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Math Help - what is jk?

  1. #1
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    what is jk?

    ok so here we go...

    we have the set up which states that only students within a certain range, can use the trombone...

    so 95 is less than equal to T which is less than equal to 185..

    now this next part i found on the internet...but it was suggested that i find the middle of the range which is 140, and so i subtract 140 from each part of the setup???what is jk?-imag0092.jpg

    so now i have this inequality that i need to rewrite with the use of absolute value bars, but the only problem is that i do not know how to set that up...any help would be appreciated and can you explain why i need to find the middle of the range and why is that being subtracted from either side. thanks
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  2. #2
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    Re: what is jk?

    we know that 95 ≤ w ≤ 185 (i am using w instead of T, to match the book).

    what we want is something that looks like:

    |w - j| ≤ k, which is the same as:

    -k ≤ w - j ≤ k

    if we add j to everything, we get:

    -k + j ≤ w ≤ k + j, which is what we have:

    k + j = 185
    -k + j = 95

    let's add the two equations, to get:

    k + j + -k + j = 185 + 95

    2j = 280

    j = 140 (see where the 140 comes in?)

    now we can find k:

    k + j = 185

    k + 140 = 185

    k = 45

    as a check, we verify the other equation as well:

    -k + j = 95

    -k + 140 = 95

    -k = -45

    k = 45.

    now we know that:

    95 ≤ w ≤ 185 is the same condition as:

    -45 + 140 ≤ w ≤ 45 + 140

    -45 ≤ w - 140 ≤ 45

    |w - 140| ≤ 45.

    it should be obvious what jk is now.
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  3. #3
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    Re: what is jk?

    Hello, slapmaxwell1!


    Students are allowed to use the trampoline if they weigh from 95 to 185 pounds.
    Express this restriction in the form |w - j| \:\le\:k
    where w is a student's weight, and j and k are constants.
    What is jk?

    Maybe a picture will clarify the situation.

    . . \begin{array}{ccccccc}\cdots & \bullet & --- & \circ & --- & \bullet & \cdots \\ & 95 && 140 && 185 \end{array}

    The middle of range is 140 pounds.
    We can see that a student's weight must be
    . . no more than 45 pounds away from the middle.

    This can be written: . |w - 140| \:\le\:45


    Hence: . j = 140,\;k = 45

    Therefore: . jk \;=\;140\cdot45 \;=\;6300
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