ม z Consider a square-based pyramid of constant density p=p with corners located at (x, y, z) = (1,1,0), (−1,1,0), (1,−1,0), (−1, −1,0), (0,0,2). Determine the coordinates of the pyramid's center of mass (z, y, z). A

A fluid has density 900 kg/m³ and flows with velocity v = xi+yj + zk, where x, y, and z are measured in meters, and the components of 7 are measured in meters per second. Find the rate of flow outward through the part of the paraboloid z = 64 x² - y² that lies above the xy plane. - Submit Question kg/s Question Help: Video Message instructor

find the centroid (x,y) of the shaded area

Center of Mass: Point masses in the plane. Suppose three point masses are placed in the ry-plane as follows (assume coordinates are given in meters). m1 = 10 kg, placed at (-2, 2), m2 = 6 kg, placed at (-3, 6), m3 = 8 kg, placed at (7, –4). Find the center of mass of the system. (1,7) = Note: your answer should be an ordered pair.

Using the fact that the centroid of a triangle lies at the intersection of the triangle's medians, which is the point that lies one-third of the way from each side toward the opposite vertex, find the centroid of the triangle whose vertices are (0,0), (a,0), and (0,b). Assume a > 0 and b>0. The centroid of the triangle is (x,y), where x = and y =