Suppose that a tank with a capacity of 30 gallons initially contains 18 gallons of pure water. A salt solution containing 3 pounds of salt per gallon is allowed to run into the tank at a rate of 18 gal/min, and thewell stirred mixture is then removed at a rate of 12 gal/min, as shown in the figure. The process is continued until the tank is filled (see figure below).Fluid InW' +1. Write an intial value problem for w, the total weight (in pounds) of salt in the tank.24+tMixture. The concentration is 63Fluid Outw = 30w(0) = 02. Determine the concentration of the salt solution in the tank at the end of the process.X lbs/gal.

Concept: Let w(t) be the amount of salt at any time t Now rate of change of w(t) is the difference…

Answered: Suppose that a tank with a capacity of…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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an ice cube is shrinking uniformly at a rate of 8 cubic inches per hour. when the cube has a volume of 27 cubic inches, at what rate is each side shrinking?
Consider a large vat containing sugar water that is to be made into soft drinks (see figure below). A B Suppose: The vat contains 230 gallons of liquid, which never changes. Sugar water with a concentration of 7 tablespoons/gallon flows through pipe A into the vat at the rate of 5 gallons/minute. • Sugar water with a concentration of 3 tablespoons/gallon flows through pipe B into the vat at the rate of 25 gallons/minute. The liquid in the vat is kept well-mixed. • Sugar water leaves the vat through pipe C at the rate of 30 gallons/minute. Let S(t) represent the number of tablespoons of sugar in the vat at time t, where t is given in minutes. (A) Write the DE model for the time rate of change of sugar in the vat: dS dt (B) Solve the differential equation to find the amount of sugar in the vat as a function of time. Your function will have an arbitrary constant K in it. Assume that K > 0. S(t) = (C) Suppose that there are 22 tablespoons of sugar in the vat at t = 0. How many tablespoons…
1:46 0.5 L Practice Problem 23.5 Unanswered powder volume.) :3 A vial of penicillin contains 3 million units of the powdered drug. How many mL of diluent is needed to make a solution containing 400000 units of this drug per cc? (Assume no mL .LTE Practice Problem 23.6 Unanswered Resubmit Submit You have just added 0.2 mL of folic acid to an IV bag. How many mg of folic acid have you added if the stock solution contains 5 mg folic
0.5 kg/L Pollutant Pure Water 15 L/min 5 L/min 1000 L 15 L/min 1000 L Pure Water with 5 kg pollutant Tank A Tank B 20 L/min For the figure shown, consider the following: • Two tanks are connected by a pipe with flow rate of 15L/min. • Tank A and Tank B each contains 1000L volume of liquid. • A pollutant with concentration of 0.5kg/L is discharged to Tank A at a rate of 15L/min, while pure water is discharged to Tank B at a rate of 5L/min. • There is an outflow of 20L/min from Tank B. • Initially, the amount of the pollutant in Tank A and in Tank B are zero and 5kg, respectively. • It is assumed that the pollutant is well mixed in each tank at any time t. Let yA(t) and yB(t) be the amount of the pollutant at any time t in Tank A and Tank B, respectively. Determine the particular solution of the corresponding system of ODES using Method of Undetermined Coefficients. What is the final equation of yA(t)? What is the final equation of yB(t)?
A concrete reservoir in the shape of a triangular prism is being filled with water at the constant rate of 2 cubic feet per minute. The reservoir is 4 feet deep, measures 6 feet across the top, and is 20 feet long (see figure). For any time t>=0, let H represent the depth of the water in the reservoir and let W represent the width of the rectangular region of water at the top. a. If the reservoir is initially empty, how long will it take to fill completely? b. How fast is the depth of the water in the reservoir changing when the reservoir is half-full? Remember to includes units. c. How fast is the rectangular area of the surface of the water changing when the reservoir is half full? Indicate units of measure.
Find the salt pls pounds
Can you find the amount of salt A in the tank at any time t?
Solve each question

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