24. Initially, a tank contains 400 L of water with 10 kg of salt in solution. Water containing 0.1 kg of salt per liter (L) is entering at a rate of 1 L/min, and the mixture is allowed to flow out of the tank at a rate of 2 L/min. Let Q(t) be the amount of salt at time t measured in kilograms. What is the right formulation of the differential equation for Q(t)? 2Q(t) O dQ = 0.1 dt - 400 + t dQ 2Q(t) = 0.1 dt 400 – t O dQ 10 2Q(t) - dt 400 400 +t O dQ = 0.1 2Q(t) dt 400 O dQ 0.1 2Q(t) dt 400 400 – t -

24. Initially, a tank contains 400 L of water with 10 kg of salt in solution. Water containing 0.1 kg of salt per liter (L) is entering at a rate of 1 L/min, and the mixture is allowed to flow out of the tank at a rate of 2 L/min. Let Q(t) be the amount of salt at time t measured in kilograms. What is the right formulation of the differential equation for Q(t)? 2Q(t) O dQ = 0.1 dt - 400 + t dQ 2Q(t) = 0.1 dt 400 – t O dQ 10 2Q(t) - dt 400 400 +t O dQ = 0.1 2Q(t) dt 400 O dQ 0.1 2Q(t) dt 400 400 – t -

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

Related questions

Q: Using the attached problem and solution as a format, find the differential equation for: A tank…

Q: A tank is filled with 1000 liters of pure water. Brine containing 0.03 kg of salt per liter enters…

Q: 1) A tank contains 100 gallons of water in which 40 pounds of salt are dissolved. A brine solution…

Q: Suppose that a large mixing tank initially holds 1200 L of water in which 25 kg of salt have been…

Q: The performance level of someone learning a skill P(t) is a function of the training time t dP and…

A: Given differential equation is dPdt=kM-Pt. where Pt is the performance level at some time t and k…

Q: Suppose that a large mixing tank initially holds 500 gallons of water in which 50 pounds of salt…

A: Thus, we need to find and first.Here, (concentration of salt in inflow).(input rate of…

Q: The body metabolizes an antibiotic over time (this is why we take it for several days at specified…

A: Let represents the concentration of the antibiotic that remains in the body at time , where is…

Q: Suppose that a large mixing tank initially holds 100 gallons of water in which 50 pounds of salt…

A: Let A(t) be the amount of salt in tank, then is the rate of change of the amount of salt in the…

Q: certain drug is administered intravenously to a patient at the continuous rate of 10 milligrams per…

A: Introduction: In mathematics, differentiation is the process of determining the derivative, or rate…

Q: A tank initially contains a solution of 14 pounds of salt in 50 gallons of water. Water with 1/5…

Q: The amount y of the drug Warfarin in a patient’s body after t hours satisfies the differential…

A: We have to find the time and the rate of dissipation of the drug increase or decrease.

Q: At t = 0, a tank of volume 300 L is filled with 100 L of water containing salt at a concentration of…

Q: Suppose that a large mixing tank initially holds 1200 L of water in which 25 kg of salt have been…

Q: A tank initially contains a solution of 7 pounds of salt in 60 gallons of water. Water with 3/10…

Q: The population of a particular type of fish in a lake would grow logistically according to the…

Q: Suppose that a large mixing tank initially holds 900 gallons of water in which 50 pounds of salt…

Q: The proportion of people in a community infected with a virus that stays active for two weeks is x…

A: The complete solutions are given below

Concept explainers

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.

Question

24. Initially, a tank contains 400 L of water with 10 kg of salt in solution. Water containing
0.1 kg of salt per liter (L) is entering at a rate of 1 L/min, and the mixture is allowed
to flow out of the tank at a rate of 2 L/min. Let Q(t) be the amount of salt at time
t measured in kilograms. What is the right formulation of the differential equation for
Q(t)?
O dQ
2Q(t)
0.1
dt
400 + t
O dQ
= 0.1
2Q(t)
dt
400 – t
-
dQ
10
2Q(t)
dt
400
400 +t
dQ
2Q(t)
= 0.1
-
dt
400
2Q(t)
400 – t
O dQ
0.1
dt
400
-

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

A tank initially contains a solution of 6 pounds of salt in 40 gallons of water. Water with 1/2 pound of salt per gallon is added to the tank at 9 gal/min, and the resulting solution leaves at the same rate. Let Q(t) denote the quantity (lbs) of salt at time t (min). (a) Write a differential equation for Q(t). Q'(t) (b) Find the quantity Q(t) of salt in the tank at time t > 0. (c) Compute the limit. lim Q(t) = t→∞ Submit Question
Suppose that a large mixing tank initially holds 700 gallons of water in which 50 pounds of salt have been dissolved. Another brine solution is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min. If the concentration of the solution entering is 2 lb/gal, determine a differential equation (in lb/min) for the amount of salt A(t) (in lb) in the tank at time t > 0. (Use A for A(t).) dA dt = ____________________ lb/min
A 90 gallon tank initially contains 10 gallons of water and 5 pounds of salt. Salt solution, at 2.5 lb/gal, begins entering the tank at a rate of 4 gal/min. Simultaneously, a 3 gal/min drain is opened. in the bottom of the tank. Let s(t) be the amount of salt in the tank at time t. Find the differential equation and initial condition for which s(t) is a solution. DO NOT SOLVE THE DIFFERENTIAL EQUATION.
A 50 gallon tank is full to the brim with pure water, and 5 gallons/minute of a brine solution with 0.3 kg/gallon salt flows into it. Since the tank is full, 5 gallons/minute of well-mixed solution flows onto the ground. Find a differential equation with initial condition for S(t) = number of kg salt in the tank and solve it for S(t).
A drug is administered intravenously at a constant rate of r mg/hour and is excreted at a rate proportional to the quantity present, with constant of proportionality k > 0. (a) Set up a differential equation for the quantity, Q, in milligrams, of the drug in the body at time t hours. Your answer will contain the unknown constants r and k. Q' = (b) Solve this differential equation, assuming there is no drug in the body initially. Your answer will contain r and k. Q = (c) What is the limiting long-run value of Q? lim Q(t) = t→∞