A parametric curve is defined by x(t) = 2t2 - 1 and y(t) = +2. At what coordinate is the tangent line to the curve horizontal? (6 points) 3 O (-1 3 ) O (0,0) O (0,4)A particle moves in a plane according to the parametric equations x(t) = 1 + 3cost, y(t) = 3sin2t. Find - > in terms of t. (6 points) O 4 sin 2t sint O 4 sin 2t cost 2costcos 2t - 8sintcost 3sin't 4 sint sin 2t + 2costcos 2t -3sin'tW Q 3. (09.02 MC) Determine |s'(4)| for position vector s(t) = . (6 points) V65 O V8 O 3 O 16. (09.01 HC) For the parametric curve defined by x(t) = 3cos2t, y(t) = 3sin2t. Part A: For the given parametric curve, determine where _ does not exist on the interval [0, rt] and determine the type of discontinuity. (3 points) dx Part B: Find the inflection point(s) of the curve on the interval [0, r]. (3 points) Part C: What is the length of the curve on the interval [0, ~ ]? (4 points)3 7. (09.01, 09.02, 0903 HC) r2 2: A submarine is traveling such that its position vector 5(1) :, where s is in miles and t is time in hours. Part A: Find the speed of the submarine at 4 hours to the nearest tenth. (4 points) Part B: Find the acceleration vector of the submarine at 4 hours. (4 points) Part c: What is the total distance traveled by the submarine in the rst 4 hours? (2 points)