Answer:
1/2
Step-by-step explanation:
The interior of the square is the region D = { (x,y) : 0 ≤ x,y ≤1 }. We call L(x,y) = 7y²x, M(x,y) = 8x²y. Since C is positively oriented, Green Theorem states that

Lets calculate the partial derivates of M and L, Mx and Ly. They can be computed by taking the derivate of the respective value, treating the other variable as a constant.
- Mx(x,y) = d/dx 8x²y = 16xy
- Ly(x,y) = d/dy 7y²x = 14xy
Thus, Mx(x,y) - Ly(x,y) = 2xy, and therefore, the line ntegral is equal to the double integral

We can compute the double integral by applying the Barrow's Rule, a primitive of 2xy under the variable x is x²y, thus the double integral can be computed as follows

We conclude that the line integral is 1/2
686 barrels left. If I'm not mistaken this should just be simple subtraction
Answer:
11°
Step-by-step explanation:
tan ∅ = 20/100 = 0.2
∅ = 11.31°
Answer:
64
Step-by-step explanation:
can be found by first finding
then taking that result and putting it into the function
.
means we are going to take the expression
and evaluate it for
:


So
.
So we have this so far:
.
was found by replacing
in
with
.