document.write( "Question 769863: x3 + 2x^2 - 9x = 18\r
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\n" ); document.write( "\n" ); document.write( " Suppose the altitude of a rising hot-air balloon is given by h = 0.04 t2 + 2t, where \"t\" is the time in seconds after the balloon leaves the ground. How long will it take for the balloon to reach an altitude of 200 feet?\r
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Algebra.Com's Answer #469082 by ramkikk66(644) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "x3 + 2x^2 - 9x = 18 \r\n" );
document.write( "2x^4 + 16x \r\n" );
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document.write( "Suppose the altitude of a rising hot-air balloon is given by h = 0.04 t2 + 2t, where \"t\" is the time in seconds after the balloon leaves the ground. How long will it take for the balloon to reach an altitude of 200 feet? \r\n" );
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document.write( "1) x^3 + 2*x^2 - 9*x - 18 = 0\r\n" );
document.write( "Can be re-written as\r\n" );
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document.write( "i.e.  because x^2 - 9 = (x+3)(x-3)\r\n" );
document.write( "So the 3 roots of the equation are\r\n" );
document.write( "x + 3 = 0 or x = -3\r\n" );
document.write( "x - 3 = 0 or x = 3\r\n" );
document.write( "x + 2 = 0 or x = -2\r\n" );
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document.write( "2) I assume you are looking for factorizing this expression.\r\n" );
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document.write( "2*x^4 + 16*x can be written as\r\n" );
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document.write( " since a^3 + b^3 = (a+b)*(a^2 + b^2 - ab)\r\n" );
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document.write( "3) \r\n" );
document.write( "h = 0.04*t^2 + 2*t\r\n" );
document.write( "For h = 200\r\n" );
document.write( "200 = 0.04*t^2 + 2*t\r\n" );
document.write( "Rewriting to remove the decimals\r\n" );
document.write( "20000 = 4*t^2 + 200*t\r\n" );
document.write( "Dividing by 4 and moving all terms to one side\r\n" );
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document.write( "This is a standard quadratic equation. Solved using factorization\r\n" );
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document.write( "t = -100 or t = 50\r\n" );
document.write( "Since time cannot be negative,\r\n" );
document.write( "t = 50 sec to achieve a height of 200 ft.\r\n" );
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