A circle has an initial radius of 50 ft when the radius begins decreasing at the rate of 4 ft/min. What is the rate in the change of area at the instant that the radius is 10 ft? Write an equation relating the area of a circle, A, and the radius of the circle, r. (Type an exact answer, usingz as needed.) Differentiate both sides of the equation with respect to t. dA dr dt dt (Type an exact answer, using x as needed. Type an expression using r as the variable.) The rate of change of the area is (Type an exact answer in terms of x.) f / min. f / min. ft/min. ft.
A circle has an initial radius of 50 ft when the radius begins decreasing at the rate of 4 ft/min. What is the rate in the change of area at the instant that the radius is 10 ft? Write an equation relating the area of a circle, A, and the radius of the circle, r. (Type an exact answer, usingz as needed.) Differentiate both sides of the equation with respect to t. dA dr dt dt (Type an exact answer, using x as needed. Type an expression using r as the variable.) The rate of change of the area is (Type an exact answer in terms of x.) f / min. f / min. ft/min. ft.
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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Transcribed Image Text:A circle has an initial radius of 50 ft when the radius begins decreasing at the rate of 4 ft/min. What is the rate in the change of area at the instant that the radius is 10 ft?
Write an equation relating the area of a circle, A, and the radius of the circle, r.
|(Type an exact answer, using a as needed.)
Differentiate both sides of the equation with respect to t.
dA
dr
dt
dt
(Type an exact answer, using a as needed. Type an expression using r as the variable.)
The rate of change of the area is
(Type an exact answer in terms of r.)
ft / min.
/min.
ft/min.
fi?.
ft3.
ft.
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