document.write( "Question 582407: The cabels of a suspension bridge are in the shape of a parabola. The towers supporting the cable are 400 feet apart and 100 feet high. If the cables are at the height of 10 feet ,idway between the towers, what is the height of the cable at the point 50 feet from the center of the bridge? \n" ); document.write( "
Algebra.Com's Answer #372240 by ankor@dixie-net.com(22740)\"\" \"About 
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The cables of a suspension bridge are in the shape of a parabola.
\n" ); document.write( " The towers supporting the cable are 400 feet apart and 100 feet high.
\n" ); document.write( " If the cables are at the height of 10 feet midway between the towers, what is the height of the cable at the point 50 feet from the center of the bridge?
\n" ); document.write( ":
\n" ); document.write( "Use the given information to create a quadratic equation to represent this bridge
\n" ); document.write( "Using the form: ax^2 + bx + c = y
\n" ); document.write( "left side
\n" ); document.write( "x=0, y=100, therefore c=100
\n" ); document.write( ":
\n" ); document.write( "Midway
\n" ); document.write( "x=200, y=10
\n" ); document.write( "200^2a + 200b + 100 = 10
\n" ); document.write( "40000a + 200b = 10 - 100
\n" ); document.write( "40000a + 200b = -90
\n" ); document.write( ":
\n" ); document.write( "right end
\n" ); document.write( "x=400, y=100
\n" ); document.write( "400^2a + 400b + 100 = 100
\n" ); document.write( "160000a + 400b = 0
\n" ); document.write( ":
\n" ); document.write( "Multiply the midway equation by 2, subtract from the above
\n" ); document.write( "160000a + 400b = 0
\n" ); document.write( " 80000a + 400b = -180
\n" ); document.write( "-----------------------subtraction eliminates b, find a
\n" ); document.write( "80000a = 180
\n" ); document.write( "a = 180/80000
\n" ); document.write( "a = .00225
\n" ); document.write( "find b
\n" ); document.write( "160000(.00225) + 400b = 0
\n" ); document.write( "360 + 400b = 0
\n" ); document.write( "400b = -360
\n" ); document.write( "b = -360/400
\n" ); document.write( "b = -.9
\n" ); document.write( ":
\n" ); document.write( "The equation: y = .00225x^2 - .9x + 100
\n" ); document.write( "looks like this
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-100%2C+500%2C+-20%2C+120%2C+.00225x%5E2-.9x%2B100%29+\"
\n" ); document.write( ":
\n" ); document.write( "\"what is the height of the cable at the point 50 feet from the center of the bridge?\"
\n" ); document.write( "x = 200-50
\n" ); document.write( "x = 150
\n" ); document.write( "y = .00225(150^2) - .9(150) + 100
\n" ); document.write( "y = 15.625 ft above 0
\n" ); document.write( ":
\n" ); document.write( "x = 200 + 50
\n" ); document.write( "x = 250
\n" ); document.write( "do the same as we did above \n" ); document.write( "
\n" );