Aufmann and Nation - Algebra and Trigonometry 8/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 30 / 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	10
2/2	1/1	1/5	9/9	3/3	4/4	0/8	6/6	4/4	–/2

Total

30/44 (68.2%)

Instructions

Create your course assignments by selecting questions from our bank of end-of-section exercises.

Students can view and hear additional instruction through the 2-5 minute Watch It links. Students will also find helpful links to online excerpts from their textbook, tutorials, and videos.

Every problem includes a link to the appropriate section of a complete interactive eBook, (also available through a dynamic table of contents from the student's WebAssign homepage), allowing students to highlight and take notes as they read.

Many problems include detailed stepped-out solutions, available to students at each instructor's discretion. The solutions use the same algorithmic values assigned in the problem, further driving problem-solving mastery.

This book also includes a Personal Study Plan (PSP). Once PSP is enabled for your course, your students can use chapter and section assessments to gauge their mastery of the material and generate individualized study plans that include various online, interactive multimedia resources.

- relevant textbook pages

- videos of worked examples

- tutorials

In this assignment we present several textbook question types found in Algebra and Trigonometry 8/e by Richard N. Aufmann and Richard D. Nation published by Cengage Learning.

Click here for a list of all of the questions coded in WebAssign. 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.

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 AufCAT8 0.1.030. My Notes

Graph the set.

(−∞, 7)

NO SOLUTION

(
)
[
]

NO SOL

Write the set in set-builder notation.

{x|x ≤ 7} {x|x < 7} {x|−∞ ≤ x ≤ 7} {x|−∞ ≤ x < 7}

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2. 1/1 points | Previous Answers AufCAT8 2.1.035. My Notes

Graph the equation by plotting points that satisfy the equation.

y = −2|x − 4|

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3. 1/5 points | Previous Answers AufCAT8 2.1.087.MI. My Notes

Find the x- and y-intercepts of the graph of the equation.

|x| + |y| = 5

x−intercept

(x, y)

5,0

(smaller x-value)

x−intercept

(x, y)

−5,0

(larger x-value)

y−intercept

(x, y)

0,5

(smaller y-value)

y−intercept

(x, y)

0,−5

(larger y-value)

Use the intercepts and additional points as needed to draw the graph of the equation.

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4. 9/9 points | Previous Answers AufCAT8 2.1.087.MI.SA. My Notes

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.

Find the x- and y-intercepts of the graph of the equation. Use the intercepts and additional points as needed to draw the graph of the equation.

|x| + |y| = 8

Part 1 of 6

Any point on the graph that has an x- or a y-coordinate of zero is called an intercept because at this point, the graph intersects the x- or the y-axis.

The definitions of x-intercepts and y-intercepts are as follows:

If

(x₁, 0)

satisfies an equation, then the point

(x₁, 0)

is called the x

-intercept of the graph of the equation.

If

(0, y₁)

satisfies an equation, then the point

(0, y₁)

is called the y

-intercept of the graph of the equation.

Part 2 of 6

To find the x-intercepts of

|x| + |y| = 8,

let y = 0 and solve the equation for x.

\|x\| + \|0 0 \|	=	8
x	=	±8 8

Part 3 of 6

So when y = 0, we have

x = 8

and

x = −8.

Thus, the x-intercepts are as follows. (Separate multiple ordered pairs with commas.)

(x, y) =

$$(8,0),(−8,0)

(-8,0),(8,0)

Part 4 of 6

To find the y-intercepts of

|x| + |y| = 8,

let

x = 0

and solve the equation for y.

\|0 0 \| + \|y\|	=	8
y	=	±8 8

Part 5 of 6

So when

x = 0,

we have y = 8 and

y = −8.

Thus, the y-intercepts are as follows. (Separate multiple ordered pairs with commas.)

(x, y) =

$$(0,8),(0,−8)

(0, -8),(0, 8)

Part 6 of 6

Since there are two x-intercepts and two y-intercepts, and each piece of the equation is linear, there is no need to find any additional point to graph the equation.

To draw the graph, plot the points (8, 0), (−8, 0), (0, 8), and (0, −8), and connect them.

0,0

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

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Submission Data

segment: [(-8,0),(0,8)]; segment: [(0,8),(8,0)]; segment: [(8,0),(0,-8)]; segment: [(0,-8),(-8,0)]

You have now completed the Master It.

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5. 3/3 points | Previous Answers AufCAT8 2.2.096. My Notes

A child 3 feet tall is standing near a street lamp that is 12 feet high. The light from the lamp casts a shadow as shown in the diagram below.

3 ft

(a) Find the length l of the shadow as a function of the distance d of the child from the lamppost. (Hint: Use the fact that the ratios of corresponding sides of similar triangles are equal.)

l(d) =

d3

(b) What is the domain of the function? (Enter your answer using interval notation.)

[0,∞)

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6. 4/4 points | Previous Answers AufCAT8 2.3.035. My Notes

Graph the equation by first writing the equation in slope-intercept form.

3x + y = 1

y=−3x+1

Graph the equation.

0,0

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

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Submission Data

Check the graph by finding the x- and y-intercepts.

x-intercept (x, y)

13,0

y-intercept (x, y)

0,1

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7. 0/8 points | Previous Answers AufCAT8 2.6.019. My Notes

Use the given functions f and g to find

f + g,

f − g,

fg,

and

State the domain of each. (Enter your answer for the domain in interval notation.)

f(x) =

49 − x²

, g(x) = 7 + x

f + g	=	`ƒ`(`x`)+`g`(`x`)=(49−`x`2)+(7+`x`)
domain		(−∞,∞)

f − g	=
domain

fg	=
domain

domain

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8. 6/6 points | Previous Answers AufCAT8 2.6.080. My Notes

Consider the following.

f(x) = 2x − 6, g(x) =

x + 6

Show that

(g ∘ f)(x) = x.

(g ∘ f)(x)

x − 6

Show that

(f ∘ g)(x) = x.

(f ∘ g)(x)

x + 6

−

x + 6 −

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9. 4/4 points | Previous Answers AufCAT8 2.6.085. My Notes

A water tank has the shape of a right circular cone with height 16 feet and radius 8 feet. Water is running into the tank so that the radius r (in feet) of the surface of the water is given by

r = 1.5t,

where t is the time (in minutes) that the water has been running.

(a) The area A of the surface of the water is

A = πr².

Find

A(t)

and use it to determine the area of the surface of the water when

t = 5 minutes.

(Round the area to two decimal places.)

A(t)	=	π(1.5`t`)2
A(5)	=	ft²

(b) The volume V of the water is given by

V =

πr²h.

Find

V(t)

and use it to determine the volume of the water when

t = 3 minutes.

(Hint: The height of the water in the cone is always twice the radius of the surface of the water. Round the volume to two decimal places.)

V(t)	=	13π(1.5`t`)2(3`t`)
V(3)	=	ft³

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10. –/2 points AufCAT8 2.7.018. My Notes

A graphing calculator is recommended.

The data in the table below show the distance, in feet, a ball travels for various swing speeds, in miles per hour, of a bat.

Bat speed (mph)	Distance (ft)
40	204
45	217
50	237
60	278
70	298
75	324
80	333

(a) Find the linear regression equation for these data. (Round all numerical values to three decimal places.)

y =

(b) Using the regression model, what is the expected distance a ball will travel when the bat speed is 58 miles per hour? Round to the nearest foot.
ft

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1	2	3	4	5
0/1	0/1	0/1	0/1	1/1
4/50	5/50	2/50	3/50	7/50

1	2	3	4	5	6	7	8
0/1	0/1	–/1	–/1	–/1	–/1	–/1	–/1
4/50	1/50	0/50	0/50	0/50	0/50	0/50	0/50

1	2
–/1	–/1
0/50	0/50

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Aufmann and Nation - Algebra and Trigonometry 8/e (Homework)

Current Score : 30 / 44

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

Last Saved : n/a Saving... ()

Instructions

Assignment Submission

Assignment Scoring

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