The average rate of change of function
from x = 3 to x = 4 is 4 times that from x = 1 to x = 2.
The correct option is (A).
What is the average rate of change of a function?
The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function.
Using function notation, we can define the Average Rate of Change of a function f from a to b as:

The given function is
,
Now calculating the average rate of change of function from x = 1 to x = 2.

Now, calculate the average rate of change of function from x = 3 to x = 4.

The jump from m = 10 to m = 40 is "times 4".
So option (A) is correct.
Hence, The average rate of change of function
from x = 3 to x = 4 is 4 times that from x = 1 to x = 2.
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Close off the hemisphere
by attaching to it the disk
of radius 3 centered at the origin in the plane
. By the divergence theorem, we have

where
is the interior of the joined surfaces
.
Compute the divergence of
:

Compute the integral of the divergence over
. Easily done by converting to cylindrical or spherical coordinates. I'll do the latter:

So the volume integral is

From this we need to subtract the contribution of

that is, the integral of
over the disk, oriented downward. Since
in
, we have

Parameterize
by

where
and
. Take the normal vector to be

Then taking the dot product of
with the normal vector gives

So the contribution of integrating
over
is

and the value of the integral we want is
(integral of divergence of <em>F</em>) - (integral over <em>D</em>) = integral over <em>S</em>
==> 486π/5 - (-81π/4) = 2349π/20
Answer: 1:2
Step-by-step explanation: if she sleeps 8 hours out of 24 hours, 8 goes into 24, 3 times so 1 to 2 ratio because you subtract the time she is awake from the time she is asleep
Answer:
<h3>The option A)

is correct answer.</h3><h3>The correct simplification for the given expression

is

</h3>
Step-by-step explanation:
Given expression is x to the 12th power times z to the 11th power all over x to the 2nd power times z to the 4th power.
The given expression can be written as 
<h3>To choose the correct simplification of the given expression :</h3>
Now we have to simplify the given expression as below

( by using the identity
)

( by using the identity
)


∴ 
<h3>The correct simplification for the given expression

is

</h3><h3>Hence option A)

is correct answer.</h3>
We have to see the graph to what the answer is. Sorry I wish I could help!