36. (0 points) Graph the system of inequalities. Then find the coordinates of the points of intersection of the graphs of the related equations. (a) 2 Sy ityz2 8-76-5 -4-3-2 -10 123 4 5678 (b) 12 +y of 90 O ZOOM + 31. (0 points) Calculate the difference quotient (DQ) of the given function. Simplify your answer fully. (a) 1(z) = 2. DQ (b) / (1) = = 7- 4 DQ -22. (0 points) A giant sloth fossil has lost 90.9% of its Carbon-14. (Recall that the half-life of Carbon-14 is 5750 years.) (a) What percent of Carbon-14 is left? Round your answer to the nearest tenth of a percent. ANS: (b) What is the rate of exponential decay? Round your answer to three significant figures. ANS: (c) How old is the fossil? Round your answer to the nearest year. ANS: years up\f18. (0 points) Divide using long division or synthetic division and write your answer as Remainder Quotient + Divisor (a) 2 -912 + 151 + 44 T- 5 Answer: (b) ' + 72 + 3x2 - 40x - 33 r+4 Answer: hp\f37. (0 points) In 1990, South Africa had a population of 36.80 million, and an exponential growth rate of 2.39%. (a) Find the exponential growth function. ANS: (b) Estimate the population in 2002. Round your answer to the nearest tenth of a million. ANS: million (c) After how long will the population be double what it was in 1990? Round your answer to the nearest tenth of a year. ANS: years (d) After how many years will the population be 120.0 million? Round your answer to the nearest tenth of a year. ANS: years\f25. (0 points) Find all zeros of the polynomial-including complex ones, if any. (a) 23 - 5012 +471 + 98 Zeros: (b) 3 + 212 + 7x + 14 Zeros: hp26. (0 points) Suppose the functions f and g are defined as follows. f(x) = v-5x -7 and g(r) = -6 -8 (a) Find the composition fog and find its domain using interval notation. (fog)(1) = dom(f o g) = (b) Find the composition go f and find its domain using interval notation. (go !)(I) = dom(g o J )35 29. (0 points) Given that cos (a) = 37 and a is in quadrant III, and sin (B) = 8 17 and B is in quadrant II, find the exact value of: (a) sin (a - B) DO NOT USE A CALCULATOR. (b) cos (a - B) DO NOT USE A CALCULATOR.\f19. (0 points) Use a sum or difference formula to find the exact value of tan 197 12 DO NOT USE A CALCULATOR. 20. (0 points) Evaluate the following expression exactly. DO NOT USE A CALCULATOR. in () cos (") - cos (') sin () 21. (0 points) Evaluate the given expression. Your answer should be an exact expression containing no trigonometric functions. DO NOT USE A CALCULATOR. van (sin ' (-) - com ' ( 19) ) hp27. (0 points) $6500 is deposited in a bank account with an annual interest rate of 6.50%, compounded continuously. (a) Find the exponential growth function. ANS: (b) What will the balance be after 13 years?. Round your answer to the nearest cent. ANS: $ (c) After how long will the $6500 have doubled? Round your answer to the nearest tenth of a year. ANS: years (d) After how long will there be $11000 in the bank. Round your answer to the nearest tenth of a year. ANS: years23. (0 points) Two sides and an included angle of a triangle are given (SAS). Solve the triangle. Round all sides to the nearest tenth of a unit and round all angles to the nearest tenth of a degree. 164 cm 50 B 19 cm cm 24. (0 points) Three sides of a triangle are given (SSS). Solve the triangle. Round all angles to the nearest tenth of a degree. A hp