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
Answer:
16.49
Step-by-step explanation:
21^2 - 13^2 = 272
square root 272 = 16.49
The hypotenuse^2 = leg1^2 + leg2^2
The hypotenuse is always the LONGEST side of any right triangle.
It is also the side that is opposite the right angle
Answer:
The given sequence 6, 7, 13, 20, ... is a recursive sequence
Step-by-step explanation:
As the given sequence is

- It cannot be an arithmetic sequence as the common difference between two consecutive terms in not constant.
As
, 
As d is not same. Hence, it cannot be an arithmetic sequence.
- It also cannot be a geometrical sequence and exponential sequence.
It cannot be geometric sequence as the common ratio between two consecutive terms in not constant.
As
,
, 
As r is not same, Hence, it cannot be a geometric sequence or exponential sequence. As exponential sequence and geometric sequence are basically the same thing.
So, if we carefully observe, we can determine that:
- The given sequence 6, 7, 13, 20, ... is a recursive sequence.
Please have a close look that each term is being created by adding the preceding two terms.
For example, the sequence is generated by starting from 1.

and

for n > 1.
<em>Keywords: sequence, arithmetic sequence, geometric sequence, exponential sequence</em>
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Answer: 2 x - 3 y = 6 i think but let let me know if i'm wrong