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Collingwood et al - Precalculus (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 12 / 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
10/10 –/1 2/5 0/9 –/2 –/9 –/2 –/6
Total
12/44 (27.3%)

  • Instructions

    Here are some textbook questions from Precalculus 1/e by David H. Collingwood, K. David Prince and Matthew M. Conroy, a new custom course collection created for the University of Washington mathematics department.

    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.

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1. 10/10 points  |  Previous Answers UWAPreCalc1 6.P.001. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8 9 10
1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1
1/50 1/50 1/50 1/50 1/50 1/50 1/50 1/50 1/50 2/50
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10/10
 
The absolute value function is defined by the multipart rule:
|x| = 
x    if 0 ≤ x
−xif x < 0
The graph of the absolute value function is pictured below.
WebAssign Plot
(a) Calculate:
|0|, |3|, |−1|.

|0| =  Correct: Your answer is correct.
|3| =  Correct: Your answer is correct.
|−1| =  Correct: Your answer is correct.


(b) Solve for x. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
|x| = 4
  x =
−4, 4
Correct: Your answer is correct.
 
|x| = 0
  x =
0
Correct: Your answer is correct.
 
|x| = −6
  x =
DNE
Correct: Your answer is correct.

(c) Sketch the graph of
y = 
1
2
x + 5 and y = |x|
 in the same coordinate system.

Incorrect: Your answer is incorrect.

Find where the two graphs intersect.
(x, y) =
−103​, 103​
Correct: Your answer is correct.
(smaller x-value)
(x, y) =
10, 10
Correct: Your answer is correct.
(larger x-value)

Find the area of the region bounded by the two graphs.
Correct: Your answer is correct. square units
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2. –/1 points UWAPreCalc1 6.P.005. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Express the area of the shaded region below as a function of x. The dimensions in the figure are centimeters.
cm2
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3. 2/5 points  |  Previous Answers UWAPreCalc1 6.P.010. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5
0/1 1/1 0/1 1/1 –/1
1/50 1/50 1/50 1/50 0/50
Total
2/5
 
Pagliacci Pizza has designed a cardboard delivery box from a single piece of cardboard, as pictured.
(a) Find a polynomial function
v(x)
 that computes the volume of the box in terms of x.
v(x)
 =
x(50− 2x)(20 − 2x)
Incorrect: Your answer is incorrect.

What is the degree of v?
Correct: Your answer is correct.

(b) Find a polynomial function
a(x)
 that computes the exposed surface area of the closed box in terms of x.
a(x)
 =
1000 − 4x2
Incorrect: Your answer is incorrect.

What is the degree of a?
Correct: Your answer is correct.

What are the explicit dimensions if the exposed surface area of the closed box is 600 sq. inches? (Round your dimensions to three decimal places. Enter your answers as a comma-separated list.)
in
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4. 0/9 points  |  Previous Answers UWAPreCalc1 6.P.012. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8 9
0/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1
1/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50
Total
0/9
 
The graph of a function
y = g(x)
 on the domain
−8 ≤ x ≤ 8
 consists of line segments and semicircles of radius 3 connecting the points
(−8, 0), (−6, 6), (0, 6), (6, 6), (8, 0).
(a) What is the range of g?
     Incorrect: Your answer is incorrect.

(b) Where is the function increasing? (Select all that apply.)


Where is the function decreasing? (Select all that apply.)


(c) Find the multipart formula for
y = g(x).

y = 
    if −8 ≤ x ≤ −6
if −6 ≤ x ≤ 0
if 0 ≤ x ≤ 6
if 6 ≤ x ≤ 8


(d) If we restrict the function to the smaller domain
−7 ≤ x ≤ 0,
 what is the range?
    

(e) If we restrict the function to the smaller domain
0 ≤ x ≤ 6,
 what is the range?
    
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5. –/2 points UWAPreCalc1 6.P.013. My Notes
Question Part
Points
Submissions Used
1 2
–/1 –/1
0/50 0/50
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–/2
 
(a) Simplify as far as possible.
 
1
1 + 
1
a
 − 
a
a + 1
 



(b) Find a, b, c that simultaneously satisfy these three equations.
a + b − c = 6
2a − 3b + c = 7
a + b + c = −2
(a, b, c) = 
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6. –/9 points UWAPreCalc1 19.P.002. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8 9
–/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50
Total
–/9
 
A weight is attached to a spring suspended from a beam. At time t = 0, it is pulled down to a point 11 cm above the ground and released. After that, it bounces up and down between its minimum height of 11 cm and a maximum height of 25 cm, and its height
h(t)
 is a sinusoidal function of time t. It first reaches a maximum height 0.8 seconds after starting.
(a) Follow the procedure outlined in this section to sketch a rough graph of
h(t).
 Draw at least two complete cycles of the oscillation, indicating where the maxima and minima occur.


(b) What are the mean, amplitude, phase shift and period for this function? (Assume the absolute value of the phase shift is less than the period.)
mean
amplitude
phase shift     
period

(c) Give four different possible values for the phase shift. (Enter your answers as a comma-separated list.)


(d) Write down a formula for the function
h(t)
 in standard sinusoidal form; i.e. as in the equation shown below.
y = A sin 
2π
B
(x − C)
 + D
y =


(e) What is the height of the weight after 2.4 seconds?
cm

(f) During the first 10 seconds, how many times will the weight be exactly 20 cm above the floor? (Note: This problem does not require inverse trigonometry.)
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7. –/2 points UWAPreCalc1 19.P.004. My Notes
Question Part
Points
Submissions Used
1 2
–/1 –/1
0/50 0/50
Total
–/2
 
Suppose the high tide in Seattle occurs at 1:00 a.m. and 1:00 p.m. at which time the water is 16 feet above the height of low tide. Low tides occur 6 hours after high tides. Suppose there are two high tides and two low tides every day and the height of the tide varies sinusoidally.
(a) Find a formula for the function
y = h(t)
 that computes the height of the tide above low tide at time t, where t indicates the number of hours after midnight. (In other words,
y = 0
 corresponds to low tide.)
h(t) =


(b) What is the tide height at 11:00 a.m.?
ft
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8. –/6 points UWAPreCalc1 19.P.005. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6
–/1 –/1 –/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50 0/50 0/50
Total
–/6
 
Your seat on a Ferris Wheel is at the indicated position at time
t = 0.
Let t be the number of seconds elapsed after the wheel begins rotating counterclockwise. You find it takes 3 seconds to reach the top, which is 53 feet above the ground. The wheel is rotating 12 RPM and the diameter of the wheel is 50 feet. Let
d(t)
 be your height above the ground at time t.
(a) Argue that
d(t)
 is a sinusoidal function, describing the amplitude, phase shift, period and mean.
amplitude
phase shift     
period
mean

(b) When are the first and second times you are exactly 28 feet above the ground? (Enter your answers as a comma-separated list.)
t = sec

(c) After 29 seconds, how many times will you have been exactly 28 feet above the ground?
times
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