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

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

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+(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.