The following table shows a proportional relationship between m and n
2 answers:
Answer:
Step-by-step explanation:
Notice that if you divide each n-value by its correspoding m-value, you always have 7 as a result, that means it's the constant ratio of change,
21/3 = 7
35/5 = 7
56/8 = 7
Now, this is a linear relatioship by definition, where its constant ratio is 7, but geometrically, that ratio is the slope of a linear equation.
So, we need to use the slope 7, one pair from the table and the point-slope formula
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Close off the hemisphere by attaching to it the disk
of radius 3 centered at the origin in the plane
. By the divergence theorem, we have
where is the interior of the joined surfaces
.
Compute the divergence of :
Compute the integral of the divergence over . Easily done by converting to cylindrical or spherical coordinates. I'll do the latter:
So the volume integral is
From this we need to subtract the contribution of
that is, the integral of over the disk, oriented downward. Since
in
, we have
Parameterize by
where and
. Take the normal vector to be
Then taking the dot product of with the normal vector gives
So the contribution of integrating over
is
and the value of the integral we want is
(integral of divergence of <em>F</em>) - (integral over <em>D</em>) = integral over <em>S</em>
==> 486π/5 - (-81π/4) = 2349π/20