A jogger runs around a circular track of radius 65 ft. Let (x,y) be her coordinates, where the origin is the center of the track. When the jogger's coordinates are (39, 52), her x -coordinate is changing at a rate of 15ft/s. Find (dy/dx)

Question

A jogger runs around a circular track of radius 65 ft. Let (x,y)  be her coordinates, where the origin is the center of the track. When the jogger's coordinates are (39, 52), her x -coordinate is changing at a rate of  15ft/s. Find (dy/dx)

Reiny · Accepted Answer

I think you want to find dy/dt
or else we don't need the fact that
dx/dt = 15 ft/s

x^2 + y^2 = 65^2

2x dx/dt + 2y dy/dx= 0
dy/dx = (-2x dx/dt)/(2y) = (-x dx/dt)/y

so for the given data
dy/dt = -39(15)/52 = -45/4 or -11.25 ft/s

hello · Answer

How did you solve this thx