Example 2: Consider a pond that initially contains 10 million gal of fresh water. Water containing anundesirable chemical flows into the pond at the rate of 5 million gal/yr, and the mixture in the pondflows out at the same rate. The concentration of the chemical in the incoming water varies periodicallywith time according to the expression 2 + sin 2t g/gal. Construct a mathematical model of this flowprocess and determine the amount of chemical in the pond at any time.

Answered: Image /qna-images/answer/a595a48d-a697-4c26-be8f-3ce57af62a15.jpg

Answered: Example 2: Consider a pond that…

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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Have portions of part A and B complete, however I'm not sure on how to graph the phase potraits along with the inital conditions. Ultimately needing help with parts a through c thanks!
The brine solution is recycled using a series of mixing tanks before being released outside of the tanks. Tank A receives pure water at a rate of 4 L/min. The solution is pumped to Tanks B and C at rates of 2 L/min and x L/min, respectively, from Tank A, which originally contains 500 L of brine solution in which 200 g of salt is first dissolved. At a rate of 4 L/min, Tank B from its original 400 L of brine solution in which 1000 g of salt has been dissolved pumps the solution to Tank C. At a rate of y L/min, Tank C, which originally holds 400 L of pure water, pumps the solution back to Tank B. Meanwhile, Tank C releases z L/min of solution out of the system. a. Determine the values of x, y, and z if the volume of the solution within each tank stays constant throughout time. b. Find out the brine solution's concentration coming out of each tank at time t-8 minutes. 2 L/min TANK B TANKA 4 L/min y L/min Pure water @4 L/min x L/min TANK C z L/min
In a natural habitat, the population of a certain species of snails is given by P=0.8(Ae* +500), where A and k are constants and / is the time in years starting from 1 January 2010. Over a period of 8 years from 1 January 2010 to 31 December 2017, the population decreased from 50 000 to 19 000. (i) Calculate the valucs of A and of k.
Solve number 4
Two 100L tanks are connected in line. Saline is pumped into the first tank at a rate of 5L/min at a concentration of 2kg/L. Tank 1 is initially filled with pure water, and has an overflow drain which flows into Tank 2. Tank 2 initially contains 10kg of salt dissolved in 20L of solution, and has a drain with outflow at 5L/min. Let y(t) denote the amount of salt in Tank 1. Let x(t) denote the amount of salt in Tank 2. Determine the (two) differential equations describing the rates of change of y(t) and x(t). 5 L/min →→→ Tank 1 y(t) 100 L 5 L/min Tank 2 x(t) 100 L 5 L/min →
3

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