A beam is machined to be bolted at the base and has a channel for routing cables. As shown in the figure below, the cross-sectional shape of the beam consists of a rectangular base for a raised square portion that has a semi- circular groove cut into its top. Engineering has specified a dimension of a = 4 cm for the machined beam. Determine the following: a) the centroid location, yc, along the vertical Y axis. b) the moment of inertia, Ixc, about the centroidal x axis. Submit your answer for the centroid location, yc, along the vertical Yc axis. 0.5a -2a- -0.5a a a 3at 5a+ -