A container that has 5 L of water with 1 kg salt dissolved is to be filled by pure water at arate of 0.5 L/min. The mixture is kept homogeneous by stirring and the solution is beingpumped out at twice the rate of input. Find the function of salt in the container at anygiven time.OS (1) = 0.1(100 – t)² kgS (t) = 0.01 (101)² kg

We will construct a initial value problem according to the given informations. A linear…

Answered: A container that has 5 L of water with…

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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Two tanks are connected in tandem as shown in the following figure. Each tank contains 60 gal of water. Starting at timet = 0, brine containing 3 lb/gal of salt flows into tank 1 at the rate of 2 gal/min. The mixture then enters and leaves tank 2 at the same rate. The mixtures in both tanks are stirred uniformly. It can be shown that the amount of salt in tank 2 after t min is given by A(t) = 180(1 − e−t/30) − 6te−t/30 where A(t) is measured in pounds. (Round your answers to one decimal place.) (a) What is the initial amount of salt (in lb) in tank 2? (b) What is the amount of salt (in lb) in tank 2 after 2 hr (120 min)? (c) What is the average amount of salt (in lb) in tank 2 over the first 2 hr?
A large tank is filled to capacity with 400 gallons of pure water. Brine containing 3 pounds of salt per gallon is pumped into the tank at a rate of 4 gal/min. The well-mixed solution is pumped out at the same rate. Find the number A(t) of pounds of salt in the tank at time t. A(t) = Ib
A tank is filled with 200 l of salt solution containing Qo kg of salt at time t = 0. Another salt solution with 1/4 kg of salt per liter flows into the tank at a rate of 6 lt / min. By mixing, a homogeneous water-salt mixture is obtained continuously in the tank and the mixture leaves the tank at the same speed. Find the expression Q (t) which gives the amount of salt present in the tank at time t.
A tank contains 350 liters of fluid in which 20 grams of salt is dissolved. Pure water is then pumped into the tank at a rate of 5 L/min; the well-mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t. A(t) = 9
Find the population y(t) if the birth rate is proportional to y(t) and the death rate is propors- -tional to square of y(t).
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.
A tank contains 200 liters of fluid in which 20 grams of salt is dissolved. Pure water is then pumped into the tank at a rate of 4 L/min; the well-mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t.
A tank contains 120 liters of fluid in which 50 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 3 L/min; the well-mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t. A(t) = 9
Solve v=m/4(a+K) for K.
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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