document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1112670>Question 1112670</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a parabolic trough 10 meters long 4 meters wide cross the top and 3 meters deep is filled with water at depth of 2 meters. Find the volume of the water in the through </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #727820 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=727820\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a parabolic trough 10 meters long 4 meters wide cross the top and 3 meters deep is filled with water at depth of 2 meters. Find the volume of the water in the through<BR>\n" );
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document.write( "Find the equation of the parabola.<BR>\n" );
document.write( "Make the x-axis the top of the trough.<BR>\n" );
document.write( "--> y = ax^2 - 3 and the 2 points (-2,0) and (2,0)<BR>\n" );
document.write( "0 = a*4 - 3<BR>\n" );
document.write( "a = 3/4<BR>\n" );
document.write( "--> y = 3x^2/4 -3 is the parabola.\r<BR>\n" );
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document.write( "Find the intersections of the parabola and the line y = -1.<BR>\n" );
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document.write( "-1 = 3x^2/4 - 3<BR>\n" );
document.write( "x^2 = 8/3<BR>\n" );
document.write( "x = +/- sqrt(24)/3<BR>\n" );
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document.write( "Translating the parabola up 1 unit --> the zeroes are x = +/- sqrt(24)/3 and a 3rd point is (0,-2)<BR>\n" );
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document.write( "y = ax^2 - 2<BR>\n" );
document.write( "0 = a*24/9 - 2<BR>\n" );
document.write( "a = 2*(9/24)<BR>\n" );
document.write( "a = 3/4<BR>\n" );
document.write( "--> y = 3x^2/4 - 2<BR>\n" );
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document.write( "INT(3x^2/4 -2) = x^3/4 - 2x + C<BR>\n" );
document.write( "Find area from x = 0 to x = sqrt(24)/3<BR>\n" );
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document.write( "Area of one side = (sqrt(24)/3)^3 - 2sqrt(24)/3 sq meters<BR>\n" );
document.write( "= (24/9)*sqrt(24)/3 - 2sqrt(24)/3<BR>\n" );
document.write( "= 8sqrt(24)/9 - 2sqrt(24)/3<BR>\n" );
document.write( "= 4sqrt(6)/9<BR>\n" );
document.write( "2 times --> 8sqrt(6)/9 sq meters area of the parabola<BR>\n" );
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document.write( "Vol = area*length = 80sqrt(6)/9 cubic meters\r<BR>\n" );
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document.write( " </SPAN>\n" );
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