anonymous
  • anonymous
Find the centroid of the following:
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
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anonymous
  • anonymous
Here's what I did.... \[\huge \bar{y}= \frac{\int\limits y dA}{\int\limits dA}\] \[\huge \frac{\int\limits_0^1 y\sqrt{4-y}dy}{\int\limits_{-2}^{2} 1-\frac{1}{4}x^2dx}\] \[\huge=0.342m\]
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anonymous
  • anonymous
**They only want y centroid
jim_thompson5910
  • jim_thompson5910
I would use \[\LARGE \bar{y} = \frac{1}{A}*\int_{-2}^{2}\frac{1}{2}*\left(1-\frac{1}{4}x^2\right)^2dx\] where A is the area of the blue region http://tutorial.math.lamar.edu/Classes/CalcII/CenterOfMass.aspx When I used that formula I didn't get 0.342. I got something slightly larger.

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anonymous
  • anonymous
@jim_thompson5910 It's for a statics course, so I have to do it using this particular equation. I'm not sure what I'm doing wrong
jim_thompson5910
  • jim_thompson5910
If you used your version of the formula, it would actually be this \[\huge \frac{\int\limits_0^1 4y\sqrt{1-y}dy}{\int\limits_{-2}^{2} 1-\frac{1}{4}x^2dx}\]
anonymous
  • anonymous
Oh I see my stupid error... Also I think you meant 2**, not 4
jim_thompson5910
  • jim_thompson5910
if you solve y = 1-(1/4)x^2 for x, you get x = 2*sqrt(-y+1) or x = -2*sqrt(-y+1) using symmetry, we know the two halves of the region are equal so we can integrate from y = 0 to y = 1 and then double the area so 2*2*sqrt(-y+1) = 4*sqrt(-y+1)
anonymous
  • anonymous
Ohh I didn't realize you already factored that in
anonymous
  • anonymous
Thank you!
jim_thompson5910
  • jim_thompson5910
what final answer did you get?
anonymous
  • anonymous
~0.400m
jim_thompson5910
  • jim_thompson5910
yep 2/5 = 0.4
anonymous
  • anonymous
X)

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