document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=620924>Question 620924</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An architectural engineer is designing a parabolic dome that will be 200 feet in diameter with a maximum height of 50 feet. Find the equation of the cross-sectional parabola of the dome. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #390484 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=390484\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An architectural engineer is designing a parabolic dome that will be 200 feet in diameter with a maximum height of 50 feet.<BR>\n" );
document.write( " Find the equation of the cross-sectional parabola of the dome.<BR>\n" );
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document.write( "Using the form ax^2 + bx + c = y,  in this equation c = 0<BR>\n" );
document.write( "Two equation from the information given<BR>\n" );
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document.write( "Using the axis of symmetry and max: x=100; y=50<BR>\n" );
document.write( "100^2a + 100b = 50<BR>\n" );
document.write( "10000a + 100b = 50<BR>\n" );
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document.write( "Using the x intercept: x=200; y=0<BR>\n" );
document.write( "200^2a + 200b = 0<BR>\n" );
document.write( "40000a + 200b = 0<BR>\n" );
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document.write( "Multiply the 1st equation by 2, subtract from the above equation<BR>\n" );
document.write( "40000a + 200b = 0<BR>\n" );
document.write( "20000a + 200b = 100<BR>\n" );
document.write( "---------------------subtraction eliminates b, find a<BR>\n" );
document.write( "20000a = -100<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-100%29%2F20000 ALIGN=MIDDLE  ALT=\"%28-100%29%2F20000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = -.005<BR>\n" );
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document.write( "Find b using the 1st equation, replace a with -.005<BR>\n" );
document.write( "10000(-.005) + 100b = 50<BR>\n" );
document.write( "-50 + 100b = 50<BR>\n" );
document.write( "100b = 50 + 50<BR>\n" );
document.write( "100b = 100<BR>\n" );
document.write( "b = 1<BR>\n" );
document.write( "therefore the equation for this:<BR>\n" );
document.write( "y = -.005x^2 + 1x<BR>\n" );
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document.write( "If we graph this, we can see what it will look like<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-20%2C+220%2C+-10%2C+60%2C+-.005x%5E2%2Bx%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-20%2C+220%2C+-10%2C+60%2C+-.005x%5E2%2Bx%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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