Wednesday

April 1, 2015

April 1, 2015

Posted by **POD** on Wednesday, April 30, 2008 at 8:26pm.

How many gallons of water leak out of the tank from time t=0 to t=3 minutes?

- calculus -
**Reiny**, Wednesday, April 30, 2008 at 9:29pmthe effective rate of change of the water is dV/dt = 8 - (t+1)^½ + c

so integrating we get

V = 8t - (2/3)(t+1)^(3/2) + c , where c is a constant

but when t=0 , V = 30

30 = 0 - 2/3(1)^(3/2) + c

c = 92/3

so V = 8t - (2/3)(t+1)^(3/2) + 92/3

when t = 3 minutes

V = 24 - (2/3)(4)^(3/2) + 92/3

= 24 - 16/3 + 92/3

= 148/3

so the increase is 19.3333333

but we poured in 8 gallons/min for 3 minutes which is 24 gallons.

so the leakage must be 24 - 19.3333

or 4.66666 gallons

- calculus -
**JOE**, Thursday, May 1, 2008 at 9:58amya

**Answer this Question**

**Related Questions**

math - Water is Pumped into an underground tank at a constant rate of 8 gallons ...

Math/Physics - Please check my work below and comment. A tank initially contains...

calculus(related rates) - Water is leaking out of an inverted conical tank at a ...

Calculus - Water is leaking out of an inverted conical tank at a rate of cubic ...

Calculus (pleas help!!!) - Water is leaking out of an inverted conical tank at a...

calculus - please help! - Water is leaking out of an inverted conical tank at a ...

Calculus - Water is leaking out of an inverted conical tank at a rate of 1100.0 ...

Calculus - Water is leaking out of an inverted conical tank at a rate of 1100.0...

calculus - Water is leaking out of an inverted conical tank at a rate of 60000 ...

calculus - Water is leaking out of an inverted conical tank at a rate of 1100 ...