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in the first integral , theJ Hann said:
in the first integral , the y prime is squared , so they don't cancel out each other?J Hann said:
When have you squared a real number and it came out negative?werson tan said:
The formula for finding the centroid of a shape is:
x̄ = (∑(xi * Ai)) / A
ȳ = (∑(yi * Ai)) / A
where x̄ and ȳ represent the x-coordinate and y-coordinate of the centroid, xi and yi represent the x and y coordinates of each individual point, Ai represents the area of each individual point, and A represents the total area of the shape.
The centroid of a triangle can be calculated using the formula:
x̄ = (x1 + x2 + x3) / 3
ȳ = (y1 + y2 + y3) / 3
where (x1, y1), (x2, y2), and (x3, y3) represent the coordinates of the three vertices of the triangle.
The centroid of a shape is the point where all the medians intersect. This point divides each median into two parts, with the distance from the centroid to the vertex being twice the distance from the centroid to the midpoint of the opposite side. The centroid has many important properties in geometry, such as being the center of mass and the center of gravity of a shape.
Yes, the centroid can be outside of the shape. This is possible when the shape is irregular and does not have symmetrical sides. In this case, the centroid may lie outside of the shape, but it will still divide the shape into equal areas.
The centroid of a compound shape can be calculated by finding the individual centroids of each component of the shape and then using the formula for a weighted average to find the overall centroid. This involves finding the area of each component, multiplying it by the distance of its centroid from a chosen reference point, and then dividing the sum of these values by the total area of the compound shape.
