Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Chapter 7.1, Problem 4SA
Change pressure to
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A tank initially holds 100 gal of a brine solution containing 20 lb of salt. 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. Find the amount of salt in the tank att =
20 mins
O 6.37 lbs
Ⓒ 3.76 lbs
3.67 lbs
7.36 lbs
A tank initially contains 150 gal of brine in which 80 lb of salt are dissolved. A brine containing 4 lb/gal of salt runs into the tank at the rate of 3 gal/min. The mixture is kept uniform by stirring and flows out of the tank at the rate of 2 gal/min. Let y represent the amount of salt at time t. Complete parts a through e.
A tank initially holds 80 gal of a brine solution containing8/1 lb 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 40gal of solution.e. Determine when the tank will contain the most salt
Chapter 7 Solutions
Numerical Analysis
Ch. 7.1 - Use Theorem 7.1 to prove that the boundary value...Ch. 7.1 - Show that the solutions to the BVPs in Exercise 1...Ch. 7.1 - Consider the BVP { y=cyy(a)=yay(b)=yb where c0, ab...Ch. 7.1 - Consider the BVP { y=cyy(0)=0y(b)=0 where c0. For...Ch. 7.1 - Prob. 5ECh. 7.1 - Prob. 6ECh. 7.1 - Show that the solutions to the linear BVPs {...Ch. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Apply the Shooting Method to the linear BVPs....
Ch. 7.1 - Carry out the steps of Computer Problem 1 for the...Ch. 7.1 - Apply the Shooting Method to the nonlinear BVPs....Ch. 7.1 - Carry out the steps of Computer Problem 3 for the...Ch. 7.1 - Prob. 5CPCh. 7.1 - Verify that (7.10) is a solution of the BVP for...Ch. 7.1 - Set compressibility to the moderate value c=0.01 ....Ch. 7.1 - Prob. 3SACh. 7.1 - Change pressure to p=3.5, and resolve the BVP....Ch. 7.1 - Prob. 5SACh. 7.1 - Carry out Step 5 for the reduced compressibility...Ch. 7.1 - Carry out Step 5 for increased compressibility...Ch. 7.2 - Use finite differences to approximate solutions to...Ch. 7.2 - Use finite differences to approximate solutions to...Ch. 7.2 - Use finite differences to approximate solutions to...Ch. 7.2 - Use finite differences to plot solutions to the...Ch. 7.2 - (a) Find the solution of the BVP y=y, y(0)=0,...Ch. 7.2 - Solve the nonlinear BVP 4y=ty4, y(1)=2, y(2)=1 by...Ch. 7.2 - Extrapolate the approximate solutions in Computer...Ch. 7.2 - Extrapolate the approximate solutions in Computer...Ch. 7.2 - Prob. 9CPCh. 7.2 - Use finite differences to solve the equation {...Ch. 7.2 - Solve { y=cy(1y)y(0)=0y(1/2)=1/4y(1)=1 for c0,...Ch. 7.3 - Use the Collocation Method with n=8, 16 to...Ch. 7.3 - Use the Collocation Method with n=8, 16 to...Ch. 7.3 - Carry out the steps of Computer Problem 1, using...Ch. 7.3 - Carry out the steps of Computer Problem 2, using...
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