ANSWER
[tex]f(x)= \sqrt{ 36 - {x}^{2} } [/tex]
EXPLANATION
The equation of a circle centered at the origin, with radius r units is given by
[tex] {x}^{2} + {y}^{2} = {r}^{2} [/tex]
The given circle has radius 6 cm.
The equation becomes:
[tex] {x}^{2} + {y}^{2} = {6}^{2} [/tex]
[tex]{x}^{2} + {y}^{2} = 36[/tex]
We solve for y to obtain,
[tex] {y}^{2} = 36 - {x}^{2} [/tex]
[tex]y = \pm \sqrt{ 36 - {x}^{2} } [/tex]
The top half of the circle is always positive, hence its equation is:
[tex]y = \sqrt{ 36 - {x}^{2} } [/tex]
Or
[tex]f(x)= \sqrt{ 36 - {x}^{2} } [/tex]
