document.write( "Question 79138: A bridge is built in the shape of a parabolic arch. The bridge has a span of 120 feet and a maximum height of 25 feet. Choose a suitable rectangular coordinate system and find the height of the arch at distances of 10, 30 and 50 feet from the center. \n" ); document.write( "
Algebra.Com's Answer #56822 by ankor@dixie-net.com(22740)\"\" \"About 
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A bridge is built in the shape of a parabolic arch. The bridge has a span of 120 feet and a maximum height of 25 feet. Choose a suitable rectangular coordinate system and find the height of the arch at distances of 10, 30 and 50 feet from the center.
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\n" ); document.write( "Here's one way to do it:
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\n" ); document.write( "We know that equation of a parabola is; ax^2 + bx + c = y
\n" ); document.write( "This parabola originates at 0,0 so the value of c = 0; find the values of a & b
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\n" ); document.write( "The coordinates of the vertex are given; x/y = 60, 25
\n" ); document.write( "60^2*a + 60b = 25
\n" ); document.write( "3600a + 60b = 25
\n" ); document.write( "Simplify; divide by 5
\n" ); document.write( "720x + 12b = 5
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\n" ); document.write( "The coordinates of the x intercept: x/y = 120, 0
\n" ); document.write( "120^2a + 120b = 0
\n" ); document.write( "14400a + 120b = 0
\n" ); document.write( ":
\n" ); document.write( "Multiply the 1st equation by 10 and subtract it from the 2nd equation, find a:
\n" ); document.write( "14400a + 120b = 0
\n" ); document.write( " 7200a + 120b = 50
\n" ); document.write( "------------------subtract
\n" ); document.write( " 7200a + 0b = -50
\n" ); document.write( "a = -50/7200
\n" ); document.write( "a = -.006944
\n" ); document.write( ":
\n" ); document.write( "Find b: substitute -.006944 for a in the 2nd equation:
\n" ); document.write( "14400(-.006944) + 120b = 0
\n" ); document.write( "-100 + 120b = 0
\n" ); document.write( "120b = +100
\n" ); document.write( "b = 100/120
\n" ); document.write( "b = +.8333
\n" ); document.write( ":
\n" ); document.write( "The equation of this parabola: y = -.006944x^2 + .8333x
\n" ); document.write( ":
\n" ); document.write( "A look at the graph of this:
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-10%2C+125%2C+-10%2C+30%2C+-.0069x%5E2+%2B+.83x%29+\"
\n" ); document.write( ":
\n" ); document.write( "\"find the height of the arch at distances of 10, 30 and 50 feet from the center.
\n" ); document.write( "Substitute the x values in the equation to find the y values
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\n" ); document.write( "10 feet from the center would be x=50 and x=70; this will check our equation
\n" ); document.write( "they should be equal
\n" ); document.write( " x | y
\n" ); document.write( "-------
\n" ); document.write( " 50|24.3
\n" ); document.write( " 70|24.3
\n" ); document.write( ":
\n" ); document.write( "30 feet from the center: x=30, x=90
\n" ); document.write( " 30|18.75
\n" ); document.write( " 90|18.75
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\n" ); document.write( "50 ft from center: x=10, x=110
\n" ); document.write( " 10|7.64
\n" ); document.write( "110|7.64
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\n" ); document.write( "Did all this make sense to you? \n" ); document.write( "
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