A tank contains 1000 L of pure water. Brine that contains 0.05 kg of salt per liter of water enters the tank at a rate of 5 L/min. Brine that contains 0.04 kg of salt per liter of water enters the tank at a rate of 10 L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 15 L/min. (a) How much salt is in the tank after t minutes? kg (b) How much salt is in the tank after 50 minutes? (Round the answer to one decimal place.) kg

Q: A large tank is filled to capacity with 700 gallons of pure water. Brine containing 4 pounds of salt…

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Q: A tank contains 50 kg of salt and 2000 L of water. A solution of a concentration 0.0125 kg of salt…

A: Given Initially tank contain 50 kg  salt And 2000 litre of water

Q: A tank contains 1000 liters of brine with 15 kg of dissolved salt. Pure water enters the tank at a…

A: Let x represents the amount of salt after t minutes. Given that, the initial amount of salt is 15…

Q: A tank contains 180 liters of fluid in which 10 grams of salt is dissolved. Brine containing 1 gram…

A: Let the amount of salt in grams at time t be A(t)We have given the initial amount of salt in grams…

Q: A tank contains 420 liters of fluid in which 50 grams of salt is dissolved. Brine containing 1 gram…

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Q: A tank contains 100 gal of brine made by dissolving 80 lb of salt in water. Pure water runs into the…

A: Given: tank contains 100 gal of brine made by dissolving 80 lb of salt in water The pure water runs…

Q: A tank initially contains 100 gal of pure water. Starting at t=0, a brine containing 4 Ib of salt…

A: Amount of water in tank =100 gal Amount of brine containing 4 lb of salt per gallon initially (t=0)=…

Q: In the tank of 100 liters of brine containing 50kg totally dissolved salt. Pure water is allowed to…

A: Let y(t) be the amount of salt dissolved in the tank in kilograms after t minutes. Initially amount…

Q: A tank contains 400 liters of fresh water. Brine containing 0.3 kg/L of salt runs into the tank at…

A: We need to find concentration.

Q: A population of cattle is increasing at a rate of 800 + 80 t per year, where t is measured in years.…

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Q: 2. Brine containing 3 lbs./gal of salt enters a large tank at the rate of 2 gals/minute and the…

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Q: A swimming pool whose volume is 10,000 gal contains water that is 0.02% chlorine. Starting at t=0,…

A:

Q: A swimming pool whose volume is 10,000 gal contains water that is 0.03% chlorine. Starting at t=0,…

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Q: A tank contains 60 kg of salt and 1000 L of water. A solution of concentration .03 kg of salt per…

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Q: Initially a tank contains 10 lb of salt dissolved in 100 gal of water. Assume that brine containing…

A: Given that Initially a tank contains 10 lb of salt dissolved in 100 gal of water. Let x(t) be the…

Q: A tank contains 100 gal of brine made by dissolving 60 lb of salt in water. Saltwater containing 1…

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Q: A large tank initially contains 200 gal of brine in which 15lb of salt is dissolved. Starting at t =…

A: The described process is as illustrated below,

Q: 1. A tank contains 1,000 L of water and 20 kg of dissolved salt. Fresh water is entering the tank at…

A: Here we are given that A tank contains 100 L of water and 20 kg of dissolved salt.Fresh water is…

Q: A brine solution of salt flows at a constant rate of 6 L/min into a large tank that initially held…

A: given, brine solution of salt flows at a constant rate of 6 Lmin the tank initially had 100 L of…

Q: A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 1 gram…

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Q: A large tank holds (400) gallons of brine solution with (50) pounds Q5: of salt. A concentration of…

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Q: A tank contains 150 liters of fluid in which 20 grams of salt is dissolved. Brine containing 1 gram…

A:

Q: A 20 m³ tank is full of brine with 40 kg of dissolved salt. Pure water enters the tank at a rate of…

A: A differential equation is an equation that involves derivatives or differential coefficients or…

Q: A 2000 L tank initially contains 40 kg of salt dissolved in 1000 L of water. A brine solution…

A: Given capacity of tank =2000 L initial amount of water =1000 L rate of in flow of salt =50 L/min…

Q: A 1500-L tank is initially filled with a solution that contains 3000 g of salt. A salt solution with…

A: This question can be solved using the concept of differential equation.

Q: A tank contains 200 liters of fresh water. Brine containing 2 kg/liter of salt enters the tank at…

A: Let the amount of salt be Q. Volume at any time t: 200+4-3t=200+t The concentration becomes Q200+t.…

Q: A tank contains 240 liters of fluid in which 10 grams of salt is dissolved. Pure water is then…

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Q: A solution of salt flows at a constant rate of 6 L/min into a large tank that initially held 50 L of…

A: We have, dxtdt=0.3 kg/min - 0.12 xt kg/min⇒dxtdt+ 0.12xt=0.3        ...i Calculating for P(t) and…

Q: solution well stirred leaves at 2 gal/min. The tank initially contains 20 gal of water.What is the…

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Q: A tank contains 1000L of pure water. Brine that contains 0.05kg of salt per liter of water enters…

A: In this question we set up a initial value problem and then solve it

Q: A tank initially contains 200 liters of pure water. Brine containing 2 kg per liter enters the tank…

A: 1st we will make differential equation and then solve it to find amount of salt

Q: 3. A tank contains 100 gal of brine made by dissolving 80 pounds of salt in water. Pure water runs…

A: Given

Q: A tank contains 300 liters of fluid in which 50 grams of salt is dissolved. Brine containing 1 gram…

A:

Q: A large tank initially contains 200 gal of brine in which 15 lb of salt is dissolved. Starting at…

A:

Q: A tank contains 1,158 L of brine with 15kg of dissolved salt. Pure water enters the tank at a rate…

A:

Q: A tank contains 240 liters of fluid in which 50 grams of salt is dissolved. Pure water is then…

A: Given :  The quantity of the water in the tank is 240 liters in which 50 grams of salt is dissolved.…

Q: 3. Brine containing 3lb/gal of salt enters a tank at the rate of 4gal/min and the solution…

A:

Q: A tank initially contains 200L of fresh water. Brine containing 2N/L of dissolved salt enters the…

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Q: A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 1 gram…

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Q: Brine containing 1.5 lb/gal of salt enters a tank at the rate of 2 gal/min and the mixture…

A:

Q: A tank is utilized for mixing sugar solutions which can initially contain 80 gallons of water. A…

A: To find: Amount of sugar in the tank after 10 minutes

Q: Bacteria grow in a culture at a rate proportional to the amount present. Initially, 300 strands of…

A: Solve for the doubling time

Q: In the tank of 113 liters of brine containing 50kg totally dissolved salt. Pure water is allowed to…

A: Recall: ∫1ax+bdx=lnax+ba+C lnmn=n lnm  [Power Rule]

Q: A 20 m³ tank is full of brine with 40 kg of dissolved salt. Pure water enters the tank at a rate of…

A: The  given problem we can be formulated as  a differential equation and solve.

Q: A tank contains 1780 L of pure water. A solution that contains 008 kg of sugar per liter enters a…

A: Consider the provided question, Part first: Find how much sugar in the tank initially, Since, at the…

Q: A tank contains 1000 L of brine with 15 kg of dissolvedsalt. Pure water enters the tank at a rate of…

A: Given data: A tank contains 1000 L of brine with 15 kg of dissolved salt. Consider x(t) be the…

Q: A container holds 200 gallons of brine solution containing 50 lb of salt. Initially , fresh water is…

A:

Q: A tank containing 100 gallons of brine made by dissolving 40 lbs of salt in water. Pure water runs…

A: Pure water in flow rate = 5 galmin

Q: A tank contains 150 gal of brine made by dissolving 60 pounds of salt in water. Salt water…

A:

Q: A brine solution of salt flows at a constant rate of 8 L/min into a large tank that initially held…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.