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
Rather than solve the entire problem for you, I'll give you some hints to help you get started:
1. The amplitude of your sinusoidal graph is |3|, or just 3.
2. Because of that, your graph begins at the point (0,3).
3. Because this is the cosine function, your graph descends from (0,3) to y=3 and then begins to ascend (back to y=3).
4. The coefficient of x is "one half pi," or pi/2. Call this "b".
5. The period of your function is 2pi/b. Here, b=pi/2.
Dividing, [2pi]/[pi/2] = 4.
6. Mark your horizontal axis as follows: x=0, 4, 8, 12, 16, ...
7 Draw one cycle of the cosine function with amplitude 3. It must begin at (0,3) and end at (4,3) (which covers one period).
8. Draw another cycle or two, beginning at (4,3) and ending at (8,3), and so on.
Answer:
sin∅ = 0.7311
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
sin∅ = opposite/hypotenuse
Step 1: Find our hypotenuse
14² + 15² = c²
c = √421
Step 2: Find sin∅
sin∅ = 15/√421
sin∅ = 0.731055
Answer:
The difference of fifty-four and seven times a number is written as 54 - 7x.
Step-by-step explanation: