document.write( "Question 54072This question is from textbook Algebra and Trigonometry
\n" ); document.write( ": Please help me with this problem:
\n" ); document.write( "The period of a simple pendulum is directly proportional to the square root of its length. If a pendulum has a length of 6 feet and a period of 2 seconds, to what length should it be shortened to achieve a 1 second period? \n" ); document.write( "

Algebra.Com's Answer #36326 by AnlytcPhil(1806) $\"\"$ $\"About$

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Please help me with this problem:\r\n" );
document.write( "The period of a simple pendulum is directly \r\n" );
document.write( "proportional to the square root of its length. \r\n" );
document.write( "If a pendulum has a length of 6 feet and a \r\n" );
document.write( "period of 2 seconds, to what length should it \r\n" );
document.write( "be shortened to achieve a 1 second period?\r\n" );
document.write( "\r\n" );
document.write( "           ______\r\n" );
document.write( "Period = kÖLength\r\n" );
document.write( "           _   \r\n" );
document.write( "     P = kÖL\r\n" );
document.write( "\r\n" );
document.write( "Substitute L = 6 and P = 2 and solve for k\r\n" );
document.write( "           _  \r\n" );
document.write( "     2 = kÖ6\r\n" );
document.write( "                      _\r\n" );
document.write( "Divide both sides by Ö6\r\n" );
document.write( "\r\n" );
document.write( "     2\r\n" );
document.write( "   ---- = k\r\n" );
document.write( "    Ö6\r\n" );
document.write( "\r\n" );
document.write( "Rationalize the denominator\r\n" );
document.write( "         _\r\n" );
document.write( "     2  Ö6\r\n" );
document.write( "    ------- = k\r\n" );
document.write( "     Ö6 Ö6\r\n" );
document.write( "        _\r\n" );
document.write( "      2Ö6\r\n" );
document.write( "     ----- = k\r\n" );
document.write( "       6\r\n" );
document.write( "\r\n" );
document.write( "Cancel 2 into 6\r\n" );
document.write( "      _\r\n" );
document.write( "     Ö6\r\n" );
document.write( "    ---- = k\r\n" );
document.write( "      3\r\n" );
document.write( "\r\n" );
document.write( "Now substitute\r\n" );
document.write( "\r\n" );
document.write( "        _\r\n" );
document.write( "       Ö6\r\n" );
document.write( "  k = ---- \r\n" );
document.write( "       3\r\n" );
document.write( "\r\n" );
document.write( "into the original equation\r\n" );
document.write( "\r\n" );
document.write( "           _   \r\n" );
document.write( "     P = kÖL\r\n" );
document.write( "\r\n" );
document.write( "        _ _\r\n" );
document.write( "       Ö6ÖL\r\n" );
document.write( "  P = ---- \r\n" );
document.write( "        3\r\n" );
document.write( "        __\r\n" );
document.write( "       Ö6L\r\n" );
document.write( "  P = ------ \r\n" );
document.write( "        3\r\n" );
document.write( "\r\n" );
document.write( "Now substitute P = 1\r\n" );
document.write( "\r\n" );
document.write( "        __\r\n" );
document.write( "       Ö6L\r\n" );
document.write( "  1 = ------ \r\n" );
document.write( "        3\r\n" );
document.write( "\r\n" );
document.write( "Multiply both sides by 3 to clear of fractions\r\n" );
document.write( "       __\r\n" );
document.write( "  3 = Ö6L \r\n" );
document.write( "   \r\n" );
document.write( "Square both sides of the equation\r\n" );
document.write( "\r\n" );
document.write( "  9 = 6L\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by 6\r\n" );
document.write( "\r\n" );
document.write( "9/6 = L\r\n" );
document.write( "\r\n" );
document.write( "3/2 = L\r\n" );
document.write( "\r\n" );
document.write( "  L = 3/2   \r\n" );
document.write( "  \r\n" );
document.write( "Edwin

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