6. A 50L tank initially contains 5L of brine solution where 3kg of salt have been dissolved. At t = 0, a brine solution of 1kg of salt per L is poured at a rate of 3L / min and the perfectly stirred mixture is poured out of the tank at a rate of 1.5L / min. How much salt is in the tank when it contains 10L of brine solution?

Q: A mold grows at a rate that is proportional to the amount present. Initially there is 6 oz of this…

A:

Q: 2. A tank contains 2,000 liters of brine. Brine containing 5N/liter of salt flows in at 10…

A: We will find out the initial concentration of the salt for the given problem.

Q: f. A truck travelling southwards at 40 kph and a car traveling eastward at a rate of 60 kph are…

A:

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

A: Solution :-

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

A:

Q: Consider a reservoir with a volume of 8 billion cubic feet (ft^3) and an initial pollutant…

A:

Q: A 600 litre tank initially contains 200 litres of water in which 10 grams of salt are dissolved.…

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

Q: Water is pumped from a tank at constant rate, and no more water enters the tank. If the tank…

A: To solve the following problem and find the amount of water left at 6:10pm.

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: If 10 pounds of salts is dissolved in a large tank in partially filled with 100 gallons of fluid.…

A: Given :   10 pounds of salts is dissolved in a large tank in partially filled with 100 gallons of…

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 50 – gallon tank of pure water has a brine mixture with concentration of 2 pounds per gallon…

A: Form the first order differential equation then find its solution to get amount of salt at any 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 400 gal tank initially contains 100 gal of brine containing 25 lb of salt. Brine containing 2 lb…

A: A real-life scenario can be described mathematically through a differential equation. By solving the…

Q: A tank contains 400 liters of brine. Twelve (12) liters of brine, each containing 2.50 N of…

A: Given: 400 litres of brine are kept in a tank. The tank receives 12 litres of brine each minute,…

Q: A 100-gallon tank contains 50 gallons of water. Brine, containing 2 lbs of salt per gallon, flows…

A: Given that, A 100-gallon tank contains 50 gallons of water. Brine, containing 2 lbs of salt per…

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 tank contains 10m^3 of free water, brine having a concentration of 15kgsalt/m^3 is sent into the…

A:

Q: Tank A contains 274 litres of brine holding 123 N of dissolved salt, and tank B contains 274 litres…

A:

Q: A tank contains 400 liters of brine. Twelve (12) liters of brine, each containing 2.5 N of dissolved…

A: If volume of any liquid is inside the container and some amount of liquid is entering and leaving…

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

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 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: A 400-gal tank initially contains 100 gal of brine containing 50 lb of salt. Brine containing 1 lb…

A:

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

A: The rate of change of a quantity with respect to time is the differential of that quantity. In a…

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 150 gal of water with 25 lb of salt in…

A:

Q: A mold grows at a rate that is proportional to the amount present. Initially there is 6oz of this…

A: The amount of mold at time 0 is m0. The amount of mold present after t hours is m. The rate of…

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 mold grows at a rate that is proportional to the amount present. Initially, there is 5 oz of this…

A:

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

A:

Q: A tank initially contains 100 L of a well-mixed water-and-salt solution, with salt concentration of…

A: As the solution well mixed water and solution solution and flowing out with the constant rate of 2 L…

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

A:

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: 2.21: A tank that can hold 500 gal. originally contains 200 gal. of water with 100 lbs. of salt in…

A: Originally tank can hold water =500 gal. But the water in the tank =200 gal. Salt in the solution of…

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

A: Ans =38

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

A: Question is solved.

Q: A tank initially contains 50 gal. of fresh water. Brine (water in which a certain number of pounds…

A:

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: A 50L tank initially contains 5L of brine solution where 3kg of salt have been dissolved. At t = 0,…

A: According to the given information,

Q: A solution with 35% ammonia is added at a rate of 5 liters per minute to a vat that initially…

A: Given: A solution with 35% ammonia is added at a rate of 5 liters per minute to a vat that initially…

Q: A tank with a capacity of 25 L originally contains 15 L of brine with a concentration of 5 g/L of…

A:

Q: A 50-gallon tank initially contains 10 gallons of fresh water. At t= 0, a brine solution containing…

A: We will find out the required time.

Q: Consider that sugar dissolves in water at a rate proportional to the amount still un-dissolved.…

A: 50kgs of sugar is present and at 5-hour mark there's only 20kg of sugar is left.

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.