# help with Word Problems?

Printable View

• Dec 13th 2007, 03:39 PM
Raleigh
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?

http://i103.photobucket.com/albums/m...titled2222.jpg
• Dec 13th 2007, 09:18 PM
earboth
Quote:

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?

http://i103.photobucket.com/albums/m...titled2222.jpg

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
• Dec 14th 2007, 05:27 AM
Soroban
Hello, Raleigh!

Quote:

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: . $R \:=\:6$