Kerry drew a number line starting at 0, point a, and ending at 1, point c. Halfway between points a and c, kerry added point b.
1 answer:
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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
⇒
⇒
⇒
⇒
⇒
⇒ -216π
Therefore, the required value is -216π.
Learn more about green's theorem here:
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Answer:
The total distance walked by Paulo is 3750 feet.
Step-by-step explanation:
Here the four points are<em> (-2,1) (-2,-7) (5,-7) (5,1)</em>
Moving from stop A to B, only the y coordinate changes,
the change is ,
=1-(-7) = 1+7 = 8 units
Moving from stop B to C, only the x coordinate changes,
the change is ,
=5-(-2) = 5+2 = 7 units
Moving from stop C to D, only the y coordinate changes,
the change is
=1-(-7) = 1+7 = 8 units
Moving from stop D to A, only the x coordinate changes,
the change is
=5-(-2) = 5+2 = 7 units
Thus, the total distance traveled is 8+7+8+7 = 30 units
It is given that <em>1 unit = 125 feet</em>
Thus, the total distance traveled is =
The total distance walked by Paulo is 3750 feet.