document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185067>Question 1185067</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bridge is built in the shape of a parabolic arch and is to have a span of 100 feet. The height of the arch at a distance of 40 feet from the center is to be 10 feet. Assume that the ground is the x-axis and the y-axis as the axis of the arch.\r<BR>\n" );
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document.write( "a. How high is the arch at its center approximated in two decimal places?\r<BR>\n" );
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document.write( "b. What is the horizontal length approximated to two decimal places of the arch from its axis when it’s 15 feet high? </SPAN>\n" );
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document.write( "With the origin at ground level at the center of the arch, the equation of the parabola is of the form<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax%5E2%2Bb ALIGN=MIDDLE  ALT=\"y=ax%5E2%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "We know that the height is 0 50 feet from the center of the arch and 10 feet 40 feet from the center.  Use those two points to determine the coefficients a and b.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=2500a%2Bb ALIGN=MIDDLE  ALT=\"0=2500a%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10=1600a%2Bb ALIGN=MIDDLE  ALT=\"10=1600a%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10=900a ALIGN=MIDDLE  ALT=\"-10=900a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-10%2F900=-1%2F90 ALIGN=MIDDLE  ALT=\"a=-10%2F900=-1%2F90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=2500%28-1%2F90%29%2Bb ALIGN=MIDDLE  ALT=\"0=2500%28-1%2F90%29%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=2500%2F90=250%2F9 ALIGN=MIDDLE  ALT=\"b=2500%2F90=250%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The equation of the parabola is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F90%29x%5E2%2B250%2F9 ALIGN=MIDDLE  ALT=\"y=%28-1%2F90%29x%5E2%2B250%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "a.  The height at the center of the arch is the y value when x=0.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=250%2F9 ALIGN=MIDDLE  ALT=\"y=250%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "b.  To find the width of the arch when the height is 15, find the x value when y is 15, then double that answer:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15=%28-1%2F90%29x%5E2%2B250%2F9 ALIGN=MIDDLE  ALT=\"15=%28-1%2F90%29x%5E2%2B250%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...<br><BR>\n" );
document.write( "Numerical calculations or a graphing calculator should give you x=33.91 (to 2 decimal places), so the width of the arch when the height is 15 feet is 67.82 feet.<br><BR>\n" );
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