2,2 The TUT cafeteria at the eMalahleni campus is home to an industrial juice dispenser witha volume of 20I. Initially the dispenser is filled with a juice blend containing 10% mango and90% peach juice. An orange-mango blend containing 40% orange and 60% mango is enteringthe dispenser at a rate of 4/ / hr and the well-stirred mixture leaves at a rate of 4// hr.2.2.1 Use a differential equation to model the amount of mango juice, M(1), in the dispenserat any time t and solve it. (The orange-mango blend starts to enter att=0)

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Answered: 2.2 The TUT cafeteria at the eMalahleni…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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A brine solution of salt flows at a constant rate of 3 L/min into a large tank that initially held 100 L of pure water. The solution inside the tank is kept well stirred and flows out of the tank at a rate of 2 L/min. If the concentration of salt in the brine entering the tank is 0.6 kg/L, determine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach 0.5 kg/L? ... Determine the mass of salt in the tank after t min. mass= kg
a tank in which 1 gram of chlorine is initially present in 80.38 m3 of a solution of water and chlorine. A chlorine solution concentrated at 1.49 g/m3 flows into the tank at a rate of 3 m3 /min, while the uniformly mixed solution exits the tank at 7 m3 /min. What will be the amount of chlorine present in the tank after 1 minute?
In monitoring the blood alcohol content of a person, the bloodstream, which is composed of 5L of water, could be idealized to have a single inflow by the absorption of fluids through the small intestine at a rate of 2×10-5 L/s. Blood then is filtered through the kidneys for alcohol and other toxic substances. This mixture is released through the form of urine at a rate of 1.75×10-5 L/s. Upon testing, it was found out that you have a total 6 g of alcohol within your system. You were advised to drink pure water to reduce the amount of alcohol in your body. Assume instantaneous mixing after absorption takes place. How long should your small intestine absorb pure water to reduce the amount of alcohol in your system by [H]g? NOTE: Birthdate = February 06, 2002 NOTE:[H](your birthdate)/10
A brine solution of salt flows at a constant rate of 4 L/min into a large tank that initially held 100 L of pure water. The solution inside the tank is kept well stirred and flows out of the tank at a rate of 3 L/min. If the concentration of salt in the brine entering the tank is 0.4 kg/L, determine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach 0.2 kg/L? Determine the mass of salt in the tank after t min. mass= 4(t+100) - 4x10² (t+100³) kg A
5. Suppose that sodium pentobarbital is used to anesthetize a dog. The dog is anesthetized when its bloodstream contains at least 45 milligrams (mg) of sodium pentobarbitol per kilogram of the dog's body weight. Suppose also that sodium pentobarbitol is eliminated from the dog's bloodstream at a rate which is proportional to the amount of sodium pentobarbitol in the bloodstream and that after 5 hours half of the initially prescribed sodium pentobarbitol is elliminated from the bloodstream. Set up and solve an initial value differential equation. What single dose should be administered in order to anesthetize a 50-kg dog for 1 hr?
Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing from tank A into tank B at a rate of 5 L/min and from B into A at a rate of 4 L/min. The liquid inside each tank is kept well stirred. A brine solution with a concentration of 0.1 kg/L of salt flows into tank A at a rate of 10 L/min. The (diluted) solution flows out of the system from tank A at 9 L/min and from tank B at 1 L/min. If initially, tank A contains pure water and tank B contains 10 kg of salt, determine the mass of salt in each tank at time t≥0. x(t) = 10 L/min- 0.1 kg/L y(t) = 9 L/min A x(t) 100 L x(0) = 0 kg 5 L/min What is the solution to the system? 18 4 L/min B y(t) 100 L y(0) = 10 kg ..... 1 L/min O ✔
Write an algebraic expression for the fare increase if a $200 plane ticket is increased to x dollars.
A tank with a capacity of 25 L originally contains 15 L of brine with a concentration of 5 g/L of salt. Water containing 1 g/L of salt is entering at a rate of 5 L/min, and the mixture is allowed to flow out of the tank at a rate of 4 L/min. Find the concentration (in g/L) of salt in the tank when it is on the point of overflowing.

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