Calculus

Short Answer: Type your answer below each question. Show your work.1Verify the identity.cot ? ? sec ? = csc ?2A gas company has the following rate schedule for natural gas usage in single-family residences:Monthly service charge                  $8.80Per therm service charge1st 25 therms                      $0.6686/thermOver 25 therms                  $0.85870/thermWhat 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.3The 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 isW(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.)4Complete 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).5For 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 Year6Verify the identity.(1 + tan2u)(1 – sin2u) = 17Verify the identity.cot2x + csc2x = 2csc2x – 18Verify the identity.1 + sec2xsin2x = sec2x9Verify the identity.cos(? – ?) – cos(? + ?) = 2 sin ? sin ?10The 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. YesB. No_____12.Find the vertical asymptotes, if any, of the graph of the rational function.f(x) =A. x = 0 and x = 4B. x = 0C. x = 4D. 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. 2008B. 2005C. 2006D. 2007_____14.Find the specified vector or scalar.u = -4i + 1j and v = 4i + 1j; Find .A.B. 8C. 2D. 5_____15.Find the exact value of the trigonometric function. Do not use a calculator.A. -1B.C. 1D._____16.Find the x-intercepts (if any) for the graph of the quadratic function.6×2 + 12x + 5 = 0Give 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)8A. f(x) = 6x – 14, g(x) = x8B. f(x) = 6×8 – 14, g(x) = -14C. f(x) = x8, g(x) = 6x – 14D. 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 | + 2A.B.C.D._____20.Find the reference angle for the given angle.-404°A. 44°B. 46°C. 134°D. 136°