document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1174860>Question 1174860</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I really need help with this problem, I'd appreciate a detailed explanation too because it's really important!!!\r<BR>\n" );
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document.write( "You have a flat sheet of cardboard that is 10 inches long and 8 inches wide. You need to make a box that has the maximum area. So you decide to cut out square corners of the sheet of cardboard, and fold the cardboard to make a box. Let x represent the side of each little square you cut out. Write a function for the area of the box and use your graphing calculator to graph it. \r<BR>\n" );
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document.write( "What is the maximum area of your box, and what value of x gives you that maximum area? Be sure to justify your answer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #800331 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=800331\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have a flat sheet of cardboard that is 10 inches long and 8 inches wide.<BR>\n" );
document.write( " You need to make a box that has the maximum volume.<BR>\n" );
document.write( " So you decide to cut out square corners of the sheet of cardboard, and fold the cardboard to make a box.<BR>\n" );
document.write( " Let x represent the side of each little square you cut out.<BR>\n" );
document.write( " Write a function for the volume of the box and use your graphing calculator to graph it.<BR>\n" );
document.write( "What is the maximum volume of your box, and what value of x gives you that maximum area?<BR>\n" );
document.write( " Be sure to justify your answer.<BR>\n" );
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document.write( "the dimensions of the box will be<BR>\n" );
document.write( "(10-2x) by (8-2x) by x, which is the height<BR>\n" );
document.write( "f(x) = Volume<BR>\n" );
document.write( "V = (10-2x)*(8-2x)*x<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "v = (80-20x-16x+4x^2)*x<BR>\n" );
document.write( "V = (80-36x+ 4x^2)*x<BR>\n" );
document.write( "multiply by x, arrange in the standard order<BR>\n" );
document.write( "V = 4x^3 - 36x^2 = 80x<BR>\n" );
document.write( "Graph this equation, volume is on the vertical axis, x is the horizontal<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-2%2C+5%2C+-10%2C+70%2C+4x%5E3-36x%5E2%2B80x%2C+52.5%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-2%2C+5%2C+-10%2C+70%2C+4x%5E3-36x%5E2%2B80x%2C+52.5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "calc shows max volume is when x = 1.47 inches and <BR>\n" );
document.write( "then the max vol = 52.5 cu/in (green line)<BR>\n" );
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document.write( "You can confirms this by replacing 1.47 for x in the original equation, and finding the volume </SPAN>\n" );
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