9:40 m 25 Done A cdn.discordapp.com C ACADSORT MATHS TEST PAPER VECTORS AND PARAMETRICS let u = (2, -1), v = (4, 2), and w = (1, -3) be vectors. Find the indicated expression. 1. u .v let A = (2, -1), B = (3, 1), C = (-4, 2), and D = (1,-5). Find the component form and magnitude of the vector. 1. AC + BD' find (a) a unit vector in the direction of AB and (b) a vector of magnitude 3 in the opposite direction. 1. A = (4, 0), B = (2, 1) find (a) the direction angles of u and v and (b) the angle between u and v. 1. u = (4, 3), v = (2, 5) Use an algebraic method in Exercises 15-18 to convert the polar coordinates to rectangular coordinates. Approximate exact values with a calculator when appropriate. 1. (-2.5, 250) polar coordinates of point P are given. Find all of its polar coordinates. 1. P = (-1,-27/3) eliminate the parameter / and identify the graph. Support your answer with a grapher. 1. x = 4 +ty = -8 - 5t. -3 is 5 2. x = 3 cost, y = 3 sint find a parametrization for the curve. 1. The line through the points (-1, -2) and (3, 4) -. use De Moivre's Theorem to find the indicated power of the complex number. Write your answer in (a) polar form and (b) standard form. 1. [3( cos # + i sin = ) 1 , convert the polar equation to rectangular form and identify the graph. 1. r = -3 cos 0 - 2 sin 0 analyze the graph of the polar curve. 1.r = 2 - 5 sin 0 74. Flight Engineering An airplane is flying on a bearing of 80 at 540 mph. A wind is blowing with the bearing 100 at 55 mph.8 cdn.discordapp.com use De Moivre's Theorem to find the indicated power of the complex number. Write your answer in (a) polar form and (b) standard form. = B N8 }(.;m1 + :mi) L 4 4 , convert the polar equation o rec and identify the graph 1. r==3cos# = 2sin analyze the graph of the polar curve 2-=35sing 74. Flight Engineering An airplane is flying on a bearing of 80 at 540 mph. A wind is blowing with the bearing 100 at 55 mph (a) Find the component form of the velocity of the airplane. (b) Find the actual speed and direction of the airplane. . Braking Force A 3000-1b car is parked on a street that makes an angle of 16 with the horizontal (see figure). (a) Find the force required to keep the car from rolling down the hill. (b) Find the component of the force perpendicular to the street. 16 . Baseball Hitting Brian hits a baseball straight toward a 15-ft-high fence that is 400 ft from home plate. The ball is hit when it is 2.5 ft above the ground and leaves the bat at an angle of 30 with the horizontal. Find the initial velocity needed for the ball to clear the fence