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Fourth-Degree Polynomial HW problem

  1. Oct 19, 2006 #1

    Tzz

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    This is one of my hw problems:
    "A scientist has limited data on the temperature T during a 24-hour period. If t denotes time in hours and t = 0 corresponds to midnight, find the fourth-degree polynomial that fits the information in the following table.

    t (hours) 0 10 12 16 24
    T (celcius) 0 0 1 0 0

    Please enter your answer as a product of linear factors. Enter any fractions or fractional coefficients as fractions, not as decimals."


    I assumed the form was : T(t) = ax(x-10)(x-16)(x-24)
    I found 'a' by using the given T(12)=1 and got: a = 1/1152
    Multiplying out the factors i got:
    T(t) = 1/1152*x^4 - 25/576*x^3 + 49/72*x^2 - 10/3*x

    I'm confused as to why the program says this is the wrong answer. Maybe i have some faulty arithmetic...Any ideas?
     
  2. jcsd
  3. Oct 19, 2006 #2
    looks fine to me *shrug*
     
  4. Oct 19, 2006 #3

    Tzz

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    looks like (1/1152)x(x-10)(x-16)(x-24) worked even though it said to multiply it out....thanks anyways
     
  5. Oct 19, 2006 #4
    yeah, that makes a lot of sense looking at the problem again

    "Please enter your answer as a product of linear factors."
    means that you keep it exactly as it was when it marked it correct.

    x, x-10, x-16, x-24 were our linear factors, so we'd just write it as their product:

    [tex]\frac{1}{1152}x(x-10)(x-16)(x-24) [/tex]
     
  6. Oct 20, 2006 #5

    HallsofIvy

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    Staff Emeritus
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    WHERE did it say "multiply it out"?
     
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