document.write( "Question 1205247: 1.Find the equation of the circle that passes through the points (0,0), (5,0), and (3,3). Use both geometric and algebraic solution for comparison.\r
\n" ); document.write( "\n" ); document.write( "2. The cable of a suspension bridge hangs in the shape of a parabola. The tower supporting the cable are 400 ft apart and 150 ft high. If the cable, at its lowest, is 30 ft above the bridge at its midpoint, how high is the cable 50 ft away(horizontally) from either tower? \n" ); document.write( "

Algebra.Com's Answer #841919 by ikleyn(52834) $\"\"$ $\"About$

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\n" ); document.write( "2. The cable of a suspension bridge hangs in the shape of a parabola.
\n" ); document.write( "The tower supporting the cable are 400 ft apart and 150 ft high.
\n" ); document.write( "If the cable, at its lowest, is 30 ft above the bridge at its midpoint,
\n" ); document.write( "how high is the cable 50 ft away(horizontally) from either tower?
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document.write( "Place the origin of the coordinate system half way between the towers,\r\n" );
document.write( "at the level of the bridge.\r\n" );
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document.write( "Using vertex form, write equation of a parabola \r\n" );
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document.write( "    y = ax^2 + 30.\r\n" );
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document.write( "Find the unknown coefficient \"a\" from the condition \r\n" );
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document.write( "    a*200^2 + 30 = 150  ft,\r\n" );
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document.write( "which says that the cable is suspended at the top of a tower  (for each cable and each tower).\r\n" );
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document.write( "From this equation, find \"a\"\r\n" );
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document.write( "    40000a = 150 - 30 = 120\r\n" );
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document.write( "    a =  =  = 0.003.\r\n" );
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document.write( "So, the parabola equation is\r\n" );
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document.write( "    y = 0.003*x^2 + 30.\r\n" );
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document.write( "They want you find \"y\" at x = 200-50 = 150 ft.\r\n" );
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document.write( "Substitute x= 150 into equation of the parabola and get\r\n" );
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document.write( "    y = 0.003*150^2+30 = 97.5  ft.\r\n" );
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document.write( "ANSWER.  50 ft away from either tower, the cable is 97.5 ft over the bridge.\r\n" );
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