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Larson-Algebra &Trig: Real Math, Real People 7/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 9 / 40

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

Last Saved : n/a Saving...  ()

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Question
Points
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4/4 1/2 4/4 –/8 –/4 –/2 –/15 –/1
Total
9/40 (22.5%)

  • Instructions

    Ideal for courses that require the use of a graphing calculator, Algebra & Trigonometry: Real Math, Real People, 7th Edition by Ron Larson, published by Cengage Learning, features quality exercises, interesting applications, and innovative resources to help you succeed. The WebAssign component for this textbook engages students with immediate feedback, lecture videos, and an interactive, fully customizable eBook, helping students to develop a deeper conceptual understanding of their subject matter. All even skill problems and all application problems from the textbook will be available in WebAssign.

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    Questions 1 - 3 have algorithmic solutions.

    Question 1 features the WebAssign graphing tool to graph a line.

    Question 6 features the WebAssign graphing tool to graph a quadratic. This question also demonstrates interval grading, which can grade any canonically equivalent interval and enforce proper notation.

    Question 8 is a Video Example that provides integrated video instruction and a follow up question about the concept that is presented.

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1. 4/4 points  |  Previous Answers LarATRMRP7 1.1.044.MI. My Notes
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Find the slope and y-intercept (if possible) of the equation of the line. (If an answer is undefined, enter UNDEFINED. Enter NONE if there is no y-intercept.)
2x + 3y = 6
slope Correct: Your answer is correct. seenKey

-2/3
y-intercept    (x, y) = ( Correct: Your answer is correct. seenKey

0

 , Correct: Your answer is correct. seenKey

2

 )

Sketch the line.
No Solution
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Clear Graph
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Show Key

Graph LayersToggle Open/Closed

Submission Data

Correct: Your answer is correct.
seenKey

line: y=-2/3*x+2


Solution or Explanation
2x + 3y = 6
3y = −2x + 6
y = − 
2
3
x + 2
Slope: m = − 
2
3
y-intercept: (0, 2)

Maple Generated Plot

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2. 1/2 points  |  Previous Answers LarATRMRP7 1.1.068. My Notes
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Consider the following.
Point      Line
(-7, 6)      x + y = 11
(a) Write the slope-intercept form of the equation of the line through the given point and parallel to the given line.
y =
−x−1
Correct: Your answer is correct. -x - 1

(b) Write the slope-intercept form of the equation of the line through the given point and perpendicular to the given line.
y =
x−1
Incorrect: Your answer is incorrect. x + 13


Solution or Explanation
x + y = 11
y = −x + 11
Slope: m = −1
(a) m = −1, (-7, 6)
y − 6 = −1(x + 7)
y − 6 = −x − 7
y = −x − 1
(b) m = 1, (-7, 6)
y − 6 = 1(x + 7)
y = x + 13

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3. 4/4 points  |  Previous Answers LarATRMRP7 1.2.073. My Notes
Question Part
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An open box of maximum volume is to be made from a square piece of material, 24 centimeters on a side, by cutting equal squares from the corners and turning up the sides as shown below.
(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 1 2 3 4 5 6
Volume, V 484 800 972 1024 980 864

Correct: Your answer is correct. seenKey

1024

 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?
     Correct: Your answer is correct.

(c) If V is a function of x, write the function. (If V is not a function of x, enter NONE.)
V =
4x(12−x)2
Correct: Your answer is correct. 4x(12-x)**2
Determine the domain of the function.
     Correct: Your answer is correct.


Solution or Explanation
(a)
Height, x Volume, V
1 484
2 800
3 972
4 1024
5 980
6 864
The volume is maximum when x = 4 and V = 1024 cubic centimeters.
(b)
V is a function of x.
(c) V = x(24 − 2x)2
Domain: 0 < x < 12

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4. –/8 points LarATRMRP7 1.2.076. My Notes
Question Part
Points
Submissions Used
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–/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1
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A rectangular package to be sent by the U.S. Postal Service can have a maximum combined length and girth (perimeter of a cross section) of 144 inches (see figure).
(a) Write the volume V of the package as a function of x.
V =


What is the domain of the function?
    

(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? (Enter your values in increasing order.)
× ×

Explain your answer.
From the graph, the volume occurs when x = .
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5. –/4 points LarATRMRP7 1.3.078. My Notes
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Consider the following.
(6a, 6c)
(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) = 
,


(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) = 
,
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6. –/2 points LarATRMRP7 1.3.090. My Notes
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Graph the function and determine the interval(s) for which
f(x) ≥ 0.
f(x) = x2 − 6x
No Solution
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Submission Data


Interval(s) for which f(x) ≥ 0: (Enter your answer using interval notation.)

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7. –/15 points LarATRMRP7 1.6.028. My Notes
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Show that f and g are inverse functions algebraically, graphically, and numerically.
f(x) = 
x3
6
,    g(x) = 
36x
 
(a) algebraically
f(g(x))
 		 =  f
 
 = 

g(f(x))
 		 =  g
 
 = 

(b) graphically


(c) numerically
x
f(g(x))
g(f(x))
−2
−1
0
1
4

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8. –/1 points LarATRMRP7 10.1.VE.001. My Notes
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Watch the video below then answer the question.

Finding Equation of a Circle

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