Answer:
313 shapes
Step-by-step explanation:
The nth term is 3n+1
so 3x104=312+1= 313 shapes
If the face is a square, then (l*l)
If the face is a triangle, then (b*h)(1/2)
If the face is a rectangle, then (l*w)
If the face is a circle, then (r²)(3.14)
You can then add all these faces up to get the total surface area of the prism.
Converting to spherical coordinates, we have
On the other hand, we can parameterize the boundary of
by
with
and
. Now, consider the surface element
So we have the surface integral - which the divergence theorem says the above triple integral is equal to -
as required.
9514 1404 393
Answer:
107/18
Step-by-step explanation:
Your calculator and/or knowledge of trig function values can help you evaluate this.
= 4/3(1/3) +3/4 -3(3/4) +3(3) -2(1)
= 4/9 +3/4 -9/4 +9 -2
= 107/18
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tan(30°) = 1/√3
tan(45°) = 1
tan(60°) = √3
sin(60°) = cos(30°) = √3/2