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Zill - Engineering Mathematics 7/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 3 / 21

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

Last Saved : n/a Saving...  ()

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Question
Points
1 2 3 4 5 6 7 8 9
1/1 0/1 1/4 1/1 0/1 –/2 –/4 –/4 0/3
Total
3/21 (14.3%)

  • Instructions

    Modern and comprehensive, the new seventh edition of Advanced Engineering Mathematics by Dennis G. Zill, published by Jones and Bartlett Learning, is a compendium of topics that are most often covered in courses in engineering mathematics, and is extremely flexible to meet the unique needs of courses ranging from ordinary differential equations, to vector calculus, to partial differential equations. The WebAssign component for this title includes question links to the full eBook along with useful Instructor Resources such as related PowerPoint Slides, a test bank of questions, and the Instructor Solutions Manual.

    Question 1 features standard differential equation grading that allows the general solution to be written in terms of any constant that the student chooses.

    Question 2 shows grading for an initial value problem that accepts any form of the correct solution.

    Question 3 asks for various particular solutions of a separable equation. Part (a) allows for the use of either an arbitrary constant or any specific value of C.

    Question 4 utilizes special grading to accept any function that satisfies the nonlinear differential equation, with or without an arbitrary constant.

    Question 5 exhibits implicit solution grading for an exact equation.

    Questions 6 and 8 deal with applications of initial value problems where the student predicts future values using the solution. Question 6 incorporates tolerance for the second answer to allow the use of the rounded answer from the first question, and Question 8 has the student choose the graph that depicts the shape of the solution curve.

    Question 7 demonstrates grading for the solution of a generalized initial value problem. The student is also asked to analyze the long term behavior based on how parameters are related.

    Question 9 contains an application that involves draining a conical tank. The student provides the governing differential equation and the time it takes for the tank to empty under two scenarios. This demo assignment allows many submissions and allows you to try another version of the same question for practice wherever the problem has randomized values.

Assignment Submission

For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.

Assignment Scoring

Your last submission is used for your score.

1. 1/1 points  |  Previous Answers ZillEngMath7 2.2.005. My Notes
Question Part
Points
Submissions Used
1
1/1
7/100
Total
1/1
 
Solve the given differential equation by separation of variables.
x
dy
dx
 = 4y
y=Cx4
Correct: Your answer is correct. webMathematica generated answer key
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2. 0/1 points  |  Previous Answers ZillEngMath7 2.2.027. My Notes
Question Part
Points
Submissions Used
1
0/1
3/100
Total
0/1
 
Find an explicit solution of the given initial-value problem.
1 − y2
 dx − 
1 − x2
 dy = 0,   y(0) =
1
2
y =
x +C
Incorrect: Your answer is incorrect. webMathematica generated answer key
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3. 1/4 points  |  Previous Answers ZillEngMath7 2.2.040. My Notes
Question Part
Points
Submissions Used
1 2 3 4
1/1 –/1 –/1 –/1
2/100 0/100 0/100 0/100
Total
1/4
 
Find a solution of
x 
dy
dx
 = y2 − y
 that passes through the indicated points.
(a)    
(0, 1)
y(x) =
1
Correct: Your answer is correct. webMathematica generated answer key


(b)    
(0, 0)
y(x) =
+


(c)    
1
4
, 
1
4
y(x) =


(d)    
6, 
1
8
y(x) =
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4. 1/1 points  |  Previous Answers ZillEngMath7 2.2.059. My Notes
Question Part
Points
Submissions Used
1
1/1
1/100
Total
1/1
 
Find a function whose square plus the square of its derivative is 1.
y(x) =
1
Correct: Your answer is correct. webMathematica generated answer key
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5. 0/1 points  |  Previous Answers ZillEngMath7 2.4.009. My Notes
Question Part
Points
Submissions Used
1
0/1
1/100
Total
0/1
 
Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not exact, enter NOT.)
(x − y5 + y2 sin(x)) dx = (5xy4 + 2y cos(x)) dy
515
Incorrect: Your answer is incorrect. webMathematica generated answer key
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6. –/2 points ZillEngMath7 2.7.003. My Notes
Question Part
Points
Submissions Used
1 2
–/1 –/1
0/100 0/100
Total
–/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 60 years? (Round your answer to the nearest person.)
persons

How fast is the population growing at
t = 60?
 (Round your answer to two decimal places.)
persons/yr
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7. –/4 points ZillEngMath7 2.7.043. My Notes
Question Part
Points
Submissions Used
1 2 3 4
–/1 –/1 –/1 –/1
0/100 0/100 0/100 0/100
Total
–/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 ZillEngMath7 2.8.001. My Notes
Question Part
Points
Submissions Used
1 2 3 4
–/1 –/1 –/1 –/1
0/100 0/100 0/100 0/100
Total
–/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 − 0.0005N),    N(0) = 1.
(a) Use the phase portrait concept 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 = 5?
 (Round your answer to the nearest integer.)
supermarkets
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9. 0/3 points  |  Previous Answers ZillEngMath7 2.8.017. My Notes
Question Part
Points
Submissions Used
1 2 3
0/1 –/1 –/1
1/100 0/100 0/100
Total
0/3
 
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
c Ah
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. (Assume the removed apex of the cone is of negligible height and volume.)
(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.)
Incorrect: Your answer is incorrect. seenKey

14.31

 min

(b) Suppose the tank has a vertex angle of 60° and the circular hole has radius 4 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 10 feet, how long will it take the tank to empty? (Round your answer to two decimal places.)
min
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