A thin wire has the shape of the first-quadrant part of thecircle with center the origin and radius . If the densityfunction is p(x,y)=   kxy find the mass and center ofmass of the wire.

A thin wire represented by the smooth curve C with a density p (units of mass per length) has a mass M-p ds. Find the mass of the wire C: ((xy) y=4x²,0x53) with density ply)=3+6xy. The mass of the wire is about (Round to one decimal place as needed.)

The boundary of a lamina consists of the semicircles y= 1-x² and y = 25-x² together with the portions of the x-axis that join them. Find the center of mass of the lamina if the density at any point is inversely proportional to its distance from the origin. Hint: use polar coordinates

Find the center of mass and the moment of inertia about the y-axis for a thin rectangular plate cut from the first quadrant by the lines x=6 and y = 1 if 8(x,y) = x+3y + 1. What are the coordinates of the center of mass? X y= (Type an integer or a simplified fraction.) D