document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=230357>Question 230357</A>: <I><SPAN STYLE=\"word-break: break-all;\"> pleeeeeeeeeeeeease help me! my assignment is due in 4 hours!!!!\r<BR>\n" );
document.write( "\n" );
document.write( "a box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 in. by 20 in. by cutting out equal squares of side x at each corner and then folding up the sides\r<BR>\n" );
document.write( "\n" );
document.write( "a) find a function that models the volume of the box<BR>\n" );
document.write( "b) find the values of x for which the volume is greater than 200 in^3<BR>\n" );
document.write( "c) find the largest volume that such a box can have. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #170588 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=170588\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 in. by 20 in. by cutting out equal squares of side x at each corner and then folding up the sides <BR>\n" );
document.write( "a) find a function that models the volume of the box<BR>\n" );
document.write( "Draw the picture of the rectangular piece<BR>\n" );
document.write( "Sketch the square corners that are cut out of the rectangle.<BR>\n" );
document.write( "Each square has dimensions x by x.<BR>\n" );
document.write( "Imagine folding up the sides to form a box.<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "The base of the box is (12-2x)by(20-2x) in area<BR>\n" );
document.write( "The height of the box is x<BR>\n" );
document.write( "The Volume of the box is x(12-2x)(20-2x)<BR>\n" );
document.write( "V = x(240-24x-40x+4x^2)<BR>\n" );
document.write( "V = 4x^3 - 64x^2 + 240x<BR>\n" );
document.write( "-------------------------------------<BR>\n" );
document.write( "b) find the values of x for which the volume is greater than 200 in^3<BR>\n" );
document.write( "Solve 4x^3 - 64x^2 + 240x - 200 > 0<BR>\n" );
document.write( "I graphed it and found the x value is greater than 10.928...<BR>\n" );
document.write( "But that x-value is not possible since one of the base dimensions<BR>\n" );
document.write( "is 20-2x.  So no x value gives a volume greater than 200 in^3<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "c) find the largest volume that such a box can have.<BR>\n" );
document.write( "I'll leave that to you.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );