cot θ ∙ sec θ = csc θ

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.

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.)

(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).

 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

(1 + tan²u)(1 – sin²u) = 1

cot²x + csc²x = 2csc²x – 1

1 + sec²xsin²x = sec²x

cos(α – β) – cos(α + β) = 2 sin α sin β

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.

Does the graph represent a function?

f(x) =

u = -4i + 1j and v = 4i + 1j; Find .

6x² + 12x + 5 = 0

Give your answers in exact form.

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?

h(x) = (6x – 14)⁸

h(x) = 2 | x | + 2

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