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.

Which compound inequality could be represented by the graph?

Since opening night, attendance at play a has increased steadily, while attendance at play b first rose and then fell. equations modeling the daily attendance y at each play are shown below, where x is the number of days since opening night. on what day(s) was the attendance the same at both plays? what was the attendance? play a: y = 8x + 191 play b: y = -x^2 + 26x + 126 a. the attendance was never the same at both plays. b. the attendance was the same on day 5. the attendance was 231 at both plays on that day. c. the attendance was the same on day 13. the attendance was 295 at both plays on that day. d. the attendance was the same on days 5 and 13. the attendance at both plays on those days was 231 and 295 respectively.

Find the equation of a line whose slope is 2/5 and y- intercept is 2.write your answer in the form 1) ax+by+c=02) x/a+y/b=1