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Math Help - Polynomial Trouble

  1. #1
    Junior Member phgao's Avatar
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    Polynomial Trouble

    Hi!

    Is 3^x + 3 a polynomial?
    On my sheet it is written as 3 superscript x + 3. Thanks!

    Also there is another question thanks! :

    A right square pyramid, vertex O, stands on a square base ABCD. The height is 15cm and base length is 10cm. Find:

    a. the length of the slant edge : I got that: 5 root 11.
    b. the inclination of a slant edge to the base : 64.76 degrees
    c. the inclination of a sloping face to the base : 71.57 degrees
    d. the madnitude of the angle between two adjacent sloping faces : I have no idea about this one! Please help it is the angle between the faces?! I can't picture it.

    Thanks!
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  2. #2
    Junior Member phgao's Avatar
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    To add to this some more polynomials...

    Is 5x^1.5 + 1.5x - 3 a polynomial? Why/not? And can you explain what is the power of 1.5 mean? I dont think i understand.

    Lasly, cos(5x + 1) is it a poly or not? Please explain!

    Thanks so much!
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by phgao
    Hi!

    Is 3^x + 3 a polynomial?
    On my sheet it is written as 3 superscript x + 3. Thanks!
    Thanks!
    Wikipedia's definition of a polynomial is:

    "In mathematics, a polynomial is an expression in which constants and
    variables are combined using (only) addition, subtraction, and multiplication.
    Thus, 7x2+4x−5 is a polynomial; 2/x is not."

    I would also add to this definition that only a finite number of
    additions, subtractions, and multiplications are to be allowed, as otherwise
    we will find we have allowed infinite series, which I am pretty sure is not
    intended.

    3^3+3=x \times x\times x +3,

    So yes 3^3+3 is a polynomial.

    RonL
    Last edited by CaptainBlack; February 2nd 2006 at 03:34 AM.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by phgao
    To add to this some more polynomials...

    Is 5x^1.5 + 1.5x - 3 a polynomial? Why/not? And can you explain what is the power of 1.5 mean? I dont think i understand.
    x^{1.5} means (\sqrt x)^3 when x \ge 0, and something more complicated otherwise.
    As \sqrt x is not a polynomial, 5x^{1.5} + 1.5x - 3 is not a polynomial.

    Lasly, cos(5x + 1) is it a poly or not? Please explain!

    Thanks so much!
    \cos is not a polynomial so \cos (5x + 1) is not a polynomial.

    RonL
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by phgao
    Hi!

    Is 3^x + 3 a polynomial?
    On my sheet it is written as 3 superscript x + 3. Thanks!

    Also there is another question thanks! :

    A right square pyramid, vertex O, stands on a square base ABCD. The height is 15cm and base length is 10cm. Find:

    a. the length of the slant edge : I got that: 5 root 11.
    b. the inclination of a slant edge to the base : 64.76 degrees
    c. the inclination of a sloping face to the base : 71.57 degrees
    d. the madnitude of the angle between two adjacent sloping faces : I have no idea about this one! Please help it is the angle between the faces?! I can't picture it.

    Thanks!
    Your second problem is different in nature to the first so you should repost
    it as a seperate thread.

    RonL
    Last edited by CaptainBlack; February 2nd 2006 at 03:48 AM.
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  6. #6
    Junior Member phgao's Avatar
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    Thanks!
    can you explain why power of 1.5 is the same as what you have typed:

    <br />
(\sqrt x)^3<br />

    Thanks
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  7. #7
    Grand Panjandrum
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    Quote Originally Posted by phgao
    Thanks!
    can you explain why power of 1.5 is the same as what you have typed:

    <br />
(\sqrt x)^3<br />

    Thanks
    First we need:

    \sqrt x=x^{1/2},

    this is so that the law of indices works for fractional indices. We want:

    x^{1/2}x^{1/2}=x^{1/2+1/2}=x

    So x^{1/2}=\sqrt x.

    Again by the law of indices:

    (\sqrt x)^3=x^{1/2}x^{1/2}x^{1/2}=x^{1/2+1/2+1/2}=x^{1.5}

    RonL
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  8. #8
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    Quote Originally Posted by phgao
    Thanks!
    can you explain why power of 1.5 is the same as what you have typed:

    <br />
(\sqrt x)^3<br />

    Thanks
    It actually is a definiton, not a theorem.
    We define x^{n/m} as \sqrt[m]{x^n}
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