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Sketch the region bounded by the curves, and visually estimate the location of the centroid. y = 2x, y = 0, x = 1 WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot Find the exact coordinates of the centroid.

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Answer:

the graph is in the attachment.

the coordinates of the centroid : (2/3,2/3)

Step-by-step explanation:

  • y=0 represents x-axis ( you can easily mark it on the graph)
  • now draw x=1 line.( It is a line parallel to y axis and passing through the point (1,0) )
  • y=2x is a line which passes through origin and has a slope "2"

by using these sketch the region.

I have uploaded the region bounded in the attachment. You may refer it. The region shaded with grey is the required region.

  • to find centroid:

it can be easily identified that the formed region is a triangle

  • the coordinates of three vertices of the triangle are

(1,2) , (0,0) , (1,0)

( See the graph. the three intersection points of the lines are the three vertices of the triangle)

  • for general FORMULA, let the coordinates of three vertices of a triangle PQR be P(a,b) , Q(c,d) , R(e,f)
  • then the coordinates of the centroid( let say , G) of the triangle is given by

G = [tex](\frac{a+c+e}{3}  , \frac{b+d+f}{3} )[/tex]

  • therefore , the exact coordinates of the centroid =

[tex](\frac{1+0+1}{3}, \frac{2+0+0}{3}  ) = (\frac{2}{3}, \frac{2}{3} )[/tex]

this point is marked as G in the graph uploaded.

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