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1 answer:
The number 72 should replace the question mark.
Step-by-step explanation:
Step 1:
First, we need to determine how the values inside the triangles were attained in terms of the outer values.
We get that summing the bottom values on the triangle and multiplying it with the value on top equals the value in the triangle.
For triangle 1,
For triangle 2,
For triangle 3,
Step 2:
By using the same method for the fourth triangle we have;
For triangle 4:
So the question mark equals 72.
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Rather than compute the surface integral over straight away, let's close off the hemisphere with the disk
of radius 9 centered at the origin and coincident with the plane
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is closed, we have
where is the interior of
.
has divergence
so the flux over the closed region is
The total flux over the closed surface is equal to the flux over its component surfaces, so we have
Parameterize by
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Then the flux of across
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