quadratic mean of all values of r of a circle

I did just that in post #19.
You repeated yourself in that post. We're still waiting for the answers to our questions. We can't do anything until those answers are forthcoming. Sorry.
 
I was asked, "Please reply with...":
a. "...the full and exact text of the original exercise, the complete instructions"
I answered with with the full and exact text of the original exercise, the complete instructions: "Circle 2 is twice the area of circle 1. Show that the quadratic mean of all the values of r of circle 1, is equal to the radius of circle 2."

b. "a clear listing of your thoughts and efforts so far"
I answered with a clear listing of my thoughts and efforts so far: "I have found that the relation between the radius of a circle that is twice the area of another is that the radius of the larger circle is equal to the radius of the smaller circle multiplied by square root of 2. Therefore, the result of the quadratic mean calculation must be radius of circle 1 multiplied by square root of 2. Using this information to work backwards, y must be r1 multiplied by square root of 6 (or r1 multiplied by square root of 2π). However, I do not believe the exercise is to work it backwards, but to find the correct relationship to deduce y."

Were there more questions that I missed?
 
I was asked, "Please reply with...":
a. "...the full and exact text of the original exercise, the complete instructions"
I answered with with the full and exact text of the original exercise, the complete instructions: "Circle 2 is twice the area of circle 1. Show that the quadratic mean of all the values of r of circle 1, is equal to the radius of circle 2."
Well, if that's all they've given you, so there really is no definition for "r", then there really is no way to answer this question.

Please have a talk with your instructor, regarding clarification (that is, regarding obtaining the rest of the information, which allows this question to be answerable). Thank you! ;)
 
I don't know if restating what I indicated before will help, but it is my understanding that r is the distance from the center of a concentric elementary zone (dr, for example).
 
I don't know if restating what I indicated before will help, but it is my understanding that r is the distance from the center of a concentric elementary zone (dr, for example).
I can find no reference online (other than this thread) for "concentric elementary zone", let alone how it relates to "dr" (which is a differential, maybe?). Providing the definition of this phrase, along with whatever other "understood" and otherwise supplementary material is required, might go a long way toward our being able to figure out what you're talking about.
 
I don't know if restating what I indicated before will help, but it is my understanding that r is the distance from the center of a concentric elementary zone (dr, for example).
Post - 19
Circle 2 is twice the area of circle 1. Show that the quadratic mean of all the values of r of circle 1, is equal to the radius of circle 2.

I have found that the relation between the radius of a circle that is twice the area of another is that the radius of the larger circle is equal to the radius of the smaller circle multiplied by square root of 2. Therefore, the result of the quadratic mean calculation must be radius of circle 1 multiplied by square root of 2. Using this information to work backwards, y must be r1 multiplied by square root of 6 (or r1 multiplied by square root of 2π). However, I do not believe the exercise is to work it backwards, but to find the correct relationship to deduce y.
I don't see any reference to concentricity in Post 19
 
The radii are just line segments; we should be able to use f(x) = x, to sum all possible radii.

I think we integrate x^2 from 0 to r.

My take on the exercise statement (first two sentences of post #19) is that we're supposed to show the Quadratic Mean of all possible radii up to r (r=radius of Circle 1) equals the radius of a second circle whose area is twice as big as Circle 1.

We know that Circle 2 radius = sqrt[2]*r

But, when I use the Quadratic Mean formula, I get sqrt(3)/3*r instead of sqrt(2)*r.

Could my take be correct (all possible radii), but there's a logic error in the exercise design?
 
I designed a different exercise. Does it make sense?

Circle 1 has radius r

Circle 2 has radius R

Circle 1 is three times bigger than Circle 2

Show that the Quadratic Mean of the radii of all circles smaller than Circle 1 equals R

Quadratic Mean = sqrt[1/r * int(x^2 dx, x=0..r)] = R = sqrt(3)/3*r

Area of Circle 1: Pi*r^2

Area of Circle 2: Pi*(sqrt[3]/3*r)^2 = 1/3*Pi*r^2
 
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mmm4444bot: Interesting. It could be that there is an error in the exercise and what you gave is what was intended (in your final quadratic mean, you forgot r). However, it is also an odd coincidence that 2π is about 6, which is the solution for 2 times the area.

Subhotosh Khan: There is no reference to concentricity. In an exercise that says to find a minimum volume, there is no reference to differentiation, but that is the way to the solution.

Subhotosh Khan and stapel: I tried to attach a drawing I made with Paint as to what I mean about concentric elements. It let me choose what file to upload, but there was no "OK", or "Continue" or "Upload" or anything to complete the attach.
To describe it, imagine a circle whose radius is R. A concentric element would be inside said circle with radius r and a width of dr. The sum of all dr would be R. Again, this is only a guess as to some relationship that I proposed that might lead to the solution of twice the area, unless mmm4444bot is correct about an error in the exercise..



 
… in your final quadratic mean, you forgot r …
I sure did. Fixed now, thanks.


I tried to attach a drawing I made with Paint as to what I mean about concentric elements. It let me choose what file to upload, but there was no "OK", or "Continue" or "Upload" or anything to complete the attach.
You begin by using the Manage Attachments button. On the resulting pop-up window, you click the Add Files button. That causes another pop-up window (which defaults to using your computer as the image source, instead of the web), and this window contains both the Choose File and Upload buttons. It's also explained in the FAQ. :cool:
 
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