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Adip Shelley
MTH 166, section E97N CORRECT, Fall 2017
Instructor: Richard Pellerin
WebAssign
Quiz-Ch.4 (MTH 166) (Quiz)
Current Score : 30.5 / 37.5
Due : Sunday, November 12 2017 11:59 PM EST
3/3 submissions
The due date for this assignment is past. Your work can be viewed below, but no changes can be made.
1. 1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 4.1.012.
Graph the exponential function by hand. Identify any asymptotes and intercepts and determine whether the graph of the function is increasing or decreasing.
(Enter NONE in any unused answer blanks.)
Equation of horizontal asymptote:
$$y=0
Equation of vertical asymptote:
$$none
Value of y-intercept
1
1
Value of x-intercept
none
NONE
The function is decreasing
decreasing .
2. 1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 4.2.036.
Solve the equation for x.
log3(35) = x
5
5
3. 0/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 4.4.146.
Find the time t required for a $1450 investment to double at interest rate r, compounded continuously, and triple at interest rate r, compounded continuously.
Round your results to two decimal places.
r = 5.75%
(a) double at interest rate r, compounded continuously
t = (No Response)
12.05 yr
(b) triple at interest rate r, compounded continuously
t = (No Response)
19.11 yr
4. 1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 4.2.086.
Use the properties of natural logarithms to rewrite the expression.
eln 34
34
34
5. 1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 4.4.030.
Solve the exponential equation.
3 x
27
=
4
64
3
x= 3
6. 1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 4.1.010.
Graph the exponential function by hand. Identify any asymptotes and intercepts and determine whether the graph of the function is increasing or decreasing.
(Enter NONE in any unused answer blanks.)
Equation of horizontal asymptote:
$$y=0
Equation of vertical asymptote:
$$none
Value of y-intercept
1
1
Value of x-intercept
none
NONE
The function is increasing
increasing .
7. 1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 4.4.044.
Solve the logarithmic equation.
log10(x) = –9/10
x = 0.126
0.126
8. 1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 4.3.064.
Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)
logb
x y3
z3
$$logb(x)2+3logb(y)−3logb(z)
9. 0/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 4.5.014.
Complete the table for a savings account in which interest is compounded continuously.
Initial Investment
Annual % Rate
$2200
1.8%
(No Response)
$1300
(No Response)
(No Response)
5.33
4.47
%
2360
2.4%
10.1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 4.3.082.
Condense the expression to the logarithm of a single quantity. (Assume z > 5.)
3[ln z + ln(z + 7)] − 2 ln(z − 5)
$$ln z3(z+7)3(z−5)2
11.1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 4.4.032.
Solve the exponential equation. (Round your answer to three decimal places.)
ex = 62
x = 4.127
4.127
Solution or Explanation
ex = 62
ln(ex) = ln(62)
x = ln(62)
x ≈ 4.127
Amount After 10 years
38.5
years
%
$400
$ (No Response)
Time to Double
13 years
(No Response)
15.5
years
(No Response)
years
28.9
$ (No Response)
2630
$ (No Response)
2220
$625.25
$3000.00
12.0/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 4.1.060.
Complete the table to determine the balance A for $2000 invested at rate r for t years and compounded n times per year. (Round your answers to the nearest ce
r = 3%, t = 42 years
n
1
A
$ (No Response)
6,921.39
2
$ (No Response)
6,985.18
4
$ (No Response)
7,017.77
13.1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 4.3.016.
Evaluate the logarithm using the change-of-base formula. Round your result to three decimal places.
log5(0.019)
-2.46
-2.463
14.1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 4.3.014.
Evaluate the logarithm using the change-of-base formula. Round your result to three decimal places.
log10(7)
0.845
0.845
Solution or Explanation
log(7)
ln(7)
log10(7) =
=
= ≈ 0.845
log(10)
ln(10)
15.1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 4.4.040.
Solve the logarithmic equation.
ln x = −14
x=
$$1e14
16.1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 4.2.032.
Solve the equation for x.
log11(11) = x
1
1
17.0.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 4.2.010.MI.
Write the logarithmic equation in exponential form. For example, the exponential form of log5 25 = 2 is 52 = 25.
log
1
1
= -8
100,000,000
10
-8
-8
= 100,000,000
Your answer must be a fraction, integer, or exact decimal.
1/100000000
$ (No Response)
18.1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 4.4.102.
Solve the logarithmic equation algebraically. Round the result to three decimal places. Verify your answers using a graphing utility. (Enter your answers as a
comma-separated list. If there is no solution, enter NO SOLUTION.)
log10 x2 = 6
x=
$$1000,−1000
19.1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 4.4.112.MI.
Solve the logarithmic equation algebraically. Approximate the result to three decimal places. (If there is no solution, enter NO SOLUTION.)
log(2x) – log(10 + √x) = 2
x = 3427.051
3427.051
20.0/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 4.4.144.
Find the time t required for a $1250 investment to double at interest rate r, compounded continuously, and triple at interest rate r, compounded continuously.
Round your results to two decimal places.
r = 8%
(a) double at interest rate r, compounded continuously
t = (No Response)
8.66 yr
(b) triple at interest rate r, compounded continuously
t = (No Response)
13.73 yr
21.1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 4.2.082.
Use the properties of natural logarithms to rewrite the expression.
ln(e2)
2
2
22.1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 4.2.034.
Solve the equation for x.
log3 3−9 = x
x = -9
-9
23.1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 4.2.040.
Use the properties of logarithms to simplify the expression.
1
log5 25
5
$$25
24.1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 4.3.010.
Consider the following.
loga
2
3
(a) Rewrite the logarithm as a ratio of common logarithms.
$$log(23)log(a)
(b) Rewrite the logarithm as a ratio of natural logarithms.
$$ln(23)ln(a)
25.1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 4.2.088.
Use the properties of natural logarithms to rewrite the expression.
ln
-5
1
e5
-5
Adip Shelley
MTH 166, section E97N CORRECT, Fall 2017
Instructor: Richard Pellerin
WebAssign
Quiz-Ch.5 (MTH 166) (Quiz)
Current Score : 35.4 / 37.5
Due : Sunday, November 19 2017 11:59 PM EST
3/3 submissions
The due date for this assignment is past. Your work can be viewed below, but no changes can be made.
1. 1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 5.4.050.
Sketch the graph of the function. Use a graphing utility to verify your sketch. (Include two full periods.)
y = sin(x + π)
2. 1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 5.6.026.
Use a calculator to approximate the value of the expression. Round your answer to the nearest hundredth. (Enter your answer in
radians.)
arccos(−0.9)
2.69
2.69
3. 1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 5.3.108.
Find two solutions of the equation. Give your answers in degrees (0° ≤ θ < 360°) and in radians (0 ≤ θ < 2π). Do not use a calculator. (Do not enter your answers with degree symbols.) (a) cos θ = 2 2 Degrees Radians $$14π $$45 (smaller values) $$74π $$315 (larger values) (b) cos θ = − 2 2 Degrees $$135 Radians $$34π (smaller values) $$225 $$54π (larger values) 4. 1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 5.4.030. Describe the relationship between the graphs of f and g. Consider amplitude, period, and shifts. The amplitude of g is four times the period of f. The graphs of f and g differ only in their phase shift. The period of g is one-fourth the period of f. The amplitude of g is one-fourth the amplitude of f. The period of g is four times the period of f. 5. 1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 5.3.100. Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.) sec 205° -1.1034 -1.1034 Solution or Explanation 1 sec 205° = ≈ -1.1034 cos 205° 6. 0.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 5.4.010. Use the graph of the function to answer the following. f(x) = cos x on the interval [−2π, 2π] (a) Find the x-intercepts of the graph of y = f(x). (Enter your answers as a comma-separated list.) x= $$−32π,−12π,12π,32π (b) Find the y-intercepts of the graph of y = f(x). (Enter your answers as a comma-separated list.) y= $$(0,1) (c) Find the intervals on which the graph of y = f(x) is increasing and the intervals on which the graph of y = f(x) is decreasing. (Enter your answers using interval notation.) $$(−π,0),(π,2π) increasing $$(−2π,π),(0,π) decreasing (d) Find the relative extrema of the graph of y = f(x). (Enter your answers as a comma-separated list of ordered pairs.) $$(−2π,1)(0,1),(2π,1) relative maxima Your answer cannot be understood or graded. More Information $$(−π,−1)(π,−1) relative minima Your answer cannot be understood or graded. More Information 7. 0.9/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 5.2.016. Sketch a right triangle corresponding to the trigonometric function of the acute angle θ. Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of θ. cos θ = 3 7 $$√407 sin θ = $$√403 tan θ = $$7√40 csc θ = $$73 sec θ = $$3√40 cot θ = 8. 1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 5.1.072. Convert the angle measure from degrees to radians. Round your answer to three decimal places. 665° 11.606 11.606 rad 9. 1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 5.3.101. Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set to the correct angle mode.) cot(-215°) -1.428 -1.4281 10.1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 5.1.060. Rewrite each angle in radian measure as a multiple of π. (Do not use a calculator.) (a) 315° $$74π rad (b) 60° $$13π rad 11.1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 5.2.078. A zip-line steel cable is being constructed for a reality television competition show. The high end of the zip-line is attached to the
top of a 50-foot pole while the lower end is anchored at ground level to a stake 50 feet from the base of the pole.
(a) Find the angle of elevation of the zip-line.
$$45
°
(b) Find the number of feet of steel cable needed for the zip-line.
$$50√2
ft
(c) A contestant takes 4 seconds to reach the ground from the top of the zip-line. At what rate is the contestant moving
down the line?
$$(25√2)2
ft/s
At what rate is the contestant dropping vertically?
$$12.5
ft/s
12.1/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 5.3.078.
Evaluate the sine, cosine, and tangent of the angle without using a calculator.
– (5π)/6
$$−0.5
sin(θ) =
$$−0.866
cos(θ) =
$$−0.577
tan(θ) =
13.1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 5.1.074.
Convert the angle measure from radians to degrees. Round to three decimal places.
3π
11
49.091
49.091 °
14.1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 5.7.020.
An electrician is running wire from the electric box on a house to a utility pole 76 feet away. The angle of elevation to the
connection on the pole is 18°. How much wire does the electrician need? (Round your answer to two decimal places.)
79.91
79.91 ft
15.1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 5.1.094.MI.
Find the length of the arc on a circle of radius r intercepted by a central angle θ. (Round your answer to two decimal places.)
Radius r
Central Angle θ
12 feet
45°
Arc Length s
9.42
9.42 feet
Solution or Explanation
π
r = 12 feet, θ = 45° =
4
π
s = rθ = 12
4
≈ 9.42 feet
= 3π feet
16.1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 5.4.052.
Sketch the graph of the function by hand. Use a graphing utility to verify your sketch. (Include two full periods.)
f(x) = 2 cos (x + π/7)
17.1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 5.1.098.
Find the radius r of a circle with an arc length s and a central angle θ. (Round your answer to two decimal places.)
Arc Length s
Central Angle θ
7 meters
π/6 radians
13.37
13.37 meters
18.1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 5.3.102.
Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in
the correct angle mode.)
csc 320°
-1.5557
-1.5557
19.1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 5.3.104.
Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in
the correct angle mode.)
tan 15π/13
0.5248
0.5248
20.1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 5.3.106.
Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in
the correct angle mode.)
cos(−27π/22)
-0.7557
-0.7557
21.1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 5.4.022.
Describe the relationship between the graphs of f and g. Consider amplitude, period, and shifts.
f(x) = cos x
g(x) = cos(x + 4π)
The graph of g is a horizontal shift of the graph of f 4π units to the left.
The graph of g has an amplitude 4 more than that of the graph of the graph of f.
The period of the graph of g is 4π units longer than the period of the graph of f.
The graph of g is a vertical shift of the graph of f 4π units upward.
The graph of g is a vertical shift of the graph of f 4π units downward.
22.1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 5.6.024.
Use a calculator to approximate the value of the expression. Round your answer to the nearest hundredth.
sin-1 (0.54)
0.570
0.57
23.1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 5.6.032.
Use a calculator to approximate the value of the expression. Round your answer to the nearest hundredth. (Enter your answer in
radians.)
tan−1 −
-1.38
87
17
-1.38
24.1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 5.1.066.
Rewrite each angle in degree measure. (Do not use a calculator.)
(a)
− 7π
2
-630
(b)
264
-630 °
22π
15
264 °
25.1.5/1.5 points | Previous AnswersLarPreCalcRMRPAlt6 5.7.019.
A ladder that is 30 feet long leans against the side of a house. The angle of elevation of the ladder is 75°. Find the height from the
top of the ladder to the ground. (Round your answer to one decimal place.)
28.98
29.0 ft
…
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