A point p is moving along a circle with equation x^2+y^2=100 at a constant rate of 3 units/sec.?

When P is 5 units above the x-axis it is moving at 3 units/sec tangentially

x^2 + y^2 = 100

2x + 2ydy/dx = 0

Slope at p is –x/y

When y = 5, x = 5√(3)

Slope is - √(3) = tan(θ)

The component along the x-axis employs cos(θ) = 1/2

Speed projection is -3 cos(θ) = -1.5 units/sec

y = 5 => x = √(100 - 5²) = 5√3, which means that the angle the circle's radius to this point makes with the x axis is 30°. Since the motion is perpendicular to this radius, the absolute values of its vertical and horizontal components must be in the ratio √3:1, where their resultant has a ratio-magnitude of 2, so the x component is half this, or 1.5 units/sec.