Stokes' theorem equates the line integral of along the curve to the surface integral of the curl of over any surface with the given curve as its boundary. The simplest such surface is the triangle with vertices (1,0,1), (0,1,0), and (0,0,1).
Parameterize this triangle (call it ) by
with and . Take the normal vector to to be
Divide this vector by its norm to get the unit normal vector. Note that this assumes a "positive" orientation, so that the boundary of is traversed in the counterclockwise direction when viewed from above.
Compute the curl of :
Then by Stokes' theorem,
where
The integral thus reduces to
Answer:
An equation or an inequality that contains at least one variable is called an open sentence. When you substitute a number for the variable in an open sentence, the resulting statement is either true or false. If the statement is true, the number is a solution to the equation or inequality.
Answer:
The Answer Is C
Step-by-step explanation:
To find the value of x you need to get x by itself. First you need to subtract 5x from both sides. You will end up with -x=-12. Then you need to divide both sides by -1 to get x by itself. You get x=12
4x=5x-12
-5x -5x
-x=-12
÷-1 ÷-1
x=12