An object is moving in the clockwise direction around the unit circle `x^(2)+y^(2)=1`. As it passes through the point `(1/2,(sqrt(3))/2)`, its y-coordinate is decreasing at the rate of 3 unit per second. The rate at which the x-coordinate changes at this point is (in unit per second)

Options

A. 2
B. `3sqrt(3)`
C. `sqrt(3)`
D. `2sqrt(3)`

Answer

B

Explanation

`x^(2)+y^(2)=1implies2x(dx)/(dt)+2y(dy)/(dt)=0`
But we have `x=1/2, y=(sqrt(3))/2` and `(dy)/(dt)=-3`, then
`1/2(dx)/(dt)=3sqrt(3)` unit per second