A plant worker is monitoring the amount of a certain chemical solution entering an empty, cylindrical tank. The tanks has a diameter of 6 meters. The rate at which the solution enters the tank is modeled by 20+6 cos (0.2r) where C is measured in kilograms (kg), t is measure in hours and 0 ≤t≤ 10 After 4 hours, the worker falls asleep and the tank springs a leak. After the leak is sprung, the solution leaves the tank at a constant rate of 15 kilograms per hour. C (t) 50. (a) How many kilograms of solution are in the tank right before the leak is sprung?
A plant worker is monitoring the amount of a certain chemical solution entering an empty, cylindrical tank. The tanks has a diameter of 6 meters. The rate at which the solution enters the tank is modeled by 20+6 cos (0.2r) where C is measured in kilograms (kg), t is measure in hours and 0 ≤t≤ 10 After 4 hours, the worker falls asleep and the tank springs a leak. After the leak is sprung, the solution leaves the tank at a constant rate of 15 kilograms per hour. C (t) 50. (a) How many kilograms of solution are in the tank right before the leak is sprung?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A plant worker is monitoring the amount of a certain chemical solution entering an empty, cylindrical
tank. The tanks has a diameter of 6 meters. The rate at which the solution enters the tank is modeled by
C (t) 20+ 6 cos (0.2r) where C is measured in kilograms (kg), t is measure in hours and 0 ≤t≤ 10
. After 4 hours, the worker falls asleep and the tank springs a leak. After the leak is sprung, the solution
leaves the tank at a constant rate of 15 kilograms per hour.
50. (a) How many kilograms of solution are in the tank right before the leak is sprung?
51. (b) Is the amount of solution in the tank increasing or decreasing at time t = 7 hours?
52. (c) If C (t) also models the rate at which the volume of solution in the tank is changing, at what
rate is the height of solution in the tank rising at time t=2 hours?
E
53. (d) Let Q (1) represent the net rate at which chemicals are added the tank. Is Q (t) continuous at
time t=4 hours? Justify your answer.
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