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

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- Dec 13th 2007, 03:39 PMRaleighhelp 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 PMearboth
Hello,

to #37:

Plug in the given values:

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

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

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

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:

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

$\displaystyle S = 2r \text{ and }D^2 = 2 S^2\text{ and }R = \frac12 \cdot D$ Therefore R = 12 - Dec 14th 2007, 05:27 AMSoroban
Hello, Raleigh!

Quote:

38. A square fits just inside a circle whole radius is $\displaystyle 3\sqrt{2}.$

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?

Code:`* - - * - * - * - - * B`

| * */ | _

|* R / *| 3√2

| / |

* / *

* * - - - - * A

* O 3√2 *

| |

|* *|

| * * |

* - - * - * - * - - *

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

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

We have a 45° right triangle.

. . $\displaystyle OB^2 \:=\:OA^2 + AB^2\quad\Rightarrow\quad R^2 \:=\:(3\sqrt{2})^2 + (3\sqrt{2})^2 \:=\:18 + 18 \:=\:36$

Therefore: .$\displaystyle R \:=\:6$