6x – 4y = 9
4y = 6x - 9
y = 6/4 x - 9/4
y = 3/2 x - 9/4 this line has slope = 3/2
perpendicular line, slope is opposite and reciprocal so slope of this line = -2/3
answer:
A. y= - 2/3 x - 4 (only this line has slope = -2/3)
Answer: D. cylinder F. prism
Step-by-step explanation:
From the given figures in the options , only cylinder and prism have two congruent parallel bases.
- A cylinder is a solid figure which has the two congruent parallel bases i.e. circles.
- A prism is a solid shape that has two parallel congruent sides which are called bases and they are joined by the lateral faces that are parallelograms.
Rest of other options do not have congruent parallel bases.
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: Two and one tenth.
Answer:
13/20
Step-by-step explanation:
65%=65/100
65/100=13/20