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If a tank holds 4500 gallons of water, which drains from the bottom of the tank in 50 minutes, then Toricelli's Law gives the volume V of water remaining in the tank after t minutes as
V = 4500(1 - 1/50t)2 0 < or = t < or = 50
1) Find the rate at which water is draining from the tank after the following amounts of time.
(a) 5 min gal/min
(b) 10 min gal/min
(c) 20 min gal/min
(d) 50 min gal/min
2) At what time is the water flowing out the fastest?
3) At what time is the water flowing out the slowest?

Respuesta :

Answer:

The response to this question can be defined as follows:

Step-by-step explanation:

[tex]v =4500 (1-\frac{t}{50})^2\\\\\to \frac{dV}{dt}= 9000 (1- \frac{t}{50})(\frac{1}{50})\\\\[/tex]

          [tex]= 180 (\frac{50-t}{50})\\\\= 3.6(50-t)\\\\[/tex]

For point a:

[tex]t=5\\\\V'=3.6\times 45 = 162\\\\ans= - 162\ \frac{gal}{min}\\\\[/tex]

For point b:

[tex]t=10\\\\V'=3.6\times 40 = 144\\\\ans= - 144 \ \frac{gal}{min}\\\\[/tex]

For point c:

[tex]t=20\\\\V'=3.6\times 30 = 108\\\\ans= - 108 \ \frac{gal}{min}\\\\[/tex]

For point d:

[tex]t=50\\\\V'=3.6\times 0 = 0\\\\ans= 0 \ \frac{gal}{min}\\\\[/tex]

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