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.
No because the box has a fixed weight as the several books weighing said pounds would most likely to be use as the x in this equation.
Number one is a square number two is quadrillateral
Answer:
1/5
Step-by-step explanation:
The maximum units is 200 and , Total revenue is $8,000
<u>Step-by-step explanation:</u>
Here we have , A manufacturer finds that the revenue generated by selling of cortan commodity is given by function R(x)=80x-0.2x^ 2 , where he maximum reveremany should be manufactured to obtain this maximum units .Let's find out:
We have following function as
. Let's differentiate this and equate it to zero to find value of x for which the function is maximum!
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
Now , Value of function at x=200 is :
⇒ 
⇒ 
⇒ 
Therefore , The maximum units is 200 and , Total revenue is $8,000