Use the divergence theorem to calculate the surface integral s f · ds; that is, calculate the flux of f across s. f(x, y, z) = (cos(z) + xy2) i + xe−z j + (sin(y) + x2z) k, s is the surface of the solid bounded by the paraboloid z = x2 + y2 and the plane z = 9.

By the divergence theorem,

where is the 3-dimensional space with boundary . We have

So the flux is given by

Converting to cylindrical coordinates lets us compute the following integral:

and the flux is then

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.