Find the moments of inertia ix, iy, i0 for a lamina that occupies the part of the disk x2 + y2 ≤ 36 in the first quadrant if the density at any point is proportional to the square of its distance from the origin. (assume that the coefficient of proportionality is k.)

Emmy kicks a soccer ball up at an angle of 45° over a level field. she watches the ball's trajectory and notices that it lands, two seconds after being kicked, about 20 m away to the north. assume that air resistance is negligible, and plot the horizontal and vertical components of the ball's velocity as a function of time. consider only the time that the ball is in the air, after being kicked but before landing. take "north" and "up" as the positive ‑ and ‑directions, respectively, and use ≈10 m/s2 for the downward acceleration due to gravity.