A large tank contains 20 liters of pure water. Then a process begins where water containing 50grams per liter of salt is pumped into the tank at a rate of 3 liters per minute. The well-mixedtank is drained at 2 liters per minute. Let y(t) be the amount of salt (in grams) in the tank att> 0 minutes since the pumping began. Set up an Initial Value Problem (IVP) for y(t) thatmodels this situation. You D O NOT need to solve the IVP.

Answered: A large tank contains 20 liters of pure…

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 tank contains 1,000 L of pure water. Brine that contains 0.05 kg of salt per liter of water enters the tank at a rate of 5 L/min. Brine that contains 0.04 kg of salt per liter of water enters the tank at a rate of 10 L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 15 L/min. Let y(t) be the amount of salt (in kg) in the tank after t minutes. (a) Find the rate of change of amount of salt in the tank after t minutes. dy dt kg min How much salt is in the tank when t = 0? y(0) How much salt (in kg) is in the tank after t minutes? y = = kg (b) How much salt (in kg) is in the tank after 50 minutes? (Round the answer to one decimal place.) y(50) = kg
Consider a storage tank containing Vo liters of pure water. Water containing salt at a concentration of co kg/liter enters the tank at a rate r liters/min. The well-mixed solution leaves the tank at the same rate. Write down an initial value problem for the amount A(t) of salt in the tank at time t. You do NOT need to solve.
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In a factory there is a 10,000 liter water tank that contains 0.01% colorant. From the beginning (t = 0) water with a dye content of 0.001% is pumped into the tank at a rate of 4 1 / min. The water leaves the tank at the same speed. Calculate the percentage of chlorine in the tank after 60 minutes (iterations) taking time intervals of one minute: - analytical form - using the approximate method of Euler and Runge Kutta of 4 order.
2. A tank is initially filled with 100 L of salt solution with a concentration of 0.12 kg/L. At time t = 0, a solution containing 0.2 kg/L of salt is poured into the tank at a rate of 3 L/min. Simultaneously, a drain is opened in the bottom of the tank allowing the solution to leave the tank at a rate of 4 L/min. The tank is well-stirred. Let x(t) represent the amount of salt (in kg) in the tank after t minutes. Find the differential equation and initial condition for which x(t) is a solution. DO NOT SOLVE THE DIFFERENTIAL EQUATION. (t)= S t x' (t) = , x(0) =
A tank is initially filled with 400 gal of salt solution with a concentration of 0.08 lb/gal. At time t = 0, pure water is poured into the tank at a rate of 2 gal/min. Simultaneously, a drain is opened at the bottom of the tank allowing the solution to leave the tank at a rate of 3 gal/min. The tank is well-stirred. Let x(t) represent the amount of salt (in lb) in the tank after t min. Write down the initial value problem that x(t) satisfies. DO NOT SOLVE the initial value problem.

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