6. Find the center of mass of the rectangular lamina with vertices (0,0), (6,0), (0, 24)...
please answer 5-7 in detail 5. Find the center of mass of the rectangular lamina with vertices (0.0), (21.0). (0.12), and (21. 12) for the density p = kxy. Ans: 6. Find the mass of the triangular lamina with vertices (0, 0), (12, 24), and (24,0) for the density p = kxy. Ans: 7. Find the area of the portion of the of the surface z = 4x + 8y that lies above the region R = {(x, y): x...
Problem 11 A lamina of constant density ρ(z, y) = l is bounded by the triangle with vertices (0, 0), (4,0) and (4, 2) (a) Find the lamina's moment of inertia Iy with respect to the y-axis. (b) Find the lamina's moment of inertia I with respect to the r-axis. Problem 11 A lamina of constant density ρ(z, y) = l is bounded by the triangle with vertices (0, 0), (4,0) and (4, 2) (a) Find the lamina's moment of...
Evaluate the integral [c F.dr. F(x, y) = (x + y) i + (3x - cos y) j where is the boundary of the region that is inside the square with vertices (0,0), (4,0),(4,4), (0,4) but is outside the rectangle with vertices (1, 1), (3,1),(3,2), (1,2). Assume that C is oriented so that the region R is on the left when the boundary is traversed in the direction of its orientation.
Find the center of mass of the lamina that occupies the region R with the given density function. R = {y = 0, y = -x = 1,33 = 1,3 = 4}; 0(x, y) = kx
mass AND center of gravity (G)(3pts) Find the mass and the center of gravity of the lamina with density 6(x, y)r y enclosed by the ellypse: y 4 (G)(3pts) Find the mass and the center of gravity of the lamina with density 6(x, y)r y enclosed by the ellypse: y 4
Find the center of mass of the lamina (thin plate) corresponding to the region 0 lessthanorequalto y lessthanorequalto 4 - x^2 in the xy plane if the density of the plate is proportional to the distance from the r axis.
3) (1.25 point) Find the center of mass of the lamina that occupies the region R with the given density function. 4 R = {y = 0, y = x
3) (1.25 point) Find the center of mass of the lamina that occupies the region with the given density function. R = {y = 0, y = x = 1,= 4}; 8(x,y) = kx?
3) (1.25 point) Find the center of mass of the lamina that occupies the region R with the given density function. R = {y = 0, y = -x = 1,x = 4}: 8(x,y) = kx?
3) (1.25 point) Find the center of mass of the lamina that occupies the region R with the given density function. 4 R = 0, y = 4}; 8(x,y) = kx?