# Thread: help with Word Problems?

1. ## 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?

2. Originally Posted by Raleigh
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

3. 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: . $R \:=\:6$