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 on the amount present initially (d) EXPLAIN IN TERMS OF DIRECTION FIELD. (DO NOT SOLVE THE DIFFERENTIAL EQUATION)
Homework Answers
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...
7. Consider the following scenario. A pond containing 500,000 gal of water is initially free of a certain toxin. Wa...
7. Consider the following scenario. A pond containing 500,000 gal of water is initially free of a certain toxin. Water containing 0.02 g/gal of the toxin flows into the pond at a rate of 250 gal/hour and water also flows out of the pond at the same rate. Assume that the toxin is uniformly distributed throughout the pond. Let Q(t) be the amount of the toxin in the pond at time t (hours). Write down an initial value together with...
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...
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...
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...
(10p) (b) Use the Laplace transform method to find Q1 (t); Q2 (t) in terms of convolution products
(10p) (b) Use the Laplace transform method to find Q1 (t); Q2
(t) in terms of convolution products
2. Consider the two interconnected tanks shown in the figure below. 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...
A tank initially contains 500 gallons of water in which 40 pounds of salt is initially dissolved in the water
A tank initially contains 500 gallons of water in which 40 pounds of salt is initially dissolved in the water. Brine (a water-salt mixture) containing 0.4 pounds of salt per gallon flows into the tank at the rate of 5 gal/min, and the mixture (which is assumed to be perfectly mixed) flows out of the tank at the same rate of 5 gal/min. Let y(t) be the amount of salt (in pounds) in the tank at time t. a) Set up...
at any time i. Also find the limiting amount of salt in the tank - A...
at any time i. Also find the limiting amount of salt in the tank - A tank contains 100 gal of water and 50 oz of salt. Water containing a salt concentration of (1 + i sin t) oz/gal flows into the tank at a rate of 2 gal/min, and the mixture in the tank flows out at the same rate. (a) Find the amount of salt in the tank at any time. (b) Plot the solution for a time...
4. A tank with a capacity of 500 gal originally contains 200 gal of water with...
4. A tank with a capacity of 500 gal originally contains 200 gal of water with 100 lb of salt in solution. Water containing 1 lb of salt per gallon is entering at a rate of 3 gal/min, and the mixture is allowed to flow out of the tank at a rate of 2 gal/min. Find the amount of salt in the tank at any time prior to the instant when the solution begins to overflow. Find the concentration (in...
Each of the tanks shown in Figure 3.2.9 contains a brine solution. Assume that Tank 1...
Each of the tanks shown in Figure 3.2.9 contains a brine solution. Assume that Tank 1 initially contains 30 gallons (gal) of water and 55 ounces (oz) of salt, and Tank 2 initially contains 20 gal of water and 26 oz of salt. Water containing 1 oz/gal of salt flows into Tank 1 at a rate of 1.5 gal/min, and the well-stirred solution flows from Tank 1 to Tank 2 at a rate of 3 gal/min. Additionally, water containing 3...
7. Consider the following scenario. A pond containing 500,000 gal of water is initially free of a certain toxin. Water containing 0.02 g/gal of the toxin flows into the pond at a rate of 250 gal/hour and water also flows out of the pond at the same rate. Assume that the toxin is uniformly distributed throughout the pond. Let Q(t) be the amount of the toxin in the pond at time t (hours). Write down an initial value together with...
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...
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...
(10p) (b) Use the Laplace transform method to find Q1 (t); Q2
(t) in terms of convolution products
2. Consider the two interconnected tanks shown in the figure below. 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...
at any time i. Also find the limiting amount of salt in the tank - A tank contains 100 gal of water and 50 oz of salt. Water containing a salt concentration of (1 + i sin t) oz/gal flows into the tank at a rate of 2 gal/min, and the mixture in the tank flows out at the same rate. (a) Find the amount of salt in the tank at any time. (b) Plot the solution for a time...
4. A tank with a capacity of 500 gal originally contains 200 gal of water with 100 lb of salt in solution. Water containing 1 lb of salt per gallon is entering at a rate of 3 gal/min, and the mixture is allowed to flow out of the tank at a rate of 2 gal/min. Find the amount of salt in the tank at any time prior to the instant when the solution begins to overflow. Find the concentration (in...
Each of the tanks shown in Figure 3.2.9 contains a brine solution. Assume that Tank 1 initially contains 30 gallons (gal) of water and 55 ounces (oz) of salt, and Tank 2 initially contains 20 gal of water and 26 oz of salt. Water containing 1 oz/gal of salt flows into Tank 1 at a rate of 1.5 gal/min, and the well-stirred solution flows from Tank 1 to Tank 2 at a rate of 3 gal/min. Additionally, water containing 3...
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