The area of the ellipse
is given by

To use Green's theorem, which says

(
denotes the boundary of
), we want to find
and
such that

and then we would simply compute the line integral. As the hint suggests, we can pick

The line integral is then

We parameterize the boundary by

with
. Then the integral is


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Notice that
kind of resembles the equation for a circle with radius 4,
. We can change coordinates to what you might call "pseudo-polar":

which gives

as needed. Then with
, we compute the area via Green's theorem using the same setup as before:






Roughly 2,365,200,000. If you have muiltiple choices round up to the nearest
Answer:
The legs of a triangle with a hypotenuse that measures 15 units long have lengths that are equal to 15 times the sine or cosine of the given angle.
leg 1 = (15 units) x (cos 19) = 14.18 units
leg 2 = (15 units) x (sin 19) = 4.88 units
The lengths of the legs are 14.18 units and 4.88 units.
Answer:

Step-by-step explanation:
Option 1:
Using the following rule:

Put in our expression,
a = 2
n = 3
m = 2


Option 2:
Using the following rule:

Since our expression is the same as multiplying 2³ with itself, we can write it as a multiplication.

If we compare this with
, we can see that
a = 2
n = 3
m = 3 (in this case, n and m are equal)


Answer: 