<p>BB Pg. 807 # 14</p>
<p>I missed that one today. It's probably super esay, but I just couldn't figure it out with the 5 minutes I had left...lol</p>
<p>
[QUOTE]
however, i'm also interested in how arachnotron knew to add them together, because his way sounds better!
[/QUOTE]
</p>
<p>That's just realizing that you need one in terms of the other, so you just combine then rearrange. You get used to it after doing a lot of problems :) </p>
<p>@ Quicksandslowly: </p>
<p>If p is a factor of n+3 and n+10, that means that n+10 is a whole number multiple of n+3; represent it like this: </p>
<p>n+10/p = k(n+3)/p</p>
<p>rearrange and solve to get: </p>
<p>k = 10/n+3 (the multiple)</p>
<p>Since n+10 is an integer multiple of n+3, find the value of "n" which makes k a whole, positive number. The only one that works is 7, so the answer is <a href="B">b</a> **</p>
<p>(no it wasn't easy. It took me a few minutes to solve it)</p>
<p>Thanks Arachnotron! Wow, I would never have figured that one out lol.</p>
<p>Haha, let's just hope nothing like that shows up on this coming test, or we're all screwed :P</p>
<p>Haha for sure!</p>
<p>
[QUOTE]
blue book pg 684 number 15.collegeboard one.
[/QUOTE]
</p>
<p>Apply the pythagorean theorem once to get the length of the diagonal from the midpoint, A, to the corner of the cube:</p>
<p>(1)^2 + (2)^2 = 5 </p>
<p>Diagonal = sqrt(5). </p>
<p>Then apply the pythagorean theorem again with the sqrt(5) side and the length from the corner to B: </p>
<p>(sqrt(5))^2 + (1)^2 = 6 </p>
<p>Length of AB = sqrt(6) -> <a href="D">b</a>**</p>
<p>
[QUOTE]
There is a cube with a volume of 8. What is the distance from the center of the cube to a vertex? how is this solved?
[/QUOTE]
</p>
<p>Volume = l^3 = 8
length of a side, then is cube root of 8 = 2. </p>
<p>Now, to solve this, we find the length of the total diagonal in the cube using the 3D pythagorean theorem: </p>
<p>sqrt( 3 * 2^2 ) = d^2 </p>
<p>2*sqrt 3 = distance from one corner of the cube to another. To find the distance from the center to the corner, we simply divide this by 2, to yield ** sqrt 3 **</p>
<p>Conveniently ignoring the message in the first post, I ask you to prove this. GO!</p>
<p>Some numbers have the special property that they cannot be expressed as the product of two smaller numbers, e.g., 2, 3, 5, 7, etc. Such numbers are called prime numbers, and they play an important role, both in pure mathematics and its applications. The distribution of such prime numbers among all natural numbers does not follow any regular pattern, however the German mathematician G.F.B. Riemann (1826 - 1866) observed that the frequency of prime numbers is very closely related to the behavior of an elaborate function </p>
<pre><code>ζ(s) = 1 + 1/2s + 1/3s + 1/4s + ...
</code></pre>
<p>called the Riemann Zeta function. The Riemann hypothesis asserts that all interesting solutions of the equation</p>
<pre><code>ζ(s) = 0
</code></pre>
<p>lie on a certain vertical straight line. This has been checked for the first 1,500,000,000 solutions. A proof that it is true for every interesting solution would shed light on many of the mysteries surrounding the distribution of prime numbers.</p>
<p>I could see this as a practice problem in Barron's for Math II. It's well documented that they hate everyone who buys their books.</p>
<p>Jeez, I can solve SAT problems, not Millenium Prize Problems :D</p>
<p>Coward :P. It can't be THAT hard. I mean it's just simple advanced (oxymoron?) analytical math theory.</p>
<p>sadeas's questions answer is B.</p>
<p>thanks arachnotron!</p>
<p>Haha, I could SO see barron's asking something like that. Man did that book get me into mathematical shape, though...</p>