1) A water 3000 litter water tank is being filled up by the minute.

Question

The rate at which the water is entering the tank can be described as Q′(t) = 3√t, where t is measured in minutes.

a) Determine how much water will be poured into the tank within an hour.

b) At what time will the tank actually be full?

Answer 1

Q'=3sqr(t)

integrate

Q(t)=2t^1.5+c

Q(60)= 2(60)^1.5+c

in 60 minutes 2(60)^1.5 liters flow into the tank

=120sqr60

=240sqr15

=about 929.76 Liters

it fills up in 3000/240sqr15= 3000/929.76 hrs

=about 3.23 hours

=about 193 minutes 36 seconds

= 3 hrs 13 min 36 sec