Question

A tank initially contains 150 gal of brine in which 60 lb of salt are dissolved....

A tank initially contains 150 gal of brine in which 60 lb of salt are dissolved. A brine containing 4 ​lb/gal of salt runs into the tank at the rate of 6 ​gal/min. The mixture is kept uniform by stirring and flows out of the tank at the rate of 5 ​gal/min. Let y represent the amount of salt at time t. Complete parts a through f.

a. At what rate​ (pounds per​ minute) does salt enter the tank at time​ t?

b. What is the volume of brine in the tank at time​ t?

c. At what rate​ (pounds per​ minute) does salt leave the tank at time​ t?

d. Write down and solve the initial value problem describing the mixing process.

e. What is the solution to the initial value​ problem?

f. Find the concentration of salt in the tank 27 min after the process starts.

Thank you in advance. Please show your work and explain.

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A large tank contains 800 gal of water in which 42 lb of salt are dissolved....
A large tank contains 800 gal of water in which 42 lb of salt are dissolved. Brine containing 2 lb of of dissolved salt per gal is pumped into the tank at a rate of 4 gal per minute, and the mixture, kept uniform by stirring, is pumped out at the same rate. (a) Find the amount x(t) of salt in the tank, at time t. (b) How long will it take for the amount of salt in the tank...
A tank contains 100 gal of brine made by dissolving 80 lb of salt in water....
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 of 4 gal/min, and the mixture, kept uniform by stirring runs out at the same rate. Find the amount of salt in the tank at t=8 min.
Suppose the tank in the figure below initially contains 800 gals of water in which 190...
Suppose the tank in the figure below initially contains 800 gals of water in which 190 lbs of salt is dissolved. Brine runs in at a rate of 10 gal min and each gallon contains .5 lb of dissolved salt. The mixture in the tank is kept uniform by stirring. The brine solution is withdrawn from the tank at a rate of 8 gals min. Let s(t) represent the amount of salt in the tank at anytime t, and develop...
A tank contains 40 lb of salt dissolved in 400 gallons of water. A brine solution...
A tank contains 40 lb of salt dissolved in 400 gallons of water. A brine solution is pumped into the tank at a rate of 4 gal/min; it mixes with the solution there, and then the mixture is pumped out at a rate of 4 gal/min. Determine A(t), the amount of salt in the tank at time t, if the concentration of salt in the inflow is variable and given by cin(t) = 2 + sin(t/4) lb/gal.
A tank contains 70 lb of salt dissolved in 200 gallons of water. A brine solution...
A tank contains 70 lb of salt dissolved in 200 gallons of water. A brine solution is pumped into the tank at a rate of 2 gal/min; it mixes with the solution there, and then the mixture is pumped out at a rate of 2 gal/min. Determine A(t), the amount of salt in the tank at time t, if the concentration of salt in the inflow is variable and given by cin(t) = 2 + sin(t/4) lb/gal.
A 500​-gal tank initially contains 100 gal of brine containing 75 lb of salt. Brine containing...
A 500​-gal tank initially contains 100 gal of brine containing 75 lb of salt. Brine containing 2 lb of salt per gallon enters the tank at a rate of 5 ​gal/s, and the​ well-mixed brine in the tank flows out at the rate of 3 ​gal/s. How much salt will the tank contain when it is full of​ brine?
A tank initially contains 50 gal of pure water. Brine containing 4 lb of salt per...
A tank initially contains 50 gal of pure water. Brine containing 4 lb of salt per gallon enters the tank at 2 ​gal/min, and the​ (perfectly mixed) solution leaves the tank at 3 ​gal/min. Thus, the tank is empty after exactly 50 min. ​(a) Find the amount of salt in the tank after t minutes. ​(b) What is the maximum amount of salt ever in the​ tank?
A tank is filled with 10 gallons of brine in which is dissolved 5 lb of...
A tank is filled with 10 gallons of brine in which is dissolved 5 lb of salt. Brine containing 3 lb of salt per gallon enters the tank at a rate of 2 gal per minute, and the well-stirred mixture is pumped out at the same rate. (a) Find the amount of salt in the tank at any time t. (b) How much salt is in the tank after 10 minutes? (c) How much salt is in the tank after...
A 110 gallon tank initially contains 5 lbs salt dissolved in 60 gallons of water. Brine...
A 110 gallon tank initially contains 5 lbs salt dissolved in 60 gallons of water. Brine containing 1 lb salt per gallon begins to flow into the tank at the rate of 3 gal/min and the well-mixed solution is drawn off at the rate of 1 gal/min. How much salt is in the tank when it is about to overflow? (Round your answer to the nearest integer.)
A tank initially holds 100 gal of brine solution. At t = 0, fresh water is...
A tank initially holds 100 gal of brine solution. At t = 0, fresh water is poured into the tank at the rate of 5 gal/min, while the well-stirred mixture leaves the tank at the same rate. After 20 min, the tank contains 20/e lb of salt. Find the initial concentration of the brine solution inside the tank. Ans.: 0.20 lb/gal
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT