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Math Help - help with Word Problems?

  1. #1
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    help with Word Problems?

    I have tried really hard to get started on these, but I am completely lost...could anyone please help me get started?


    Last edited by Raleigh; December 13th 2007 at 06:59 PM.
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  2. #2
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    Quote Originally Posted by Raleigh View Post
    I have tried really hard to get started on these, but I am completely lost...could anyone please help me get started?


    Hello,

    to #37:

    Plug in the given values:

    A(60)=500 \cdot e^{-0,013 \cdot 60} \approx 229.2

    Plug in the given values and solve the equation for t:

    100=500 \cdot e^{-0.013 \cdot t}~\iff~\frac15 = e^{-0.013 \cdot t}~\iff~t = \dfrac{\ln\left(\frac15\right)}{-0.013}\approx 123.8

    to #38:

    If
    - r is the radius of the smaller circle,
    - R is the radius of the larger circle,
    - d is the diagonal of the smaller square,
    - D is the diagonal of the larger square,
    - s is the side of the smaller square and
    - S is the side of the larger square

    then you have:

    d = 2r\text{ and }d^2 = 2s^2 therefore s = 6

    S = 2r \text{ and }D^2 = 2 S^2\text{ and }R = \frac12 \cdot D Therefore R = 12
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  3. #3
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    Hello, Raleigh!

    38. A square fits just inside a circle whole radius is 3\sqrt{2}.
    There is second square that fits around that circle
    and a second circle around the second square.
    What is the radius of the second circle?
    Are they trying to be funny? . . . That first square is irrelevant!
    Code:
          * - - * - * - * - - * B
          |  *             */ |   _
          |*           R  /  *| 3√2
          |             /     |
          *           /       *
          *         * - - - - * A
          *         O   3√2   *
          |                   |
          |*                 *|
          |  *             *  |
          * - - * - * - * - - *

    The radius of the first circle is: . OA = 3\sqrt{2}

    The radius of the second circle is: . R \:=\:OB

    We have a 45 right triangle.
    . . OB^2 \:=\:OA^2 + AB^2\quad\Rightarrow\quad R^2 \:=\:(3\sqrt{2})^2 + (3\sqrt{2})^2 \:=\:18 + 18 \:=\:36

    Therefore: . R \:=\:6

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