A 105-kg horizontal platform is a uniform disk of radius 1.77 m and can rotate about the vertical axis through its center. A 62.9-kg person stands on the platform at a distance of 1.17 m from the center and a 28.5-kg dog sits on the platform near the person, 1.39 m from the center. Find the moment of inertia of this system, consisting of the platform and its population, with respect to the axis.