Geometry

Discussion in 'Other Pre-University Math' started by nycmathguy, Aug 3, 2021.

  1. nycmathguy

    nycmathguy

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    Section 1.8
    Question 61

    See attachment.

    Let me see.

    For part (a), I know that the area of a square is side squared or A = s^2, where s = x for this problem. I think the answer is r(x) = x^2.

    For part (b), the area of the circular base is pi•r^2.
    I think the answer is A(r) = pi•r^2.

    For part (c), I must find (A ° r)(x).

    I know that (A ° r)(x) = A(r(x)).

    I know that r(x) = x^2 from part (a).

    I conclude that A(r(x)) = A(x^2).

    If I am correct, how do I interpret A(x^2)?


    20210803_040658.jpg
     
    nycmathguy, Aug 3, 2021
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  2. nycmathguy

    MathLover1

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    r(x)=x/2

    A=r^2*pi

    (A \circ r)(x)=A(r(x))
    (A \circ r)(x)=A(x/2)
    (A \circ r)(x)=(x/2)^2*pi
    (A \circ r)(x)=(x^2/4)*pi
    (A \circ r)(x)=(1/4)x^2*pi
     
    MathLover1, Aug 3, 2021
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  3. nycmathguy

    nycmathguy

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    What did I do wrong?

    (A\circ r)(x) = (A ° r)(x). Yes?
     
    nycmathguy, Aug 4, 2021
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  4. nycmathguy

    MathLover1

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    r(x) = x^2 => that was wrong
    should be
    r(x)=x/2
     
    MathLover1, Aug 4, 2021
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  5. nycmathguy

    nycmathguy

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    Why is r(x) = x/2, which means (1/2) times x?
     
    nycmathguy, Aug 4, 2021
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  6. nycmathguy

    MathLover1

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    take a look at picture, diameter of the circle is equal to the side x
    => radius is half of it
     
    MathLover1, Aug 5, 2021
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  7. nycmathguy

    nycmathguy

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    Yes, I see it now.
     
    nycmathguy, Aug 5, 2021
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