document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=164928>Question 164928</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular piece of cardboard with perimeter 30 in., two parallel and equally spaced creases are made. The cardboard is then folded to make a prism with open ends that are equilateral triangles.  Find the volume of the prism as a function of x and what is the domain of V(x)? Thanks to those who can help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #121609 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=121609\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A rectangular piece of cardboard with perimeter 30 in., two parallel and equally spaced creases are made. The cardboard is then folded to make a prism with open ends that are equilateral triangles. Find the volume of the prism as a function of x and what is the domain of V(x)? <BR>\n" );
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document.write( "Let x = the 3 equal distances, between the two folds<BR>\n" );
document.write( "then<BR>\n" );
document.write( "3x = width of the cardboard<BR>\n" );
document.write( "and<BR>\n" );
document.write( "Let L = the length of cardboard<BR>\n" );
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document.write( "Perimeter:<BR>\n" );
document.write( "2(3x) + 2L = 30<BR>\n" );
document.write( "Simplify divide by 2<BR>\n" );
document.write( "3x + L = 15<BR>\n" );
document.write( "L = (15-3x)<BR>\n" );
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document.write( "Find the height (h) of the equilateral triangle with sides = x<BR>\n" );
document.write( "h^2 + (x/2)^2 = x^2<BR>\n" );
document.write( "h^2 = x^2 - (x/2)^2<BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2-%28x%2F2%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2-%28x%2F2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Vol of a triangular prism = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >*L*w*h<BR>\n" );
document.write( "In this problems<BR>\n" );
document.write( "L = (15-3x)<BR>\n" );
document.write( "w = x<BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2-%28x%2F2%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2-%28x%2F2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "V(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >*(15-3x)*x*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2-%28x%2F2%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2-%28x%2F2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can tell by L, (15-3x), that x has to be less than 5 (the domain)<BR>\n" );
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document.write( "If you graph this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-3%2C+6%2C+-10%2C+25%2C+.5%2A%2815-3x%29%2Ax%2Asqrt%28x%5E2-%28x%2F2%29%5E2%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The max volume when x = 3.33, Domain 0 to <+5 </SPAN>\n" );
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