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ser-zykov [4K]
3 years ago
11

A robotic machine fills containers with an acid solution at the rate of 50 + 5 t milliliters (mL) per second, where t is in seco

nds and 0 ≤ t ≤ 60 . How many mL are put into a container in 60 seconds? Evaluate your answer to a whole number.
Mathematics
1 answer:
Alika [10]3 years ago
7 0

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.

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