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Hughes-Hallett et al - Applied Calculus 5/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 4 / 34

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 10
2/2 2/4 –/1 –/2 –/6 –/5 –/1 –/3 –/6 –/4
Total
4/34 (11.8%)

  • Instructions

    The fifth edition of Applied Calculus by Deborah Hughes-Hallett, Patti Frazer Lock, Andrew M. Gleason, and Daniel E. Flath, published by John Wiley & Sons, includes a focus on creative conceptual and modeling problems. This text provides readers with deeper skills needed to apply calculus on the job and highlights connections with real-world concerns. The WebAssign component for this textbook gives students immediate feedback, provides worked solutions on select questions, and includes links to the complete eBook.

    Question 1 requires a numerical answer for the slope and accepts only an ordered pair in the form (x, y) for the y-intercept.

    Question 2 accepts any equivalent form of the desired equation. Try entering an equation with both variables on one side, then try an equivalent equation solved for one of the variables.

    Question 3 gives a randomized table of values to use to create a unique formula graded with our special regression grading.

    Question 4 demonstrates grading based on the values of the coefficients.

    Question 5 utilizes a fill-in-the-blank table to assist the student with determining the final answer.

    Question 6 specifies that the student should simplify the expression and the grading reflects this requirement.

    Question 7 gives the student the flexibility to answer with any correct trigonometric function. Enter in the answer in terms of cosine, then try an answer in terms of sine.

    Question 8 demonstrates interval grading, which can grade any canonically equivalent interval and enforce proper notation.

    Question 9 grades the integral and enforces correct form and notation while also allowing all mathematically correct answers.

    Question 10 features a solution and uses differential equation grading to test the validity of the answer. It accepts any correct form of the answer and runs student's responses through a series of tests to ensure the assumptions and requirements of the question are met. 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.

    The answer key and solutions will display after the first submission for demonstration purposes. Instructors can configure these to display after the due date or after a specified number of submissions.

Assignment Submission

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Assignment Scoring

Your last submission is used for your score.

1. 2/2 points  |  Previous Answers HHApCalc5 1.2.006. My Notes
Question Part
Points
Submissions Used
1 2
1/1 1/1
1/100 1/100
Total
2/2
 
Determine the slope and the y-intercept of the line whose equation is given.
3x + 2y = 16
slope Correct: Your answer is correct. seenKey

-3/2

 y-intercept
(x, y) = 
0,8
Correct: Your answer is correct. webMathematica generated answer key
 

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2. 2/4 points  |  Previous Answers HHApCalc5 1.5.009. My Notes
Question Part
Points
Submissions Used
1 2 3 4
0/1 1/1 0/1 1/1
1/100 1/100 1/100 1/100
Total
2/4
 
An air freshener starts with 40 grams and evaporates. In each of the following cases, write a formula for the quantity, Q grams, of air freshener remaining t days after the start and sketch a graph of the function.
(a) The decrease is 2 grams a day.
Q(t)=40−2t
Incorrect: Your answer is incorrect. webMathematica generated answer key

Sketch a graph of the function.

Correct: Your answer is correct.

(b) The decrease is 15% a day. (Note: Use the general exponential function.)
Q(t)=40(1720​)t
Incorrect: Your answer is incorrect. webMathematica generated answer key

Sketch a graph of the function.

Correct: Your answer is correct.

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3. –/1 points HHApCalc5 1.5.036. My Notes
Question Part
Points
Submissions Used
1
–/1
0/100
Total
–/1
 
Aircraft require longer takeoff distances, called takeoff rolls, at high altitude airports because of diminished air density. The table shows how the takeoff roll for a certain light airplane depends on the airport elevation. (Takeoff rolls are also strongly influenced by air temperature; the data shown assume a temperature of 0°C.)
Elevation (ft) Sea level 1,000 2,000 3,000 4,000
Takeoff roll (ft) 635 696 763 836 916
Determine a formula for this particular aircraft that gives the takeoff roll d as an exponential function of airport elevation h. (In your calculations, round the ratio between takeoff roll distances to three decimal places.)
d =

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4. –/2 points HHApCalc5 1.6.022. My Notes
Question Part
Points
Submissions Used
1 2
–/1 –/1
0/100 0/100
Total
–/2
 
Write the function in the form
P = P0at.
 (Round a to four decimal places.)
P = 3e−0.2t
P =


Does the function represent exponential growth or exponential decay?
    

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5. –/6 points HHApCalc5 1.7.009. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6
–/1 –/1 –/1 –/1 –/1 –/1
0/100 0/100 0/100 0/100 0/100 0/100
Total
–/6
 
The half-life of nicotine in the blood is 2 hours. A person absorbs 0.4 mg of nicotine by smoking a cigarette. Fill in the following table with the amount of nicotine remaining in the blood after t hours.
t (hours) 0 2 4 6 8 10
Nicotine (mg) 0.4
Estimate the length of time (in hours) until the amount of nicotine is reduced to 0.07 mg.
hours

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6. –/5 points HHApCalc5 1.8.006. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5
–/1 –/1 –/1 –/1 –/1
0/100 0/100 0/100 0/100 0/100
Total
–/5
 
If
f(x) = x2 + 1,
 find and simplify the following.
(a)    f(t + 5) =


(b)    f(t2 + 4) =


(c)    f(4) =


(d)    2f(t) =


(e)    (f(t))2 + 4 =

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7. –/1 points HHApCalc5 1.10.018. My Notes
Question Part
Points
Submissions Used
1
–/1
0/100
Total
–/1
 
Find a possible formula for the graph.
f(x) =
WebAssign Plot

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8. –/3 points HHApCalc5 4.3.047. My Notes
Question Part
Points
Submissions Used
1 2 3
–/1 –/1 –/1
0/100 0/100 0/100
Total
–/3
 
In a chemical reaction, substance C combines with substance D to form substance Y. At the start of the reaction, the quantity of C present is c grams, and the quantity of D present is d grams. At time t seconds after the start of the reaction, the quantity of Y present is y grams. Assume
c < d
 and
y ≤ c.
 For certain types of reactions, the rate of the reaction, in grams/sec, is given by the following.
Rate = k(c − y)(d − y),     k is a positive constant
(a) For what values of y is the rate nonnegative? (Enter your answer using interval notation.)


Graph the rate against y.


(b) Use your graph to find the value of y at which the rate of the reaction is fastest.
y =

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9. –/6 points HHApCalc5 6.6.048. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6
–/1 –/1 –/1 –/1 –/1 –/1
0/100 0/100 0/100 0/100 0/100 0/100
Total
–/6
 
If appropriate, evaluate the following integrals by substitution. If substitution is not appropriate, do not evaluate and enter NONE. (Use C for the constant of integration. Remember to use absolute values where appropriate.)
(a)    
x sin(x2) dx


(b)    
x2 sin x dx


(c)    
x2
1 + x2
 dx


(d)    
x
(1 + x2)2
 dx


(e)    
x3ex2 dx


(f)    
sin x
2 + cos x
 dx

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10. –/4 points HHApCalc5 9.R.022. 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 rate of growth of a tumor is proportional to the size of the tumor.
(a) Write a differential equation satisfied by S, the size of the tumor, in mm, as a function of time, t. (Use k as a constant of proportionality.)
dS
dt
 =


(b) Find the general solution to the differential equation.
S =


(c) If the tumor is 5 mm across at time
t = 0,
 what does that tell you about the solution?
S(t) =


(d) If, in addition, the tumor is 8 mm across at time
t = 3,
 what does that tell you about the solution? (Round your answer to four decimal places.)
S(t) =

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