A conical pendulum consists of a mass m, attached to a string of fixed length L, that travels around a circle of radius r at a fixed velocity v. As the velocity of the mass is increased, both the radius and angle x increase. Given that v^2 = r*g*tan(x), where g is a gravitational constant, find the relationship between the related rates
a) dv/dt and dx/dt
b) dv/dt and dr/dt