An object is moving along a circle of radius 5 . When the object is at the point (−4,3) , the y value of its position is changing at the rate of 9 units per second. How fast is the x value of its position changing at that moment?

x^2 + y^2 = 25

2x dx/dt + 2y dy/dt = 0

2(-4) dx/dt + 2(3)(9) = 0
-8 dx/dt + 54 = 0
dx/dt = 54/8 = 27/4 = 6.75

makes sense; the particle is moving up to the right.