.) The balloon's radius is increasing at a rate of 2 ft/ min at the instant the radius is 3 ft. (Simplify your answer.)
X 3.11.19 ft3 How fast is the balloon's radius increasing at the instant the radius is 3 ft? A spherical balloon is inflating with helium at a rate of 72n min Write an equation relating the volume of a sphere, V, and the radius of the sphere, r. 4 V=Tr° (Type an exact answer, using a as needed.) Differentiate both sides of the equation with respect to t. dV dr 4xr2 dt dt (Type an exact answer, using n as needed. Type an expression using r as the variable.) The balloon's radius is increasing at a rate of 2 ft/ min at the instant the radius is 3 ft. (Simplify your answer.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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All or majority of the answers are given. Please explain step by step with detail on how the answer came to be. Please do not just list the math steps, explain with words on the steps take or what you did in each step please.
Transcribed Image Text:3.11.19
ft3
How fast is the balloon's radius increasing at the instant the radius is 3 ft?
A spherical balloon is inflating with helium at a rate of 72n
min
Write an equation relating the volume of a sphere, V, and the radius of the sphere,r.
4
V=
=7 (Type an exact answer, using t as needed.)
Differentiate both sides of the equation with respect to t.
dV
dr
4ar
dt
%3D
dt
(Type an exact answer, using n as needed. Type an expression using r as the variable.)
The balloon's radius is increasing at a rate of 2 ft/min at the instant the radius is 3 ft.
(Simplify your answer.)
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