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Math Help - volume of solid without f(x)

  1. #1
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    volume of solid without f(x)

    How would you find the volume of a solid rotating about y-axis if you were not given f(x)?, or better yet, how would you come up with the equation of f(x)?
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  2. #2
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    You could use various points(x and y coordinates)and implement the proper regression analysis to find an equation. Then revolve.

    There are linear regressions, cubic regressions, quartic and quintic regressions, exponential, etc.

    A lot of the calculators do these analyses.

    For example, suppose we had x values, respectively, of 0,1,2,3,4

    y values of 0,2,5,7,11

    I ran these through my calculator and got an equation of

    y=\frac{5}{24}x^{4}-\frac{19}{12}x^{3}+\frac{91}{24}x^{2}-\frac{5}{12}x

    Hope this helps a little.
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  3. #3
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    ohh ok,

    how would I enter values into my TI-83 to find an equation?

    or does it only work with TI-89

    I mean, I know how to plot the data, but i'm not sure if TI-83 is capable of producing an equation.
    If not, how would I derive an equation based on the x,y values?
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  4. #4
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    You need some sort of tech to derive the equation. Even a simple linear regression is rather cumbersome, let alone anything higher. I don't know if an 83 will do it or not. I use a Voyage 200 and a TI-92. They certainly do. The 89 will. If you have Excel, it will do it.

    If you can gain access to an 89 or Excel, let me know and I can show you the steps.
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  5. #5
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    Quote Originally Posted by ch2kb0x View Post
    ohh ok,

    how would I enter values into my TI-83 to find an equation?

    or does it only work with TI-89

    I mean, I know how to plot the data, but i'm not sure if TI-83 is capable of producing an equation.
    If not, how would I derive an equation based on the x,y values?
    I've done galactus' example with a TI83.

    1. Store the x-values into list L1
    2. Store y-values into list L2

    3. Use STAT - CALC - 7QuartReg
    4. add L1, L2, Y3 (you find the y-variable at VARS - Y-VARS

    5. Press ENTER

    You'll get the coefficients of quartic function.
    Attached Thumbnails Attached Thumbnails volume of solid without f(x)-regr_glgti83.gif  
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  6. #6
    Eater of Worlds
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    There ya' go. I wasn't sure if an 83 would or not. Now we know. That is exactly what my Voyage 200 gave me except I converted to fractions to make it look better.
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  7. #7
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    thank you so much, both of you. thanks.
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