Find the center of mass of the following plane region with variable density. describe the distribution of mass in the region. the triangular plate in the first quadrant bounded by y equals x, xequals0, and y equals 2 minus x with rho left parenthesis x comma y right parenthesisequals14 x plus 3 y plus 7.

When the solutions to each of the two equations below are graphed in the xy-coordinate plane, the graphs of the solutions intersect at two places. write the y-cordninates of the points of intersection in the boxes below in order from smallest to largest. y=2x y=x^2-3

The cross-sectional areas of a right triangular prism and a right cylinder are congruent. the right triangular prism has a height of 6 units, and the right cylinder has a height of 6 units. which conclusion can be made from the given information? the volume of the triangular prism is half the volume of the cylinder. the volume of the triangular prism is twice the volume of the cylinder. the volume of the triangular prism is equal to the volume of the cylinder. the volume of the triangular prism is not equal to the volume of the cylinder.

Write the point-slope form of the line passing through (2, -12) and parallel to y=3x.