Find Centroid of Bounded Region: Accurate to 0.001

In summary, a centroid is the geometric center of a shape or bounded region, important for determining stability and balance, calculating moments of inertia, and designing engineering and architectural projects. It is calculated by finding the weighted average of smaller centroids within the shape. When we say "accurate to 0.001", it means the coordinates of the centroid will be rounded to the nearest 0.001 unit for increased precision. The centroid can also be calculated for irregular shapes by dividing them into smaller shapes or using advanced mathematical techniques.
  • #1
johnnyyy
2
0
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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  • #2
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.
 
  • #3
Start by plotting the curves. The picture would show you that your first answer was not even in the region enclosed.
 

1. What is a centroid?

A centroid is the geometric center of a shape or bounded region. It is the point at which the area of the shape can be evenly distributed in all directions.

2. Why is it important to find the centroid of a bounded region?

Finding the centroid of a bounded region is important for various reasons. It can help determine the stability and balance of objects or structures, aid in the calculation of moments of inertia, and assist in the design of various engineering and architectural projects.

3. How is the centroid of a bounded region calculated?

The centroid of a bounded region can be calculated by dividing the shape into smaller, known geometrical shapes (such as triangles or rectangles), finding the centroid of each smaller shape, and then using the weighted average of these centroids to determine the overall centroid of the bounded region.

4. What does "accurate to 0.001" mean in relation to finding the centroid?

When we say "accurate to 0.001", it means that the coordinates of the centroid will be rounded to the nearest 0.001 unit. This level of accuracy is commonly used in scientific and engineering calculations to ensure precision and minimize error.

5. Can the centroid of a bounded region be calculated for irregular shapes?

Yes, the centroid of a bounded region can be calculated for irregular shapes. This is done by dividing the shape into smaller, irregular shapes and following the same process as mentioned in question 3 to find the overall centroid. Advanced mathematical techniques, such as integration, can also be used to find the centroid of irregular shapes.

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