A lamina occupies the part of the rectangle 0 ≤ x ≤ 8, 0 ≤ y ≤ 6 and the density at each point is given by the function p(x, y) = 1x + 6y + 2. A. What is the total mass? B. Where is the center of mass? (¯¯) (00)

please provide the correct soloution and circle the final answer! 2.6

The base of a three-dimensional figure is bound by the y-axis and the curve x = -3y2 + 6 on the interval [-1, 1]. Vertical cross sections that are perpendicular to the y-axis are right triangles with a height equal to 6. Find the numerical volume of the figure. 3-2 -1LA2 6 7 O V= 48 O V= 30 45 O V = 3 O V=

Let the region R be the area enclosed by the function f (x) = x°, the horizontal line y = -1 and the vertical lines x = О and x — 2. If the region R is the base of a solid such that each cross section perpendicular to the x-axis is a square, find the volume of the solid. You may use a calculator and round to the nearest thousandth. 14 13 12 11 10 8 7 6. 5 4 3 2 1 -1 3