Problem # $1($Tribology$)$

A surface profile consists of $10$ triangular asperities having a constant flank angle q and peak$-$to$-$ valley heights of $1,2,3,4,5,6,7,8,9,10,$ see Fig. $2\mathrm{.}1.$ If all of the valleys are at an arbitrary datum, calculate $($a$)$ the position of the mean line relative to the datum and $($b$)$ the $R_a$ value of the profile $($Arithmetic mean roughness$)$