Dettonville Answers - Recent questions and answers in Math
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Powered by Question2AnswerAnswered: How to find the measures of the angles?
/questions/33/how-to-find-the-measures-of-the-angles?show=34#a34
x is even.<br />
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y is a multiple of 5.<br />
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x + 10x + y = 180.<br />
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11x + y = 180.<br />
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Since x is even, there is nothing you can multiply 11 by which will get you to a number whose last digit is 5. Therefore, y must be a multiple of 10.<br />
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x must equal 10, because there is nothing else you can multiply 11 by that is an even number, that ends with a 0 and does not exceed 180.<br />
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110 + y = 180.<br />
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y = 70.<br />
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The first angle is 10, the second angle is 100, and the third angle is 70.Math/questions/33/how-to-find-the-measures-of-the-angles?show=34#a34Tue, 29 Jul 2014 00:35:00 +0000Answered: What is the millionth term in the sequence?
/questions/15/what-is-the-millionth-term-in-the-sequence?show=32#a32
<p>
The differences between each pair of consecutive terms seems to go like this:</p>
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3, 5, 7, 9, ...</p>
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Consider the sequence of perfect squares</p>
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1, 4, 9, 16, 25, ...</p>
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If we take the differences between each pair of consecutive terms with this sequence, we get:</p>
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3, 5, 7, 9, ...</p>
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There appears to be a pattern here, where the sequence involves perfect squares.</p>
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In order to match up the terms, we can add 7 to each term to get:</p>
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7+1 = 8,<br>
7+4 = 11,<br>
7+9 = 16,<br>
7+16 =23,<br>
7+25 =32,<br>
...,<br>
\(7+n^2\)<br>
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where n represents the nth term of the sequence. </p>
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Then the millionth term would be...drum roll...<br>
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=\(7+(1,000,000)^2\)<br>
= \(7+(10^6)^2\)<br>
= \(7+10^{12}\)<br>
= 1,000,000,000,007 <img alt="wink" height="20" src="http://www.dettonville.org/forum/qa-plugin/wysiwyg-editor/plugins/smiley/images/wink_smile.gif" title="wink" width="20"></p>
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</p>Math/questions/15/what-is-the-millionth-term-in-the-sequence?show=32#a32Tue, 15 Jul 2014 21:22:23 +0000How do you use Geometer Sketchpad to model a clock?
/questions/30/how-do-you-use-geometer-sketchpad-to-model-a-clock
How do you use Geometer Sketchpad to model a clock?Math/questions/30/how-do-you-use-geometer-sketchpad-to-model-a-clockFri, 11 Jul 2014 01:10:31 +0000Answered: Which right triangles have area equal to perimeter?
/questions/21/which-right-triangles-have-area-equal-to-perimeter?show=27#a27
(a,b,c)= (5,12,13), (6,8,10), (6,25,29), (7,15,20), (9,10,17)Math/questions/21/which-right-triangles-have-area-equal-to-perimeter?show=27#a27Thu, 10 Jul 2014 20:20:14 +0000Answered: What is Fermat's Last Theorem?
/questions/13/what-is-fermats-last-theorem?show=25#a25
<p>
Many of us are familiar with the Pythagorean Theorem. This theorem has many proofs.</p>
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<p>
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The Pythagorean Triples (a,b,c) represent the lengths of the two legs and hypotenuse of right triangles and satisfy the Pythagorean Theorem equation<br>
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\(a^2 + b^2 = c^2\)<br>
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We can find infinitely many triples. For example, multiply the triplet (3,4,5) by any positive integer and it also satisfies Pythagorean's Theorem<br>
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Fermat’s Last Theorem states that there are no positive integers that satisfy the equation with higher degree than 2. That is, for every triple (a,b,c), the following inequalities are always true.<br>
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\(a^3 + b^3 ≠ c^3\)<br>
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\(a^4 + b^4 ≠ c^4\)<br>
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\(a^5 + b^5 ≠ c^5\)<br>
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. . .<br>
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\(a^n + b^n ≠ c^n\)<br>
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In general, it says that there are no positive integers (a,b,c) that satisfy the equation \(a^n + b^n = c^n\), for any integer n greater than 2.<br>
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This math problem was proposed by Pierre de Fermat in 1637, and after more than 300 years and many incorrect proofs published, Andrew Wiles finally solved the enigma in 1995. It took him 8 years to solve the problem!</p>Math/questions/13/what-is-fermats-last-theorem?show=25#a25Thu, 10 Jul 2014 18:52:01 +0000Answered: 80 sided polygon?
/questions/16/80-sided-polygon?show=23#a23
It is called an octacontagon!Math/questions/16/80-sided-polygon?show=23#a23Thu, 10 Jul 2014 14:23:26 +0000Answered: How do you find the volume of a sphere?
/questions/14/how-do-you-find-the-volume-of-a-sphere?show=22#a22
Volume equals 4 over 3 multiplied by pi multiplied by the radius cubed.Math/questions/14/how-do-you-find-the-volume-of-a-sphere?show=22#a22Thu, 10 Jul 2014 14:23:21 +0000How to prove that there must be two distinct integers in A whose sum is 104?
/questions/19/how-prove-that-there-must-two-distinct-integers-whose-sum-104
Let A be any set of 20 distinct integers chosen from the academic progression 1,4,7,...100. Prove that there must be two distinct integers in A whose sum in 104.Math/questions/19/how-prove-that-there-must-two-distinct-integers-whose-sum-104Thu, 10 Jul 2014 14:18:09 +0000Answered: Pythagorean's Thereom?
/questions/17/pythagoreans-thereom?show=18#a18
\( a^2+b^2=c^2\) You square the sides of the triangleMath/questions/17/pythagoreans-thereom?show=18#a18Thu, 10 Jul 2014 14:15:32 +0000Why does this always result in 1?
/questions/12/why-does-this-always-result-in-1
Take any natural number. If even, divided by 2. If odd, multiply by 3 and add 1. No matter what number you choose, doing this repeatedly would eventually result to 1. Why does this happen?<br />
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A proof is most desirable :)Math/questions/12/why-does-this-always-result-in-1Thu, 10 Jul 2014 13:02:10 +0000Answered: How do you connect the boxes?
/questions/10/how-do-you-connect-the-boxes?show=11#a11
<p>
Here is the answer:</p>
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<img alt="" src="/questions/?qa=blob&qa_blobid=13463894889446467402" style="width: 434px; height: 431px;"></p>Math/questions/10/how-do-you-connect-the-boxes?show=11#a11Wed, 09 Jul 2014 20:42:29 +0000Answered: Who is the truth teller?
/questions/3/who-is-the-truth-teller?show=4#a4
<p>Brutus has to be a liar, because in this game, it's impossible for anyone to say that he or she is a liar. Caesar is a liar, because if he was telling the truth, it would mean that he himself would be a liar, so therefore, he is not a truth teller, and he must be a liar. So since Caesars' statement was a lie, the opposite of what he said must be true. The opposite of what Caesar said would be; if one of us is a liar, then not all of us are liars. What that really means is that there is at least one truth teller among them. So that must mean that Augustus is a truth teller. To sum it up: Brutus- liar, Caesar- liar, Augustus- truth teller.</p>
Math/questions/3/who-is-the-truth-teller?show=4#a4Sun, 27 Oct 2013 13:42:05 +0000