3. Initially, 120 gal of a brine solution containing 3/8 lb of salt per gallon is held by a tank. At the starting time, another brine solution containing 1 lb of salt per gallon is poured into the tank at the rate of 3 gal/min, while the well-stirred mixture leaves the tank at the rate of 8 gal/min. (a) Find the amount of salt in the tank at any time t. (b) Find the amount of salt in the tank when the tank contains exactly 60 gal of brine.

Q: Suppose a 1000L tank contains 400 L of fresh water at time t = 0. At that time, a salt water…

A: The solution of above question is written below.

Q: Suppose a 1000 L tank contains 100 L of fresh water at time t = 0. At that time, a salt water…

A: The rate of change of a substance in a container is determined by the concentrations as well as the…

Q: A tank contains initially 400 liters of brine holding 100 kg of salt in solution. Water containing…

A:

Q: 4. A large tank contains 100 gal of brine in which initially 50 lbs of salt are dissolved. Brine…

A:

Q: A tank contains 300 gal of water and 100 gal of pollutants. Fresh water is pumped into the tank at…

A: Fresh water is pumped into the tank at the rate of 2 gal/min, and the well stirred mixtureleaves at…

Q: 2. A tank initially contains 1000 gallons of fresh water. Brine containing 3 lbs/gallon of salt…

A: The time taken for the quantity of salt to reach 100 lbs is 16.80555 minutes

Q: Tank A contains 80 gallons of water in which 20 pounds of salt has been dissolved. Tank B contains…

A: Given, tank A contains 80 gallons of water in which 20 pounds of salt has been dissolved. Tank B…

Q: Suppose that a quantity y = y(t) increases at a rate that is proportional to the square of the…

A: Given that a quantity y=y(t) increases at a rate that is proportional to the square of the amount…

Q: The population of a bacteria culture grows at a rate of P = 100(2)n, where P is the population and n…

A:

Q: If a quantity grows/decays at a rate proportional to its size, its growth can be expressed as dQ/dt…

A:

Q: Tank # 1 initially holds 50 gals of brine with a concentration of 1 lb/gal, while Tank # 2 initially…

A: The working principle here will be Rate of change of salt=Inflow of salt-outflow of salt. The amount…

Q: Tank A initially holds 100 gallons of brine that contains 150 pounds af salt, and tank B holds 100…

A: Tank A initially holds 100 gallons of brine that contains 150 pounds of salt.Tank B holds 100…

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: When air expands adiabatically (without gaining or losing heat), its pressure P C where C is a…

A:

Q: Consider three connected lakes, A, B, and C, where lake B has a volume of 2650 km, and water flows…

A:

Q: The number of customers in a store is modeled by the function P that satisfies the logistical…

A:

Q: Find the Bolution to Hhe initial value problem - Please Write the folution with the computer.

A: Solution of Linear Differential Equation with Constant Coefficients: The general form of linear…

Q: the radiator in a car is filled with a solution of 60% antifreeze and 40% water. the manufacturer of…

A: In a 3.6 L radiator, the quantity of antifreeze is given by: In a 3.6 L radiator, the quantity of…

Q: A tank contains 400 liters of brine. Twelve (12) liters of brine, each containing 2.5 N of dissolved…

A: If volume of any liquid is inside the container and some amount of liquid is entering and leaving…

Q: A large tank initially contains 50 liters of brine in which there is dissolved 5 grams of salt.…

A:

Q: A tank initially contains 400 gal of fresh water. At time t= 0, a brine solution with a…

A: As per Bartleby answering guidelines if a questions has multiple subparts then an expert is expected…

Q: Lake Taal has a volume of 458 cubic km, and its rate of inflow and outflov are both 175 cubic…

A:

Q: Solve the initial value problem dz/dt=cost−2sint, z(0)=5.

A:

Q: 3) For an ideal gas, the pressure is related to temperature and volume by the formula 8.31T V . If…

A:

Q: Michael just started a new job as an assembly line worker. The job requires him to assemble 300…

A: given that k=0.15                      y'=0.15(300-y) also                     y'=k(M-y), y(0)=y0…

Q: Based on historical data for population growth rates and the initial number of eagles present in a…

A: Topic-basic maths

Q: A bacteria culture starts with 960 bacteria and grows at a rate proportional to its size. After 4…

A: The exponential growth formula is given by: P(t)=P0 ekt...(1) where P0 is initial population, k is a…

Q: When air expands adiabatically (without gaining or losingheat), its pressure P and volume V are…

A: Pressure and Volume are related by equation At a instant

Q: 1. A tank contains 80 gallons (gal) of pure water. A brine solution with 2 Ib/gal of salt enters at…

A: Given that, a tank contains 80 gallons (gal) of pure water. A brine solution with 2 lb/gal of salt…

Q: 2) A tank, which has a capacity of 100 L, is initially half full of a solution that contains 50g of…

A:

Q: Assume that the dynamics of caffeine absorption are given by Ct+1 = 0.87Ct , where t is time in…

A: NOTE: Refresh your page if you can't see any equations. . the given equation is  compare this…

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

A: Given:-amount of brine in the tank=1000 gallonssalt are dissolved in brine=500 lbsrate of fresh…

Q: Tank A contains 402 litres of brine holding 123 N of dissolved salt, and tank B contains 402 litres…

A:

Q: A 500-gal tank initially contains 100 gal of brine containing 50 lb of salt. Brine containing 2 Ib…

A: Given:   Equation data is given

Q: A large mixing tank initially contains 500 gallons of water in which 40 pounds of salt have been…

A: Given, A large mixing tank initially contains 500 gallons of water in which 40 pounds of salt have…

Q: A tank contains 1000 liters of brine. Brine containing 0.4 kg/liter of salt flows in at 10…

A: Let st= The amount of salt at time t. The brine flows in at the rate 10 liters/minute and flows out…

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: 4) For an ideal gas, the pressure is related to temperature and volume by the formula 8.317 P = If…

A:

Q: A cup of coffee cools at rate proportional to the difference between the constant room temperature…

A:

Q: Two tanks are connected as in Figure Q2b. Tank 1 initially contains 20 kilograms of salt dissolved…

A: Here we will use differential equation to solve this problem

Q: A tank contains 50 gallons of a solution composed of 90% water and 10% alcohol. A second solution…

A:

Q: A cylindrical tank holds 22 liters of water. At time t = 0, two taps are opened simultaneously, the…

A: Please check step 2 for the solution.

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: 4. A tank contains 400 liters of brine. 12 liters of brine each containing 2.5 N of dissolved salt,…

A:

Q: The amount of decay of a certain radioactive element is given by -0.04t Yoe' where t equals time in…

A: The amount of decay of the radioactive element is given as follows. y=y0e-0.04t where t is the time…

Q: Tank A contains 407 litres of brine holding 181 N of dissolved salt, and tank B contains 407 litres…

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…

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.