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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

If a tank holds 5000 gallons of water, which drains from the bottom of the tank in 40 minutes, then Torricelli’s Law gives the volume V of water remaining in the tank after t minutes as

V = 5000 ( 1 + 1 40 t ) 2      0 t 40

Find the rate at which water is draining from the tank after (a) 5 min, (b) 10 min, (c) 20 min, and (d) 40 min. At what time is the water flowing out the fastest? The slowest? Summarize your findings.

To determine

To find: the rate at which water is draining from the tank after

(a) 5 min

(b) 10 min

(c) 20 min

(d) 40 min

Explanation

1) Formula:

Chain rule ddxfgx= f'gx* g'x

2) Given:

Volume of water remaining V=50001-140t2

3) Calculation:

Volume of water remaining is V=50001-140t2

Therefore volume of water drained is v=5000-50001-140t2

Take derivative with respect to time t.

dvdt=ddt5000-50001-140t2

Using difference formula

dvdt=ddt(5000)-ddt50001-140t2

Using chain rule

dvdt=-100001-140t-140

dvdt=250(1-140t)

(a) Now substitute t=5,

dvd</

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