Center of Gravity and probability

mathgirl2010
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Greetings! I'm new to the forum. I am a math major with a concentration in probability. A relative wants me to find the center of gravity of the pipe. I attached a diagram below. I have no clue how to find it. I have never seen anything like this before. I know that you integrate over the x and y regions to find the center of gravity. Also, the diagram I was sent does not have a coordinate system. I would greatly appreciate it if someone could point me in the right direction.
 

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I don't understand the diagram. What's the triangle in the diagram on the left supposed to show?

Anyhow, you can approximate the pipe as being made up of 2 cylinders and two tori. You can then figure out the center of mass of each before combining them with the formula Mx_com = m1x1 + m2x2. Depending on the level of accuracy you want, you can even approximate the pipe as being made up of 3 hollow cylinders connecting at right angles.
 
Thanks for your response. I think the triangle is suppose resemble a rig with weights on it.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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