Respuesta :
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 [tex]c(t)[/tex] 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.
[tex]\int\limits^{20}_{0} {c'(t)} \, dt =\int\limits^{20}_0 {(180+3t)} \, dt[/tex]
[tex]\int\limits^{20}_{0} {c'(t)} \, dt =\left[180t+\dfrac{3}{2}t^2\right]^{20}_0[/tex]
[tex]\int\limits^{20}_{0} {c'(t)} \, dt =3600+600[/tex]
[tex]\int\limits^{20}_{0} {c'(t)} \, dt =4200[/tex]
So, the amount of the chemical flows into the tank during the firs 20 minutes is 4200 liters.
