Question

A chemical flows into a storage tank at a rate of (180+3t) liters per minute, where t is the time in minutes and 0<=t<=60

Answer 1

Answer:

The amount of the chemical flows into the tank during the firs 20 minutes is 4200 liters.

Step-by-step explanation:

Consider the provided information.

A chemical flows into a storage tank at a rate of (180+3t) liters per minute,

Let $c(t)$ is the amount of chemical in the take at t time.

Now find the rate of change of chemical flow during the first 20 minutes.

$\int\limits^{20}_{0} {c'(t)} \, dt =\int\limits^{20}_0 {(180+3t)} \, dt$

$\int\limits^{20}_{0} {c'(t)} \, dt =\left[180t+\dfrac{3}{2}t^2\right]^{20}_0$

$\int\limits^{20}_{0} {c'(t)} \, dt =3600+600$

$\int\limits^{20}_{0} {c'(t)} \, dt =4200$

So, the amount of the chemical flows into the tank during the firs 20 minutes is 4200 liters.