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

In summary, the conversation discusses finding the x and y coordinates of the centroid of the area bounded by the parabola y = x^2 and the line y = 10m. The person has attempted to integrate the equation and has gotten a value of 21, but is unsure if it is correct. They also mention calculating the area of the enclosed parabola.
  • #1
khutch2212
4
0
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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  • #2
OK, show us what you have tried.
 
  • #3
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.
 
  • #4
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?
 

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

What is the centroid of a parabola?

The centroid of a parabola is the point where all the mass of the parabola is evenly distributed. It is also known as the center of mass or center of gravity.

How is the centroid of a parabola calculated?

The centroid of a parabola can be calculated using the formula (2/3)*a, where 'a' is the distance from the vertex to the focus of the parabola.

Why is the centroid of a parabola important?

The centroid of a parabola is important because it helps in determining the stability and balance of the parabola. It is also used in various applications such as engineering, physics, and mathematics.

What is the significance of the centroid being located on the axis of symmetry?

The axis of symmetry is the line that divides the parabola into two equal halves. Since the centroid is located on the axis of symmetry, it means that the parabola is balanced and has equal mass on both sides.

Can the centroid of a parabola be outside the parabola?

No, the centroid of a parabola will always be located within the parabola. This is because the centroid represents the center of mass, and all the mass of the parabola is within its boundaries.

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