Question

A valve in a full 6000 gallon water tank is slowly opening. Water flows out of the tank through the valve. The flow rate in gallons per hour is given by the function f(t)=300 t^2 where t is in minutes.
How much water flows out the tank in the first 7 minutes?
How many minutes does it take for the tank to be completely empty?

Answer 1

300(7)^2=

Answer 2

2,100^2=

Answer 3

i tried that its not the answer

Answer 4

http://answers.yahoo.com/question/index?qid=20080710170950AAexzaz

Answer 5

maybe this will help

Answer 6

sorry i couldnt be of more help to you.

Answer 7

i got 34,300 for the first part

Answer 8

\(f(t)=300t^2\) is the flow rate, so integrating \(f\) over some interval \([a,b]\) would tell you how much flows out over \([a,b]\).

"The first 7 minutes" gives you an interval to work with: \([0,7]\).
So find
\[\int_0^7f(t)~dt\]
The second question asks how long it takes until the amount of water in the tank reaches 0, i.e. how long it takes for the amount of water that has flowed out to be 6000 gal. Starting at time \(t=0\), you must find \(k\) such that
\[\int_0^kf(t)~dt=6000\]