A tank with a capacity of 700 gal originally contains 100 gal of water with 100 lb of salt in solution. Watercontaining 2 lb of salt per gallon is entering at a rate of 4 gal/min, and the mixture is allowed to flow out of the tank at arate of 6 gal/min. Let Q(t) be the amount of salt (in pounds) inside the tank at time t>0. ONLY SET UP the initialvalue problem that Q(t) needs to satisfy. You don't need to solve this problem.

Given thata tank with a capacity of 700 gal originally contains 100 gal of water with100 lb of salt…

Answered: A tank with a capacity of 700 gal…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Two tanks are connected in tandem as shown in the following figure. Each tank contains 60 gal of water. Starting at timet = 0, brine containing 3 lb/gal of salt flows into tank 1 at the rate of 2 gal/min. The mixture then enters and leaves tank 2 at the same rate. The mixtures in both tanks are stirred uniformly. It can be shown that the amount of salt in tank 2 after t min is given by A(t) = 180(1 − e−t/30) − 6te−t/30 where A(t) is measured in pounds. (Round your answers to one decimal place.) (a) What is the initial amount of salt (in lb) in tank 2? (b) What is the amount of salt (in lb) in tank 2 after 2 hr (120 min)? (c) What is the average amount of salt (in lb) in tank 2 over the first 2 hr?
Identical tanks T₁ and T₂ initially contain 40 liters each of pure water. Starting at to = 0, a solution containing 20 grams of salt per liter is pumped into T₁ at 5 L/min and drained from T₁ into T₂ at the same rate. The resulting mixture in T2 is also drained at the same rate. Find the concentrations K₁(t) and K₂(t) in tanks T₁ and T₂ for t > 0. (a) Write a differential equation for K₁(t). d dt d dt K₁(t) = (b) Write a differential equation for K₂(t) in terms of K₁ (t) and K₂(t). K₂(t) = = 5 K₂(t) (K₁ (t)-K₂ (t)) 40 20 4000 (5t +40)² = (c) Find the concentration of salt in T₂ at any time t> 0. 500t² (5t+40)² lim K₂(t) t→∞ (d) What does the concentration of salt in T2 approach as t→∞. X X =
A 100-L tank was initially empty, but is to be filled with salt-and-water solution. The way the solution is being poured into the tank is through a device the controls the rate at which it is being poured. The controller ensures the solution is being poured at time t (minutes) with the expression (1 + cos(2t)) in liters per minute. It follows that the amount of salt for every liter of the solution being poured at time t (minutes) is described by the expression 0.2(1 + cos(2t)) in kilograms. This implies the rate the salt- and-water solution being poured into the tank alternately gets faster and slower. Determine which of the following differential equation describing the salt concentration S in the solution at any time t. O A. dS dt OB. dS dt OC. dS dt O D. dS dt = 0.2(1 + cos 21) ² = = = -0.2(1 + cos 21) ² 0.2 (1 + cos 21) ² 0.2 2 (1 + cos 21) ²
Please don't provide handwritten solution .....
After 2010 population and housing census, the birth rate in Ghana increased dramatically. Suppose that the number of babies born(in thousands per year) was given by b(t)=5 +2t, t is from 0 to 10 ,where t s time in years after the end of the 2010. I) How many babies in total were born during this time period (I.e the first ten years after the 2010 population census? 2)Find time To such that the total number of babies born from the 2010 census up to To was precisely 14 thousand.
3. A large tank with the capacity of 500 gallons is fully filled with pure water. Brine containing 2 pounds of salt per gallons is pumped into the tank at a rate of 5 gal/min. Find the amount A(t) pounds of salt in the tank at timer minutes, if the well-mixed solution is pumped out (a) with the same rate as the entering one; and (b) with the rate of 10 gal/min. In case (a), how much salt is in the tank after a long time? In case (b), what is the concentration of the solution in the tank by the time it is empty? (c) Let everything be the same except that, initially, the tank is filled with 250 gallons of pure water, while the well-stirred solution is pumped out with the flow rate of 2.5 gal/min. Find (t). What is the concentration of the solution in the tank by the time it is fully filled? Hint: (a) The volume of the solution in the tank at time (b) The volume of the solution in the tank at time minutes is V(t)= 500 gallons minutes is V(t)=500-5r gallons (c) The volume of the solution…
Consider a storage tank containing Vo liters of pure water. Water containing salt at a concentration of co kg/liter enters the tank at a rate r liters/min. The well-mixed solution leaves the tank at the same rate. Write down an initial value problem for the amount A(t) of salt in the tank at time t. You do NOT need to solve.

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS