A jogger runs around a circular track of radius 70 ft. let (x,y) be her coordinates, where the origin is the center of the track. When the jogger's coordinates are (42,56), her x-coordinate is changing at a rate of 19 ft/s. Find dy/dt.
So we have a circle of radius 90 ft by drawing a diagram you can see that she must be going around the track in the clockwise direction x = 70*cos(a*t) y = 70*sin(a*t) given at point (42, 56) dx/dt = 19 ft/s 42 = 70*cos(a*t) cos(a*t) = 42/70 56 = 70*sin(a*t) sin(a*t) = 56/70 find dx/dt and dy/dt dx/dt = -70*a*sin(a*t) dy/dt = 70*a*cos(a*t) 19 = -70*a*sin(a*t) 19 = -70*a*56/70 a = -19/56 so dy/dt = 70*a*cos(a*t) dy/dt = 70*(-19/56)*(42/70) dy/dt = -19*42/56 dy/dt = -14.25
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