A tank contains 100 gal of brine made by dissolving 80 lb of salt in water. Pure water runs into the tank at the rate 4 gal/min and the mixture, kept uniform by stirring, runs out at the same rate. The outflow runs into a second tank which contains 100 gal of pure water ini- tially and the mixture, kept uniform by stirring, runs out at the same rate. Find the amount of salt in the second tank after 1 hr. a) 27.4lb b) 40.4 lb o 17 4 Ib

Q: An open tank with a 200L capacity is half-filled with pure water. A salt solution with a…

A: Let’s set up a differential equation. We are given r1 = 15L/h, r2 = 10L/h, c1 = 10g/L, V(0) = 100L…

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 1500 gallons tank initially contains 600 gallons of water with 5 Ibs of salt dissolved in it.…

A: Please ensure that the concentration of entering water is 2t lbs/gal. ( It is not clear from the…

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

A:

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: 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: A tank initially contains 100 gal. gf salt solution, where 50 Ibs. of salt is added. Salt solution…

A:

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 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: A van is 5 km due north of a pus at 2:00 PM. if the van is traveling northward at the rate of 60 kph…

A: The rate at which the distance between bus and van is changing is solved below

Q: • A tank contains 968 L of brine with 15kg of dissolved salt. Pure water enters the tank at a rate…

A: Solution : We have given that a tank contains 968 L of brine with 15kg of dissolved salt. Pure…

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

A:

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: Intially, 32 grams of salt was dissolved in a containing 8-liters of water. Asult water solution…

A:

Q: There is a large mixing tank that initially holds 120 gallons of brine (water in which salt has been…

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 100 gallon tank is filled with brine containing 60 pounds of dissolved salt. Water runs into the…

A: As this is a multiple question according to the Bartleby Answering rule, only first question is to…

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

A:

Q: A container contains 80 liters of pure water. A brine solution with 2 kg/L of salt enter at 2 L/min,…

A:

Q: A tank contains 1,000 gal of brine in which 500 lb of salt are dissolved. Fresh water runs into the…

A: Form the first order differential equation and solve using separation of variables.

Q: A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 2 grams…

A: A tank contains 200 liters of fluid with 30 gm salt is dissolved.2 gm of salt per liter is pumped…

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: A tank contains 40 L of solution containing 2g of substance per liter. Salt water containing 3g of…

A: Initially there is 40*2 = 80 grams Let Q be the amount of substance in the tank and dQ/dt be the…

Q: A tank contains 80 gallons of pure water. A brine solution with 2lb/gal of salt enters at 2 gal/min,…

A: Given: r1=2 galsmin., r2=2 galsmin.,  c1=2 lbsgal,, v0=80 gallons, x0=0

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

A:

Q: gallon is poured into the tank at a rate of 2 gal/min, while the well-stirred mixture leaves the…

A:

Q: In a water bottling process, one-liter bottles are filled through a system that provides filtered…

A:

Q: continuous IV is infusing at 40 mL/h.  How many milliliters will infuse in 30 minutes?

A: 1 hour is equal to 60 minutes.

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

A:

Q: A spherical drop of liquid evaporates at a rate proportional to tis surface area. If a given drop…

A: Given: The drop evaporates to 18 of its volume in 5 minutes

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

A:

Q: vulcanizing shop has a trapezoidal drum that is 5 meters long, 1.5 meter wide at the top, 1 meter…

A: Solution of the problem as follows

Q: A tank originally contains 385 litres of brine holding 470 N of dissolved salt. Eight litres/min of…

A: We will find out the required solution.

Q: A tank contains 400 gallons of fluid in which 50 lb. of salt is dissolved. Brine containing 2 Ib/gal…

A: Given that : A tank contains 400 gallons of fluid in which 50 lb of salt is dissolved.

Q: A worker on a scaffolding 85 feet above the ground needs to lift a 115 pound bucket of cement from…

A:

Q: · A tank contains 968 L of brine with 15kg of dissolved salt. Pure water enters the tank at a rate…

A:

Q: A vessel with 500 gallons of beer contains 4% alcohol (by volume). Beer with 7% alcohol is pumped…

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: A stream containing 80 grams per liter of a dye is pumped into a mixing tank with 400 liters of…

A: The answer is 32kg

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

A:

Q: A 131 L mixing tank initially contains 58 L of brine solution with 310 g of dissolved salt. Brine…

A:

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

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.