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Larson - Algebra & Trig 11/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 30 / 32

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 13
0/1 1/1 0/1 2/2 1/1 2/2 3/3 1/1 3/3 3/3 7/7 2/2 5/5
Total
30/32 (93.8%)

  • Instructions

    Engage your students and prepare them for success in your course and beyond with the student-focused approach of Ron Larson and WebAssign in Algebra and Trigonometry, 11th edition. Developed through learning design principles, Larson removes barriers to learning and offers a carefully planned and inclusive experience for all students. Students facing readiness gaps will overcome them with new "Review & Refresh" exercises, Skills Refresher videos, and more.

    Question 1 enforces that the answer is written as a complex number and includes a Master It and solution.

    Question 2 grades all solutions written as a list. The prompt alerts the student to enter a comma-separated list of answers.

    Question 3 contains expression grading where any equivalent form of the expression is accepted. Also included are a Master It tutorial, Watch It, and solution.

    Question 4 demonstrates grading for factored expressions in the first answer blank. Also included are a Master It tutorial, Watch It, and solution.

    Question 5 highlights grading used for an expanded logarithm per the question instructions.

    Question 6 shows one of many prompts used to indicate to the student what to enter when there is no answer. Also included are a Watch It and a solution.

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

    Question 8 features an image with a randomized value in addition to equation grading, which allows any equivalent form of the requested equation.

    Question 9 exhibits an expandable matrix answer blank that grades the matrix as a whole, and also handles answers for matrices that cannot be computed. Also included are a Master It tutorial, Watch It, and solution.

    Question 10 demonstrates the functionality of the expanded problem (EP) question type. Students are required to show their intermediate work before arriving at the final answer.

    Question 11 demonstrates one of the many ways proofs can be automatically graded.

    Questions 12 and 13 are examples of Review and Refresh exercises found at the end of each section. These exercises will help the student reinforce previously learned skills and concepts and prepare for the next section. 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. 0/1 points  |  Previous Answers LarAT11 1.5.018.MI. My Notes
Question Part
Points
Submissions Used
1
0/1
3/100
Total
0/1
 
Perform the operation and write the result in standard form. (Simplify your answer completely.)
(6 − 5i)(3 − 2i)
3
Incorrect: Your answer is incorrect. webMathematica generated answer key


Solution or Explanation
(6 − 5i)(3 − 2i) = 18 − 12i − 15i + 10i2
 = 18 − 27i − 10 = 8 − 27i

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2. 1/1 points  |  Previous Answers LarAT11 2.3.020. My Notes
Question Part
Points
Submissions Used
1
1/1
2/100
Total
1/1
 
Find the zeros of the function algebraically. (Enter your answers as a comma-separated list.)
f(x) = 9x3 − 36x2 − x + 4
x =
−13​,13​,4
Correct: Your answer is correct. webMathematica generated answer key
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3. 0/1 points  |  Previous Answers LarAT11 2.5.050.MI. My Notes
Question Part
Points
Submissions Used
1
0/1
2/100
Total
0/1
 
Write an equation for the function whose graph is described.
the shape of
f(x) = |x|,
 but shifted three units to the left and five units down
g(x) =
35
Incorrect: Your answer is incorrect. webMathematica generated answer key


Solution or Explanation
f(x) = |x| moved 3 units to the left and 5 units down.
g(x) = |x + 3| − 5

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4. 2/2 points  |  Previous Answers LarAT11 3.4.062.MI. My Notes
Question Part
Points
Submissions Used
1 2
1/1 1/1
2/100 2/100
Total
2/2
 
Write the polynomial as the product of linear factors.
g(x) = x2 + 10x + 18
g(x) =
(x−√7+5)(x+√7+5)
Correct: Your answer is correct. webMathematica generated answer key
List all the zeros of the function. (Enter your answers as a comma-separated list. Enter all answers using the appropriate multiplicities.)
x =
−5−√7,√7−5
Correct: Your answer is correct. webMathematica generated answer key


Solution or Explanation
g(x) = x2 + 10x + 18
By the Quadratic Formula, the zeros of g(x) are as follows.
x = 
−10 ± 
100 − 72
2
 = 
−10 ± 
28
2
 = −5 ± 
7
 
g(x) = (x + 5 + 
7
)(x + 5 − 
7
)

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5. 1/1 points  |  Previous Answers LarAT11 5.3.049. My Notes
Question Part
Points
Submissions Used
1
1/1
2/100
Total
1/1
 
Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)
ln xyz9
ln(x) + ln(y) + 9ln(z)
Correct: Your answer is correct. webMathematica generated answer key
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6. 2/2 points  |  Previous Answers LarAT11 6.1.034. My Notes
Question Part
Points
Submissions Used
1 2
1/1 1/1
1/100 1/100
Total
2/2
 
Find (if possible) the complement and supplement of the angle. (If not possible, enter IMPOSSIBLE.)
55°
complement Correct: Your answer is correct. seenKey

35

 ° supplement Correct: Your answer is correct. seenKey

125

 °


Solution or Explanation
Complement: 90° − 55° = 35°
Supplement: 180° − 55° = 125°

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7. 3/3 points  |  Previous Answers LarAT11 6.3.057. My Notes
Question Part
Points
Submissions Used
1 2 3
1/1 1/1 1/1
1/100 1/100 1/100
Total
3/3
 
Evaluate the sine, cosine, and tangent of the angle without using a calculator. (If an answer is undefined, enter UNDEFINED.)
5π
3
sin θ =
−√32​
Correct: Your answer is correct. webMathematica generated answer key
cos θ =
12​
Correct: Your answer is correct. webMathematica generated answer key
tan θ =
−√3
Correct: Your answer is correct. webMathematica generated answer key
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8. 1/1 points  |  Previous Answers LarAT11 6.7.048. My Notes
Question Part
Points
Submissions Used
1
1/1
2/100
Total
1/1
 
A buoy oscillates in simple harmonic motion as waves go past. The buoy moves a total of 2.5 feet from its low point to its high point (see figure), and it returns to its high point every 12 seconds. Write an equation that describes the motion of the buoy if its high point is at t = 0, in terms of its height h.
h=54​cos(πt6​)
Correct: Your answer is correct. webMathematica generated answer key

2.5 ft


Solution or Explanation
At t = 0, buoy is at its high point  right double arrow implies  h = a cos(ωt).
Distance from high to low = 2|a| = 2.5
|a| = 
5
4
Returns to high point every 12 seconds:
Period: 
2π
ω
 = 12  right double arrow implies  ω = 
π
6
 
h = 
5
4
 cos
πt
6
 

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9. 3/3 points  |  Previous Answers LarAT11 10.2.032.MI. My Notes
Question Part
Points
Submissions Used
1 2 3
1/1 1/1 1/1
2/100 2/100 2/100
Total
3/3
 
If possible, find AB. (If not possible, enter IMPOSSIBLE in any cell of the matrix.)
A = 
0−12
803
5−16
,    B = 
4−1
4−5
18
AB =

Correct: Your answer is correct. seenKey

[-2, 21; 35, 16; 22, 48]

State the dimension of the result. (If not possible, enter IMPOSSIBLE in both answer blanks.)
Correct: Your answer is correct. seenKey

3

 × Correct: Your answer is correct. seenKey

2

Solution or Explanation
A is 3 × 3, B is 3 × 2 right double arrow implies AB is 3 × 2.
A = 
0−12
803
5−16
,    B = 
4−1
4−5
18
AB = 
0−12
803
5−16
4−1
4−5
18
 = 
−221
3516
2248

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10. 3/3 points  |  Previous Answers LarAT11 6.1.080.EP. My Notes
Question Part
Points
Submissions Used
1 2 3
1/1 1/1 1/1
2/100 2/100 2/100
Total
3/3
 
Consider an arc on a circle of radius r intercepted by a central angle θ.
r = 20 feet,  θ = 45°
Convert 45° to exact radian measure.
45° =
π4​
Correct: Your answer is correct. webMathematica generated answer key rad
Find the exact length (in ft) of the arc.
5π
Correct: Your answer is correct. webMathematica generated answer key ft
Give a decimal approximation for the length (in ft) of the arc. (Round your answer to two decimal places.)
Correct: Your answer is correct. seenKey

15.71

 ft
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11. 7/7 points  |  Previous Answers LarAT11 4.PS.005. 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
1/100 2/100 2/100 2/100 2/100 1/100 1/100
Total
7/7
 
Use the figure to show that
|d2 − d1| = 2a.
The x y-coordinate plane is given. A curve with 2 parts, 5 labeled points, and 2 dashed line segments are graphed.
  • The first part of the curve enters the window in the second quadrant, goes down and right becoming more steep, changes direction at the first labeled point (−a, 0), goes down and left becoming less steep, and exits the window in the third quadrant.
  • The second part of the curve enters the window in the first quadrant, goes down and left becoming more steep, goes through the second labeled point (x, y), continues down and left becoming more steep, changes direction and the third labeled point (a, 0), goes down and right becoming less steep, and exits the window in the fourth quadrant.
  • The fourth point is labeled (−c, 0) and is located on the negative x-axis some distance to the left of the first labeled point.
  • The fifth point is labeled (c, 0) and is located on the positive x-axis some distance to the right of the third labeled point.
  • The first dashed line segment is labeled d1, begins at (x, y), goes down and slightly left, and ends at (c, 0).
  • The second dashed line segment is labeled d2, begins at (x, y), goes down and left, crosses the y-axis, continues down and left, and ends at (−c, 0).
By definition, a hyperbola is the set of all points
(x, y)
 in a plane for which the Correct: Your answer is correct. seenKey

absolute value of the difference

 of the distances from the foci
(−c, 0)
 and
c
Correct: Your answer is correct. webMathematica generated answer key , 0
 is a constant. First find the value of
d2 − d1
 in the case that
(x, y)
 is the vertex
(a, 0).
The distance d2 from the vertex
(a, 0)
 to the focus
(−c, 0)
 is
a+c
Correct: Your answer is correct. webMathematica generated answer key . The distance d1 from vertex
(a, 0)
 to the other focus
(c, 0)
 is
c−a
Correct: Your answer is correct. webMathematica generated answer key . Therefore,
d2 − d1 = 
2
Correct: Your answer is correct. webMathematica generated answer key
 a.
The chosen vertex has x-coordinate a > 0, thus
d2 − d1 Correct: Your answer is correct. seenKey

=

 |d2 − d1|.
By the definition of a hyperbola, for any point
(x, y)
 we have that
|d2 − d1|
 is constant. This means the value of
|d2 − d1|
 for Correct: Your answer is correct. seenKey

any
(x, y)
 is the same as the value for
(a, 0).
 Thus, it is shown that
|d2 − d1| = 2a.
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12. 2/2 points  |  Previous Answers LarAT11 3.4.118. My Notes
Question Part
Points
Submissions Used
1 2
1/1 1/1
3/100 3/100
Total
2/2
 
Consider the following inequality.
|7x + 6| ≥ 27
Solve the inequality. (Enter your answer using interval notation.)
(−∞,−337​]∪[3,∞)
Correct: Your answer is correct. webMathematica generated answer key
Graph the solution set.
Use the tools to enter your answer.
Created with Raphaël 2.1.0-10-8-6-4-20246810
Created with Raphaël 2.1.0

NO SOLUTION

Help
Correct: Your answer is correct.

Created with Raphaël 2.1.0-10-8-6-4-20246810
Created with Raphaël 2.1.0

NO SOLUTION

seenKey

(-infinity, -4.71428571]; [3, infinity)
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13. 5/5 points  |  Previous Answers LarAT11 4.2.095. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5
1/1 1/1 1/1 1/1 1/1
2/100 5/100 2/100 1/100 2/100
Total
5/5
 
Consider the following quadratic function.
f(x) = x2 + 4x
Write the quadratic function in standard form.
f(x) =
(x+2)2 −4
Sketch its graph.
No Solution
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Submission Data

Identify the vertex and axis of symmetry.
vertex (x, f(x))
= 
−2,−4
axis of symmetry
x=−2
Identify the x-intercept(s). (Enter your answers as a comma-separated list.)
x =
0,−4
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