$[30$ pts$]$ For the T$-$beam shown below, find $($a$)$ the $(\stackrel{}{x}\frac{,}{b}ar(Y))$ centroid location. Show all work for each centroid location, including organizing the information in a table. Note the location of the origin. Next, $($b$)$ find $\frac{?}{\text{b}\text{a}\text{r}}(I{)}_x,$ the moment of inertia about the centroidal $x-$axis. Finally, $($c$)$ find $\frac{?}{\text{b}\text{a}\text{r}}(I{)}_y,$ the moment of inertial about the centroid $y-$axis. Hint: Once you find the centroid location, draw the centroidal axis to help visualize.