Pre-Calculus Midterm

Sigchi4life
Category:
Calculus
Price: $5 USD

Question description

Short Answer: Type your answer below each question. Show your work.

1. Verify the identity. Show your work.

 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? Show your work.

What is the charge for using 45 therms in one month? Show your work.

Construct a function that gives the monthly charge C for x therms of gas.

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.) Show your work.

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. Show your work.

(c)  Find the y-intercept. Show your work.

f(x) = x2(x + 2)

(a).

(b).

(c).

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

Verify the identity. Show your work.

(1 + tan2u)(1 - sin2u) = 1

Verify the identity. Show your work.

cot2x + csc2x = 2csc2x - 1

Verify the identity. Show your work.

1 + sec2xsin2x = sec2x

Verify the identity.Show your work.

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

The following data represents the normal

10 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. Show your work.

.

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? Explain

12. Find the vertical asymptotes, if any, of the graph of the rational function. Show your work.

f(x) =

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? Show your work.

14. Find the specified vector or scalar. Show your work.

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

15. Find the exact value of the trigonometric function. Do not use a calculator.

16. Find the x-intercepts (if any) for the graph of the quadratic function.

6x2 + 12x + 5 = 0

Give your answers in exact form. Show your work.

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? Show your work.

18. Find functions f and g so that h(x) = (f ∘ g)(x).

h(x) = (6x - 14)8

19. Begin by graphing the standard absolute value function f(x) = | x |. Then use transformations of this graph to describe the graph the given function.

h(x) = 2 | x | + 2

20. Find the reference angle for the given angle. Show your work.

-404°


Tutor Answer

(Top Tutor) Daniel C.
(997)
School: Boston College
PREMIUM TUTOR
Studypool has helped 1,244,100 students
Ask your homework questions. Receive quality answers!

Type your question here (or upload an image)

1831 tutors are online

Brown University





1271 Tutors

California Institute of Technology




2131 Tutors

Carnegie Mellon University




982 Tutors

Columbia University





1256 Tutors

Dartmouth University





2113 Tutors

Emory University





2279 Tutors

Harvard University





599 Tutors

Massachusetts Institute of Technology



2319 Tutors

New York University





1645 Tutors

Notre Dam University





1911 Tutors

Oklahoma University





2122 Tutors

Pennsylvania State University





932 Tutors

Princeton University





1211 Tutors

Stanford University





983 Tutors

University of California





1282 Tutors

Oxford University





123 Tutors

Yale University





2325 Tutors