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Larson - Precalculus 11/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 16 / 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 1/1 0/2 1/1 4/4 3/3 0/1 3/3 0/3 3/5 0/2 0/5
Total
16/32 (50.0%)

  • 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 Precalculus, 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 a 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 is a multi-part question which shows one of many prompts used to indicate to the student what to enter when there is no answer.

    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 to 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 LarPCalc11 2.4.018.MI. My Notes
Question Part
Points
Submissions Used
1
0/1
2/100
Total
0/1
 
Perform the operation and write the result in standard form. (Simplify your answer completely.)
(6 − 5i)(2 − 2i)
2−22y
Incorrect: Your answer is incorrect. webMathematica generated answer key


Solution or Explanation
(6 − 5i)(2 − 2i) = 12 − 12i − 10i + 10i2
 = 12 − 22i − 10 = 2 − 22i

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2. 1/1 points  |  Previous Answers LarPCalc11 1.5.020. My Notes
Question Part
Points
Submissions Used
1
1/1
1/100
Total
1/1
 
Find the zeros of the function algebraically. (Enter your answers as a comma-separated list.)
f(x) = 4x3 − 32x2 − x + 8
x =
8,.5,−.5
Correct: Your answer is correct. webMathematica generated answer key
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3. 1/1 points  |  Previous Answers LarPCalc11 1.7.050.MI. My Notes
Question Part
Points
Submissions Used
1
1/1
2/100
Total
1/1
 
Write an equation for the function whose graph is described.
the shape of
f(x) = |x|,
 but shifted seven units to the left and nine units down
g(x) =
|x+7|−9
Correct: Your answer is correct. webMathematica generated answer key


Solution or Explanation
f(x) = |x| moved 7 units to the left and 9 units down.
g(x) = |x + 7| − 9

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4. 0/2 points  |  Previous Answers LarPCalc11 2.5.062.MI. My Notes
Question Part
Points
Submissions Used
1 2
0/1 0/1
2/100 1/100
Total
0/2
 
Write the polynomial as the product of linear factors.
g(x) = x2 + 10x + 20
g(x) =
(x−(5+√5))(x+(5+√5))
Incorrect: Your answer is incorrect. 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−√5,−(5−√5)
Incorrect: Your answer is incorrect. webMathematica generated answer key


Solution or Explanation
g(x) = x2 + 10x + 20
By the Quadratic Formula, the zeros of g(x) are as follows.
x = 
−10 ± 
100 − 80
2
 = 
−10 ± 
20
2
 = −5 ± 
5
 
g(x) = (x + 5 + 
5
)(x + 5 − 
5
)

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5. 1/1 points  |  Previous Answers LarPCalc11 3.3.049. My Notes
Question Part
Points
Submissions Used
1
1/1
1/100
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 xyz2
ln(x)+ln(y)+2ln(z)
Correct: Your answer is correct. webMathematica generated answer key
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6. 4/4 points  |  Previous Answers LarPCalc11 4.1.034. My Notes
Question Part
Points
Submissions Used
1 2 3 4
1/1 1/1 1/1 1/1
1/100 1/100 1/100 1/100
Total
4/4
 
Find (if possible) the complement and supplement of each angle. (If not possible, enter IMPOSSIBLE.)
(a)    115°
complement     Correct: Your answer is correct. seenKey

IMPOSSIBLE

 °
supplement     Correct: Your answer is correct. seenKey

65

 °

(b)    135°
complement     Correct: Your answer is correct. seenKey

IMPOSSIBLE

 °
supplement     Correct: Your answer is correct. seenKey

45

 °

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7. 3/3 points  |  Previous Answers LarPCalc11 4.4.061. 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. 0/1 points  |  Previous Answers LarPCalc11 4.8.048. My Notes
Question Part
Points
Submissions Used
1
0/1
1/100
Total
0/1
 
A buoy oscillates in simple harmonic motion as waves go past. The buoy moves a total of 8.5 feet from its low point to its high point (see figure), and it returns to its high point every 6 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(t)=−8.5cos(π3​t)
Incorrect: Your answer is incorrect. webMathematica generated answer key

8.5 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| = 8.5
|a| = 
17
4
Returns to high point every 6 seconds:
Period: 
2π
ω
 = 6  right double arrow implies  ω = 
π
3
 
h = 
17
4
 cos
πt
3
 

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9. 3/3 points  |  Previous Answers LarPCalc11 8.2.032.MI. 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
 
If possible, find AB. (If not possible, enter IMPOSSIBLE in any cell of the matrix.)
A = 
0−14
803
7−18
,    B = 
4−1
4−7
16
AB =

Correct: Your answer is correct. seenKey

[0, 31; 35, 10; 32, 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 = 
0−14
803
7−18
,    B = 
4−1
4−7
16
AB = 
0−14
803
7−18
4−1
4−7
16
 = 
031
3510
3248

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10. 0/3 points  |  Previous Answers LarPCalc11 4.1.051.EP. My Notes
Question Part
Points
Submissions Used
1 2 3
0/1 0/1 0/1
1/100 1/100 1/100
Total
0/3
 
Consider an arc on a circle of radius r intercepted by a central angle θ.
r = 12 feet,  θ = 30°
Convert 30° to exact radian measure.
30° =
π6​
rad
Find the exact length (in ft) of the arc.
4π
ft
Give a decimal approximation for the length (in ft) of the arc. (Round your answer to two decimal places.)
ft
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11. 3/5 points  |  Previous Answers LarPCalc11 4.1.073. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5
0/1 1/1 0/1 1/1 1/1
1/100 1/100 1/100 1/100 1/100
Total
3/5
 
Prove that the area of a circular sector of radius r with central angle θ is
A = 
1
2
θr2,
 where θ is measured in radians.
Let r be the radius of circle C and θ be a central angle of the circle measured in radians.
A circle with radius r has a shaded sector. The first side of the sector starts at the top of the circle and ends at the center of the circle. The second side of the sector starts at the top right of the circle and ends at the center of the circle. The angle formed between the two edges at the center of the circle is labeled θ.
The ratio of the shaded area of the sector and area of the circle is proportional to the ratio of the central angle θ and Incorrect: Your answer is incorrect. seenKey

2π

 . This is given by the following proportion.
area of sector
Correct: Your answer is correct. seenKey

area of circle
 = 
measure of central angle of sector
Incorrect: Your answer is incorrect. seenKey

measure of central angle of circle
Let A represent the area of the sector. Substitute this variable and the known quantities into this proportion and solve for A.
A
πr2
Correct: Your answer is correct. webMathematica generated answer key
 = 
θ
2π
A = 
πr2
Correct: Your answer is correct. webMathematica generated answer key
θ
2π
 = 
1
2
r2θ
This gives the area of the sector of radius r with central angle θ measured in radians as desired.


Solution or Explanation
area of circle = πr2
area of sector
area of circle
 = 
measure of central angle of sector
measure of central angle of circle
 
area of sector
πr2
 = 
θ
2π
area of sector = (πr2)
θ
2π
 = 
1
2
r2θ
A circle with radius r has a shaded sector. The first side of the sector starts at the top of the circle and ends at the center of the circle. The second side of the sector starts at the top right of the circle and ends at the center of the circle. The angle formed between the two edges at the center of the circle is labeled θ.
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12. 0/2 points  |  Previous Answers LarPCalc11 2.5.118. My Notes
Question Part
Points
Submissions Used
1 2
0/1 0/1
1/100 1/100
Total
0/2
 
Consider the following inequality.
|5x + 2| ≥ 37
Solve the inequality. (Enter your answer using interval notation.)
[x≥7]
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

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13. 0/5 points  |  Previous Answers LarPCalc11 2.6.073. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5
0/1 0/1 0/1 0/1 0/1
1/100 3/100 1/100 1/100 1/100
Total
0/5
 
Consider the following quadratic function.
f(x) = x2 + 6x
Write the quadratic function in standard form.
f(x) =
x2+6x
Incorrect: Your answer is incorrect. webMathematica generated answer key
Sketch its graph.
No Solution
Help
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Clear Graph
Delete Layer
Fill
Show Key

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Submission Data

Incorrect: Your answer is incorrect.
seenKey

parabola: x^2+6*x
Identify the vertex and axis of symmetry.
vertex (x, f(x))
= 
−2,−8
Incorrect: Your answer is incorrect. webMathematica generated answer key
axis of symmetry
−2
Incorrect: Your answer is incorrect. webMathematica generated answer key
Identify the x-intercept(s). (Enter your answers as a comma-separated list.)
x =
−4, 0
Incorrect: Your answer is incorrect. webMathematica generated answer key
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