A) 17.9 cm
We have:
[tex]f=+15 cm[/tex] is the focal length of the mirror (for concave mirror, the focal length is positive)
[tex]p=91.5 cm[/tex] is the distance between the object and the mirror
[tex]q=?[/tex] is the distance between the image and the mirror
We can then use the mirror equation to find q:
[tex]\frac{1}{f}=\frac{1}{p}+\frac{1}{q}\\\frac{1}{q}=\frac{1}{f}-\frac{1}{p}=\frac{1}{15 cm}-\frac{1}{91.5 cm}=0.056 cm^{-1}\\q=\frac{1}{0.056 cm^{-1}}=17.9 cm[/tex]
B) -5.0 cm
The height of the image can be determined by using the magnification equation:
[tex]\frac{q}{p}=-\frac{h_i}{h_o}[/tex]
where
[tex]h_i = ?[/tex] is the heigth of the image
[tex]h_o = 25.4 cm[/tex] is the height of the object
Substituting and re-arranging the formula, we find
[tex]h_i = -h_o \frac{q}{p}=-(25.4 cm)\frac{17.9 cm}{91.5 cm}=-5.0 cm[/tex]
And the negative sign means the image is inverted.
