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Consider a large vat containing sugar water that is to be made into soft drinks (see figure below). A B Suppose: • The vat contains 260 gallons of liquid, which never changes. ● Sugar water with a concentration of 5 tablespoons/gallon flows through pipe A into the vat at the rate of 5 gallons/minute. • Sugar water with a concentration of 4 tablespoons/gallon flows through pipe B into the vat at the rate of 20 gallons/minute. • The liquid in the vat is kept well-mixed. • Sugar water leaves the vat through pipe C at the rate of 25 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)= Il B

Consider a large vat containing sugar water that is to be made into soft drinks (see figure below). A B Suppose: • The vat contains 260 gallons of liquid, which never changes. ● Sugar water with a concentration of 5 tablespoons/gallon flows through pipe A into the vat at the rate of 5 gallons/minute. • Sugar water with a concentration of 4 tablespoons/gallon flows through pipe B into the vat at the rate of 20 gallons/minute. • The liquid in the vat is kept well-mixed. • Sugar water leaves the vat through pipe C at the rate of 25 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)= Il B

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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→ Consider a large vat containing sugar water that is to be made into soft drinks (see figure below). A B Suppose: • The vat contains 260 gallons of liquid, which never changes. • Sugar water with a concentration of 5 tablespoons/gallon flows through pipe A into the vat at the rate of 5 gallons/minute. Su water with a concentration of 4 tablespoons/gallon flows through pipe B into the vat at the rate of 20 gallons/minute. • The liquid in the vat is kept well-mixed. • Sugar water leaves the vat through pipe C at the rate of 25 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 M # $ 2 Oll O %
Transcribed Image Text:→ Consider a large vat containing sugar water that is to be made into soft drinks (see figure below). A B Suppose: • The vat contains 260 gallons of liquid, which never changes. • Sugar water with a concentration of 5 tablespoons/gallon flows through pipe A into the vat at the rate of 5 gallons/minute. Su water with a concentration of 4 tablespoons/gallon flows through pipe B into the vat at the rate of 20 gallons/minute. • The liquid in the vat is kept well-mixed. • Sugar water leaves the vat through pipe C at the rate of 25 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 M # $ 2 Oll O %
Suppose: • The vat contains 260 gallons of liquid, which never changes." ● Sugar water with a concentration of 5 tablespoons/gallon flows through pipe A into the vat at the rate of 5 gallons/minute. ● Sugar water with a concentration of 4 tablespoons/gallon flows through pipe B into the vat at the rate of 20 gallons/minute. • The liquid in the vat is kept well-mixed. • Sugar water leaves the vat through pipe C at the rate of 25 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 will be present 3 minutes later? tablespoons с O ¤ ✓ # 4 5 Oll 6 & 7 * 8
Transcribed Image Text:Suppose: • The vat contains 260 gallons of liquid, which never changes." ● Sugar water with a concentration of 5 tablespoons/gallon flows through pipe A into the vat at the rate of 5 gallons/minute. ● Sugar water with a concentration of 4 tablespoons/gallon flows through pipe B into the vat at the rate of 20 gallons/minute. • The liquid in the vat is kept well-mixed. • Sugar water leaves the vat through pipe C at the rate of 25 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 will be present 3 minutes later? tablespoons с O ¤ ✓ # 4 5 Oll 6 & 7 * 8
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