A five-gallon bucket is full of pure water. Suppose we begin by dumping salt into the bucket at a rate of 0.25 pound per minute. Also, we open the spigot so that 0.5 gallon per minute leaves the bucket. (Assume that pure water is added to keep the bucket full.) If the salt water solution is always well mixed, what is the amount of salt in the bucket in the long-run? Show your work and explain thoroughly.

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

A: Solution :-

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

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Q: 4. A large tank contains 100 gal of brine in which initially 50 lbs of salt are dissolved. Brine…

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A: Let's find.

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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)How quickly is the water leaving the barrel over the first two seconds? b)Will the water drain…

A: The solution is given below in the next step:

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: Alice measures a radioactive sample at 1400 counts/minute on a Geiger counter. If the radioactive…

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A: Solve by making differential equation

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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: A tank is initially filled with 1000 gal. of salt solution containing 500 H of salt. Fresh water…

A: Let At the amount of salt at the time t Then the rate of change of the amount of salt dAdt=0lbL.10…

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A: Given :Half life of Palladium-100= 4 days

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A:

Q: In monitoring the blood alcohol content of a person, the bloodstream, which is composed of 5L of…

A: Given: Bloodstream is composed of 5L of water The rate of single inflow, by absorption of fluids…

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A:

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

A:

Q: A tank contains 1,000 gal of brine in which 500 lb of salt are dissolved. Fresh water runs into the…

A: Form the first order differential equation and solve using separation of variables.

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Q: air containing 30% oxygen passes slowly into a 3 gallon flask initially filled with pure oxygen and…

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Q: Tank A contains 499 litres of brine holding 192 N of dissolved salt, and tank B contains 499 litres…

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: In a water bottling process, one-liter bottles are filled through a system that provides filtered…

A:

Q: 1. A tank contains 80 gallons (gal) of pure water. A brine solution with 2 Ib/gal of salt enters at…

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

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A: Let x(t) and y(t) be the mass of salt in tanks T1 and T2 respectively. Fresh water follows into tank…

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

A:

Q: A tank contains 100 L of water. A salt solution containing 2 kg of salt per liter flow in at the…

A:

Q: Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional to…

A:

Q: A tank contains 1,000 gallons of brine in which 500 lbs of salt are dissolved. Fresh water runs into…

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Q: A 500-gal tank initially contains 100 gal of brine containing 50 lb of salt. Brine containing 2 Ib…

A: Given:   Equation data is given

Q: A 100 gallon tank is filled with brine containing 60 pounds of dissolved salt. Water runs into the…

A: Form the differential equation of first order and solve to get the answer.

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 (L) of a solution consisting of 100 kg of salt dissolved in water. Pure…

A: Consider, is the Rate of pure water is pumped into the tank is equal to 5 L/s. Formula used,

Q: In monitoring the blood alcohol content of a person, the bloodstream, which is composed of 5L of…

A: To determine the equation to determine the amount of alcohol in the body at a time.

Q: A tank contains 400L of fresh water. By mistake, 100kg of salt is poured into the tank instead 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 tank contains 50 gallons of a solution composed of 90% water and 10% alcohol. A second solution…

A:

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

A:

Q: In a chemical reaction, substance A decomposes at a rate proportional to the amount of A present. It…

A: This decomposition reaction of first order, because rate is directly proportional to the…

Q: A tank contains 2000 liters (L) of a solution consisting of 182 kg of salt dissolved in water. Pure…

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:

Q: Answer correctly, comprehensively, and neatly. Thank you. A vertical liquid storage tank shaped like…

A: A vertical liquid storage tank shaped like a cone has a radius of 8 m at the top and 22 m high.…

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.