Question: A person moves from the origin along the positive y-axis pulling a weight at the end of a 12-meter rope (see figure). Initially, the weight

A person moves from the origin along the positive y-axis pulling a weight at the end of a 12-meter rope (see figure). Initially, the weight is located at the point (12, 0).

12 10 00 8 y 6- 4 2 12 X Weight (x,

(a) Show that the slope of the tangent line of the path of the weight is

y) 24 6 8 10 12 X

(b) Use the result of part (a) to find the equation of the path of the weight. Use a graphing utility to graph the path and compare it with the figure.(c) Find any vertical asymptotes of the graphs in part (b).(d) When the person has reached the point (0, 12), how far has the weight moved?

12 10 00 8 y 6- 4 2 12 X Weight (x, y) 24 6 8 10 12 X

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