(b) USING tan 45" = 1 and tan 60 = V3, PROVE that . . . . . .... i. (2 points) H = =+ y ii. (2 points) H = x + v3(y -1)(c) (3 points) USE the method of substitution (linear systems!) to obtain the exact value of y as ...... V/3 3+ v3 y - or y - V3 - 1 2 (1)(d) (1 point) Is there enough information to find I? Justify your reasoning. 32. CONSIDER the TABLE of values below: X y First differences Second differences (if need be) -2 4 0 3 4 (a) (2 points) COMPLETE the differences column above, and CONCLUDE that the relation is quadratic. (b) (5 points) If the relation can be modelled by y = ar + by+ c. (2) determine the values of a, b, and c.(c) [3 points} Using your answer to part b} above. re-mfte the relation in vertex Farm, that is. in the Farm y=a(:rh}2+k [3) 33. (1 point) DISTINGUISH between similar triangles and congruent triangles. 34. An equation is given. For each equation, find an angle that satisfies it, or state whether the angle does not exist (DNE). (a) (1/2 point) sin A = 0.5151 (a) (b) (1/2 point) sin B = 1.2345 (b) (c) (1/2 point) cos C' = 0.1010 ( c ) (d) (1/2 point) cos D = 2.2222 (d) (e) (1/2 point) tan E = 3.4343 (e)35. DESCRIBE the general conditions under which one can use . .. . .. (a) (1 point) sine law (b) (1 point) cosine law . . . . . 36. CONSIDER the linear system ar + 2y = 5 (4) 3x + by = c (5) FIND suitable values of a, b, c for which the linear system will have . . . . . . (a) (3 points) infinite number of solutions (b) (3 points) one solution (c) (3 points) no solution38. (3 points) EXPLAIN how to use the distance formula to classify triangles and quadrilaterals. APPLICATION/30 39. (4 points) FIND the equation of the perpendicular bisector of the points A(-2, 5) and B(2, -3). [Leave your answer in the general form, namely ar + by + c = 0.]d0. {4 points} If the solutlm of the linear syntan M + by = '13 In: + my = 12 is (31 2). determine the values of a and b. 41. (5 points} SOLVE a triangle MUG in which a = 4 cm. 6 = 3.2 cm. and r: = 3.5 cm. {6) {7) 42. {II points) LIST ILL the values of b for which the quadratic 3.3:2 +u: 8 can be factored over the integers. For each value of b chosen. Gimme the emaciated DISCRIHIIIW. and slum that it is a perfect quart. 43. {3 points) The sun of the squares of four consecutive kite-gem is 630. FIND the integers. 44. (4 points) The girls' soccer team held a fund-raising car wash. They charged $5 for each car and $8 for each van. They washed 44 cars and collected $262. How many of each type of vehicle did they wash? 45. A harbour ferry service has about 210, 000 riders per day for a fare of $2. The port authority wants to increase the fare to help with increasing operational costs. Research has shown that for every $0.10 increase in the fare. the number of riders will drop by 10, 000. The port authority established a relation, defined by R = 1000p/2 1 4000p | 480000, (8) where R represents the revenue from fares and p represents the number of $0.10 increases in the fare. (a) (3 points) What increase in the fare will maximize the revenue