Find Centroid of Bounded Region: Accurate to 0.001

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SUMMARY

The discussion focuses on finding the centroid of the region bounded by the equations y = 1.5x² − 14x + 23.5 and x − y = 8, requiring an accuracy of 0.001. A participant reported an incorrect answer of (7/3, 59/52) and expressed difficulty with calculations. Forum members emphasized the importance of showing work and suggested plotting the curves to visualize the bounded region, which is crucial for accurate centroid calculation.

PREREQUISITES
  • Understanding of calculus, specifically integration techniques.
  • Familiarity with coordinate geometry and plotting functions.
  • Knowledge of centroid calculation methods for bounded regions.
  • Ability to use graphing tools or software for visual representation.
NEXT STEPS
  • Learn how to calculate centroids using integration methods.
  • Explore graphing software like Desmos or GeoGebra for visualizing functions.
  • Study the process of finding intersections of curves to define bounded regions.
  • Review the use of the Fundamental Theorem of Calculus in area calculations.
USEFUL FOR

Students in calculus courses, mathematics educators, and anyone involved in geometric analysis or computational geometry.

johnnyyy
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Find the centroid of the region bounded by y = 1.5x2 − 14x + 23.5, and x − y = 8. You should enter the coordinates of your answer either as decimals or fractions. Your answer must be accurate to within 0.001.

I got a wrong answer of (7/3, 59/52), I'm having problems plugging in the numbers. Any help would be appreciated.

Mod note: Warning issued because now work was shown and the template was not used.
 
Last edited by a moderator:
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You should use the HW template and post questions like these in the appropriate HW forum.

If you still want help, please show your work.
 
Start by plotting the curves. The picture would show you that your first answer was not even in the region enclosed.
 

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