3a. A tank contains 100 liters of syrup with sugar concentration 20 g/liter. Syrup is pumped out of the tank at rate 3 liter/min, and syrup with sugar concentration 10 g/liter is pumped in at a rate of 2 liter/min. Find the the amount of sugar (in grams) in the tank at time t minutes.

Q: A sewage disposal plant has a big concrete holding tank of 100,000-gal capacity. It is 3⁄4 full of…

A: Let V(t) be the volume of liquid in the tank at time t. Let Vo be the initial volume of liquid in…

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

A:

Q: . A tank contains 1,500 liters of water and 20 kg. of dissolved salt. Fresh water is entering the…

A: Using mixing problem formula we find the general amount of salt at any time t minutes and then…

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 131 L mixing tank initially contains 65 L of brine solution with a concentration of 7 g/L. Brine…

A:

Q: A bucket that has a mass of 10 kg when filled with sand needs to be lifted to the top of a 30 meter…

A: Mass of rope = 0.1kg/mMass of rope on bucket = 0.1kg/m*1m = .1kg…

Q: A tank contains 60L of water contaminated with Mercury at a concentration of 0.03 mg/L. Clean water…

A: Here we need to find and then solve the differential equation for the concentration of mercury using…

Q: A 20 m tank is full of brine with 40 kg of dissolved salt. Pure water enters the tank at a rate of…

A: In this question, we find the amount of solt when the takl half full. given that  Initial amount of…

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 80 gal of a brine solution containing - Ib of salt per gallon. At t = 0,…

A: Since you posted a question with multiple parts, we will solve the first three subparts for you. To…

Q: A tank originally contains 380 liters of brine holding 450 N of dissolved salt. Eight liters/min of…

A: It is given that a tank contain 380 liters of brine and holding 450 N of dissolved salt, the rate of…

Q: A tank initially holds 80 of brine solution containing 1/8 b of salt per gallon. At t-0. another…

A:

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

A:

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: 2. A tank initially holds 70 gal of a brine solution containing 2 pounds of salt per gallon. Att =…

A:

Q: A 2000 L tank initially contains 40 kg of salt dissolved in 1000 L of water. A brine solution…

A: Given capacity of tank =2000 L initial amount of water =1000 L rate of in flow of salt =50 L/min…

Q: 5. A tank originally contains 100 gallons of fresh water. Then water containing 2 lb of salt per 2…

A: We will find out the required value.

Q: A tank contains 1,500 liters of water and 20 kg. of dissolved salt. Fresh water is entering the tank…

A:

Q: A large tank initially contains 100 liters of brine in which there is dissolved 5 grams of salt.…

A:

Q: A bucket that has a mass of 15 kg when filled with sand needs to be lifted to the top of a 25 meter…

A:

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: 1) A tank whose volume is 50L initially contains 20L of water. A solution containing 10g/L of salt…

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 large rank contains 100 gal of brine in which 10 ib of salt is dissolved, Brine containing 0.2 Ib…

A:

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

A: "Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: A tank with capacity of Ig000 liters contains 800 liters of water in which are dissolved 23400 arams…

A:

Q: A tank initially holds 100 gal of brine solution containing 1 lb of salt. At t=0 another brine…

A:

Q: A bucket that has a mass of 10 kg when filled with sand needs to be lifted to the top of a 20 meter…

A: Given: Mass of bucket = 10kg Mass of the rope = 0.1kg/m Height of the Building = 20 meter

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

A: Since you posted a question with multiple parts, we will solve the first three subparts for you. To…

Q: A bucket that has a mass of 10 kg when filled with sand needs to be lifted to the top of a 30 meter…

A: Given:    Mass of the bucket =10 kg   Mass of the rope =0.2 kg/m  Height of the building =30 m…

Q: A bucket that has a mass of 25 kg when filled with sand needs to be lifted to the top of a 20 meter…

A:

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 bucket that has a mass of 15 kg when filled with sand needs to be lifted to the top of a 20 meter…

A: We are given that the mass of the bucket is 15 kg, the height of the building is 20 meter, the…

Q: A bucket that has a mass of 25 kg when filled with sand needs to be lifted to the top of a 25 meter…

A: If an object moves in a straight line by a continuous force, F(x), the work done by the force from…

Q: A tank initially contains 50 gal of sugar water having a concentration of 2 lb of sugar for each gal…

A: Given:   A tank initially contains 50 gal of sugar water having a concentration of 2 lb of sugar for…

Q: 3. A tank contains 1,500 liters of water and 20 kg. of dissolved salt. Fresh water is entering the…

A:

Q: Brine containing 3 lbs per gal of salt enters a large tank at the rate of 2 gal/min and the mixture…

A: We are given that, a brine containing 3 lbs per gal of salt enters a large tank at the rate of 2…

Q: Brine containing 1.5 lb/gal of salt enters a tank at the rate of 2 gal/min and the mixture…

A:

Q: 4. A tank contains 150 gal of brine made by dissolving 60 pounds of salt in water. Salt water…

A: Given:       Initially there are 150 gal in the tank.   There are 60 pounds of salt in water.   The…

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 bucket that has a mass of 10 kg when filled with sand needs to be lifted to the top of a 10 meter…

A:

Q: A 20 m³ tank is full of brine with 40 kg of dissolved salt. Pure water enters the tank at a rate of…

A: The  given problem we can be formulated as  a differential equation and solve.

Q: A 30 m³ tank is full of brine with 40 kg of dissolved salt. Pure water enters the tank at a rate of…

A: Volume of the tank is 30 m3 The tank is full of brine with 40 kg of dissolved salt. Pure water…

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

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

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.