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:
y=-12/11
Step-by-step explanation:
y-(-12/11)=0(x-(-12/13))
y+12/11=0(x+12/13)
y+12/11=0
y=-12/11
Since the slope equals 0, then the line is horizontal.
For the 2nd part of 2. just plug in what you have for G in your previous graph into the equation. This will give you H for all 5 columns . Like 3×8(-1+5)= h = 3× 32= 96 so H should equal 96 and so on as far as this function.
For number 3. The equation is given so just plug in your T for time which is 3 seconds, so...-16(3)^2+90(3) = H the height at 3 seconds. I'm doing it in my head but should be the height is 414. You should also say whether it's ft or inches etc because the teacher or yourself left that out of the equation which is also vital lol.