Suppose a brine containing 2 kg of salt per liter runs into a tank initially filled with 500 L of water containing 50 kg of salt. The brine enters the tank at a rate of 5 L/min. The mixture, kept uniform by stirring, is flowing out at the rate of 10 L/min. Find the amount of salt in the tank after 10 min. Find the concentration, in kilograms per liter, of salt in the tank after 10 min. When will the tank empty?

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A: 1st we will make differential equation for amount of drug in the body and then solve it to get exact…

Q: Consider a tank with volume 100 liters containing a salt solution. Suppose a solution with 2…

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Q: A tank contains initially 400 liters of brine holding 100 kg of salt in solution. Water containing…

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A: (a) A 600 litre tank initially contains 200 liters of water. 10 grams of salt are dissolved in it.…

Q: A tank contains 300 gal of water and 100 gal of pollutants. Fresh water is pumped into the tank at…

A: Fresh water is pumped into the tank at the rate of 2 gal/min, and the well stirred mixtureleaves at…

Q: A tank initially contains 200 L of fresh water. Brine containing 2.5 N/L of dissolved salt runs into…

A: Let "s" represents the quantity of salt in the tank. dSdt=(8×2.5)-8S200dSdt+0.04S=20   and S(0)=0…

Q: A 1500 gallon tank initially contains 600 gallons of water with 5 lbs of salt dissolved in it. Water…

A: This question is related to differetial equations, we will solve it using given information.

Q: Assume that Laguna Lake has a volume of 480km^3 and that its rate of inflow (from Lake Huron) and…

A:

Q: Initially a tank holds 100 gal of a brine solution containing 4 lb of salt. At t = 0, brine…

A: We will find out the required time.

Q: A 1,000-liter tank initially contains 200 liters of brine containing 100 kg of salt. Brine…

A: Given that, A 1,000-liter tank initially contains 200 liters of brine containing 100 kg of salt.…

Q: Tank A initially holds 100 gallons of brine that contains 150 pounds af salt, and tank B holds 100…

A: Tank A initially holds 100 gallons of brine that contains 150 pounds of salt.Tank B holds 100…

Q: A container that has 5 L of water with 1 kg salt dissolved is to be filled by pure water at a rate…

A: Solve by making differential equation

Q: A tank originally contains 380 liters of brine holding 450 N of dissolved salt. Eight liters/min of…

A: It is given that a tank contain 380 liters of brine and holding 450 N of dissolved salt, the rate of…

Q: A tank contains 2,000 L of brine. Brine containing 5 kg/L of salt flows in at 10 L/min, and the…

A:

Q: There is a large mixing tank that initially holds 120 gallons of brine (water in which salt has been…

A:

Q: A tank contains 80 galloons (gal) of pure water. A brine solution with 2 lb/gal of salt enters at 2…

A: Given that, A tank contains 80 galloons (gal) of pure water. A brine solution with 2 lb/gal of salt…

Q: A 200g-tank holds 100 gallons of fresh water upon first. At t = 0, a 5 gal/min salt solution…

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A:

Q: Worker A is a loader and worker B is an unloader. Worker A can load a truck in 10mins, while worker…

A: The time taken by worker A to load the truck is = 10 min  The time taken by the worker B to unload…

Q: A tank with a capacity of 400 gal originally contains 150 gal of water with 25 lb of salt in…

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Q: A large tank initially contains 50 liters of brine in which there is dissolved 5 grams of salt.…

A:

Q: A tank contains 4000 liters (L) of a solution consisting of 120 kg of salt dissolved in water. Pure…

A: Here, ri = 4, ci = 0, r0 = 5, The differential equation is There is no inflow of salt, thus the…

Q: Suppose you have a 200-gallon tank full of fresh water. A drain is opened that removes 3 gal/sec…

A: Let the concentration of brine =x lb/gal Amount of salt entering in per minute = 2 gal1 min×x lb1…

Q: A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 2 grams…

A: A tank contains 200 liters of fluid with 30 gm salt is dissolved.2 gm of salt per liter is pumped…

Q: At 12:00 p.m. a tank contains 150 g of salt dissolved in 8 L of water. Pure water begins flowing…

A: Since you have asked multiple questions, we will solve the first one for you. If you want any…

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A:

Q: A tank contains 1000 liters (L) of a solution consisting of 170 kg of salt dissolved in water. Pure…

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Q: If 150 g of copper at initial temperature of 50 °C gains 6930 J of heat when it is cooled to 170°C.…

A:

Q: A tank contains 80 gallons of pure water. A brine solution with 2lb/gal of salt enters at 2 gal/min,…

A: Given: r1=2 galsmin., r2=2 galsmin.,  c1=2 lbsgal,, v0=80 gallons, x0=0

Q: A 450 gal tank initially contains 110 gal of brine containing 52 Ib of salt. Brine containing 1lb of…

A:

Q: A tank with a capacity of 400 gal originally contains 100 gal of water with 200 lb of salt in…

A: A tank with a capacity of 400 gal originally contains 100 gal of water with 200 lb of salt in…

Q: A tank contains 200 gallon of salt water with 150 lbs of dissolved salt. Salt water with 5 lbs of…

A:

Q: Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds of salt…

A: We need to find amount after one hour.

Q: If a IV fluid bag is Flowing out of a 1.0 liter bag at the rate of 0.4 cc/min how long will it take…

A: Total volume of fluid flowing out =1.0 litre rate of flowing =0.4 cc/min

Q: A tank contains 5000 liters (L) of a solution consisting of 182 kg of salt dissolved in water. Pure…

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Q: Tank A contains 402 litres of brine holding 123 N of dissolved salt, and tank B contains 402 litres…

A:

Q: A large mixing tank initially contains 500 gallons of water in which 40 pounds of salt have been…

A: Given, A large mixing tank initially contains 500 gallons of water in which 40 pounds of salt have…

Q: A tank contains 1000 liters of brine. Brine containing 0.4 kg/liter of salt flows in at 10…

A: Let st= The amount of salt at time t. The brine flows in at the rate 10 liters/minute and flows out…

Q: A 100-gallon tank contains 5O gallons of water. Brine, containing 2 Ibs of salt per gallon, flows…

A: Ans =38

Q: Assume that Laguna Lake has a volume of 480km^3 and that its rate of inflow (from Lake Huron) and…

A:

Q: There's a tank containing 50 L of a solution into which 10 g of salt is dissolved in. A solution…

A: image is attached

Q: A 200-gal tank is half full of distilled water.At time t = 0, a solution containing 0.5 lb / gal of…

A:

Q: We have a mixing tank that contains 100 gallons of water into which 5 pounds of sugar have been…

A: According to question. Initial amount of water in tank= 100gallons Initial amount of sugar = 5 pound

Q: A 150 mg per L solution of drug is administered intravenously at a rate of 30 mL per hr to a patient…

A: Given that: A 150 mg per L solution of drug is administered intravenously at a rate of 30 mL per hr…

Q: A stream containing 80 grams per liter of a dye is pumped into a mixing tank with 400 liters of…

A: The answer is 32kg

Q: A 100L-capacity tank initially holds 80L of fresh water. A brine solution is poured into the tank at…

A: A brine solution is poured into the tank at the rate of 4 L/hr, while the well-stirred mixture…

Q: In a room containing of air 20,000 m3 of air, 600 m3 of fresh air flows in per minute, and the…

A:

Q: A tank contains 1000 liters (L) of a solution consisting of 195 kg of salt dissolved in water. Pure…

A: Solution is given below:

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.