natural gas usage
Short Answer: Type your answer below each question. Show your work.
1
Verify the identity.
cot θ ∙ sec θ = csc θ
2
A gas company has the following rate schedule for natural gas usage in single-family residences:
Monthly service charge $8.80
Per therm service charge
1st 25 therms $0.6686/therm
Over 25 therms $0.85870/therm
What is the charge for using 25 therms in one month?
What is the charge for using 45 therms in one month?
Construct a function that gives the monthly charge C for x therms of gas.
3
The wind chill factor represents the equivalent air temperature at a standard wind speed that would produce the same heat loss as the given temperature and wind speed. One formula for computing the equivalent temperature is
W(t) =
where v represents the wind speed (in meters per second) and t represents the air temperature . Compute the wind chill for an air temperature of 15°C and a wind speed of 12 meters per second. (Round the answer to one decimal place.)
4
Complete the following:
(a) Use the Leading Coefficient Test to determine the graph’s end behavior.
(b) Find the x-intercepts. State whether the graph crosses the x-axis or touches the x-axis and turns around at each intercept.
(c) Find the y-intercept.
f(x) = x2(x + 2)
(a).
(b).
(c).
5
For the data set shown by the table,
a. Create a scatter plot for the data. (You do not need to submit the scatter plot)
b. Use the scatter plot to determine whether an exponential function or a logarithmic function is the best choice for modeling the data.
Number of Homes Built in a Town by Year
6
Verify the identity.
(1 + tan2u)(1 – sin2u) = 1
7
Verify the identity.
cot2x + csc2x = 2csc2x – 1
8
Verify the identity.
1 + sec2xsin2x = sec2x
9
Verify the identity.
cos(α – β) – cos(α + β) = 2 sin α sin β
10
The following data represents the normal monthly precipitation for a certain city.
Draw a scatter diagram of the data for one period. (You do not need to submit the scatter diagram). Find the sinusoidal function of the form that fits the data.
Multiple Choice: Type your answer choice in the blank next to each question.
_____11.
The graph below shows the percentage of students enrolled in the College of Engineering at State University. Use the graph to answer the question.
Does the graph represent a function?
A. Yes
B. No
_____12.
Find the vertical asymptotes, if any, of the graph of the rational function.
f(x) =
A. x = 0 and x = 4
B. x = 0
C. x = 4
D. no vertical asymptote
_____13.
The formula A = 118e0.024t models the population of a particular city, in thousands, t years after 1998. When will the population of the city reach 140 thousand?
A. 2008
B. 2005
C. 2006
D. 2007
_____14.
Find the specified vector or scalar.
u = -4i + 1j and v = 4i + 1j; Find .
A.
B. 8
C. 2
D. 5
_____15.
Find the exact value of the trigonometric function. Do not use a calculator.
A. -1
B.
C. 1
D.
_____16.
Find the x-intercepts (if any) for the graph of the quadratic function.
6×2 + 12x + 5 = 0
Give your answers in exact form.
A.
B.
C.
D.
_____17.
Use the compound interest formulas A = Pert and A = P to solve.
Suppose that you have $11,000 to invest. Which investment yields the greater return over 10 years: 6.25% compounded continuously or 6.3% compounded semiannually?
A. $11,000 invested at 6.25% compounded continuously over 10 years yields the greater return.
B. Both investment plans yield the same return.
C. $11,000 invested at 6.3% compounded semiannually over 10 years yields the greater return.
_____18.
Find functions f and g so that h(x) = (f ∘ g)(x).
h(x) = (6x – 14)8
A. f(x) = 6x – 14, g(x) = x8
B. f(x) = 6×8 – 14, g(x) = -14
C. f(x) = x8, g(x) = 6x – 14
D. f(x) = (6x)8, g(x) = -14
_____19.
Begin by graphing the standard absolute value function f(x) = | x |. Then use transformations of this graph to graph the given function.
h(x) = 2 | x | + 2
A.
B.
C.
D.
_____20.
Find the reference angle for the given angle.
-404°
A. 44°
B. 46°
C. 134°
D. 136°
attachment
3.png
attachment
5.png
attachment
10.png
attachment
11.png
attachment
12.png
attachment
14.png
attachment
16.png
attachment
17.png
attachment
19.png