<p>t^2-k^2<6
t+k>4
14. If t and k are positive integers in the inequalities above and t>k, what is the value of t?
a.1
b.2
c.3
d.4
e.5</p>
<ol>
<li><p>Semicircular arcs AB,AC,BD,CD divide the circle above into regions. The points show along the diameter AD divide it into 6 equal parts. If AD=6, what is the total area of the shaded regions?
a.4pi
b.5pi
c.6pi
d.12pi
e.24pi
Picture:Image</a> - TinyPic - Free Image Hosting, Photo Sharing & Video Hosting</p></li>
<li><p>Any 2 points determine a line. If there are 6 points in a plane, no 3 of which lie on the same line, how many lines are determined by pairs of these 6 points?
a.15
b.18
c.20
d.30
e.36</p></li>
<li><p>A certain function f has a property that f(x+y) = f(x)+ f(y) for all values of x and y. Which of the following statements must be true when a = b?
I.f(a+b)=2f(a)
II.f(a+b)=[f(a)]^2
III.f(b)+f(b) = f(2a)</p></li>
</ol>
<ol>
<li>Plug in a and b to the thing given to get f(a+b)=f(a)+f(b)</li>
</ol>
<p>Now try to manipulate I, II, III to match that.</p>
<p>I. I.f(a+b)=2f(a)</p>
<p>Because a=b, this can be rewritten as f(a+a). Based on f(x+y) = f(x)+ f(y), f(a+a)=f(a)+f(a)=2f(a). So, I is true.</p>
<p>II. f(a+b)=[f(a)]^2</p>
<p>Same logic as for I. f(a+b)=f(a+a)=f(a)+f(a)=2f(a). However, 2f(a) is not the same as [f(a)]^2 (I’m sure you can figure that out yourself). So, II is not true.</p>
<p>III. f(b)+f(b) = f(2a)</p>
<p>Work backwards on this one. f(b)+f(b) has to equal f(b+b) based on f(x+y) = f(x)+ f(y). So, since a=b, f(b+b)=f(a+a)=f(2a). Therefore, III is true.</p>
<p>So, your answer should be I and III only.</p>
<p>Just watch, I’m gonna be completely wrong. :)</p>
<p>T>K </p>
<h2>Plug in T. 9 - K^2 <6. 2 works. 3+2 >4 so yes So C?</h2>
<p>Split it in the diameter ofthe large circle</p>
<h2>Try to go from one half of the large circle. Then subtract the 2nd largest half circle in there. Then add the shaded half circle etc.</h2>
<h2>I remember doing this. 6 P 3 is it 20? I forgot. Don’t want to draw it out do it and youll get it</h2>
<ol>
<li>
I and III ? @314159265. We are right!</li>
</ol>
<p>18.
It’s actually 6C2 = 15 because you want to know how many ways there are to pair 2 points out of 6, so order doesn’t matter.
An intuitive way to do this is to take one point, and see that there are 5 other possible points it can connect to to make a line. For the second point, there are 4 possibilities since you already counted the possibility with the first point. And so on, so it’s 5+4+3+2+1 =15.</p>
<p>lol fail. Yeah 6 c 2. I remember I drew 6 points and drew em and found out it was 5 4 3 2 1</p>