Part of a cross-country skier's path can be described with the vector function r = < 2 + 6t + 2 cos(t), (15 − t)(1 − sin(t))> for 0 ≤ t ≤ 15 minutes, with x and y measured in meters. the derivatives of these functions are given by x′(t) = 6 − 2sin(t) and y′(t) = −15cos(t) + tcos(t) − 1 + sin(t). find the slope of the path at time t = 4. show the computations that lead to your answer. find the time when the skier's horizontal position is x = 60. find the acceleration vector of the skier when the skier's horizontal position is x = 60. find the speed of the skier when he is at his maximum height and find his speed in meters/min. find the total distance in meters that the skier travels from t = 0 to t = 15 minutes.

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answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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answer: i believe the answer is e

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