A tank contains 200 gallons of liquid. Five gallons of brine per minute flow into the tank, and each gallon of brine contains 2 pounds of salt. Five gallons of brine flow out of the tank per minute. Assume that the tank is kept well stirred.
A. Find a differential equation for the number of pounds of salt in the tank. Assuming the tank intially contains 50 pounds of salt, solve this differential equation.
B. How much salt is in the tank after one hour?
C. At what time will there be 399 lbs of salt in the tank?
A tank contains 200 gallons of liquid. Five gallons of brine per minute flow into the...
please solve all three questions, will upvote thank you 1) A tank contains 200 gallons of water in which 50 pounds of salt are dissolved. A brine solution containing 4 pounds of salt per gallon is pumped into the tank at the rate of 6 gallons per minute. The mixture is stirred well and is pumped out of the tank at the same rate. Let A(t) represent the amount of salt in the tank at time t a) Write down...
A tank contains 150 gallons of brine whose salt concentration is 2 pounds per gallon. Three gallons of brine whose salt concentration is 4 pounds per gallon flow into the tank each minute. At the same time 3 gallons of the mixture flows out each minute. If the mixture is kept uniform by constant stirring, find the salt content of the brine as a function of the time t. Approximately how long will it take until there are 240 pounds...
h A tank initially has 200 gallons of a solution that contains 25 lb. of dissolved salt. brine solution with a concentration of 21b of salt/gallon is admitted into the tank at a rate of 4 gallons per minute. The well-stirred solution is drained at the same rate. How long will it take for the tank to have 100 lb. of dissolved salt? Round your answer to the nearest minute.
1) Given a tank initially contains 200 gallons of brine (salt mixed with water) in which 150 lbs of salt is dissolved. A salt solution consisting of 0.5×(1 + e^(-0.02t)) lb. of salt per gallon (where t is time in unit of minute) is flowing into the tank at a rate of 10 gal./min and the mixed solution is drained from tank at the same rate. Find the amount of the salt in the tank after 1 hour. (10 points)...
A 120-gallon tank initially contains 90 pounds of salt dissolved in 90 gallons of water. Brine containing 2 1b/gal of salt flows into the tank at the rate of 4 cal/min, and the well-stirred mixture flows out of the tank at the rate of 3 gal/min. How much salt does the tank contain when it is full? (At 30 minutes, there is approximately 202 pounds of salt present in the tank.)
2. A tank contains 100 gallons of pure water. Beginning at t O, a salt water solution containing 0.2 pounds of salt per gallon is pumped into the tank at a rate of 3 gallons per minute. At the same time, a drain is opened at the bottom of the tank which allows the mixture to leave the tank at a rate 3 gallons per minute. Assume the solution is kept perfectly mixed. (a) What will be concentration of salt...
2. A tank contains a 100 gallons of pure water. Brine containing pound salt per gallon enters the tank at thratof 2 Let x(t) represent the amount of salt in the tank after t min. and the well-mixed solution flows out at the rate of 4ツ· a. Find the differential equation which relates( and , the initial condition and the domain of x() dr b. Find the particular solution of this equation. c. What is the most amount of salt...
Can you show all the steps please? A salt tank contains 50 lbs of salt dissolved in a 300 gallon tank. A brine mixture with a concentration of 2 lbs of salt per gallon is pumped into the tank at a rate of 3 gallons per minute. The mixture is distributed uniformly in the tank and the mixture is drained at the same rate of 3 gallons per minute input rate of brine 3 gal/min constant 300 gal A Set...
Question 2 (32 points) A large tank is filled to capacity with 200 gallons of pure water. Brine containing 5 pounds of salt per gallon is pumped into the tank at a rate of 18 gallons per minute. The well-mixed solution is pumped out at the same rate. Find the amount of salt in pounds after 10 minutes. (round to the nearest tenth of a pound) Your Answer: Answer
2. A tank initially contains 100 gallons of salt solution in which 20 pounds of salt is dissolved. Starting at time 0, a solution containing 3 pounds of salt per gallon flows into the tank at a rate of 4 gallons per minute. The mixture is kept uniform by stirring and the well-mixed solution simultancously flows out of the tank at the same rate. Determine the amount of salt in the tank after 10 minutes, when the amount of salt...