Question

Find the center of mass of a thin plate of constant density

delta δ covering the region bounded by the parabola y=(3/2)x²and the line y=6.

Answer 1

To find the center of mass of a thin plate with a constant density delta covering the region bounded by the parabola y= (3/2)x² and the line y = 6, we can use calculus.

Step-by-step explanation:

To find the center of mass of a thin plate with a constant density delta covering the region bounded by the parabola y= (3/2)x² and the line y = 6, we can use calculus.

1. First, we need to find the mass of the plate. To do this, we integrate the surface mass density over the region bounded by the parabola and the line.
2. Then, we can find the moments about the x-axis and y-axis by integrating x and y multiplied by the surface mass density, respectively.
3. Finally, we divide the moments by the total mass to find the coordinates of the center of mass.