CALCULUS:EARLY TRANSCENDENTALS-PACKAGE
3rd Edition
ISBN: 9780135182543
Author: Briggs
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 9.5, Problem 24E
Stirred tank reactions For each of the following stirred tank reactions, carry out the following analysis.
- a. Write an initial value problem for the mass of the substance.
- b. Solve the initial value problem.
24. A 1500-L tank is initially filled with a solution that contains 3000 g of salt. A salt solution with a concentration of 20 g/L flows into the tank at a rate of 3 L/min. The thoroughly mixed solution is drained from the tank at a rate of 3 L/min.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
2. A tonk initially contains 1oO gallons of brine
whose concentration is 2 lb/gal. Brine whose salt
concentration is 2 /gal flows nto the tank ot the
rate of 3 gal per minute. The well-stirred mixture
Hows out at a rate of e ga/min. Find salt content
of the brine and its concentration ofter Y2 hbur.
A tank contains 40 L of a chemical solution prepared by dissolving 80 g of a soluble substance in fresh water. Fluid containing 2 g of this
sutstance per liter runs in at the rate of 3 L/min and the well-stirred mixture runs out at the same rate. Find the amount of substance in
the tank after 20 minutes.
O a. 70 grams
O b. 80 grams
O c. 60 grams
O d. 90 grams
3.
A tank contains 80 gals. of pure water. A
brine solution with 2 lbs/gal of salt enters at
2 gals/min, and the well-stirred mixture
leaves at the same rate. Find (a) the amount
of salt in the tank at any time
O a. 80 Ibs
O b. 41.3 lbs
c. 23 Ibs
O d. 27.73 lbs
Chapter 9 Solutions
CALCULUS:EARLY TRANSCENDENTALS-PACKAGE
Ch. 9.1 - What are the orders of the equations in Example 2?...Ch. 9.1 - What is the solution of the initial value problem...Ch. 9.1 - Solve the initial value problem in Example 4a with...Ch. 9.1 - Suppose the initial conditions in Example 5a are...Ch. 9.1 - In Example 7, if the height function were given by...Ch. 9.1 - Consider the differential equation y(t) + 9y(t) =...Ch. 9.1 - If the general solution of a differential equation...Ch. 9.1 - Does the function y(t) = 2t satisfy the...Ch. 9.1 - Does the function y(t) = 6e3t satisfy the initial...Ch. 9.1 - The solution to the initial value problem y(t) = 2...
Ch. 9.1 - Explain why the graph of the solution to the...Ch. 9.1 - Verifying general solutions Verify that the given...Ch. 9.1 - Verifying general solutions Verify that the given...Ch. 9.1 - Verifying general solutions Verify that the given...Ch. 9.1 - Verifying general solutions Verify that the given...Ch. 9.1 - Verifying general solutions Verify that the given...Ch. 9.1 - Verifying general solutions Verify that the given...Ch. 9.1 - Verifying general solutions Verify that the given...Ch. 9.1 - Verifying general solutions Verify that the given...Ch. 9.1 - Verifying general solutions Verify that the given...Ch. 9.1 - Verifying general solutions Verify that the given...Ch. 9.1 - Verifying solutions of initial value problems...Ch. 9.1 - Verifying solutions of initial value problems...Ch. 9.1 - Verifying solutions of initial value problems...Ch. 9.1 - Verifying solutions of initial value problems...Ch. 9.1 - Finding general solutions Find the general...Ch. 9.1 - Finding general solutions Find the general...Ch. 9.1 - Finding general solutions Find the general...Ch. 9.1 - Finding general solutions Find the general...Ch. 9.1 - Finding general solutions Find the general...Ch. 9.1 - Finding general solutions Find the general...Ch. 9.1 - Finding general solutions Find the general...Ch. 9.1 - Finding general solutions Find the general...Ch. 9.1 - General solutions Find the general solution of the...Ch. 9.1 - General solutions Find the general solution of the...Ch. 9.1 - General solutions Find the general solution of the...Ch. 9.1 - General solutions Find the general solution of the...Ch. 9.1 - Solving initial value problems Solve the following...Ch. 9.1 - Solving initial value problems Solve the following...Ch. 9.1 - Solving initial value problems Solve the following...Ch. 9.1 - Solving initial value problems Solve the following...Ch. 9.1 - Solving initial value problems Solve the following...Ch. 9.1 - Solving initial value problems Solve the following...Ch. 9.1 - Solving initial value problems Find the solution...Ch. 9.1 - Solving initial value problems Find the solution...Ch. 9.1 - Solving initial value problems Find the solution...Ch. 9.1 - Solving initial value problems Find the solution...Ch. 9.1 - Motion in a gravitational field An object is fired...Ch. 9.1 - Prob. 44ECh. 9.1 - Harvesting problems Consider the harvesting...Ch. 9.1 - Harvesting problems Consider the harvesting...Ch. 9.1 - Draining tanks Consider the tank problem in...Ch. 9.1 - Prob. 48ECh. 9.1 - Explain why or why not Determine whether the...Ch. 9.1 - A second-order equation Consider the differential...Ch. 9.1 - Another second-order equation Consider the...Ch. 9.1 - Drug infusion The delivery of a drug (such as an...Ch. 9.1 - Logistic population growth Widely used models for...Ch. 9.1 - Free fall One possible model that describes the...Ch. 9.1 - Chemical rate equations The reaction of certain...Ch. 9.1 - Tumor growth The growth of cancer tumors may be...Ch. 9.2 - Assuming solutions are unique (at most one...Ch. 9.2 - Prob. 2QCCh. 9.2 - Prob. 3QCCh. 9.2 - Notice that the errors in Table 9.1 increase in...Ch. 9.2 - Explain how to sketch the direction field of the...Ch. 9.2 - Prob. 2ECh. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - Identifying direction fields Which of the...Ch. 9.2 - Direction fields A differential equation and its...Ch. 9.2 - Prob. 8ECh. 9.2 - Direction fields with technology Plot a direction...Ch. 9.2 - Prob. 10ECh. 9.2 - Direction fields with technology Plot a direction...Ch. 9.2 - Sketching direction fields Use the window [2, 2] ...Ch. 9.2 - Sketching direction fields Use the window [2, 2] ...Ch. 9.2 - Sketching direction fields Use the window [2, 2] ...Ch. 9.2 - Sketching direction fields Use the window [2, 2] ...Ch. 9.2 - Sketching direction fields Use the window [2, 2] ...Ch. 9.2 - Increasing and decreasing solutions Consider the...Ch. 9.2 - Increasing and decreasing solutions Consider the...Ch. 9.2 - Increasing and decreasing solutions Consider the...Ch. 9.2 - Increasing and decreasing solutions Consider the...Ch. 9.2 - Logistic equations Consider the following logistic...Ch. 9.2 - Logistic equations Consider the following logistic...Ch. 9.2 - Logistic equations Consider the following logistic...Ch. 9.2 - Logistic equations Consider the following logistic...Ch. 9.2 - Two steps of Eulers method For the following...Ch. 9.2 - Two steps of Eulers method For the following...Ch. 9.2 - Two steps of Eulers method For the following...Ch. 9.2 - Two steps of Eulers method For the following...Ch. 9.2 - Errors in Eulers method Consider the following...Ch. 9.2 - Errors in Eulers method Consider the following...Ch. 9.2 - Prob. 31ECh. 9.2 - Prob. 32ECh. 9.2 - Prob. 33ECh. 9.2 - Prob. 34ECh. 9.2 - Prob. 35ECh. 9.2 - Prob. 36ECh. 9.2 - Prob. 37ECh. 9.2 - Equilibrium solutions A differential equation of...Ch. 9.2 - Prob. 39ECh. 9.2 - Prob. 40ECh. 9.2 - Equilibrium solutions A differential equation of...Ch. 9.2 - Equilibrium solutions A differential equation of...Ch. 9.2 - Direction field analysis Consider the first-order...Ch. 9.2 - Eulers method on more general grids Suppose the...Ch. 9.2 - Analyzing models The following models were...Ch. 9.2 - Prob. 47ECh. 9.2 - Analyzing models The following models were...Ch. 9.2 - Convergence of Eulers method Suppose Eulers method...Ch. 9.2 - Stability of Eulers method Consider the initial...Ch. 9.3 - Which of the following equations are separable?...Ch. 9.3 - Write y(t) = (t2 + 1)/y3 in separated form.Ch. 9.3 - Find the value of the constant C in Example 2 with...Ch. 9.3 - Find the value of the constant C in Example 3 with...Ch. 9.3 - What is a separable first-order differential...Ch. 9.3 - Is the equation t2y(t)=t+4y2 separable?Ch. 9.3 - Is the equation y(t)=2yt separable?Ch. 9.3 - Explain how to solve a separable differential...Ch. 9.3 - Solving separable equations Find the general...Ch. 9.3 - Solving separable equations Find the general...Ch. 9.3 - Solving separable equations Find the general...Ch. 9.3 - Solving separable equations Find the general...Ch. 9.3 - Solving separable equations Find the general...Ch. 9.3 - Solving separable equations Find the general...Ch. 9.3 - Solving separable equations Find the general...Ch. 9.3 - Solving separable equations Find the general...Ch. 9.3 - Solving separable equations Find the general...Ch. 9.3 - Solving separable equations Find the general...Ch. 9.3 - Solving separable equations Find the general...Ch. 9.3 - Solving separable equations Find the general...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solutions of separable equations Solve the...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solutions in implicit form Solve the following...Ch. 9.3 - Solutions in implicit form Solve the following...Ch. 9.3 - Solutions in implicit form Solve the following...Ch. 9.3 - Solutions in implicit form Solve the following...Ch. 9.3 - Solutions in implicit form Solve the following...Ch. 9.3 - Solutions in implicit form Solve the following...Ch. 9.3 - Logistic equation for a population A community of...Ch. 9.3 - Logistic equation for an epidemic When an infected...Ch. 9.3 - Explain why or why not Determine whether the...Ch. 9.3 - Implicit solutions for separable equations For the...Ch. 9.3 - Implicit solutions for separable equations For the...Ch. 9.3 - Orthogonal trajectories Two curves are orthogonal...Ch. 9.3 - Orthogonal trajectories Use the method in Exercise...Ch. 9.3 - Applications 44.Logistic equation for spread of...Ch. 9.3 - Free fall An object in free fall may be modeled by...Ch. 9.3 - Free fall Using the background given in Exercise...Ch. 9.3 - Torricellis law An open cylindrical tank initially...Ch. 9.3 - Chemical rate equations Let y(t) be the...Ch. 9.3 - Tumor growth The Gompertz growth equation is often...Ch. 9.3 - Blowup in finite time Consider the initial value...Ch. 9.3 - Analysis of a separable equation Consider the...Ch. 9.4 - Verify by substitution that y(t) = Cekt b/k is a...Ch. 9.4 - Prob. 2QCCh. 9.4 - Prob. 3QCCh. 9.4 - Prob. 4QCCh. 9.4 - In general, what is the equilibrium temperature...Ch. 9.4 - The general solution of a first-order linear...Ch. 9.4 - Prob. 2ECh. 9.4 - What is the general solution of the equation y'(t)...Ch. 9.4 - Prob. 4ECh. 9.4 - First-order linear equations Find the general...Ch. 9.4 - First-order linear equations Find the general...Ch. 9.4 - First-order linear equations Find the general...Ch. 9.4 - First-order linear equations Find the general...Ch. 9.4 - First-order linear equations Find the general...Ch. 9.4 - First-order linear equations Find the general...Ch. 9.4 - Initial value problems Solve the following initial...Ch. 9.4 - Initial value problems Solve the following initial...Ch. 9.4 - Initial value problems Solve the following initial...Ch. 9.4 - Initial value problems Solve the following initial...Ch. 9.4 - Initial value problems Solve the following initial...Ch. 9.4 - Initial value problems Solve the following initial...Ch. 9.4 - Stability of equilibrium points Find the...Ch. 9.4 - Stability of equilibrium points Find the...Ch. 9.4 - Stability of equilibrium points Find the...Ch. 9.4 - Stability of equilibrium points Find the...Ch. 9.4 - Stability of equilibrium points Find the...Ch. 9.4 - Stability of equilibrium points Find the...Ch. 9.4 - Loan problems The following initial value problems...Ch. 9.4 - Loan problems The following initial value problems...Ch. 9.4 - Loan problems The following initial value problems...Ch. 9.4 - Loan problems The following initial value problems...Ch. 9.4 - Newtons Law of Cooling Solve the differential...Ch. 9.4 - Newton's Law of Cooling Solve the differential...Ch. 9.4 - Newtons Law of Cooling Solve the differential...Ch. 9.4 - Prob. 30ECh. 9.4 - Intravenous drug dosing The amount of drug in the...Ch. 9.4 - Optimal harvesting rate Let y(t) be the population...Ch. 9.4 - Endowment model An endowment is an investment...Ch. 9.4 - Explain why or why not Determine whether the...Ch. 9.4 - Prob. 36ECh. 9.4 - A bad loan Consider a loan repayment plan...Ch. 9.4 - Prob. 38ECh. 9.4 - Special equations A special class of first-order...Ch. 9.4 - Prob. 40ECh. 9.4 - Special equations A special class of first-order...Ch. 9.4 - Prob. 42ECh. 9.4 - Prob. 43ECh. 9.4 - Prob. 44ECh. 9.4 - General first-order linear equations Consider the...Ch. 9.4 - Prob. 46ECh. 9.4 - Prob. 47ECh. 9.4 - General first-order linear equations Consider the...Ch. 9.5 - Explain why the maximum growth rate for the...Ch. 9.5 - Prob. 2QCCh. 9.5 - Prob. 3QCCh. 9.5 - Explain how the growth rate function determines...Ch. 9.5 - Prob. 2ECh. 9.5 - Explain how the growth rate function can be...Ch. 9.5 - Prob. 4ECh. 9.5 - Is the differential equation that describes a...Ch. 9.5 - What are the assumptions underlying the...Ch. 9.5 - Describe the solution curves in a predator-prey...Ch. 9.5 - Prob. 8ECh. 9.5 - Solving logistic equations Write a logistic...Ch. 9.5 - Solving logistic equations Write a logistic...Ch. 9.5 - Designing logistic functions Use the method of...Ch. 9.5 - Designing logistic functions Use the method of...Ch. 9.5 - Prob. 19ECh. 9.5 - Prob. 20ECh. 9.5 - Solving the Gompertz equation Solve the Gompertz...Ch. 9.5 - Prob. 22ECh. 9.5 - Stirred tank reactions For each of the following...Ch. 9.5 - Stirred tank reactions For each of the following...Ch. 9.5 - Stirred tank reactions For each of the following...Ch. 9.5 - Stirred tank reactions For each of the following...Ch. 9.5 - Prob. 31ECh. 9.5 - Growth rate functions a.Show that the logistic...Ch. 9.5 - Solution of the logistic equation Use separation...Ch. 9.5 - Properties of the Gompertz solution Verify that...Ch. 9.5 - Properties of stirred tank solutions a.Show that...Ch. 9.5 - Prob. 36ECh. 9.5 - RC circuit equation Suppose a battery with voltage...Ch. 9.5 - U.S. population projections According to the U.S....Ch. 9 - Explain why or why not Determine whether the...Ch. 9 - Prob. 2RECh. 9 - General solutions Use the method of your choice to...Ch. 9 - General solutions Use the method of your choice to...Ch. 9 - General solutions Use the method of your choice to...Ch. 9 - Prob. 6RECh. 9 - General solutions Use the method of your choice to...Ch. 9 - General solutions Use the method of your choice to...Ch. 9 - General solutions Use the method of your choice to...Ch. 9 - Prob. 10RECh. 9 - Solving initial value problems Use the method of...Ch. 9 - Prob. 12RECh. 9 - Solving initial value problems Use the method of...Ch. 9 - Prob. 14RECh. 9 - Solving initial value problems Use the method of...Ch. 9 - Solving initial value problems Use the method of...Ch. 9 - Solving initial value problems Use the method of...Ch. 9 - Solving initial value problems Use the method of...Ch. 9 - Direction fields Consider the direction field for...Ch. 9 - Direction fields The direction field for the...Ch. 9 - Eulers method Consider the initial value problem...Ch. 9 - Equilibrium solutions Find the equilibrium...Ch. 9 - Equilibrium solutions Find the equilibrium...Ch. 9 - Equilibrium solutions Find the equilibrium...Ch. 9 - Equilibrium solutions Find the equilibrium...Ch. 9 - Logistic growth The population of a rabbit...Ch. 9 - Logistic growth parameters A cell culture has a...Ch. 9 - Logistic growth in India The population of India...Ch. 9 - Stirred tank reaction A 100-L tank is filled with...Ch. 9 - Newtons Law of Cooling A cup of coffee is removed...Ch. 9 - A first-order equation Consider the equation...Ch. 9 - A second-order equation Consider the equation...
Additional Math Textbook Solutions
Find more solutions based on key concepts
Exercises 5-10 refer to the function
graphed in the accompanying figure.
5.
Does f(−1) exist?
Does exist?
Doe...
University Calculus: Early Transcendentals (3rd Edition)
The percentage of doctors that are prescribing the medication after 0 month, 1 month, 2 months, 3 months, 5 mon...
Calculus and Its Applications (11th Edition)
Locating critical points Find the critical points of the following functions. Assume a is a nonzero constant. 3...
Calculus, Single Variable: Early Transcendentals (3rd Edition)
1. On a real number line the origin is assigned the number _____ .
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
The conversion of 16 L into cups rounded to hundredth place.
Glencoe Math Accelerated, Student Edition
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
- 3. A container with 300 gal of alcoholic beverages contains 3% alcohol (by volume). Beer with 8% is pumped into the container at a rate of 4gal/min and the mixture is pumped out at the same rate. What is the amount of alcohol after 30min.arrow_forwardA water tank that initially contains 140 L of solution in which 20 g of salt was dissolved. A solution with a salt concentration of 4 g/L is added at a rate of 6 L/min. The solution is mixed well and was drained from the tank at a rate of 4 L/min. Find the answer for the following question. 1) Find the concentration of the solution in the tank after 30 minutes.arrow_forwardA tank initially contains 500 gallons of water and 30 pounds of salt dissolved in it. Water enters the tank at the rate of 3 gal/min with concentration 4 lb/gal of salt in it. The well-mixed solution leaves the tank at the rate of 3 gal/min. Write the initial value problem for finding the concentration of salt in the tank (you do not need to solve it).arrow_forward
- 9. A large tank contains 100 gallons of brine in which 10 lbs. of salt is dissolved. Brine containing 0.2 lbs. of salt to the gallon runs into the tank at the rate of 6 gal/min. The mixture, kept uniform by stirring, runs out of the tank at the rate of 4 gal/min. Find the amount of salt in the solution in the tank at the end of t min.arrow_forwardA tank contains 200 liters of brine holding 50 kg of salt in solution. Water containing 125 g of salt per liter flows into the tank at the rate of 12 liters per minute, and the mixture, kept uniform by stirring, flows out at the same rate. Find the time it takes for the concentration in the tank to be equal to 0.23 kg/L. Topic: Applications of 1st Order DEarrow_forwardA tank initially contains 200 liters of fresh water. Brine containing 2.5 N/liter of dissolved salt runs into the tank at the rate of 8 liters/min and the mixture kept uniform by stirring runs out at the same rate. After 15 minutes, what is the concentrations of the salt in the mixture? 1.8 N/L 2.1 N/L 0.82 N/L O 1.1 N/Larrow_forward
- 1. A tank initially holds 80 gal of a brine solution containing - Ib of salt per gallon. At t = 0, another brine solution containing 1 lb of salt per gallon is poured into the tank at the rate of 4 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. Determine when the tank will be empty. c. Determine when the tank will hold 40 gal of solution. d. Find the amount of salt in the tank when the tank contains exactly 40 gal solution. e. Determine when the tank will contain the most salt.arrow_forwardBrine containing 3 lbs per gal of salt enters a large tank at the rate of2 gal/min and the mixture well stirred leaves at 1.5 gal/min. If the tankcontains initially 100 gal of water, with 4 lbs of dissolved salt.a. Find the mount of salt in the tank at any time t in minutes.b. Find the amount of salt in the tank after 4 mins.arrow_forward1. A tank initially holds 80 gal of a brine solution containing Ib of salt per gallon. At t = 0, another brine solution containing 1 Ib of salt per gallon is poured into the tank at the rate of 4 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. Determine when the tank will be empty. c. Determine when the tank will hold 40 gal of solution. d. Find the amount of salt in the tank when the tank contains exactly 40 gal of solution. e. Determine when the tank will contain the most salt.arrow_forward
- . A large mixing tank currently contains 300 gallons of water, into which 8 pounds of sugar have been mixed. A tap will open, pouring 20 gallons of water per minute into the tank at the same time sugar is poured into the tank at a rate of 2 pounds per minute. Find the concentration (pounds per gallon) of sugar in the tank after t minutes.arrow_forwardA 500 gal capacity tank initially contains a salt solution consisting of 200 gal of water and 3 lbs of salt/gal. A solution of 2 Ib/gal flows in at the rate of 3 gal/min and the resulting mixture flows out at the rate of 2 gal/min. What is the concentration in the tank when it starts to overflow? O 2.352 Ib/gal O 1.873 lb/gal O 1032 lb O 2.064 lb/galarrow_forwardA tank initially contains 100 gal of brine in which 50 lb of salt are dissolved. A brine containing 2 lb/gal of salt runs into the tank at the rate of 5 gal/min. The mixture is kept uniform by stirring and flows out of the tank at the rate of 4 gal/ min. 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. Find the concentration of salt in the tank 25 min after the process starts.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY
Solution of Differential Equations and Initial Value Problems; Author: Jefril Amboy;https://www.youtube.com/watch?v=Q68sk7XS-dc;License: Standard YouTube License, CC-BY