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:
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Answer: she must sell 6 large photos and 6 small photos
Step-by-step explanation: and how I knew that is I multiplied 6 40 times and that gives you 240 and if you multiply 6 ten times that gives you 60 so 240 plus 60 is $300
Answer:
Laura will need to order 3 pizza boxes and Laura will need to spend $37.50.
Step-by-step explanation:
Answer:
8/27
Step-by-step explanation:
2 2/3 = 8/3
8/3 divided by 9 =
8/3 x 1/9 =
8/27
Simplify <span><span><span>12</span>x</span><span><span>12</span>x</span></span> to <span><span>x2</span><span>x2</span></span>
<span><span><span>x2</span>−<span>34</span>y=−2</span><span><span>x2</span>−<span>34</span>y=−2</span></span>
2 Simplify <span><span><span>34</span>y</span><span><span>34</span>y</span></span> to <span><span><span>3y</span>4</span><span><span>3y</span>4</span></span>
<span><span><span>x2</span>−<span><span>3y</span>4</span>=−2</span><span><span>x2</span>−<span><span>3y</span>4</span>=−2</span></span>
3 Subtract <span><span>x2</span><span>x2</span></span> from both sides
<span><span>−<span><span>3y</span>4</span>=−2−<span>x2</span></span><span>−<span><span>3y</span>4</span>=−2−<span>x2</span></span></span>
4 Multiply both sides by <span>44</span>
<span><span>−3y=(−2−<span>x2</span>)×4</span><span>−3y=(−2−<span>x2</span>)×4</span></span>
5 Regroup terms
<span><span>−3y=4(−2−<span>x2</span>)</span><span>−3y=4(−2−<span>x2</span>)</span></span>
6 Divide both sides by <span><span>−3</span><span>−3</span></span>
<span><span>y=<span><span>4(−2−<span>x2</span>)</span><span>−3</span></span></span><span>y=<span><span>4(−2−<span>x2</span>)</span><span>−3</span></span></span></span>
7 Simplify <span><span><span>4(−2−<span>x2</span>)</span><span>−3</span></span><span><span>4(−2−<span>x2</span>)</span><span>−3</span></span></span> to <span><span>−<span><span>4(−2−<span>x2</span>)</span>3</span></span><span>−<span><span>4(−2−<span>x2</span>)</span>3</span></span></span>
<span><span>y=−<span><span>4(−2−<span>x2</span>)</span>3</span></span></span>
