By the divergence theorem, the surface integral over
is
where
denotes the space bounded by
. Assuming the vector field is given to be
then
Converting to spherical coordinates, we take
so that the triple integral becomes
Now the integral over
alone will be the difference of the integral over
and the integral over
, i.e.
We can parameterize the points in
by
so that the integral over
is
So, the integral over
alone evaluates to
The area of a square increases by a factor 2n when its perimeter increases by a factor of n
<h3>How to determine the perimeter and area of each square?</h3>
Start by calculating the side length of each square
From the diagram, we have the following side lengths in ascending order
Square 1 = 2
Square 2 = 4
Square 3 = 8
<u>The perimeter</u>
This is calculated as:
P = 4 * Side length
So, we have:
Perimeter Square 1 = 4 * 2 = 8
Perimeter Square 2 = 4 * 4 = 16
Perimeter Square 3 = 4 * 8 = 32
Hence, the perimeters of the squares are 8, 16 and 32
<u>The area</u>
This is calculated as:
A = Side length^2
So, we have:
Area Square 1 = 2^2 = 4
Area Square 2 = 4^2 = 16
Area Square 3 = 8^2 = 64
Hence, the areas of the squares are 4, 16 and 64
<h3>What happens to the area of a square when its perimeter increases by a factor of n?</h3>
Using the computations in (a), the area of a square increases by a factor 2n when its perimeter increases by a factor of n
Read more about area and perimeter at:
brainly.com/question/24571594
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Answer:
p = 18
Step-by-step explanation:
given : n = -3
p = 2n^2
p=2*(-3)^2
p=2*8
p=18
Answer:
The first number line.
Step-by-step explanation:
In the first number line, both lines decrease, which is the same as the word problem says. Hope this helps!
Answer:
777,223 meters squared
Step-by-step explanation:
To find the amount of carpeting, we must find the area of the floor of Tom's bedroom.
To find area, we multiply the length and width of the rectangle.
999 x 777 = 776,223
Remember, when we find the area, we must give the answer in square units.
Our final answer is 777,223 meters squared