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7. Consider the following scenario. A pond containing 500,000 gal of water is initially free of a certain toxin. Wa...
A pond initially contains 4,000,000 gal of water and an unknown amount of an undesirable chemical
Chapter 1, Section 1.1, Question 17ab A pond initially contains 4,000,000 gal of water and an unknown amount of an undesirable chemical. Water containing 0.05 grams of this chemical per gallon flows into the pond at a rate of 100 gal/h.The mixture flows out at the same rate, so the amount of water in the pond remains constant. Assume that the chemical is uniformly distributed throughout the pond. (a) Write a differential equation for the amount of chemical in the pond at...
A tank initially contains 980 gal of pure water.
A tank initially contains 980 gal of pure water. Brine containing 3.3 lb/gal of salt is poured into the tank at a rate of 7 gal/min. Suppose the solution in the tank is instantly well mixed and drained out at a rate of 9 gal/min. Let Q = Q(t) be the quantity of salt in the tank at time t minutes. What is the initial condition? Set up the differential equation for the quantity of salt in the tank: Find the particular solution: When does...
Calc 4 question
A tank initially contains 1000 gal of water and some chemical inside that. Water containing .001 gram of the chemical flows into the tank at a rate 20 gal/min and flows out at the same rate. The chemical is uniformly distributed throughout the pond. (a) Write a differential equation for the amount of the chemical at the pond at any time t. (b) How much chemical will be there after a very long time? (c) Does the limiting amount depend...
A small pond initially contains 2,000 litres of fresh water. Polluted water flows in at a...
A small pond initially contains 2,000 litres of fresh water. Polluted water flows in at a rate of 5 litres per hour. Water fows out of the pond at the same rate. The concentration of pollutant in the inflow, c(t), is given by c(t) = 2 +5e-* grams per litre. Originally there is no pollutant in the pond. Which of the following differential equation models describes the total mass Q of pollutant in the pond over time? dQ dt 10...
(1) A tank is filled with 300 liters (L) of contaminated water initially containing 3 kg...
(1) A tank is filled with 300 liters (L) of contaminated water initially containing 3 kg of toxin. Pure water is pumped in to the tank at a rate of 40 L/min, mixes instantaneously, and the mixture is pumped out at the same rate (40 L/min). Let y(t) be the amount of toxin present in the tank at time t. Write the differential equation and the initial value that models this scenario. (a) Find the particular solution, y(t). Put a...
Consider the two interconnected tanks shown in Figure 7.1.6. Tank 1 initially contains 30 gal of ...
Consider the two interconnected tanks shown in Figure 7.1.6.
Tank 1 initially contains 30 gal of water and 25 oz of salt, and
Tank 2 initially contains 20 gal of water and 15 oz of salt. Water
containing 1 oz/gal of salt flows into Tank 1 at a rate of 1.5
gal/min. The mixture flows from Tank 1 to Tank 2 at a rate of 3
gal/min. Water containing 3 oz/gal of salt also flows into Tank 2
at a...
Consider the two interconnected tanks shown in the following figure. 1 g/min 3 galimin 1 oz...
Consider the two interconnected tanks shown in the following figure. 1 g/min 3 galimin 1 oz 30/gal 4 galimin Q un salt Q.) o salt Tank 1 Tank 2 4 l/min Tank 1 initially contains 60 gal of water and 25 oz of salt, and Tank 2 initially contains 44 gal of water and 15 oz of salt. Water containing 1 oz/gal of salt flows into Tank 1 at a rate of 3 gal/min. The mixture flows from Tank 1...
7.2.6 A swimming pool has a volume of 50 m. A mass C (in kg) of chlorine is dissolved in the pool water. Starting at a time 0, water containing a con- centration of 0.1 C/V chlorine is pumped in...
7.2.6 A swimming pool has a volume of 50 m. A mass C (in kg) of chlorine is dissolved in the pool water. Starting at a time 0, water containing a con- centration of 0.1 C/V chlorine is pumped into the swimming pool at a rate of 0.02 m3/min, and the water flows out at the same rate. a) Present the differential equation for the chlorine mass O). b) Find the solution O(t) to this equation. c) What is the...
3. A 1000-gallon tank initially contains 800 gallons of water with 3 lbs of salt dissolved...
3. A 1000-gallon tank initially contains 800 gallons of water with 3 lbs of salt dissolved in it. A water-salt mixture with a concentration of 0.4 lb of salt per gallon enters the tank at a rate of 8 gal/hr. The liquid in the tank is well-mixed and is pumped out of the tank at a rate of 10 gal/hr. Suppose you were asked to find an expression for the amount of salt in the tank at time t. (a)...
2. A tank contains a 100 gallons of pure water. Brine containing pound salt per gallon...
2. A tank contains a 100 gallons of pure water. Brine containing pound salt per gallon enters the tank at thratof 2 Let x(t) represent the amount of salt in the tank after t min. and the well-mixed solution flows out at the rate of 4ツ· a. Find the differential equation which relates( and , the initial condition and the domain of x() dr b. Find the particular solution of this equation. c. What is the most amount of salt...
A small pond initially contains 2,000 litres of fresh water. Polluted water flows in at a rate of 5 litres per hour. Water fows out of the pond at the same rate. The concentration of pollutant in the inflow, c(t), is given by c(t) = 2 +5e-* grams per litre. Originally there is no pollutant in the pond. Which of the following differential equation models describes the total mass Q of pollutant in the pond over time? dQ dt 10...
Consider the two interconnected tanks shown in Figure 7.1.6.
Tank 1 initially contains 30 gal of water and 25 oz of salt, and
Tank 2 initially contains 20 gal of water and 15 oz of salt. Water
containing 1 oz/gal of salt flows into Tank 1 at a rate of 1.5
gal/min. The mixture flows from Tank 1 to Tank 2 at a rate of 3
gal/min. Water containing 3 oz/gal of salt also flows into Tank 2
at a...
Consider the two interconnected tanks shown in the following figure. 1 g/min 3 galimin 1 oz 30/gal 4 galimin Q un salt Q.) o salt Tank 1 Tank 2 4 l/min Tank 1 initially contains 60 gal of water and 25 oz of salt, and Tank 2 initially contains 44 gal of water and 15 oz of salt. Water containing 1 oz/gal of salt flows into Tank 1 at a rate of 3 gal/min. The mixture flows from Tank 1...
7.2.6 A swimming pool has a volume of 50 m. A mass C (in kg) of chlorine is dissolved in the pool water. Starting at a time 0, water containing a con- centration of 0.1 C/V chlorine is pumped into the swimming pool at a rate of 0.02 m3/min, and the water flows out at the same rate. a) Present the differential equation for the chlorine mass O). b) Find the solution O(t) to this equation. c) What is the...
3. A 1000-gallon tank initially contains 800 gallons of water with 3 lbs of salt dissolved in it. A water-salt mixture with a concentration of 0.4 lb of salt per gallon enters the tank at a rate of 8 gal/hr. The liquid in the tank is well-mixed and is pumped out of the tank at a rate of 10 gal/hr. Suppose you were asked to find an expression for the amount of salt in the tank at time t. (a)...
2. A tank contains a 100 gallons of pure water. Brine containing pound salt per gallon enters the tank at thratof 2 Let x(t) represent the amount of salt in the tank after t min. and the well-mixed solution flows out at the rate of 4ツ· a. Find the differential equation which relates( and , the initial condition and the domain of x() dr b. Find the particular solution of this equation. c. What is the most amount of salt...
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