Use the divergence theorem to calculate the outward flux of f=r|r|f=r|r| where r=⟨x, y,z⟩r=⟨x, y,z⟩ across ss: the hemisphere z=16−x2−y2‾‾‾‾‾‾‾‾‾‾‾‾√z=16−x2−y2 and the disk x2+y2≤16x2+y2≤16 in the xyxy-plane.

With (?) you have divergence

Then by the divergence theorem, the flux is

where denotes the interior of the region with boundary .

Convert to spherical coordinates to set up the volume integral as

honesty mood

step-by-step explanation:

ratio is 2 : 9

the answer is three

13.5 : 3