What's 3 quarters in change
2 answers:
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Treat 
as the boundary of the region 
, where is the part of the surface 
bounded by . We write
with
.
By Stoke's theorem, the line integral is equivalent to the surface integral over of the curl of 
. We have
so the line integral is equivalent to
where
is a vector-valued function that parameterizes . In this case, we can take
with
and 
. Then
and the integral becomes
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with
By Stoke's theorem, the line integral is equivalent to the surface integral over
so the line integral is equivalent to
where
with
and the integral becomes
Answer:
Step-by-step explanation:
The base of the pyramid we need to study is a hexagon.
Let's look at the attached image of an hexagon to understand how we are going to find the area of this figure.
Notice that an hexagon is the combination of 6 exactly equal equilateral triangles in our case of size "2x" (notice that the "radius" of the hexagon is given as "2x")
Therefore the area of the hexagon is going to be 6 times the area of one of those equilateral triangles.
We know the area of a triangle is the product of its base times its height, divided by 2:
We notice that the triangle's height is exactly what is called the "apothem" of the hexagon (depicted in green in our figure) which measures , so replacing this value in the formula above for the area of one of the triangles:
Then we multiply this area times 6 to get the total area of the hexagon (6 of these triangles):
Area of hexagon =
which is the last option given in the list.
