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	<title>Precal Blog</title>
	<link>http://prec.alcul.us</link>
	<description>Well is the enemy of better.</description>
	<lastBuildDate>Wed, 01 Feb 2012 04:34:28 +0000</lastBuildDate>
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		<title>Proving Identities</title>
		<description><![CDATA[Today we started out class with another proof by induction example.  The problem was: Prove n is greater than or equal to 2, a(x1+x2+x3+&#8230;+xn)=ax1+ax2+ax3+&#8230;+axn  n=2,   a(x1+ax2) =ax1=ax2 (distributive property)  TRUE! Now we have to continue the problem by assuming n=k, a(x1+x2+x3+..+xk)+ax1+ax2+ax3+&#8230;axk The next step is to assume k+1, a(x1+x2+x3+&#8230;+xk+xk+1)=ax1+ax2+ax3+&#8230;+axk+axk+1 The left part of the equation can [...]]]></description>
		<link>http://prec.alcul.us/index.php/2012/proving-identities/</link>
			</item>
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		<title>Learning the Pythagorean Properties</title>
		<description><![CDATA[Most of us are familiar with the Pythagorean Theorem of a²+b²=c², well on Monday we learned how that can apply to our unit circle and the 8 different Pythagorean Properties.If you look at the unit circle and create a right triangle with a point on the center of the circle and on the border, then [...]]]></description>
		<link>http://prec.alcul.us/index.php/2012/learning-the-pythagorean-properties/</link>
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		<title>I CAN BUILD THE PYTHAGOREAN TRIG PROPERTIES</title>
		<description><![CDATA[&#60;&#60;WE STARTED OFF THE CLASS WITH A BASIC PROOF BY INDUCTION PROBLEM THAT WAS&#8230; 2+2²+3²+4²+&#8230;. 2^K = 2^(K+1) +2 2+2²+3²+4²&#8230; 2^K+2^(K+1) = 2^(K+2) &#8211; 2 2^(K+1) + 2^(K+1) = 2^(K+2) 2(2^K+1) = 2^(K+2) Q.E.D. #TOMBSTONE #HAVINFUNYET ? NEXT WE LEARNED THE #PYTHAGOREAN, #QUOTIENT, AND #RECIPROCAL PROPERTIES&#8230; #PYTHAGOREAN&#8230; 1) SIN²X+COS²X=1   1A) SIN²X=1-COS²X       1B) COS²X=1-SIN²X 2)1+COT²X=CSC²X   2A) [...]]]></description>
		<link>http://prec.alcul.us/index.php/2012/i-can-build-the-pythagorean-trig-properties/</link>
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		<title>More Work with Proof by Induction</title>
		<description><![CDATA[Today in #bienprecal, we did some more solving of proof by induction equations. The first one we did was 2+4+6+8+&#8230;+2n=. The steps we used to solve this are as follows: 1. Find what the equation equals. 2+4+6+8+&#8230;+2n=n²+n 2. Assume Pk (do this by changing all the n&#8217;s to k&#8217;s) 2+4+6+8+&#8230;+2k=k²+k 3. Prove Pk+1 is true (do [...]]]></description>
		<link>http://prec.alcul.us/index.php/2012/more-work-with-proof-by-induction/</link>
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		<title>Proof By Induction (Day 2)</title>
		<description><![CDATA[We dove right into class today. We review how to do the proof by induction. After we tried a problem we tried something a little more difficult.  Proving 1^2+2^2+3^2+&#8230;+2n=n(n+1)(2n+1/6) First: Prove That the First Domino Falls n=1 1^2=1(1+1)(2*1+1/6) simplify 4=4 The first domino falls! Second: Assume another domino falls  1^2+2^2+3^2+&#8230;+2k=k(k+1)(2k+1/6)  1^2+2^2+3^2+&#8230;+2(k+1)=(k+1)((k+1)+1)(2(k+1)+1/6) Sence  1^2+2^2+3^2+&#8230;+2n=k(k+1)(2k+1/6) We can subsitute in [...]]]></description>
		<link>http://prec.alcul.us/index.php/2012/proof-by-induction-day-2/</link>
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		<title>Proof by Induction&#8211;Fun with Dominos</title>
		<description><![CDATA[Well, ladies and gents, we started today with dominos again. We set up our patterns, spelling out &#8220;calc&#8221; and/or setting up straight lines. Some patterns fell over right away (success!); others, unfortunately, did not. However, it was these so-called &#8220;failures&#8221; that provided the greatest learning examples. After dominos, we were given our board problem: 1+3+5+7+ [...]]]></description>
		<link>http://prec.alcul.us/index.php/2012/proof-by-induction-fun-with-dominos/</link>
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		<title>Proof by Induction</title>
		<description><![CDATA[For proof by induction, you  start with an equation where the sum of odd numbers  (2n-1) = n^2   in  1+3+5+&#8230;. Then there  are things to proof by induction that must be true in order to prove that this equation works for everything. The first number must work &#38; that every other number must work. To prove this [...]]]></description>
		<link>http://prec.alcul.us/index.php/2012/proof-by-induction/</link>
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		<title>Creating Blog Posts and Dominoes</title>
		<description><![CDATA[With the dawn of a new semester, the class was introduced to the blog today. We were told the basic rules, such as posting an important title and filling the post with information learned in class. Besides the website we also started a project involving dominoes. First we watched a few really cool videos of domino [...]]]></description>
		<link>http://prec.alcul.us/index.php/2012/creating-blog-posts-and-dominoes/</link>
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		<title>The Domino Effect</title>
		<description><![CDATA[Today was our first day of the new semester.  In pre-calculus class we watched a few videos of epic domino sequences. Below is another cool one: We then split up into groups to create our own mini versions of these domino sequences.  My group is going to create a sinusoid shape out of the 58 [...]]]></description>
		<link>http://prec.alcul.us/index.php/2012/the-domino-effect/</link>
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		<title>Determining Graphs for Polynomial and Rational Functions</title>
		<description><![CDATA[Equation to look of graphs: Even exponent: Both ends point the same direction Odd exponent: Each end points a different direction Positive coefficient: as x??, p(x) ?? Negative coefficient: as x??, p(x) ?-? Turns = degree – 1 Branches = zeros =      degree A zero of multiplicity bigger than 2 flattens the graph out [...]]]></description>
		<link>http://prec.alcul.us/index.php/2011/determining-graphs-for-polynomial-and-rational-functions/</link>
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