At the county fair, the operator of a game guesses a contestant's weight. For each pound the operator's guess differs from the contestant's weight, the contestant will receive $3. A contestant weighing a pounds received $15 when the operator guessed 120 pounds. Which of the following equations could be used to solve for the weight of the contestant? ( ) A. 3 x - 15 = 120 B. 3 x - 120 = 15 3. Find the general solution u(r, y) of each of the following partial differ- ential equations. Find the particular solution up(x, y) which satisfies the given condition. (a) 3ur - 5uy =0, u(0, y) = sin y. (b) 2ur - 3uy = cos x, u(x, x) =x2. (c) rus + yuy = 2ry, u(x, x?) = 2. (d) ur + ruy = (y - }x2)2, u(0,y) = ev. (e) yur - 2ryuly = 2xu, u(0, y) =y3. (f) 2rus + yuy - x - u =0, u(1, y) = 1. 1. Find the values of X for all possible values of the variable (truth table) a. X=4+BC b. X = ABC+ AB Question 2 a) Determine L cos(at + b); where a and b are constants. ( 3 marks ) Hint: Use a suitable compound angle identity. b) Given that 2x - x = sint; x(0) = 0, show by Laplace transform that X(S) = (2-5)(53+1) ' Solve fully to obtain x in terms of t. ( 12 marks ) Test for symmetry with respect to the line 0 = 1/2, the polar axis, and the pole. (Select all that apply r = 5 cos 30 O symmetric with respect to the pole O symmetric with respect to the polar axis O symmetric with respect to 0 = 1/2