document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=388388>Question 388388</A>: <I><SPAN STYLE=\"word-break: break-all;\"> you decide to make a box. You have one piece of plastic with dimensions 15 in x 10 in, with squares cut from the corners to fold up the sides. <BR>\n" );
document.write( "a. Write an equation that represents the volume of the box without a cover.<BR>\n" );
document.write( "b. Graph your equation on graphing calculator<BR>\n" );
document.write( "c. Use a graph to find the dimensions of the box, to the nearest whole numbers, with the maximum volume.\r<BR>\n" );
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document.write( "THANK YOU SO VERY VERY VERY MUCH!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #274815 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=274815\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The piece of plastic is 15\" by 10\".<BR>\n" );
document.write( "The squares cut from each corner are x\" by x\".<BR>\n" );
document.write( "The volume of the box made from folding up the sides after the square corners have been removed can be expressed by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+x%28B%29 ALIGN=MIDDLE  ALT=\"V+=+x%28B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where B is the area of the bottom of the box and x is the height of the box sides:<BR>\n" );
document.write( "The area of the box bottom can be expressed by:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+=+%2810-2x%29%2815-2x%29 ALIGN=MIDDLE  ALT=\"B+=+%2810-2x%29%2815-2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the volume equation becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+x%2810-2x%29%2815-2x%29 ALIGN=MIDDLE  ALT=\"V+=+x%2810-2x%29%2815-2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+x%28150-50x%2B4x%5E2%29 ALIGN=MIDDLE  ALT=\"V+=+x%28150-50x%2B4x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+4x%5E3-50x%5E2%2B150x ALIGN=MIDDLE  ALT=\"V+=+4x%5E3-50x%5E2%2B150x\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is the equation for the volume of the box.<BR>\n" );
document.write( "The graph of this cubic equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C10%2C-50%2C140%2C4x%5E3-50x%5E2%2B150x%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C10%2C-50%2C140%2C4x%5E3-50x%5E2%2B150x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From the graph, you can see that the relative maximum (of y, the volume) occurs at about x = 2 (it's really 1.96187390745...), so the dimensions of the square cut-outs would be 2\" by 2\" to obtain the maximum volume. </SPAN>\n" );
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