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.
There are 2001 items in that set.
So n(A) = 2001
We can individually count them all out, which is very slow and tedious, or we can use the formula
n-m+1
where,
m = starting value
n = ending value
In this case,
m = 0
n = 2000
So,
n-m+1 = 2000-0+1 = 2001
This formula only works if we increase the number by 1 each time (eg: 6, 7, 8, etc)
Answer:
The correct answer is option A
Step-by-step explanation:
The volume of a cylinder is given by

Substituting the values of radius and height in above equation, we get -

Answer:
The wide of river is 
Step-by-step explanation:
In this problem we know that
Triangles DEG and DEF are congruent by ASA (Angle-Side-Angle) Congruence
therefore
EG=EF
