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Calculus / Calculus: Early Transcendentals 1 / Chapter 1.1 / Problem 64E

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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Draining a tank (Torricelli’s law) A cylindrical tank with

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QUESTION:

Draining a tank (Torricelli's law) A cylindrical tank with a cross-sectional area of \(100\mathrm{\ cm}^2\) is filled to a depth of 100 cm with water. At t = 0, a drain in the bottom of the tank with an area of \(10\mathrm{\ cm}^2\) is opened allowing water to flow out of the tank. The depth of water in the tank at time \(t \geq 0\) is \(d(t)=(10-2.2 t)^{2}\).

a. Check that d(0) = 100, as specified.

b. What is an appropriate domain for d?

c. At what time is the tank first empty?

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QUESTION:

Draining a tank (Torricelli's law) A cylindrical tank with a cross-sectional area of \(100\mathrm{\ cm}^2\) is filled to a depth of 100 cm with water. At t = 0, a drain in the bottom of the tank with an area of \(10\mathrm{\ cm}^2\) is opened allowing water to flow out of the tank. The depth of water in the tank at time \(t \geq 0\) is \(d(t)=(10-2.2 t)^{2}\).

a. Check that d(0) = 100, as specified.

b. What is an appropriate domain for d?

c. At what time is the tank first empty?

ANSWER:

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