In each of Problems 21 through 24, draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y as t → ∞. If this behavior depends on the initial value of v at t = 0, describe this dependency. Noté that the right-hand sides of hese equations depend on t as well as y; therefore, their solutions can. xhibit more complicated behavior than those in the text. G21. y=-3+t-y %3D

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 74E
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Question
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Question 21 as it appears in the textbook
b. How much
long time? Doe-
was present ini
27. Newton's lav
20.
The direction field of Figure 1.1.10.
object changes at
temperature of the
(the ambient air te
temperature is 20
differential equat
that the different
object is above
N 28. For
the text that the
For larger, mo
that the drag
а. Wri
of mass
FIGURE 1.1.10
Problem 20.
In each of Problems 21 through 24, draw a direction field for the
given differential equation. Based on the direction field, determine the
behavior of y as t → ∞. If this behavior depends on the initial value of
y at t = 0, describe this dependency. Noté that the right-hand sides of
these equations depend on t as well as y; therefore, their solutions can
exhibit more complicated behavior than those in the text.
square
veloci
b. D
c. I
velo
G 21. y=-3+1-y
G 22. y= te-24 – 2y
23. y = 3r-1 – y²
© 24. y =-y-
it w
29.
A
patient.
bloods
tissues
25. A spherical raindrop evaporates at a rate proportional to its
surface area. Write a differential equation for the volume of the
raindrop as a function of time.
the ar
26. A pond initially contains 1,000,000 L of water and an unknown
amount of an undesirable chemical. Water containing 0.01 g of this
chemical per liter flows into the pond at a rate of 300 L/h. The
mixture flows out at the same rate, so the amount of water in the pond
remains constant. Assume that the chemical is uniformly distributed
throughout the pond.
a. Write a differential equation for the amount of chemical in
the pond at any time.
Transcribed Image Text:b. How much long time? Doe- was present ini 27. Newton's lav 20. The direction field of Figure 1.1.10. object changes at temperature of the (the ambient air te temperature is 20 differential equat that the different object is above N 28. For the text that the For larger, mo that the drag а. Wri of mass FIGURE 1.1.10 Problem 20. In each of Problems 21 through 24, draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y as t → ∞. If this behavior depends on the initial value of y at t = 0, describe this dependency. Noté that the right-hand sides of these equations depend on t as well as y; therefore, their solutions can exhibit more complicated behavior than those in the text. square veloci b. D c. I velo G 21. y=-3+1-y G 22. y= te-24 – 2y 23. y = 3r-1 – y² © 24. y =-y- it w 29. A patient. bloods tissues 25. A spherical raindrop evaporates at a rate proportional to its surface area. Write a differential equation for the volume of the raindrop as a function of time. the ar 26. A pond initially contains 1,000,000 L of water and an unknown amount of an undesirable chemical. Water containing 0.01 g of this chemical per liter flows into the pond at a rate of 300 L/h. The mixture flows out at the same rate, so the amount of water in the pond remains constant. Assume that the chemical is uniformly distributed throughout the pond. a. Write a differential equation for the amount of chemical in the pond at any time.
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