Use Stokes' theorem for both parts, which equates the surface integral of the curl to the line integral along the surface's boundary.
a. The boundary of the hemisphere is the circle 
in the plane 
, where the curl is 
. Green's theorem applies here, so that
which means the value of the line integral is 3 times the area of the circle, or 
.
b. The closed sphere has no boundary, so by Stokes' theorem the integral is 0.
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The surface area of a cone is equal to the base plus the lateral area.
The base is a circle, and has a diameter of 16 meters.
The radius is always half the diameter, so it is 8 meters.
The area of a circle = πr², where r is the radius. π(8)² = 64π ≈ 201.06193
The area of the base is ≈ 201.06193.
To find the lateral area of the cone, we need to find the slant height.
Since the height, radius, and slant height of the cone form a right triangle, we can use the Pythagorean Theorem to find the slant height with what we are given.
radius² + height² = slant height²
8² + 37² = slant height²
64 + 1369 = slant height²
1433 = slant height²
slant height = √1433
The lateral area of a cone is equal to πrl, where r = radius and l = slant height.
πrl = π(8)(√1433) ≈ 951.39958
(there are other formulas which do the same thing, but it doesn't matter.)
Now we add the lateral area and base together to find our surface area.
201.06193 + 951.39958 = 1152.46151 which rounds to C. 1,152 m².
The fish weighed 660 because 2÷132 is 66×10=660
Answer:
the answer is gay
Step-by-step explanation:
I Logan is gay cause he asked people who liked carrots and carrots are gay
