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Larson-Precalc: Real Math, Real People 7/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 7 / 58

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 11 12
4/4 1/2 –/4 –/8 –/4 2/2 –/15 –/4 –/1 –/1 –/12 –/1
Total
7/58 (12.1%)

  • Instructions

    Precalculus: Real Math, Real People, 7th Edition by Ron Larson, published by Cengage Learning, is an ideal student and instructor resource for courses that require the use of a graphing calculator. The quality and quantity of the exercises, combined with interesting applications and innovative resources, make teaching easier and help students 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.

    Question 1 has a Watch It.

    Questions 1 and 10 have a Master it.

    Questions 1 - 3 and 9 - 11 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 10 features equation grading to grade the equation of an ellipse in standard form.

    Question 11 illustrates vector grading.

    Question 12 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 LarPreCalcRMRP7 1.1.044.MI. My Notes
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4/4
 
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.)
3x + 5y = 15
slope Correct: Your answer is correct. seenKey

-3/5
y-intercept    (x, y) = ( Correct: Your answer is correct. seenKey

0

 , Correct: Your answer is correct. seenKey

3

 )

Sketch the line.
No Solution
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Clear Graph
Delete Layer
Fill
Show Key

Graph LayersToggle Open/Closed

Submission Data

Correct: Your answer is correct.
seenKey

line: y=-3/5*x+3


Solution or Explanation
3x + 5y = 15
5y = −3x + 15
y = − 
3
5
x + 3
Slope: m = − 
3
5
y-intercept: (0, 3)

Maple Generated Plot

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2. 1/2 points  |  Previous Answers LarPreCalcRMRP7 1.1.068. My Notes
Question Part
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Submissions Used
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0/1 1/1
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1/2
 
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 =
11x−yx+41
Incorrect: Your answer is incorrect. -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+13
Correct: Your answer is correct. 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 points LarPreCalcRMRP7 1.2.073. My Notes
Question Part
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–/4
 
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

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 NONE.)
V =

Determine the domain of the function.
    

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4. –/8 points LarPreCalcRMRP7 1.2.076. My Notes
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–/8
 
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 120 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 LarPreCalcRMRP7 1.3.078. My Notes
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–/4
 
Consider the following.
(3a, 3c)
(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. 2/2 points  |  Previous Answers LarPreCalcRMRP7 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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Correct: Your answer is correct.
seenKey

parabola: y=x^2-6*x

Interval(s) for which f(x) ≥ 0: (Enter your answer using interval notation.)
(−∞,0],[6,∞)
Correct: Your answer is correct. webMathematica generated answer key

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7. –/15 points LarPreCalcRMRP7 1.6.028. My Notes
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–/15
 
Show that f and g are inverse functions algebraically, graphically, and numerically.
f(x) = 
x3
3
,    g(x) = 
33x
 
(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. –/4 points LarPreCalcRMRP7 4.3.054. My Notes
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–/4
 
Use the given function values and the trigonometric identities to find the indicated trigonometric functions.
sin 30° = 
1
2
,     tan 30° = 
3
3
(a)     csc 30°


(b)     cot 60°


(c)     cos 30°


(d)     cot 30°

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9. –/1 points LarPreCalcRMRP7 10.2.022. My Notes
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Find the vector z, given u = ‹-1, 1, 2›, v = ‹2, -2, -1›, and w = ‹0, 0, -5›. Use a graphing utility to verify your answer.
z = 7u + v −
1
5
 		w
z =

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10. –/1 points LarPreCalcRMRP7 9.2.014.MI. My Notes
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–/1
 
Find the standard form of the equation of the ellipse with the given characteristics and center at the origin.
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11. –/12 points LarPreCalcRMRP7 1.7.018. My Notes
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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
 =


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
−1
0
1
2
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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 (6, −1) and passing through the point (6, 2).
    
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