Q2 (10 points) use the green-stokes formula in order to compute the vector line integral: (z + y') dx + (2x - z) dy + (x- - y) dz where t is the triangle with vertices (1, 0, 0), (0, 1,0) and (0, 0, 2) traversed in the direction implied by the order in which the vertices were given (i. e. from the 1st to the 2nd, to the 3rd and then back to the 1st one).

has the underlying vector field

with curl

Parameterize by

with , .

The implied orientation of the curve is counter-clockwise when viewing from the first octant (each of greater than 0), so that the normal vector to is pointing upward and away from the origin. Take this vector to be

Then by Stokes' theorem, the line integral is equivalent to

blue marble is 15 times out of 50 = 15/50 reduces to 3/10

landing on tails is 24 out of 50 = 24/50 reduces to 12/25

to find the probability of both multiply together:

3/10 x 12/25 = 3 x 12 / 10 x 25 = 36/250

if you multiplied the numerator and denominator by 10 you get 360/2500.

the answer is 360/2500

c

step-by-step explanation:

at least i think its