Water Tank

[Mooch22]

A water tank at Camp Newton holds 1200 gallons of water at time t=0. During the time interval 0 (less than or equal to) t (less than or equal to) 18 hours, water is pumped into the tank at the rate

W(t) = 95(Sq. rt(t))(sin^2(t/6)) gallons per hour.

During the same time interval, water is removed from the tank at the rate

R(r) = 275(sin^2(t/3)) gallons per hour.

a.) Is the amount of water in the tank increasing at time t=15? Why?

b.) To the nearest whole number, how many gallons of water are in the tank at time t=18?

c.) At what time t, for 0 (less than or equal to) t (less than or equal to) 18, is the amount of water in the tank at an absolute minimum?

d.) For t>18, no water is pumped into the tank, but water continues to be removed at the rate R(t) until the tank becomes empty. Let k be the time at which the tank becomes empty. Find, but don't solve, an equation involving an integral expression that can be used to find the value of k.

**Help please!!! :roll:

 

[happy]

What have you done on this so far?

 

[Mooch22]

I don't know where to start... I have drawn my picture and observed the graph.

 

[skeeter]

a.) Is the amount of water in the tank increasing at time t=15? Why?

hint: what is the sign of W(15) - R(15) ? what does that tell you in terms of the rate of change of water in the tank?

b.) To the nearest whole number, how many gallons of water are in the tank at time t=18?

wouldn't a function for total water in the tank in gallons be ...

\(\displaystyle 1200 + \int_0^t W(x) - R(x) dx\) ???

c.) At what time t, for 0 (less than or equal to) t (less than or equal to) 18, is the amount of water in the tank at an absolute minimum?

wouldn't the value of W(t) - R(t) change sign from negative to positive for the total water in the tank to be a minimum?

d.) For t>18, no water is pumped into the tank, but water continues to be removed at the rate R(t) until the tank becomes empty. Let k be the time at which the tank becomes empty. Find, but don't solve, an equation involving an integral expression that can be used to find the value of k.

you should be able to answer this now ... since I gave you a function to answer part (b).