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
x= 1st integer and then x+1 x+2 and x+3 all add up to 326
x + x+1 + x+2 + x+3 = 326
4x +6 = 326
4x= 320 (divide both sides by 4)
x=80
the Second number is 81
Answer:
Oxygen; 34.01°C
Step-by-step explanation:
The oxygen freezes first as it has a higher (warmer) freezing point. For both to freeze, the temperature must drop a further 34.01°C as:
-218.79 - (-252.8)
= 252.8 - 218.79
= 34.01
Answer:
9 red shirts
Step-by-step explanation:
30 x 0.30 = 9 red shirts