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51. (b) Is the amount of solution in the tank increasing or decreasing at time - 7 hours?

51. (b) Is the amount of solution in the tank increasing or decreasing at time - 7 hours?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 74E
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Solve 51 (b) Only in 20 min plz i need urgently plz I will give you thumb up so plz solve in 20 min plz
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? - 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.
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? - 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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