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:
(a) none of the above
Step-by-step explanation:
The largest exponent in the function shown is 2. That makes it a 2nd-degree function, also called a quadratic function. The graph of such a function is a parabola -- a U-shaped curve.
The coefficient of the highest-degree term is the "leading coefficient." In this case, that is the coefficient of the x² term, which is 1. When the leading coefficient of an even-degree function is positive, the U curve has its open end at the top of the graph. We say it "opens upward." (When the leading coefficient is negative, the curve opens downward.)
This means the bottom of the U is the minimum value the function has. For a quadratic in the form ax²+bx+c, the horizontal location of the minimum on the graph is at x=-b/(2a). This extreme point on the curve is called the "vertex."
This function has a=1, b=1, and c=3. The minimum of the function is where ...
x = -b/(2·a) = -1/(2·1) = -1/2
This value is not listed among the answer choices, so the correct choice for this function is ...
none of the above
__
The attached graph of the function confirms that the minimum is located at x=-1/2
_____
<em>Additional comment</em>
When you're studying quadratic functions, there are few formulas that you might want to keep handy. The formula for the location of the vertex is one of them.
Answer:
-2
or
-2/1
Explanation:
**Slope = rise/run**
By counting the distance between the points, from (0,3) to (1,1) , it went down 2 units and right by 1 unit
15 feet is what I came up with.
Answer:
$5,875
Step-by-step explanation:
Interest = Principal x Time x Interest Rate
Interest = $5000 x 3.5 x 0.05
Interest = $875
Total Balance will be
$5000 + $875
= $5,875
in 3.5 years
