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.
Answer:
7) a= 20
8) m= 5
9)n = 5
10) b = 8
Step-by-step explanation:
7) 18+2=-2+2+a
>> 20 = a >> a = 20
18 + 2 = 20 so that isolates the variable leaving a = 20
8) -7+12 = m -12+12
>>> 5 = m >> m = 5
-7 + 12 = 5 so that again isolates the variable leaving m = 5
9) <u>-8(7</u> + <u>7n</u>) = -336
>> -56+56 + -56n = -336+56
>>> -56n/-56 = -280/-56
>>>> n = 5
use distributive property, cancel out necessary numbers, isolate the variable. leaving n = 5.
10) -140 = <u>-7(-4 </u>+ <u>3b)</u>
>> -140 = 28 - 21b >> -140-28 = -21b +28-28 ( flipped the numbers)
>>> -168/-21 = -21b /-21
>>>> 8 = b >> b =8
Hope it helps!
Answer:
Equation: 8=4b
b=2
Explanation:
The green line equals 8 and the black time equals 2b+2b. So to form an equation where the green line equals the black line it would look like: 8=2b+2b
8 being the green line
2b+2b being the black line
Then the directions tell us to combine like terms, like terms are terms that are the same such as 2b in this problem, and to combine them means to add them together.
So, 2b+2b= 4b
So the answer is, 8= 4b
In order to solve this equation divide both sides by 4.
Which leaves you with: 8/4= b
Now solve 8/4:
Which gives you:
b=2
Answer:
You <u>solve</u> the equation.
Step-by-step explanation:
The process of finding variable values that make the equation true is called <em>solving</em> the equation.
