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Larson - Precalc w/Limits: A Graphing Approach 8e (Homework)

James Finch

Math - High School, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : – / 51

Due : Tuesday, January 28, 2020 00:00 EST

Last Saved : n/a Saving...  ()

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  • Instructions

    Precalculus with Limits: A Graphing Approach, 8th edition, written by Ron Larson and Paul Battaglia and published by Cengage Learning, provides the clear instruction, precise mathematics, and thorough coverage students and teachers depend on. This program uses strong pedagogy and integrated technology to show students how precalculus is used by real people to solve real-life problems and make real-life decisions.

    The WebAssign enhancement to this textbook, which includes an interactive eBook, is a fully customizable online solution that empowers students to learn, not just do homework. Insightful tools save time and highlight exactly where students are struggling. Students get an engaging experience, instant feedback, and better outcomes. A total win-win!

    Question 1 demonstrates the calcPad's ability to enforce the specific form of an equation in an answer.

    Questions 2 and 3 feature a variety of grading modes, including multiple choice, numerical, and algebraic grading. Question 2 always has a solution.

    Question 4 shows the ability to grade ordered pairs.

    Question 5 demonstrates how WebAssign can approach one problem with multiple methods.

    Question 6 accepts coefficients of an equation rounded to a specified decimal place.

    Question 7 requires the evaluations of the the sine, cosine, and tangent of the angle to be entered in simplest form.

    Question 8 gives a randomized graph and asks the student to enter the correct answer in a specific form based on the graph. This question also features a Master It.

    Question 9 features vector grading in the calcPad.

    Question 10 asks a question related to the concept explored in an embedded video. 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 points LarPCalcLimAGA8 1.1.072. My Notes
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Submissions Used
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–/2
 
Consider the following.
Point      Line
(−6, 5),
 		     x + y = 9
(a) Write the slope-intercept form of the equation of the line through the given point and parallel to the given line.
(No Response) webMathematica generated answer key

(b) Write the slope-intercept form of the equation of the line through the given point and perpendicular to the given line.
(No Response) webMathematica generated answer key


Solution or Explanation
x + y = 9
y = −x + 9
Slope: m = −1
(a)    
m = −1, (−6, 5)
y − 5 = −1(x + 6)
y − 5 = −x − 6
y = −x − 1

(b)    
m = 1, (−6, 5)
y − 5 = 1(x + 6)
y = x + 11
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2. –/6 points LarPCalcLimAGA8 1.2.075. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6
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–/6
 
An open box of maximum volume is to be made from a square piece of material, 26 centimeters on a side, by cutting equal squares from the corners and turning up the sides as shown below.
26 − 2x
26 − 2x
(a) The table shows the volume V (in cubic centimeters) of the box for various heights x (in centimeters). Use the table to estimate the maximum volume.
Height, x Volume, V
1 576
2 968
3 1200
4 1296
5 1280
6 1176

(No Response) seenKey

1296

 cubic centimeters

(b) Plot the points (x, V) from the table in part (a). Does the relation defined by the ordered pairs represent V as a function of x?
    

(c) If V is a function of x, write the function. (If V is not a function of x, enter DNE.)
V = (No Response) webMathematica generated answer key

Determine the domain of the function. (Enter your answer using interval notation. If V is not a function of x, enter DNE.)
(No Response) webMathematica generated answer key

(d) Use a graphing utility to plot the points from the table in part (a) with the function from part (c).


How closely does the function represent the data?
    


Solution or Explanation
(a)
Height, x Volume, V
1 576
2 968
3 1200
4 1296
5 1280
6 1176
The volume is maximum when
x = 4
 and
V = 1296
 cubic centimeters.

(b)
WebAssign Plot

V is a function of x.
(c) V = x(26 − 2x)2
Domain: (0, 13)


(d)
WebAssign Plot

The function fits the data points; Answers will vary.
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3. –/7 points LarPCalcLimAGA8 1.2.076. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7
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–/7
 
A rectangular package to be sent by a shipping company can have a maximum combined length and girth (perimeter of a cross section) of 108 inches. (See figure.)
(a) Write the volume V of the package as a function of x.
V = (No Response) webMathematica generated answer key

What is the domain of the function? (Enter your answer using interval notation.)
(No Response) webMathematica generated answer key

(b) Use a graphing utility to graph your function. Be sure to use an appropriate window setting.



(c) What dimensions will maximize the volume of the package?
x = (No Response) seenKey

18

 in
y = (No Response) seenKey

36

 in

Explain your answer.
From the graph, the (No Response) seenKey

maximum

 volume occurs when x = (No Response) seenKey

18

 .
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4. –/2 points LarPCalcLimAGA8 1.3.084. My Notes
Question Part
Points
Submissions Used
1 2
–/1 –/1
0/100 0/100
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–/2
 
Consider the following.
(7a, 7c)
(a) Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even.
(x, y) = 
(No Response) webMathematica generated answer key


(b) Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is odd.
(x, y) = 
(No Response) webMathematica generated answer key
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5. –/15 points LarPCalcLimAGA8 1.6.026. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
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0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100
Total
–/15
 
Show that f and g are inverse functions algebraically, graphically, and numerically.
f(x) = 
x3
2
,    g(x) = 
32x
 
(a) algebraically
f(g(x))
 		 =  f
 		(No Response) (2x)^(1/3)
 
 =  (No Response) x

g(f(x))
 		 =  g
 		(No Response) x^3/2
 
 =  (No Response) x

(b) graphically


(c) numerically
x
f(g(x))
g(f(x))
−2 (No Response) seenKey

-2

 		(No Response) seenKey

-2
−1 (No Response) seenKey

-1

 		(No Response) seenKey

-1
0 (No Response) seenKey

0

 		(No Response) seenKey

0
1 (No Response) seenKey

1

 		(No Response) seenKey

1
4 (No Response) seenKey

4

 		(No Response) seenKey

4
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6. –/12 points LarPCalcLimAGA8 1.7.018. My Notes
Question Part
Points
Submissions Used
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–/12
 
Use the regression feature of a graphing utility to find a linear model for the data. (Round your coefficients to one decimal place.)
WebAssign Plot
y
 = (No Response) webMathematica generated answer key

Use the graphing utility to decide how closely the model fits the data graphically and numerically.
(a) graphically

(b) numerically (For the linear equation, round your answers to one decimal place.)
x linear equation given data
−2 (No Response) seenKey

5.6

 		(No Response) seenKey

6
−1 (No Response) seenKey

4.4

 		(No Response) seenKey

4
0 (No Response) seenKey

3.2

 		(No Response) seenKey

3
1 (No Response) seenKey

2.0

 		(No Response) seenKey

2
2 (No Response) seenKey

0.8

 		(No Response) seenKey

1
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7. –/4 points LarPCalcLimAGA8 4.3.052. My Notes
Question Part
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–/4
 
Use the function values and the trigonometric identities to evaluate each trigonometric function.
sin(30°) = 
1
2
,     tan(30°) = 
3
3
(a)     csc(30°)
(No Response) webMathematica generated answer key

(b)     cot(60°)
(No Response) webMathematica generated answer key

(c)     cos(30°)
(No Response) webMathematica generated answer key

(d)     cot(30°)
(No Response) webMathematica generated answer key


Solution or Explanation
sin(30°) = 
1
2
, tan(30°) = 
3
3
(a)    csc(30°) = 
1
sin(30°)
 = 2
(b)    cot(60°) = tan(90° − 60°) = tan(30°) = 
3
3
(c)    cos(30°) = 
sin(30°)
tan(30°)
 = 
1
2
3
3
 = 
3
2
3
 = 
3
2
(d)    cot(30°) = 
1
tan(30°)
 = 
3
3
 = 
3
3
3
 = 
3
 
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8. –/1 points LarPCalcLimAGA8 9.2.012.MI. My Notes
Question Part
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1
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–/1
 
Find the standard form of the equation of the ellipse with the given characteristics and center at the origin.
(No Response) webMathematica generated answer key
WebAssign Plot


Solution or Explanation
Vertices: (±4, 0) right double arrow implies a = 4

Endpoints of minor axis:
0, ±
4
2
 right double arrow implies b		 = 
4
2
 
x2
a2
 + 
y2
b2
 = 1
x2
42
 + 
y2
(4/2)2
 = 1
x2
16
 + 
4y2
16
 = 1

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9. –/1 points LarPCalcLimAGA8 10.2.020. My Notes
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–/1
 
Find the vector z, given u = ‹-4, 4, 3›, v = ‹1, -1, -2›, and w = ‹5, 5, -5›. Use a graphing utility to verify your answer.
z = 7u + v −
1
5
 		w
z = (No Response) webMathematica generated answer key


Solution or Explanation
z = 7
−4, 4, 3
 + 
1, −1, −2
 − 
1
5
5, 5, −5
 = 
−28, 26, 20
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10. –/1 points LarPCalcLimAGA8 9.1.VE.001. My Notes
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Watch the video below then answer the question.


Find the equation of the circle with center (7, −1) and passing through the point (7, 2).
    
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