Let surface S be the boundary of the solid object enclosed by x^2+z^2=4, x+y=6, x=0, y=0, and z=0. and, let f(x, y,z)=(3x)i+(x+y+2z)j + (3z)k be a vector field (for example, the velocityfaild of a fluid flow). the solid object has five sides, S1:bottom(xy-plane), S2:left side(xz-plane), S3 rear side(yz-plane), S4:right side, and S5:cylindrical roof. a. Sketch the solid object.
b. Evaluate the flux of F through each side of the object (S1,S2,S3,S4,S5).
c. Find the total flux through surface S.

a. I've attached a plot of the surface. Each face is parameterized by

• with and ;

• with and ;

• with and ;

• with and ; and

• with and .

b. Assuming you want outward flux, first compute the outward-facing normal vectors for each face.

Then integrate the dot product of f with each normal vector over the corresponding face.

c. You can get the total flux by summing all the fluxes found in part b; you end up with 42π - 56/3.

Alternatively, since S is closed, we can find the total flux by applying the divergence theorem.

where R is the interior of S. We have

The integral is easily computed in cylindrical coordinates:

as expected.

speed

ratio of distance traveled to time interval

net force

vector sum of forces on object

object

source of diverging light rays either luminous or illuminated

don't remove my answer im trying my best to answer them

explanation:

layers of the earth affect the waves and these effects are seen on instruiments such as seimometers