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.
The equation would be:
x - 9 < 4
Simplify (add 9)
Solution: x < 13
Answer:
20 feet
Step-by-step explanation:
1st piece = x
2nd piece = 2x
3rd piece = 6x
x+2x+6x=180
9x=180
x=20
so the first piece is 20 feet, the second is 40, and the third is 120.
Answer: A. UWV and UWZ are complementary angles.
B.They do not overlap, so UWV and VWX are supplementary angles
Step-by-step explanation:
Complementary angles add up to 90.
Supplementary angles do not overlap.
