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Zill and Wright - Advanced Engineering Math 5/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 19 / 21

Due : Sunday, January 27, 2030 00:00 EST

Last Saved : n/a Saving...  ()

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19/21 (90.5%)

  • Instructions

    Here are some textbook questions from Advanced Engineering Mathematics 5/e by Dennis G. Zill and Warren S. Wright published by Jones & Bartlett Learning.

    Every problem includes a link to the appropriate section of a complete interactive eBook, (also available through a dynamic table of contents from the student's WebAssign homepage), allowing students to highlight and take notes as they read.

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1. –/1 points ZillEngMath5 2.2.005. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Solve the given differential equation by separation of variables.
x
dy
dx
 = 6y
y =
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2. –/1 points ZillEngMath5 2.2.027. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Find an explicit solution of the given initial-value problem.
1 − y2
 dx − 
1 − x2
 dy = 0,   y(0) =
1
2
y =
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3. –/4 points ZillEngMath5 2.2.032. My Notes
Question Part
Points
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1 2 3 4
–/1 –/1 –/1 –/1
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–/4
 
Find a solution of
x 
dy
dx
 = y2 − y
 that passes through the indicated points.
(a)    
(0, 1)

y(x) =


(b)    
(0, 0)

y(x) =


(c)    
1
3
, 
1
3

y(x) =


(d)    
4, 
1
6

y(x) =
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4. –/1 points ZillEngMath5 2.2.047. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Find a function whose square plus the square of its derivative is 1.
y(x) =
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5. –/1 points ZillEngMath5 2.4.009. My Notes
Question Part
Points
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1
–/1
0/50
Total
–/1
 
Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not exact, enter NOT.)
(x − y6 + y2 sin x) dx = (6xy5 + 2y cos x) dy
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6. –/2 points ZillEngMath5 2.7.003. My Notes
Question Part
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1 2
–/1 –/1
0/50 0/50
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–/2
 
The population of a town grows at a rate proportional to the population present at time t. The initial population of 500 increases by 5% in 10 years. What will be the population in 20 years? (Round your answer to the nearest person.)
persons

How fast is the population growing at
t = 20?
 (Round your answer to two decimal places.)
persons/yr
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7. –/4 points ZillEngMath5 2.7.041. My Notes
Question Part
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1 2 3 4
–/1 –/1 –/1 –/1
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–/4
 
In one model of the changing population
P(t)
 of a community, it is assumed that
 
dP
dt
 = 
dB
dt
 − 
dD
dt
,
where
dB/dt and dD/dt
 are the birth and death rates, respectively.
(a) Solve for
P(t) if dB/dt = k1P and dD/dt = k2P.
 (Assume
P(0) = P0.)

P(t) =


(b) Analyze the cases
k1 > k2, k1 = k2, and k1 < k2.


For
k1 > k2,
 one has the following.
    

For
k1 = k2,
 one has the following.
    

For
k1 < k2,
 one has the following.
    
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8. –/4 points ZillEngMath5 2.8.001. My Notes
Question Part
Points
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1 2 3 4
–/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50
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–/4
 
The number
N(t)
 of supermarkets throughout the country that are using a computerized checkout system is described by the initial-value problem
dN
dt
 = N(1 − 0.0002N),    N(0) = 1.
(a) Use the phase portrait concept of Section 2.1 to predict how many supermarkets are expected to adopt the new procedure over a long period of time.
supermarkets

By hand, sketch a solution curve of the given initial-value problem.


(b) Solve the initial-value problem and then use a graphing utility to verify the solution curve in part (a).
N(t) =


How many supermarkets are expected to adopt the new technology when
t = 10?
 (Round your answer to the nearest integer.)
supermarkets
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9. –/3 points ZillEngMath5 2.8.015. My Notes
Question Part
Points
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1 2 3
–/1 –/1 –/1
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–/3
 
Suppose water is leaking from a tank through a circular hole of area
Ah
 at its bottom. When water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to
cAh
2gh
,
 where
c (0 < c < 1)
 is an empirical constant.

A tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom.
(a) Suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. The differential equation governing the height h in feet of water leaking from a tank after t seconds is
 
dh
dt
 = − 
5
6h3/2
.
In this model, friction and contraction of the water at the hole are taken into account with
c = 0.6,
 and g is taken to be
32 ft/s2.
 See the figure below. If the tank is initially full, how long will it take the tank to empty? (Round your answer to two decimal places.)
minutes

(b) Suppose the tank has a vertex angle of 60° and the circular hole has radius 2 inches. Determine the differential equation governing the height h of water. Use
c = 0.6
 and
g = 32 ft/s2.

dh
dt
 =


If the height of the water is initially 11 feet, how long will it take the tank to empty? (Round your answer to two decimal places.)
minutes
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