A shallow reservoir has a one-square-kilometer water surface and an average water depth of 2 meters.Initially it is filled with fresh water, but at time t=0 water contaminated with a liquid pollutant begins flowinginto the reservoir at the rate of 400 thousand cubic meters per month. The well-mixed water in the reservoirflows out at the same rate. Your first task is to find the amount x(t) of pollutant (in millions of liters) in thereservoir after t months. The incoming water has a pollutant concentration of c(t) = 20 liters per cubic meter(L/m³). Verify that the graph of x(t) resembles the steadily rising curve shown here, which approachesasymptotically the graph of the equilibrium solution x(t) = 40 that corresponds to the reservoir's long-termpollutant content. How long does it take the pollutant content in the reservoir to reach 10 million liters?x(t) =40-30-20-10-01020t

Given Data: Let us consider the given the reservoir has one square kilo meter water surface and an…

Answered: A shallow reservoir has a…

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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A tank contains 2100 L of pure water. Solution that contains 0.01 kg of sugar per liter enters the tank at the rate 4 L/min, and is thoroughly mixed into it. The new solution drains out of the tank at the same rate. (a) How much sugar is in the tank at the begining? y(0) = (kg) (b) Find the amount of sugar after t minutes. y(t) = (kg) (c) As t becomes large, what value is y(t) approaching? In other words, calculate the following limit. lim y(t) = (kg) 00+7
Please tell me what goes into each box thank you
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.
A brine solution of salt flows at a constant rate of 5 L/min into a large tank that initially held 100 L of brine solution in which was dissolved 0.15 kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the brine entering the tank is 0.03 kg/L, determine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach 0.01 kg/L? Determine the mass of salt in the tank after t min. mass= kg
We have a large tank filled with 50 liters of pure water. there is a salt solution of concentration 20 g/L flowing into the tank at a rate of 2 L/min. The well mixed solution is flowing out of the tank at a rate of 1 L/min. find the concentration of salt in the tank as a function of time. no need to worry about the tank overflowing.
The function f(x) = |ax - b| + c|x| : x in (-∞, ∞), where a > 0. b > 0 , c > 0 Find the condition if f(x) attains minimum value only at one point.
A brine solution of salt flows at a constant rate of 6 L/min into a large tank that initially held 100 L of brine solution in which was dissolved 0.1 kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the brine entering the tank is 0.02 kg/L, determine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach 0.01 kg/L?
Mrs. Santa has a ball of cheese wrapped in red wax and decided to cut in half, to share with her visitors. The diameter of the cheese (excluding the wax) is 10 inches, and the wax has a thickness of 0.25 inches. (a) Find the total volume (exact) of the wax; (b) Use differential to estimate the volume of the wax.
Suppose two students are memorizing the elements on a list according to the rate of change equation: dL/dt = 0.5(1-L). L represents the fraction of the list that is memorized at any time t. (a) If one of the students knows one-third of the list at time t = 0 and the other student knows none of the list, which student is learning most rapidly at this instant? Why? (b) What does the rate of change equation predict for someone who begins with the list completely memorized? Explain.
A swimming pool whose volume is 10,000 gal contains water that is 0.01% chlorine. Starting at t=0, city water containing 0.002% chlorine is pumped into the pool at a rate of 6 gal/min. The pool water flows out at the same rate. What is the percentage of chlorine in the pool after 1 hour? When will the pool water be 0.004% chlorine? What is the percentage of chlorine in the pool after 1 hour? After 1 hour the pool will be % chlorine. (Round to four decimal places as needed.)
Initially 9 grams of salt are dissolved into 7 liters of water. Brine with concentration of salt 8 grams per liter is added at a rate of 5 liters per minute. The tank is well mixed and drained at 5 liters per minute. a) Let x be the amount of salt, in grams, in the solution after t minutes have elapsed. Find a formula for the rate of change in the amount of salt, dx/dt, in terms of the amount of salt in the solution x. dx dt b) Find a formula for the amount of salt, in grams, after t minutes have elapsed. x(t) = c) How long must the process continue until there are exactly 40 grams of salt in the tank?
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