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Math Help - finding patterns (simple)

  1. #1
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    Question finding patterns (simple)

    Do you see a pattern between these three numbers:

    time temp. (A) temp. (B)
    1-----------21--------------17
    2-----------22--------------14
    3-----------23--------------11
    4-----------24--------------8

    I know:
    the pattern from time to temp A is: t+20
    the pattern from time to temp B is: 20-(h*3)

    I need to know:
    the pattern between all of those numbers.. plz help
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by puppy_wish View Post
    Do you see a pattern between these three numbers:

    time temp. (A) temp. (B)
    1-----------21--------------17
    2-----------22--------------14
    3-----------23--------------11
    4-----------24--------------8

    I know:
    the pattern from time to temp A is: t+20
    the pattern from time to temp B is: 20-(h*3)

    I need to know:
    the pattern between all of those numbers.. plz help
    Let a be temperature A and b be temperature B.

    The equation of a line is "y = mx + b." If we call "b" the y variable and "a" the x variable, we have that the form for a line is
    b = mx + c <-- I needed to change the "b" for the y-intercept.
    So try this:
    m = \frac{b_2 - b_1}{a_2 - a_1}
    Picking the first two in the set gives:
    m = \frac{14 - 17}{22 - 21} = -3

    Pick any point on the (alleged) line:
    17 = -3 \cdot 21 + c

    17 = - 63 + c

    c = 80

    You can verify that the equation b = -3a + 80 gives the relationship between a and b.

    Obviously this will only work if there is, in fact, a linear relationship between the two data sets...

    -Dan
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  3. #3
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by puppy_wish View Post
    Do you see a pattern between these three numbers:

    time temp. (A) temp. (B)
    1-----------21--------------17
    2-----------22--------------14
    3-----------23--------------11
    4-----------24--------------8

    I know:
    the pattern from time to temp A is: t+20
    the pattern from time to temp B is: 20-(h*3)

    I need to know:
    the pattern between all of those numbers.. plz help
    I don't understand what you're asking, but I believe you want an equation to model all the answers.

    Here is what I get, we know that: a=t+20 and b=20-3t

    So I like to find the difference: a-b=t+20-(20-3t)

    Then: a-b=t+20-20+3t

    Then: a-b=4t

    Therefore: b=a-4t

    Was that what you wanted?
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  4. #4
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    [soze=3]Hello, puppy_wish![/soze]

    Do you see a pattern between these three numbers:

    \begin{array}{ccccc}\text{Time} & \text{temp A} & \text{temp B} \\ 1 & 21 & 17 \\ 2 & 22 & 14 \\ 3 & 23 & 11 \\ 4 & 24 & 8\end{array}

    I know:
    The pattern from time to temp A is: t+20
    The pattern from time to temp B is: 20 - 3t

    I need to know: the pattern between all of those numbers.

    I'm not sure what you mean by "the pattern between all of these numbers".

    You found the two separate functions: . \begin{array}{cc}A(t)\\B(t)\end{array}<br />
\begin{array}{cc}= \\ = \end{array}<br />
\begin{array}{cc}20 + t \\ 20-3t\end{array}


    How can we write a function that produces two values?
    . . Then it won't be a function.

    Maybe something like: . f(t)\;=\;(20 + t) \pm 2t

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  5. #5
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    Wow! thanx for all your great responses. All of you did the correct thing. I'm gonna take all of the answers tomorrow for class and see if they're all correct or not. THANK YOU AGAIN!
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