dS 65 = 580 dt 271 13 σ 580 -S 54 ☑ (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 11 J. 65 S(t): = 2706 ✓ 2412 - 280e 31320 Ke 54 + 13 (C) Suppose that there are 32 tablespoons of sugar in the vat at t = 0. How many tablespoons will be present 4 minutes later? 385 1501.6989900366 tablespoons Suppose: • The vat contains 280 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 25 gallons/minute. • Sugar water with a concentration of 9 tablespoons/gallon flows through pipe B into the vat at the rate of 15 gallons/minute. • The liquid in the vat is kept well-mixed. • Sugar water leaves the vat through pipe C at the rate of 40 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 38 tablespoons of sugar in the vat at t = 0. How many tablespoons will be present 3 minutes later? tablespoons
dS 65 = 580 dt 271 13 σ 580 -S 54 ☑ (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 11 J. 65 S(t): = 2706 ✓ 2412 - 280e 31320 Ke 54 + 13 (C) Suppose that there are 32 tablespoons of sugar in the vat at t = 0. How many tablespoons will be present 4 minutes later? 385 1501.6989900366 tablespoons Suppose: • The vat contains 280 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 25 gallons/minute. • Sugar water with a concentration of 9 tablespoons/gallon flows through pipe B into the vat at the rate of 15 gallons/minute. • The liquid in the vat is kept well-mixed. • Sugar water leaves the vat through pipe C at the rate of 40 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 38 tablespoons of sugar in the vat at t = 0. How many tablespoons will be present 3 minutes later? tablespoons
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
The equations have to look like the 2 pictures
Transcribed Image Text:dS
65
=
580
dt
271
13
σ 580
-S
54
☑
(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
11
J.
65
S(t):
=
2706
✓
2412 - 280e
31320
Ke 54 +
13
(C) Suppose that there are 32 tablespoons of sugar in
the vat at t = 0. How many tablespoons will be
present 4 minutes later?
385
1501.6989900366 tablespoons
Transcribed Image Text:Suppose:
• The vat contains 280 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 25 gallons/minute.
• Sugar water with a concentration of 9
tablespoons/gallon flows through pipe B into
the vat at the rate of 15 gallons/minute.
• The liquid in the vat is kept well-mixed.
• Sugar water leaves the vat through pipe C at
the rate of 40 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 38 tablespoons of sugar in
the vat at t = 0. How many tablespoons will be
present 3 minutes later?
tablespoons
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