By Stokes' theorem,

where

is the circular boundary of the hemisphere

in the

-

plane. We can parameterize the boundary via the "standard" choice of polar coordinates, setting

where

. Then the line integral is


We can check this result by evaluating the equivalent surface integral. We have

and we can parameterize

by

so that

where

and

. Then,

as expected.
Answer:
y=1/4x+3
Step-by-step explanation:
Answer:
25 ft
Step-by-step explanation:
The tree's shadow is 4 times the length of the man's shadow, so we presume the tree is 4 times the height of the man: 4 × (6 ft 3 in) = (24 ft 12 in) = 25 ft.
Answer:
30 students
Step-by-step explanation:
Yesterday: 1/3 of the 75 students (75 / 3) = 25 students
There are now 50 students remaining to give their speeches.
Today: 2/5 of the 50 students (50 / 5 = 10 x 2 ) = 20 students
50 - 20 = 30 students remaining to give their speeches.
Answer:
C
Step-by-step explanation: