A concave shaving mirror has a radius of curvature of $35.0cm$. It is positioned so that the (upright) image of man's face is $2.50$ times the size of the face. How far is the mirror from the face ?a. $5.25cm$ b. $21.0cm$ c. $10.5cm$ d. $42cm$

Step 1: Use the formula for the focal length of a spherical mirror, which is $f=\frac{R}{2}$. Step 2: Substitute the given radius $R$, which is $35.0cm$, to get $f=\frac{35.0cm}{2}=17.5cm$. Step 3: Use the mirror formula, which is $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$, where $u$ is the object distance, $v$ is the image distance, and $f$ is the focal length. Step 4: Use the magnification formula, which is $m=\frac{-v}{u}$ or $v=-\mu$, where $m$ is the magnification and $\mu$ is the image height divided by the object height. Step 5: Rearrange the mirror formula to solve for the object distance $u$, which is $u=f\left(1-\frac{1}{m}\right)$. Step 6: Substitute the values of $f$ and $m$ to get $u=-17.5\left(1-\frac{1}{2.5}\right)=-17.5\times \left(0.6\right)=-10.5cm$.