Find Centroid: x(bar), y(bar) = (?, ?)

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SUMMARY

The centroid of the region defined by the inequalities y ≤ (1/3)x², (x-3)² + y² ≤ 9, and y ≥ 0 is calculated using the moment and planar mass formulas. The specific coordinates for the centroid, x(bar) and y(bar), are not provided in the discussion, as the original poster seeks confirmation of their solution. The problem involves integrating the area defined by the given inequalities to find the centroid's coordinates.

PREREQUISITES
  • Understanding of planar mass concepts
  • Familiarity with calculating centroids in calculus
  • Knowledge of inequalities and their graphical representations
  • Experience with integration techniques for area determination
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  • Research methods for calculating centroids in calculus
  • Learn about planar mass and its applications in centroid calculations
  • Study graphical representation of inequalities and their intersections
  • Explore integration techniques for finding areas under curves
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Students in calculus, mathematicians focusing on geometry, and educators teaching centroid calculations will benefit from this discussion.

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1. Find the centroid of the region determined by the graphs of the inequalities.

y ≤ (1/3)x^(2) ; (x-3)^2 + y^(2) ≤ 9 ; y ≥ 0

x(bar) , y(bar) = (?, ?)



I did the problem, but i do not know the answer because the problem is an even number and the book only have answers for the odd problem. I would like to know the answer to this problem. I do not need to know how to do it. I just need to know the answer so I can check my work.

2. What I did was find moment using the equations. then i use the formulas for planar mass.
 
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