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




Answer:
the y coordinate is 5
Step-by-step explanation:
In the figure attached, the directed line segment is shown.
J is located at (-3, 1) and K is located at (-8, 11)
run: x2 -x1 = -8 - (-3) = -5
rise: y2 - y1 = 11 - 1 = 10
Taking J as reference, the coordinate of the point that divides the directed line segment from J to k into a ratio of 2:3 is:
c = 2/(2+3) = 0.4
(x1 + c*run, y1 + c*rise)
(-3 + 0.4*-5, 1+0.4*10)
(-5, 5)
Answer:
Yumiko should multiply the other equation by 3.
If she adds the two equations she would be left with the variable 'x'.
Step-by-step explanation:
Given the two equations are as follows:


It is given that she multiplies the first equation by 6. Therefore, (1) becomes

Now, note that the sign of the variable 'y' is negative. So, if we make the co-effecient of 'y' equal in both the cases, add them it would result in the elimination of the variable 'y'.
The co-effecient of y in Equation (2) is 6. To make it 18 like it is in Equation (1), we multiply throughout by 3.
Therefore, Equation (2) becomes:

Now, we add Equation (a) and Equation (b).


Factor: 3
Equation: 27x = 126
Answer:
Idk lol
Step-by-step explanation: