document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=388733>Question 388733</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A container with a square base, vertical sides,<BR>\n" );
document.write( "and open top is to be made from 1000 ft2 of material.<BR>\n" );
document.write( "(a) Write an equation for the volume of the con-<BR>\n" );
document.write( "tainer as a function of the length of a side of<BR>\n" );
document.write( "the base.<BR>\n" );
document.write( "(b) Write an equation for the volume of the con-<BR>\n" );
document.write( "tainer as a function of the length of the ver-<BR>\n" );
document.write( "tical side\r<BR>\n" );
document.write( "\n" );
document.write( "I can do part (a) but I am stuck on (b), Help would be greatly appreciated. Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #275099 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=275099\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a)<BR>\n" );
document.write( "The square base can be any size, so I'll call<BR>\n" );
document.write( "the sides of the base <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "I want the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000 ALIGN=MIDDLE  ALT=\"1000\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft2 of material to be a<BR>\n" );
document.write( "square also, so the sides of the container will<BR>\n" );
document.write( "all be the same height .<BR>\n" );
document.write( "that means each side of the material will be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Asqrt%2810%29 ALIGN=MIDDLE  ALT=\"10%2Asqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft2<BR>\n" );
document.write( "I'll place the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft2 base exactly in the center.<BR>\n" );
document.write( "That means the  4 sides will measure <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2Asqrt%2810%29+-+x%29%2F2 ALIGN=MIDDLE  ALT=\"%2810%2Asqrt%2810%29+-+x%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V ALIGN=MIDDLE  ALT=\"V\"   DISABLED_style= \"max-width:90%; height:auto;\" > = volume<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+x%5E2%2A%2810%2Asqrt%2810%29+-+x%29%2F2 ALIGN=MIDDLE  ALT=\"V+=+x%5E2%2A%2810%2Asqrt%2810%29+-+x%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+5%2Asqrt%2810%29%2Ax%5E2+-+x%5E3%2F2 ALIGN=MIDDLE  ALT=\"V+=+5%2Asqrt%2810%29%2Ax%5E2+-+x%5E3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Is this what you got?<BR>\n" );
document.write( "(b)<BR>\n" );
document.write( "I'll call the length of the vertical side <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%2810%2Asqrt%2810%29+-+x%29%2F2 ALIGN=MIDDLE  ALT=\"y+=+%2810%2Asqrt%2810%29+-+x%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Ok, now I can say that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+x%5E2%2Ay ALIGN=MIDDLE  ALT=\"V+=+x%5E2%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now I just have to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in terms of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "so I go back to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%2810%2Asqrt%2810%29+-+x%29%2F2 ALIGN=MIDDLE  ALT=\"y+=+%2810%2Asqrt%2810%29+-+x%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y+=++10%2Asqrt%2810%29+-+x ALIGN=MIDDLE  ALT=\"2y+=++10%2Asqrt%2810%29+-+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+10%2Asqrt%2810%29+-+2y ALIGN=MIDDLE  ALT=\"x+=+10%2Asqrt%2810%29+-+2y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now I can say<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+%2810%2Asqrt%2810%29+-+2y%29%5E2+%2Ay ALIGN=MIDDLE  ALT=\"V+=+%2810%2Asqrt%2810%29+-+2y%29%5E2+%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+%281000+-+40%2Asqrt%2810%29%2Ay+%2B+4y%5E2%29%2Ay ALIGN=MIDDLE  ALT=\"V+=+%281000+-+40%2Asqrt%2810%29%2Ay+%2B+4y%5E2%29%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+4y%5E3+-+40%2Asqrt%2810%29%2Ay%5E2+%2B+1000y ALIGN=MIDDLE  ALT=\"V+=+4y%5E3+-+40%2Asqrt%2810%29%2Ay%5E2+%2B+1000y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Check answer:<BR>\n" );
document.write( "Suppose <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+1 ALIGN=MIDDLE  ALT=\"y+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That would mean <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+10%2Asqrt%2810%29+-+2 ALIGN=MIDDLE  ALT=\"x+=+10%2Asqrt%2810%29+-+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+1%2A%281000+-+40%2Asqrt%2810%29%29+%2B+4 ALIGN=MIDDLE  ALT=\"V+=+1%2A%281000+-+40%2Asqrt%2810%29%29+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+1004+-+40%2Asqrt%2810%29 ALIGN=MIDDLE  ALT=\"V+=+1004+-+40%2Asqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The equation gives me:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+4y%5E3+-+40%2Asqrt%2810%29%2Ay%5E2+%2B+1000y ALIGN=MIDDLE  ALT=\"V+=+4y%5E3+-+40%2Asqrt%2810%29%2Ay%5E2+%2B+1000y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+4+-+40%2Asqrt%2810%29+%2B+1000 ALIGN=MIDDLE  ALT=\"V+=+4+-+40%2Asqrt%2810%29+%2B+1000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "same answer </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );