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
Answer:
Step-by-step explanation:
If you graph there would be two different regions. The first one would be

And the second one would be
.
If you rotate the first region around the "y" axis you get that

And if you rotate the second region around the "y" axis you get that

And the sum would be 2.51+4.188 = 6.698
If you revolve just the outer curve you get
If you rotate the first region around the x axis you get that

And if you rotate the second region around the x axis you get that

And the sum would be 1.5708+1.0472 = 2.618
So, this means that you are multiplying both of the numerators and denominators together to get the product
Answer:
∠ 1 = 120°
Step-by-step explanation:
Note that ∠ Q and ∠ R are congruent, that is both 30°, thus
∠ 1 = 180° - (30 + 30)° = 180° - 60° = 120°
Answer:
see below
Step-by-step explanation:
A percentage change is computed as follows:
percent change = ((new value) -(original value))/(original value) × 100%
For your first one, this looks like ...
percent change = ($25 -$75)/$75 × 100% = (-50/75) × 100% = -0.667×100%
percent change = -66.7%
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When there are a lot of similar calculations to do, I like to use a spreadsheet. See below for the other percentage changes (rightmost column).