document.write( "Question 94389: Need help please
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\n" ); document.write( "need the degree and equation:\r
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\n" ); document.write( "\n" ); document.write( "i think the degree is 4 and it is linear
\n" ); document.write( "but that is as far as I can get
\n" ); document.write( "Help Please\r
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\n" ); document.write( "llo \n" ); document.write( "
Algebra.Com's Answer #68739 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Need help please\r\n" );
document.write( "Okay\r\n" );
document.write( "need the degree and equation: \r\n" );
document.write( " n   1  2  3  4  5\r\n" );
document.write( "f(n)11 21 35 53 75 \r\n" );
document.write( "i think the degree is 4 and it is linear\r\n" );
document.write( "but that is as far as I can get\r\n" );
document.write( "Help Please \r\n" );
document.write( "Thanks\r\n" );
document.write( "llo\r\n" );
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document.write( "
\r\n" );
document.write( "n     1    2     3     4     5  \r\n" );
document.write( "f(n) 11   21    35    53    75\r\n" );
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document.write( "To find the degree:\r\n" );
document.write( "Make a difference table, by finding the\r\n" );
document.write( "difference of each adjacent pair, writing\r\n" );
document.write( "the differences until you find a line of\r\n" );
document.write( "differences that are all the same.\r\n" );
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document.write( "n     1     2      3     4     5  \r\n" );
document.write( "f(n) 11    21     35    53    75\r\n" );
document.write( "1       10     14    18    22\r\n" );
document.write( "2           4      4     4 \r\n" );
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document.write( "                 \r\n" );
document.write( "It took 2 lines of differences to find\r\n" );
document.write( "a line on which all the numbers are the \r\n" );
document.write( "same, so we know to assume a polynomial \r\n" );
document.write( "of degree 2 (a quadratic):\r\n" );
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document.write( "f(n) = An² + Bn + C \r\n" );
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document.write( "Since f(1) = 11,\r\n" );
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document.write( "f(1) = A(1)² + B(1) + C = 11\r\n" );
document.write( "f(1) = A + B + C = 11\r\n" );
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document.write( "Since f(2) = 21\r\n" );
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document.write( "f(2) = A(2)² + B(2) + C = 21\r\n" );
document.write( "f(2) = A(4) + B(2) + C = 21\r\n" );
document.write( "f(2) = 4A + 2B + C = 21\r\n" );
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document.write( "Since f(3) = 35\r\n" );
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document.write( "f(3) = A(3)² + B(3) + C = 35\r\n" );
document.write( "f(3) = A(9) + B(3) + C = 35\r\n" );
document.write( "f(3) = 9A + 3B + C = 35\r\n" );
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document.write( "So we have the system of equations:\r\n" );
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document.write( " A +  B + C = 11\r\n" );
document.write( "4A + 2B + C = 21\r\n" );
document.write( "9A + 3B + C = 35\r\n" );
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document.write( "Do you know how to solve that system of\r\n" );
document.write( "equations with matrices?  If not post\r\n" );
document.write( "again asking how.  The solution is\r\n" );
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document.write( "A=2, B=4, C=5\r\n" );
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document.write( "So\r\n" );
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document.write( "f(n) = An² + Bn + C so\r\n" );
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document.write( "f(n) = 2n² + 4n + 5\r\n" );
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document.write( "Edwin

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