A tank initially contains 1 gram of blue dye dissolved in 10 liters of water. Pure water will be added to the tank at a certain rate, and the well-mixed solution will be drained from the tank at the same rate. The tank is considered “cleaned" when the dye concentration in the tank is no more than 0.001 grams/liter. (a) If the rate at which the pure water is added ( and the tank is drained) is 2 liters/ minute, how long does it take until the tank is clean? (b) If we want to clean the tank in 5 minutes, how quickly must the pure water be poured in?

Q: A tank originally contains 80 gal of fresh water. Then water containing 1/2 lb of salt per gallon is…

A: To solve this problem, we'll use the concept of differential equations and solve for the amount of…

Q: Two tanks, each holding 100 L of liquid, are interconnected by pipes with liquid flowing from tank A…

A:

Q: A brine solution of salt flows at a constant rate of 4 L/min into a large tank that initially held…

A: Given that,  xin =0.2×4=0.8 kg/minxout=xv×3dxdt=xin-xout            →1     V=qin-qout+Vo…

Q: A brine solution of salt flows at a constant rate of 4 L/min into a large tank that initially held…

A: given,Brine solution of salt flows at a constant rate of the tank initially had  of pure…

Q: There are 200 gal of fresh water in a container (that is, there is no salt in the container…

A:

Q: A five-gallon bucket is full of pure water. Suppose we begin by dumping salt into the bucket at a…

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Q: 1. A tank initially holds 100 gallons of brine solution containing 20 lbs. of salt. At t = 0, fresh…

A: Solution...

Q: A brine solution of salt flows at a constant rate of 4 L/min into a large tank that initially held…

A: Given: In flow=4 L/min, Volume of tank=100L of water, Out flow=3 L/min and the concentration of salt…

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…

Q: If a sample of tomato juice is determined to have a [H3O+][H3O+] concentration of 3.16×10−63.16×10−6…

A:

Q: Consider 2 intercomected tank. Tank A initially contains 180 L of water and log of salt, and tank B…

A: Given Information:Tank A has 180L of water and 10g of salt whereas tank B has 100L of water and 25g…

Q: Calculus Question

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Q: A brine solution of salt flows at a constant rate of 4 L/min into a large tank that initially held…

A: given,brine solution of salt flows at a constant rate of the tank initially had  of pure…

Q: 1. Mr. Pein has an aquarium that has a volume of 2000 mL and contains freshwater fish. One day, Mr.…

A: Notation used: vin = volumetric inflow rate of water mLminvf   = volumetric outflow rate of water…

Q: Sehr put $1,000 into a savings account that earns 4%/a in interest, calculated simply. How much will…

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.