Let ????C be the positively oriented square with vertices (0,0)(0,0), (2,0)(2,0), (2,2)(2,2), (0,2)(0,2). Use Green's Theorem to
bonufazy [111]
Answer:
-48
Step-by-step explanation:
Lets call L(x,y) = 10y²x, M(x,y) = 4x²y. Green's Theorem stays that the line integral over C can be calculed by computing the double integral over the inner square of Mx - Ly. In other words
Where Mx and Ly are the partial derivates of M and L with respect to the x variable and the y variable respectively. In other words, Mx is obtained from M by derivating over the variable x treating y as constant, and Ly is obtaining derivating L over y by treateing x as constant. Hence,
- M(x,y) = 4x²y
- Mx(x,y) = 8xy
- L(x,y) = 10y²x
- Ly(x,y) = 20xy
- Mx - Ly = -12xy
Therefore, the line integral can be computed as follows
Using the linearity of the integral and Barrow's Theorem we have
As a result, the value of the double integral is -48-
Answer:
483 with a remainder of 3
Step-by-step explanation:
4 8 3
---------------------------------
6 5 | 3 1 3 9 8
2 6 0
------------------
5 3 9
5 2 0
---------------------
1 9 8
1 9 5
------------------------------
3
Hope I explain myself :/
Answer: 105 and angel 2 are alternate exterior angles, angle 2 is 105 degrees. Angles 1 and 2 and supplementary so 180-105 is 75. Angle 1 measures 75 degrees.
Step-by-step explanation:
The answer is A.