$10($a$).$ A concave mirror in an amusement park has a radius of curvature of $4\mathrm{.}0$ m $.$ A child stands in front of the mirror so that she appears $3\mathrm{.}0$ times taller than her actual height. If the image is upright, how far is she standing from the mirror? $($Use both Magnification and Mirror Equations$)$

$($b$).$ An object is $1\mathrm{.}0$ m in front of a mirror. A virtual image is formed $10\mathrm{.}0$ m behind the mirror. What is the radius of curvature of the mirror?