A particle moves along the parabola y=x^2 in the first quadrant and its x-coordinate increases at a steady 10m/s. How fast is the angle of inclination of the line joining the particle to the origin changing when x = 3m?

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As the angle inclination changes, so will the x and y coordinates.  Three rates need to be considered to answer this question, d(theta)/dt, dx/dt and dy/dt.  The only one given is dx/dt which is 10 m/s.  Since the particle travels the path y=x^2, dy/dt = 2x*dx/dt by taking the derivative with respect to t.

dy/dt = 2x*dx/dt = 2(3)(10) = 60.

To find d(theta)/dt:

A triangle is drawn using the line that makes the angle of inclination.  At x=3, the y-value is 9, since y = x^2 = 3^2 = 9.

Theta is the angle formed by the x-axis and the line that...

(The entire section contains 2 answers and 317 words.)

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