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:
12 fives and 18 tens
Step-by-step explanation:
solving this we need 2 different equations
one for he total bills and one for the total money
x+y=30
that is total bills
5x+10y=240
combining both equations we can use elimination method and get
12 five dollar bills and 18 ten dollar bills
Answer:
This triangle is a scalene triangle.
Step-by-step explanation:
A scalene triangle means that all of the sides are different.
Hope this helps!
The time intervals when the riders could see Niagara falls are; 0.834 < t < 1.416 and (3.084, 3.666)
<h3>How to interpret Cycle Graphs?</h3>
From the diagram attached, we can say that;
Period = 2π/k
where;
k = 2π/2.25
k = 8π/9
Thus;
h(t) = -(48/2) cos (8π/9)t + ((48/2) + 0.5)
h(t) = -24cos (8π/9)t + 24.5
Riders can see Niagara falls if they are higher than 41 meters above the ground. Thus;
41 = -24cos (8π/9)t + 24.5
41 - 24.5 = -24cos (8π/9)t
16.5 = -24cos (8π/9)t
-0.6875 = cos (8π/9)t
cos⁻¹0.6875 = (8π/9)t
t = 0.834 min
Thus, time interval is between;
0.834 < t < (2.25 - 0.834)
⇒ 0.834 < t < 1.416 and
(2.25 + 0.834) < t < (2.25 + 1.416)
⇒ (3.084, 3.666)
Read more about Cycle Graphs at; brainly.com/question/24461724
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