Question

A robotic machine fills containers with an acid solution at the rate of 50 + 5 t milliliters (mL) per second, where t is in seconds and 0 ≤ t ≤ 60 . How many mL are put into a container in 60 seconds? Evaluate your answer to a whole number.

Answer 1

Answer:

12,000

Step-by-step explanation:

The machine fills the containers at a rate of 50+5t milliliters (mL) per second.

Therefore, the rate of change of the number of containers, N is:

$\dfrac{dN}{dt}=50+5t, 0\leq t\leq 60$

$dN=(50+5t)dt\\ Taking integrals of both sides\\\int dN=\int (50+5t)dt\\N(t)=50t+\frac{5t^2}{2}+C (C a constant of integration)\\\\When t=0, , No containers are filled, therefore: N(t)=0\\0=50(0)+\frac{5(0)^2}{2}+C\\C=0\\ Therefore, N(t)=50t+2.5t^2$

When t=60 seconds

$N(60)=50(60)+2.5(60)^2\\N(60)=12000 mL$

Therefore, 12,000 milliliters of acid solution are put into a container in 60 seconds.