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Thread: quadratic mean of all values of r of a circle

  1. #21
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    Not at all. It is ill-defined. Listen to Stapel.

  2. #22
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    I did just that in post #19.

  3. #23
    Elite Member stapel's Avatar
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    Cool

    Quote Originally Posted by ray5450 View Post
    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.

  4. #24
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    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?

  5. #25
    Elite Member stapel's Avatar
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    Cool

    Quote Originally Posted by ray5450 View Post
    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!

  6. #26
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    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).

  7. #27
    Elite Member stapel's Avatar
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    Quote Originally Posted by ray5450 View Post
    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.

  8. #28
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    Quote Originally Posted by ray5450 View Post
    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
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  9. #29
    Elite Member mmm4444bot's Avatar
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    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?
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

  10. #30
    Elite Member mmm4444bot's Avatar
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    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
    Last edited by mmm4444bot; 07-02-2017 at 03:51 PM. Reason: Typo
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

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