Question

If an appliance is plugged into a common household outlet, the wattage consumed is not constant. Instead, it varies at a high frequency according to the model Upper W equals StartFraction Upper V squared Over Upper R EndFraction equals StartFraction left parenthesis 163 sine 120 pi t right parenthesis squared Over 95 EndFraction , where V is the voltage and R is a constant that measures the resistance of the appliance. Use the identity cosine left parenthesis 2 theta right parenthesis equals 1 minus 2 sine squared theta to determine values of a, c, and omega so that Upper W equals a cosine left parenthesis omega t right parenthesis plus c. Check your answer by graphing both expressions for W on the same coordinate axes. Find the equation for W, using the values of a, c, and omega. aequals nothing (Type an integer or decimal rounded to the nearest tenth as needed.) cequals nothing (Type an integer or decimal rounded to the nearest tenth as needed.) omegaequals nothing (Type an exact answer in terms of pi.)

Answer #1

given appliance lugged into power supplly

given wattage model

W = V^2/R = [163*sin(120*pi*t)]^2/95

comparing

V = 163*sin(120*pi*t)

and

R = 95 ohms

identity

cos(2*theta) = 1 - 2*sin^2(theta)

hence

W = [163*sin(120*pi*t)]^2/95 =
279.673684*sin^2(120*pi*t) = 139.836842105263(1 -
cos(240*pi*t))

W = a*cos(wt) + c

comapring

a = -139.83684

w = 240*pi

c = 139.83

the graphs for two equations is as under

W = V^2/R = [163*sin(120*pi*t)]^2/95

Consider the inverse cosine function, defined by
y equals cosine Superscript negative 1 Baseline xy=cos−1x
or
y equals arccosine xy=arccosx.
Complete parts (a) through (d).
(a) What is its domain?
nothing
(Type your answer in interval notation. Simplify your answer.
Type an exact answer, using
piπ
as needed. Use integers or fractions for any numbers in the
expression.)
(b) What is its range?
nothing
(Type your answer in interval notation. Simplify your answer.
Type an exact answer, using
piπ
as...

The temperature in Middletown Park at 6:00 AM last Sunday was
49.2 degrees Fahrenheit. The temperature was changing at a rate
given by r left parenthesis t right parenthesis equals 3.29 cosine
left parenthesis StartFraction pi t Over 12 EndFraction right
parenthesis plus 0.032 where t is in hours after 6:00 AM last
Sunday. ROUND ALL ANSWERS TO 2 DECIMAL PLACES. At 10:00 AM last
Sunday, the temperature in the park was increasing at a rate of
about 1.68 degrees...

The number of U.S. travelers to other countries during the
period from 1990 through 2009 can be modeled by the polynomial
function
Upper P left parenthesis x right parenthesis equals negative
0.00530 x cubed plus 0.1014 x squared plus 1.043 x plus
45.43P(x)=−0.00530x3+0.1014x2+1.043x+45.43
where
xequals=0
represents 1990,
xequals=1
represents 1991, and so on and P(x) is in millions. Use this
function to approximate the number of U.S. travelers to other
countries in each given year.
(a) 1990 (b) 2000 (c)...

Given the probability distributions shown to the right,
complete the following parts.
a. Compute the expected value for each distribution.
b. Compute the standard deviation for each distribution.
c. What is the probability that x will be at least 3 in
Distribution A and Distribution B?
d. Compare the results of distributions A and B.
Distribution A
Distribution B
x Subscript ixi
P(Xequals=x Subscript ixi)
x Subscript ixi
P(Xequals=x Subscript ixi)
0
0.030.03
0
0.490.49
1
0.080.08
1
0.230.23
2...

1)
100,709
79,677
47,982
92,189
74,995
80,964
73,768
98,821
84,535
61,753
78,061
44,544
80,986
79,359
82,841
67,361
86,766
92,379
63,708
51,565
61,170
63,654
73,598
67,210
57,866
74,535
56,526
94,385
54,897
50,392
46,724
65,956
78,528
60,835
89,116
(a) Find the sample mean.
(b) Find the sample standard deviation. The sample standard
deviation is defined as is equals StartRoot StartFraction Upper
Sigma left parenthesis x minus x overbar right parenthesis squared
Over n minus 1 EndFraction EndRoots=Σx−x2n−1.
(c) Construct a 98% confidence...

A 0.01 significance level is used for a hypothesis test of the
claim that when parents use a particular method of gender?
selection, the proportion of baby girls is greater than 0.5. Assume
that sample data consists of 55 girls in 100 ?births, so the sample
statistic of StartFraction 11 Over 20 EndFraction results in a z
score that is 1 standard deviation above 0. Complete parts? (a)
through? (h) below. Click here to view page 1 of the Normal...

Researchers wondered if there was a difference between males and
females in regard to some common annoyances. They asked a random
sample of males and females, the following question: "Are you
annoyed by people who repeatedly check their mobile phones while
having an in-person conversation?" Among the
517517
males surveyed,
168168
responded "Yes"; among the
545545
females surveyed,
204204
responded "Yes." Does the evidence suggest a higher proportion
of females are annoyed by this behavior? Complete parts (a)
through (g)...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 9 minutes ago

asked 11 minutes ago

asked 17 minutes ago

asked 19 minutes ago

asked 21 minutes ago

asked 52 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago