Finding the Centroid of a Parabola: Calculating Coordinates for y = 10m

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Homework Help Overview

The discussion revolves around finding the centroid of the area bounded by the parabola described by the equation y = x² and the horizontal line y = 10m. Participants are exploring the mathematical reasoning involved in calculating the coordinates of the centroid for this specific setup.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss integration limits based on intersections with the line y = 10m and the x-axis. There are attempts to calculate the area under the curve and questions about the correctness of the integration results.

Discussion Status

Some participants are actively sharing their attempts at integration and questioning the interpretation of the problem. Guidance has been offered regarding the need to calculate the area of the enclosed region to assist in finding the centroid.

Contextual Notes

There is mention of specific integration limits derived from the intersection points, and participants are considering the implications of the area being bounded by the parabola and the line y = 10m.

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The equation y = x2 describes a parabola. Find the x and y coordinates of the centroid of the area bounded by this curve, and the line y = 10m
 
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OK, show us what you have tried.
 
I tried to intergrate from -3.16 to 3.16, b/c if you draw a perpinduclar line down from y=10 it intersects the x-axis at those two values. I integrate the given equation y=x^2, but the number I got was 21, so i do not know if it is correct.
 
I think this problem is asking you to determine the centroid of the area below y = 10 m and above y = x^2. Can you calculate the area of the enclosed parabola?
 

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