Answer:
52.9
numbers 0-4 the number stays the same
numbers 5-9 the number goes up one
Answer:10x^2y^2
Step-by-step explanation:
5x2 X 2y2=10x^2y^2
Because I've gone ahead with trying to parameterize
directly and learned the hard way that the resulting integral is large and annoying to work with, I'll propose a less direct approach.
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
. Then by the divergence theorem, since the region
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

with
and
. Take the normal vector to
to be

Then the flux of
across
is




9514 1404 393
Answer:
47 -6√10
Step-by-step explanation:
As you know, the area of a square is the square of the side length. It can be helpful here to make use of the form for the square of a binomial.
(a -b)² = a² - 2ab + b²
(√2 -3√5)² = (√2)² - 2(√2)(3√5) + (3√5)²
= 2 - 6√10 + 3²(5)
= 47 -6√10
__
<em>Check</em>
√2-3√5 ≈ -5.29399 . . . . . . . . note that a negative value for side length makes no sense, so this isn't about geometry, it's about binomials and radicals
(√2-3√5)² ≈ 28.02633
47 -6√10 ≈ 28.02633
Step 1: Find the slope:

This gives you
, but we need to find b.
To find b, substitute in one (x,y) pair and it doesn't matter which one. I'll go with (4,-2):
![\begin{aligned}-2&=-\dfrac{3}{2}(4)+b\\[0.5em]-2&=-6+b\\[0.5em]4&=b\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D-2%26%3D-%5Cdfrac%7B3%7D%7B2%7D%284%29%2Bb%5C%5C%5B0.5em%5D-2%26%3D-6%2Bb%5C%5C%5B0.5em%5D4%26%3Db%5Cend%7Baligned%7D)
Now take that b-value and plug in into the slope-intercept form:

It's always a good idea to toss in the other x-value from the other point, to make sure it checks out.