Suppose a 1000 L tank contains 400 L of fresh water at time t= 0. At that time, a salt water solution of concentration 2 g/L enters the tank at the rate of 4 L/mín. The well-mixed solution flows out of the tank at the rate of 1 L/mín. Which of thefollowing initial value problems correctly model the amount M(t) of salt in the tank at time t?M400 + 34= 8, M(0) = 0dtMdt= 8, M(0) = 0400tM= 4, M(0) = 0dt400tM+400 + 3t= 4, M(0) - 0dtO None of the others

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Answered: Suppose a 1000L tank contains 400 L of…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

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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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4. 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 0.2 kg/L, deter- mine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach 0.1 kg/L?
A tank contains 210 liters of fluid in which 50 grams of salt is dissolved. Pure water is then pumped into the tank at a rate of 3 L/min; the well-mixed solution is pumped out at the same rate. Let the A(t) be the number of grams of salt in the tank at time t. Find the rate at which the number of grams of salt in the tank is changing at time t. Find the number A(t) of grams of salt in the tank at time t.
Set up an I.V.P. and solve using the following: Suppose a large mixing tank initially holds 500 liters of pure water. A brine solution is pumped into the tank at a rate of 3 L/min with a concentration of 0.2 kilograms of salt per liter. If the well-stirred solution is pumped out at the same rate, find the number of kilograms of salt in the tank at time t, A(t).
Consider a large vat containing sugar water that is to be made into soft drinks (see figure below). A B Suppose: The vat contains 230 gallons of liquid, which never changes. Sugar water with a concentration of 7 tablespoons/gallon flows through pipe A into the vat at the rate of 5 gallons/minute. • Sugar water with a concentration of 3 tablespoons/gallon flows through pipe B into the vat at the rate of 25 gallons/minute. The liquid in the vat is kept well-mixed. • Sugar water leaves the vat through pipe C at the rate of 30 gallons/minute. Let S(t) represent the number of tablespoons of sugar in the vat at time t, where t is given in minutes. (A) Write the DE model for the time rate of change of sugar in the vat: dS dt (B) Solve the differential equation to find the amount of sugar in the vat as a function of time. Your function will have an arbitrary constant K in it. Assume that K > 0. S(t) = (C) Suppose that there are 22 tablespoons of sugar in the vat at t = 0. How many tablespoons…
A tank contains 200 gal of liquid. Initially, the tank contains pure water. At time t = 0, brine containing 3 lb/gal of salt begins to pour into the tank at a rate of 2 gal/min, and the well-stirred mixture is allowed to drain away at the same rate. How many minutes must elapse before there are 100 lb of salt in the tank?
6. A 50 gallons tank initially contains 10 gal of fresh water. At t = 0, a brine solution containing 1 lb of salt per gallon is poured into the tank at the rate of 4 gal/min, while the well-stirred mixture leaves the tank at the rate of 2 gal/min. Find a. the amount of time required for overflow to occur b. the amount of salt in the tank at the moment of overflow
2. A large tank initially contains 100 gallons of brine in which 10 lb of salt is dissolved. Starting at t = 0, pure water flows into the tank at the rate of 5 gal/min. The mixture is kept uniform by stirring, and the well-stirred mixture simultaneously flows out at the slower rate of 2 gal/min. a) How much salt is in that tank at the end of 15 min and what is the concentration at that time? b) If the capacity of the tank is 250 gallons, what is the concentration at the instant the tank overflows?
A 60-gal tank initially contains 10 gal of fresh water. At t = 0, a brine solution containing 1 Ib of salt per gallon is poured into the tank at the rate of 4 gal/min, while the well-stirred mixture leaves the tank at the rate of 2 gal/min. Find the amount of time required for overflow to occur.

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