math help

Test Preparation
1

<p><a href="http://img18.imageshack.us/img18/6024/8n5j.png%5B/url%5D"&gt;http://img18.imageshack.us/img18/6024/8n5j.png&lt;/a> </p>

<p><a href="http://img821.imageshack.us/img821/9673/sk9w.png%5B/url%5D"&gt;http://img821.imageshack.us/img821/9673/sk9w.png&lt;/a&gt;&lt;/p>

2

<p>1) The area of a circle is pi*r^2
the result of the problem is r^2, being thereby the square of the radius which is an integer.
The answers are diameters. Divide them by 2 and rule out each non-integer results.
11/2=5.5 False
5/2=2.5 False
7/2=3.5 False
9/2=4.5 False
12/2=6 Right answer.</p>

<p>2) the diagonal of a square is sqrt(2) times the side. (Pythagorean formula)
Therefore you have (x+4)<em>sqrt(2)=x+8
x</em>sqrt(2)+4*sqrt(2)=x+8 Quite simple isn’t t…
x(sqrt(2)-1)=8-4sqrt(2) Finish the algebra
…
…
x=4sqrt(2) Answer is D
I advise you to write that down clearly to apprehend completely the question. I didn’t finish the solution because it wouldn’t be clear anyway and I’m too tired (Sorry) to write it on Latex.</p>

<p>Sorry for my English. It’s been a while I didn’t use it ;)</p>

3

<p>thnx u i got the first one it’s pretty simple :wink: </p>

<p>but i didn’t get the second :confused: </p>

<p>thnx u :D</p>

4

<p>The ratio of the diagonal to the side of the square is sqrt(2):1 (45-45-90 triangles!). So x+8 = (x+4) sqrt(2). Solve for x.</p>

<p>(Correct LaTeX would be \sqrt{2} but writing equations here in LaTeX language might be confusing to newcomers)</p>

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<p>thnx i got it :)</p>

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<p><a href=“http://img96.imageshack.us/img96/4739/skbd.jpg[/url]”>http://img96.imageshack.us/img96/4739/skbd.jpg&lt;/a&gt;&lt;/p&gt;

<p><a href=“http://img833.imageshack.us/img833/6386/b68j.jpg[/url]”>http://img833.imageshack.us/img833/6386/b68j.jpg&lt;/a&gt;&lt;/p&gt;

<p>any help plz :>></p>

7

<p>1) The slope is equal to -2/3. Let be D(X,4) because it belongs to the line l
Then you have (4-(-2))/(X)=-2/3
6<em>3</em>(-1/2)=x
x=-9
So D(-9,4)
You can conclude that BD=3 (Just find the dfference between the x’s as they are on the same horizontal line)</p>

<p>2) It’s already done…</p>

8

<ol>
<li>x^2 - 81 = (x-9)(x+9), dividing numerator and denominator by x-9 gives x+9 = t^2 → x = t^2 - 9, E.</li>
</ol>

9

<p>My bad, I didn’t click on the right link and thought it was the same exercise. Thanks MITer94</p>