document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1043488>Question 1043488</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cable wire was tied to both ends of a 240 meters long bridge such that the cable hangs in the form of a parabola. The lowest point of the cable is 60 meters below the bridge.\r<BR>\n" );
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document.write( "a.) Find the equation of the cable wire, assuming that the origin is the lowest point of the cable.\r<BR>\n" );
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document.write( "b.) Using the equation, find the width of the rope at a point 38 meters above its lowest point.\r<BR>\n" );
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document.write( "c.) suppose a 180 neters rope will be tied horizontally to the cable wire. How high above the lower point of the cable wire should the rope be? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #658797 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=658797\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A cable wire was tied to both ends of a 240 meters long bridge such that the cable hangs in the form of a parabola. The lowest point of the cable is 60 meters below the bridge.<BR>\n" );
document.write( "a.) Find the equation of the cable wire, assuming that the origin is the lowest point of the cable.<BR>\n" );
document.write( "Use the form ax^2 + bx + c = y; lowest point is at origin; c = 0<BR>\n" );
document.write( "Two given points: x= -120; y = 60 and x = +120; y = 60; two equations<BR>\n" );
document.write( "-120^2a - 120b + 0 = 60<BR>\n" );
document.write( "+120x^2 + 120b + 0 = 60<BR>\n" );
document.write( "Use elimination<BR>\n" );
document.write( "14400a - 120b = 60<BR>\n" );
document.write( "14400a + 120b = 60 <BR>\n" );
document.write( "-------------------Addition eliminates b, find a<BR>\n" );
document.write( "28800a = 120<BR>\n" );
document.write( "a = 120/28800<BR>\n" );
document.write( "a = .004167<BR>\n" );
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document.write( "Find b using 120^2(.001467) + 120b = 60<BR>\n" );
document.write( "60 + 120b = 60<BR>\n" );
document.write( "b = 0<BR>\n" );
document.write( "The equation: y = .004167x^2<BR>\n" );
document.write( "looks like this, green line is the bridge<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-150%2C+150%2C+-20%2C+80%2C+.004167x%5E2%2C+60%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-150%2C+150%2C+-20%2C+80%2C+.004167x%5E2%2C+60%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "b.) Using the equation, find the width of the rope at a point 38 meters above its lowest point.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-150%2C+150%2C+-20%2C+80%2C+.004167x%5E2%2C+60%2C+38%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-150%2C+150%2C+-20%2C+80%2C+.004167x%5E2%2C+60%2C+38%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, blue line is 38 ft above the min<BR>\n" );
document.write( "//////////////////Sent this before I was done, the rest of the problem://///////<BR>\n" );
document.write( "Calculate, find x when y=38<BR>\n" );
document.write( ".004167x^2 = 38<BR>\n" );
document.write( "x^2 = 38/.004167<BR>\n" );
document.write( "x^2 = 9119.3<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289119.3%29 ALIGN=MIDDLE  ALT=\"sqrt%289119.3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = +95.5<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x = -91.5<BR>\n" );
document.write( "the length of the rope then, 2(91.5) = 191 ft<BR>\n" );
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document.write( "c.) suppose a 180 meters rope will be tied horizontally to the cable wire. How high above the lower point of the cable wire should the rope be? <BR>\n" );
document.write( "x will be half of 180, +/-90<BR>\n" );
document.write( "y = .004167(90^2)<BR>\n" );
document.write( "y = 33.75 <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-150%2C+150%2C+-20%2C+80%2C+.004167x%5E2%2C+60%2C+33.75%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-150%2C+150%2C+-20%2C+80%2C+.004167x%5E2%2C+60%2C+33.75%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >; blue line is 33.75 ft above min </SPAN>\n" );
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