Use a CAS to find the mass and center of gravity of the lamina with density δ . A lamina bounded by the graph of y = cos x , y = sin x , x = 0 , and x = π / 4 ; δ = 1 + 2 .
Use a CAS to find the mass and center of gravity of the lamina with density δ . A lamina bounded by the graph of y = cos x , y = sin x , x = 0 , and x = π / 4 ; δ = 1 + 2 .
Suppose the solid W in the figure is the spherical half-shell consisting of
the points above the xy-plane that are between concentric spheres
centered at the origin of radii 4 cm and 10 cm. Suppose the density 8 of the
material increases linearly with the distance from the origin, and that at the
inner surface the density is 8 g/cm³ while at the outer surface it is
10 g/cm.
(a) Using spherical coordinates, write d as a function of p. Enter p as rho.
8(e) = 25/9(rho-4)
(5.0
(b) Set up the integral to calculate the mass of the shell in the form below. If
necessary, enter o as phi, and 0 as theta.
B D
CLI 25/9(rho-4)rho^2sinphi
"OP Ópdp
A = 0
B = 2pi
C = 0
D= pi/2
(Drag to rotate)
E- 4
F= 10
(c) Find the mass of the shell.
4536pi
CSCZ
dz
Where y is the cirele 12-il=
Find the center of mass of a thin plate of constant density covering the region bounded by the parabola y = 2x and the line y = 8.
The center of mass is locatod at (x. ) =D
(Simplify your answer. Type an ordered pair.)
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