) A tank contains 1700 L of pure water. Solution that contains 0.04 kg of sugar per liter enters the tank at the rate 6 L/min, and is thoroughly mixed into it. The new solution drains out of the tank at the same rate. (a) How much sugar is in the tank at the begining? y(0) = 0 (kg) (b) Find the amount of sugar after t minutes. y(t) = (kg) (c) As t becomes large, what value is y(1) approaching ? In other words, calculate the following limit. lim y(t) = (kg)

Q: A tank contains 90 liters of fluid in which 40 grams of salt is dissolved. Pure water is then pumped…

A: Given that a tank contains 90 liters of fluid which has 40 grams of salt. If pure water is added to…

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

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

Q: A tank initially contains 100 gal of pure water. Starting at time t = 0, a brine containing 6lb of…

A: Given: Let us consider a tank holds 100 gallons of pure water at first. A brine containing 6lb of…

Q: 6) A chemical flow into a storage tank at a rate of 180 + 3t liters per minute, where 0st< 60. Find…

A: Given: Rate of flow of chemical in tank in liters per min: dVdt=180+3t 0≤t≤60

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 radioactive material is known to decay at the rate proportional to the amount present. If…

A: Given A radioactive material is known to decay at the rate proportional to the amount present.…

Q: A tank contains 120 gal of brine made by dissolving 85 Ibs of salt in water. Pure water runs into…

A:

Q: A tank contains 180 liters of fluid in which 10 grams of salt is dissolved. Brine containing 1 gram…

A: Let the amount of salt in grams at time t be A(t)We have given the initial amount of salt in grams…

Q: . A tank contains 100 gal of brine made by dissolving 80 pounds of salt in water. Pure water runs…

A:

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 100 gal of brine made by dissolving 80 lb of salt in water. Pure water runs into the…

A: Many real-life problems can be modeled using differential equations. This is one of the significant…

Q: (b) A tank contains 50 gal of water in which initially 6 kg of salt are dissolved. Water containing…

A:

Q: Initially a tank contains 10 lb of salt dissolved in 100 gal of water. Assume that brine containing…

A: Given that Initially a tank contains 10 lb of salt dissolved in 100 gal of water. Let x(t) be the…

Q: A tank initially holds 1 cubic meter of a brine solution containing 20 kg of salt. Att= 0, fresh…

A:

Q: A tank initially holds 410 liters of brine solution containing 7 kg of salt. At t=0, another brine…

A:

Q: The tank shown in the figure was filled with 100 liters of substance A in a concentration of 10g /…

A: Given: The tank having 100 liters of substance A in a concentration of 10g / L. Material A is fed…

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

A: Solution...

Q: A tank initially holds 50 gal of a brine solution containing 2 Ib of salt. At t = 0 another brine…

A: Given data:- Volume of brine solution, Vo=50 gal Containing salt, a=2 At t=0 any Brine solution…

Q: 1. A tank contains 1,000 L of water and 20 kg of dissolved salt. Fresh water is entering the tank at…

A: Here we are given that A tank contains 100 L of water and 20 kg of dissolved salt.Fresh water is…

Q: A brine solution of salt flows at a constant rate of 6 L/min into a large tank that initially held…

A: given, brine solution of salt flows at a constant rate of 6 Lmin the tank initially had 100 L of…

Q: A tank contains 5001 of a solution consisting of 30 kg of salt dissolved in water. Pure water umped…

A:

Q: A brine solution of salt flows at a constant rate of 5 L/min into a large tank that initially held…

A: Given that, A brine solution of salt flows at constant rate of 5L/min, initial volume is 100L, and…

Q: 3 The altitude of a triangle is increasing at a rate of 8 cm/s while its area is increasing at the…

A:

Q: 1. A brine solution of salt flows at a constant rate of 8 L/min into a large tank that initially…

A: Answer is mentioned below As per the guidelines we are suppose to answer only one question. Please…

Q: a. A tank holds 1000 liters of water, in which 15 kg of salt is dissolved. Pure water enters the…

A:

Q: A tank initially holds 1 cubic meter of a brine solution containing 20 kg of salt. Att = 0, fresh…

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: 3. A large tank contains 1 0001 of pure water. A brine solution containing 0.1 kg of salt per litre…

A:

Q: A solution of salt flows at a constant rate of 6 L/min into a large tank that initially held 50 L of…

A: We have, dxtdt=0.3 kg/min - 0.12 xt kg/min⇒dxtdt+ 0.12xt=0.3        ...i Calculating for P(t) and…

Q: 4. A tank initially holds 80 gal of a brine solution containing 1/8 lb of salt per gallon. At t = 0,…

A:

Q: 10. A ladder 15 feet long leans against a vertical wall. Suppose that when the bottom of the ladder…

A: In the question we have to find the rate of rising of top end.

Q: A brine solution of salt flows at a constant rate of 5 L/min into a large tank that initially held…

A: A tank contains 100L solution in which 0.3 kg of salt was dissolved.  Let, x(t) be the mass of the…

Q: A tank contains 120 gal of brine made by dissolving 85 lbs of salt in water. Pure water runs into…

A:

Q: 1. A tank contains 45 liters of a chemical solution prepared by dissolving 80 g of a soluble…

A: Initial condition t= 0min of tank45 liters = Amount of solution in tank, v080g        = Amount of…

Q: A brine solution of salt flows at a constant rate of 7​L/min into a large tank that initially held…

A:

Q: A brine solution of salt flows at a constant rate of 8 L/min into a large tank that initially held…

A:

Q: A brine solution of salt flows at a constant rate of 8 L/min into a large tank that initially held…

A:

Q: Consider a tank used in hydrodynamic experiments. After one experiment the tank contains 200 L of a…

A: y=amount of salt at time t  ............the water is fresh

Q: A brine solution of salt flows at a constant rate of 8 L/min into a large tank that initially held…

A:

Q: A tank contains 240 liters of fluid in which 50 grams of salt is dissolved. Pure water is then…

A: Given :  The quantity of the water in the tank is 240 liters in which 50 grams of salt is dissolved.…

Q: 2. A tank contains 120 gal of brine made by dissolving 85 Ibs of salt in water. Pure water runs into…

A:

Q: A brine solution of salt flows at a constant rate of 7 L/min into a large tank that initially held…

A: Let x(t) be the mass of salt in the tank at the time t.xi(t) be the amount of solution coming in to…

Q: A tank contains 150 liters of fluid in which 20 grams of salt is dissolved. Pure water is then…

A:

Q: A tank contains 70 gallons of pure water. A brine solution with 2 lbs / gal of salt enters at 2.25…

A: We convert this problem into a differential equation then solve the differentials equation.

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A: Given: dSdt=4  cm/secdVdt|r=4 cm=?

Q: A tank is initially filled to its capacity with 250 liters of pure water. At t=0, the brine…

A: Amount of water in the tank initially is given as: 250 litres Rate of brine pumped into the tank is…

Q: Tank B, a 30-litre tank, initially contains 6 grams of salt in 15 litres of water. At t = 0,…

A:

Q: The population of bacteria in a culture grows at a rate proportional to the number of bacteria…

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.