A beam with an inverted tee$-$shaped cross section is subjected to positive bending moments of Mz

$=5$kN$*$m$.$ The cross$-$sectional dimensions of the beam are shown. Determine:

$($a$)$ The centroid location, the moment of inertia about the z axis, and the controlling section

modulus about the z axis.

$($b$)$ The bending stress at points H and K $.$ State whether the normal stress is tension or

compression.

$($c$)$ The maximum bending stress produced in the cross section. State whether the stress is

tension or compression.

Please explain each step most especially how y at point h is $30$ and how y at point k is $80.$