Which is NOT true about a direct proportion?
2 answers:
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Answer:
Point C: (4, 0)
Step-by-step explanation:
Parallelograms are quadrilaterals with two pairs of parallel sides, this means they will have the same slope between two line segments.
point slope form between two points: y - y1 = m (x - x1)
point A (2, 6) and D (4,4):
slope: point form, 6 - 4 = m(2 - 4)
2 = -2m
m (slope) = =
now that you know the change in position, apply this to vertice B to get the position of the final vertice.
B(2, 2)
C (2 +2, 2-2) = C(4, 0)
The final position of C vertice for parrallelogram A(2,6), B(2,2), D(4,4) will be C(4,0)
It looks like the integral is
where <em>C</em> is the circle of radius 2 centered at the origin.
You can compute the line integral directly by parameterizing <em>C</em>. Let <em>x</em> = 2 cos(<em>t</em> ) and <em>y</em> = 2 sin(<em>t</em> ), with 0 ≤ <em>t</em> ≤ 2<em>π</em>. Then
Another way to do this is by applying Green's theorem. The integrand doesn't have any singularities on <em>C</em> nor in the region bounded by <em>C</em>, so
where <em>D</em> is the interior of <em>C</em>, i.e. the disk with radius 2 centered at the origin. But this integral is simply -2 times the area of the disk, so we get the same result: .