A lamina occupies the part of the disk x2+y2=1 in the first quadrant. Find its center of mass if the density at any point is proportional to its distance from the x-axis

Q: Suppose that a cylindrical container of radius r and height L is filled with a liquid with volume V…

A: Consider the given:  Express volume in terms of “h”, “r” and “w”.…

Q: Find the centroid of a thin, flat plate covering the region enclosed by the parabola y2 = x and the…

A: Given information:

Q: Find the centroid of the triangular region cut from the first quadrant by the line x + y = 3.

A: We will find the x and y-intercept of the triangle.  To find x-intercept we plug y=0 and find x…

Q: Find the area of the surface when y = vx, from (4, 2) to (9, 3) is rotated about the x-axis.

A: Surface area formula for rotating about x-axis is S=∫2πydS where dS=1+dydx2dx

Q: A thin plate (R) occupies the smaller region cut from the ellipse x² +4y² =12 by the parabola x =…

A: Given that a thin plate  (R) occupies the smaller region cut from the ellipse x2+4y2=12 by…