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:
x = 54° y = 126°
Step-by-step explanation:
Interior angles of a triangle = 180°
Therefore x = 180 - 80 - 46 = 54°
y = 180 - x = 180 - 54 = 126°
Answer:
Step-by-step explanation:
divide 20 by four
20/4=5/1
now 10 and 15 can both be divided by 5 since 5 is the greatest common factor
10/15=2/3
Answer:
y= 6971 -7 x OR y = -7x + 6971
Step-by-step explanation:
the 6971 is the original number you started with, you are now decreasing by 7, so you use the value of -7. The x is the number of years that pass by, so the variable x affects the number 7 because it says decreases by 7 per year. The x does not go with 6971 as that number doesn't get directly affected.