A 2000 L tank initially contains 40 kg of salt dissolved in 1000 L of water. A brine solution containing 0.02 kg/L of salt flows into the tank at a rate of 50 L/min. The solution is kept thoroughly mixed, and the mixture flows out at a rate of 25 L/min. (b) Find the time of overflow.

Q: A container initially contains 15 L of water in which there is 30 g of salt dissolved. A solution…

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Q: A tank contains 52 gallons of a solution composed of 85% water and 15% alcohol. A second solution…

A: Please see the answer below

Q: a tank initialy holds 80 gallon of a brine solution containing 1/8 lb of salt per gallon. at t=0,…

A:

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 freshly brewed cup of coffee has temperature 95°C in a  20°C room. When its temperature is 70°C,…

A: Given that, Initial temperature of coffee is T0=95°C, surrounding temperature is Ts=20°C. Also,…

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: A tank contains 100 liters of brine, with 50 kg total dissolved salt. Saltwater, with a…

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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: We will find out the required time.

Q: A sewage disposal plant has a big concrete holding tank of 100,000-gal capacity. It is % full of…

A: Let M(t) be the mass of the organic material in the tank at time t and Mt=CtVt, where C(t) and V(t)…

Q: a tank initialy holds 80 gal. of a brine solution containing 1/8 lb of salt per gallon. at t=0,…

A:

Q: A tank contains 57 gallons of a solution composed of 85% water and 15% alcohol. A second solution…

A:

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

A:

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

A: Schematic diagram of the given situation:…

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

A: Given: The amount of water at 3:56 PM is 10452 L and amount of water at 4:12 PM on same day  is 8092…

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

A: The amount of salt remaining after 5 minutes is 45.24 lb. And the calculation is uploaded below

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 contains 48 gallons of a solution composed of 85% water and 15% alcohol. A second solution…

A:

Q: A tank has 72 gallons of water. Brine solution with 2lbs of salt per gallon of solution enters at a…

A: here we can use differential equation to solve this question.

Q: A tank contains 45 gallons of a solution composed of 85% water and 15% alcohol. A second solution…

A: image is attached

Q: The cost of installing insulation in a particular two-bedroom home is $2400. Present monthly heating…

A: Given: The cost of installing insulation in a particular two-bedroom home is $2400. Present monthly…

Q: A tank contains 60 gallons of a solution composed of 85% water and 15% alcohol. A second solution…

A:

Q: A certain bacteria culture grows at a rate proportional to its size. If 10,000 bacteria grow at the…

A: Given: A certain bacteria culture grows at a rate proportional to its size.

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

A:

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

A:

Q: A 100 L mixing tank initially contains 50 L of brine solution with 16 g/L concentration. Brine…

A: Let V be the volume of the tank. Thus, Vt=50+4+2-5t       =50tL where, t is the time in minutes.

Q: A tank contains 200 liters of fresh water. Brine containing 2 kilograms per liter of salt enters the…

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

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

A:

Q: A tank contains 60 gallons of a solution composed of 85% water and 15% alcohol. A second solution…

A: A tank contains total solution 60 gallons Compose of 85% water = 51 gallons And 15% alcohol = 9…

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: A tank initially contains 100 gallons of brine whose salt concentration is 3 lb/gal. Freshwater is…

A: We will make a differential equation for amount of salt and then will solve it to get amount of salt…

Q: A tank contains 60 gallons of a solution composed of 85% water and 15% alcohol. A second solution…

A:

Q: A tank contains 50 gallons of a solution composed of 85% water and 15% alcohol. A second solution…

A: Consider the given information. Let y is the number of gallons of alcohol in the tank with rate of…

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 300 gallon tank initially contains 90 gallons of brine containing 400 Ibs. of salt. Brine…

A: Given the tank contains 90 gallons of brine containing 400 lbs of salt.  The above figure shows the…

Q: A tank contains 60 gallons of a solution composed of 85% water and 15% alcohol. A second solution…

A: Given ,  A tank contains 60 gallons of a solution composed of 85% water and 15% alcohol. A second…

Q: A tank contains 400L of fresh water. By mistake, 100kg of salt is poured into the tank instead of…

A:

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: An apple pie with an initial temperature of 170 -C is removed from the oven and left to cool in a…

A:

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

A:

Q: The number of germs in a certain culture increases at a rate proportional to the number present. If…

A:

Q: A tank initially contains 40 gal of sugar water having a concentration of 3 lb of sugar for each…

A: A tank initially contains 40 gal of sugar water having a concentration of 3 lb of sugar for each…

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 54 gallons of a solution composed of 85% water and 15% alcohol. A second solution…

A: Consider the given information. Let y is the number of gallons of alcohol in the tank with rate of…

Q: A 60-gal tank initially contains 10 gal of fresh water. At t = 0, a brine solution containing 1 Ib…

A:

Q: The population of a certain bacteria culture was 49,271 after 15 hours had elapsed. After another 22…

A: Given that the population of a certain bacteria culture was 49,271 after 15 hours had elapsed.After…

Q: A tank initially holds 80 gal of a brine solution containing of salt per gallon. At t=0, another…

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.