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Stewart et al - College Algebra 8/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 44 / 44

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
2/2 2/2 11/11 10/10 5/5 7/7 4/4 1/1 2/2
Total
44/44 (100.0%)

  • Instructions

    WebAssign provides a wide range of exercises that enable you to:
    • Build problem-solving skills (#1-5: Read Its, Watch Its, (optional) Master It Tutorials, Problem-Solving Exercises, and Focus on Modeling Exercises)
    • Develop Conceptual Understanding (#6-7: Explore Its and Expanded Problems)
    • Address Readiness Gaps (#8-9: Review Questions and College Math Readiness Bootcamp Exercises)
    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

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. 2/2 points  |  Previous Answers SColAlg8 4.5.019. My Notes
Question Part
Points
Submissions Used
1 2
1/1 1/1
1/50 1/50
Total
2/2
 
  • This exercise type will build problem-solving skills.
  • Read It links are available as a learning tool under each question so students can quickly jump to the corresponding section of the eTextbook.

Consider the following.
200(1.02)6t = 1,700
(a)
Find the exact solution of the exponential equation in terms of logarithms.
t =
16​log1.02​(1700200​)
Correct: Your answer is correct. Exactly!
(b)
Use a calculator to find an approximation to the solution, rounded to six decimal places.
t = Correct: Your answer is correct. Amazing job!
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2. 2/2 points  |  Previous Answers SColAlg8 4.5.095.MI. My Notes
Question Part
Points
Submissions Used
1 2
1/1 1/1
1/50 2/50
Total
2/2
 
  • This exercise type will build problem-solving skills.
  • Master It tutorials are an optional student-help tool available within select questions for just-in-time support. Students can use the tutorial to guide them through the problem-solving process step-by-step using different numbers.
  • Students get just-in-time learning support with Watch It videos that contain narrated and closed-captioned videos walking students through the proper steps to solve a similar problem.

A small lake is stocked with a certain species of fish. The fish population is modeled by the function
P = 
18
1 + 4e−0.6t
where P is the number of fish (in thousands) and t is measured in years since the lake was stocked.
(a)
Find the fish population after 4 years. (Round your answer to the nearest whole fish.)
Correct: Your answer is correct. fish
(b)
After how many years will the fish population reach 9,000 fish? (Round your answer to two decimal places.)
Correct: Your answer is correct. yr

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3. 11/11 points  |  Previous Answers SColAlg8 5.3.013.MI.SA. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8 9 10 11
1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1
1/50 1/50 1/50 1/50 1/50 1/50 1/50 1/50 1/50 1/50 2/50
Total
11/11
 
  • This exercise type will build problem-solving skills.
  • Master It tutorials—Standalone are embedded, step-by-step tutorials used to help students understand each step required to solve the problem, before inputting their final answer.

This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.

Tutorial Exercise
Find the partial fraction decomposition of the rational function.
 
8
(x − 1)(x + 1)
Step 1
Consider the following rational function.
r(x) = 
P(x)
Q(x)
 = 
8
(x + 1)(x − 1)
Is the polynomial
Q(x)
 factored completely into linear and irreducible quadratic factors?
     Correct: Your answer is correct.
Amazing work.
Which describes the polynomial
Q(x)?
 (Select all that apply.)
Correct: Your answer is correct.

Way to go!
Does more than one case describe the factors of the polynomial
Q(x)?
     Correct: Your answer is correct.
Good work.
Which of the following forms is the partial fraction decomposition of the given function?
     Correct: Your answer is correct.
Nice work.
Use the partial fraction decomposition found above to simplify the equation
P(x) = Q(x)r(x).
8 = A 
$$x+1
Correct: Your answer is correct. webMathematica generated answer key
 + B 
$$x−1
Correct: Your answer is correct. webMathematica generated answer key
Equate coefficients in the simplified equation above to create a system of equations.
A + B = 0 Correct: Your answer is correct. seenKey

0
A − B = 8 Correct: Your answer is correct. seenKey

8
Solve the system of equations for A and B.
A = 4 Correct: Your answer is correct. seenKey

4

 B = -4 Correct: Your answer is correct. seenKey

-4
Find the partial fraction decomposition of the rational function.
$$4x−1​−4x+1​
Correct: Your answer is correct. webMathematica generated answer key Terrific!
You have now completed the Master It.

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4. 10/10 points  |  Previous Answers SColAlg8 4.2.052. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8 9 10
1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1
1/50 1/50 1/50 1/50 1/50 1/50 1/50 1/50 1/50 1/50
Total
10/10
 
  • This exercise type will build problem-solving skills.
  • Problem-solving exercises in most sections highlight and apply a specific problem-solving principle from the prologue.

Show that the minimum value of
f(x) = 3ex + 3e−x
 is 6. (Do not use a graphing device. PS: Establish subgoals. First find the minimum value for
x ≥ 0.)
We know that
3ex
 is Correct: Your answer is correct. and
3e−x
 is Correct: Your answer is correct. , so
f(x) = 3ex + 3e−x
 is Correct: Your answer is correct. on
(0, ∞)
 and its Correct: Your answer is correct. value on that interval is
f(0) = 3e0 + 3e0 =
Correct: Your answer is correct. . But f is Correct: Your answer is correct. , so because it is Correct: Your answer is correct. on
(0, ∞),
 it is Correct: Your answer is correct. on
(−∞, 0).
 Therefore, its absolute Correct: Your answer is correct. value is indeed
f(0) =
Correct: Your answer is correct. .
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5. 5/5 points  |  Previous Answers SColAlg8 2.FoM.021. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5
1/1 1/1 1/1 1/1 1/1
1/50 1/50 1/50 1/50 1/50
Total
5/5
 
  • Problem-solving exercises in most sections highlight and apply a specific problem-solving principle from the prologue.
  • Focus on Modeling exercises show how math can be applied to real-life situations by utilizing modeling techniques.

In these problems you are asked to find a function that models a real-life situation and then use the model to answer questions about the situation. Use the Guidelines for Modeling with Functions to help you answer these questions.
Consider the following problem: A farmer has 2,800 feet of fencing and wants to fence off a rectangular field that borders a straight river. The farmer does not need a fence along the river (see the figure).
An image is given of a rectangular field bordered on three sides by a fence and along the bottom by a straight river. The length of the left and right side of the fence are both labeled x. The area enclosed by the fence and river is labeled A.
What are the dimensions of the field of largest area that can be fenced? (Let x be the width of the field in feet and l be the length of the field in feet.)
(a)
Experiment with the problem by drawing several diagrams illustrating the situation. Calculate the area of each configuration, and use your results to estimate the dimensions of the largest possible field (in feet). (Round your answers to the nearest hundred feet.)
x = Correct: Your answer is correct. ft l = Correct: Your answer is correct. ft
(b)
Find a function that models the area of the field in terms of one of its sides.
A(x) =
x(2800−2x)
Correct: Your answer is correct. Amazing job!
(c)
Use your model to solve the problem, and compare with your answer to part (a). (Enter your answers in feet).
x = Correct: Your answer is correct. ft l = Correct: Your answer is correct. ft
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6. 7/7 points  |  Previous Answers SColAlg8 4.1.EI.003. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7
1/1 1/1 1/1 1/1 1/1 1/1 1/1
2/50 2/50 1/50 2/50 1/50 1/50 1/50
Total
7/7
 
  • This exercise type will develop conceptual understanding.
  • Explore It exercises engage students with interactive learning modules that include video and explorations. The module is also available to use for studying in the eTextbook

Review the Explore It, then use it to complete the exercise below.
Click here to access the Explore It in a new window.
Suppose you invest $1 in an account that is compounded continuously and you wish to double your money.
(a)
How many years will it take for the money to double when the interest rate is 1%? (Enter your answer to the nearest hundredth of a year.)
Correct: Your answer is correct. yrs
(b)
How many years will it take for the money to double when the interest rate is 2%? (Enter your answer to the nearest hundredth of a year.)
Correct: Your answer is correct. yrs
(c)
How many years will it take for the money to double when the interest rate is 4%? (Enter your answer to the nearest hundredth of a year.)
Correct: Your answer is correct. yrs
(d)
How many years will it take for the money to double again (that is, for the initial investment of $1 to be worth $4) when the interest rate is 4%? (Enter your answer to the nearest hundredth of a year.)
Correct: Your answer is correct. yrs
(e)
How many years will it take for the money to double yet again (that is, for the initial investment of $1 to be worth $8) when the interest rate is 4%? (Enter your answer to the nearest hundredth of a year.)
Correct: Your answer is correct. yrs
(f)
For the case of continuous compounding, what do the results of parts (a) through (c) above suggest about the effect doubling the interest rate will have on the length of time it takes for an initial investment to double in value?
     Correct: Your answer is correct.
(g)
For the case of continuous compounding and a fixed interest rate, what do the results of parts (c) through (e) above suggest about the length of time it takes for an initial amount of money to double?
     Correct: Your answer is correct.
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7. 4/4 points  |  Previous Answers SColAlg8 7.2.040.EP. My Notes
Question Part
Points
Submissions Used
1 2 3 4
1/1 1/1 1/1 1/1
1/50 1/50 1/50 1/50
Total
4/4
 
  • This exercise type will develop conceptual understanding.
  • Expanded Problems enhance student understanding by going beyond a basic exercise and asking students to solve each step of the problem in addition to their final answer.

Consider an ellipse with the given characteristics. Find the following additional characteristics.
Foci:
(0, ±6),
 vertices:
(0, ±10)
Center
(x, y)
 =
0,0
Correct: Your answer is correct.
Major axis Correct: Your answer is correct. Length of major axis Correct: Your answer is correct. Impressive work!
Find an equation for the ellipse that satisfies the given conditions.
x264​+y2100​=1
Correct: Your answer is correct. Fantastic job!
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8. 1/1 points  |  Previous Answers SColAlg8 P.7.027. My Notes
Question Part
Points
Submissions Used
1
1/1
3/50
Total
1/1
 
  • This exercise type will address readiness gaps.
  • Review questions in the prerequisites/fundamentals chapter prepare students for success.

Perform the multiplication or division and simplify.
4x
x2 − 36
 · 
x + 6
16x
14(x−6)​
Correct: Your answer is correct. Very nice!

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9. 2/2 points  |  Previous Answers wacollmathbootcamp1 5.3.001.defective My Notes
Question Part
Points
Submissions Used
1 2
1/1 1/1
1/50 1/50
Total
2/2
 
  • This exercise type will address readiness gaps.
  • The College Math Readiness Bootcamp contains a formative student assessment on prerequisite topics needed for success and targeted learning modules for areas where students struggled.

Solve the inequality.
−4x − 5 < 3
x>−2
Correct: Your answer is correct.
Graph the solution on the number line.
Use the tools to enter your answer.
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