Since each table had 7 women and 3 men at each table, that would mean each table has 10 people. Since there are 9 tables he was waiting on, and 10 people at each table, multiply 9 x 10, and you will find that he served 90 people in total.
Answer:
x/5
Step-by-step explanation:
To get the inverse function you need to leave the x alone and then switch variables ( f(x) = y)
f(x) = 5x
y = 5x
y/5 = x
Now that x is alone you switch the x for y and the y for x and you get:
x/5 = y
And this new y is the inverse function of f(x) ( f^-1(x))
f^-1(x) = x/5
Answer:
0.03
Step-by-step explanation:
6 is greater then 5, so you add 1 to 2 making 0.03
<h3>
Answer: (n-1)^2</h3>
This is because we have a list of perfect squares 0,1,4,9,...
We use n-1 in place of n because we're shifting things one spot to the left, since we start at 0 instead of 1.
In other words, if the answer was n^2, then the first term would be 1^2 = 1, the second term would be 2^2 = 4, and so on. But again, we started with 0^2 = 0, so that's why we need the n-1 shift.
You can confirm this is the case by plugging n = 1 into (n-1)^2 and you should find the result is 0^2 = 0. Similarly, if you tried n = 2, you should get 1^2 = 1, and so on. It appears you already wrote the answer when you wrote "Mark Scheme".
All of this only applies to sequence A.
side note: n is some positive whole number.
Given that you mention the divergence theorem, and that part (b) is asking you to find the downward flux through the disk
, I think it's same to assume that the hemisphere referred to in part (a) is the upper half of the sphere
.
a. Let
denote the hemispherical <u>c</u>ap
, parameterized by

with
and
. Take the normal vector to
to be

Then the upward flux of
through
is



b. Let
be the disk that closes off the hemisphere
, parameterized by

with
and
. Take the normal to
to be

Then the downward flux of
through
is


c. The net flux is then
.
d. By the divergence theorem, the flux of
across the closed hemisphere
with boundary
is equal to the integral of
over its interior:

We have

so the volume integral is

which is 2 times the volume of the hemisphere
, so that the net flux is
. Just to confirm, we could compute the integral in spherical coordinates:
