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The line integral along the given positively oriented curve is -216π. Using green's theorem, the required value is calculated.
<h3>What is green's theorem?</h3>
The theorem states that,

Where C is the curve.
<h3>Calculation:</h3>
The given line integral is

Where curve C is a circle x² + y² = 4;
Applying green's theorem,
P = 9y³; Q = -9x³
Then,



⇒ 
Since it is given that the curve is a circle i.e., x² + y² = 2², then changing the limits as
0 ≤ r ≤ 2; and 0 ≤ θ ≤ 2π
Then the integral becomes

⇒ 
⇒ 
⇒ 
⇒ 
⇒ ![-108[2\pi - 0]](https://tex.z-dn.net/?f=-108%5B2%5Cpi%20-%200%5D)
⇒ -216π
Therefore, the required value is -216π.
Learn more about green's theorem here:
brainly.com/question/23265902
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Answer:
8.80
Step-by-step explanation:
68% you have to divide 17 by 25 and then move the decimal
Answer:
21.9
Step-by-step explanation:
The altitude of an isosceles triangle bisects the base. So, x represents the hypotenuse of a right triangle with legs of 9 and 20. It can be found using the Pythagorean theorem:
x^2 = 9^2 +20^2 = 81 +400
x = √481 ≈ 21.932
The length x is about 21.9 units.