document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=54909>Question 54909</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618073639/algebrahomeworkh>Applied College Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> 74. An open box is to be made from a square piece of cardboard of dimensions 30 inches by 30 inches by cutting out squares of area x^2 from each corner.<BR>\n" );
document.write( "a. Express the volume V of the box as a function of x.<BR>\n" );
document.write( "b. State the domain of V. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #37162 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=37162\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 74. An open box is to be made from a square piece of cardboard of dimensions 30 inches by 30 inches by cutting out squares of area x^2 from each corner.<BR>\n" );
document.write( "a. Express the volume V of the box as a function of x.<BR>\n" );
document.write( "b. State the domain of V.<BR>\n" );
document.write( "Each side of the square would look like x--------x, if the length started out as 30 inches, then each side would be 30-2x.<BR>\n" );
document.write( "V=L*W*H<BR>\n" );
document.write( "The height is x.<BR>\n" );
document.write( "Length and width are the same because it has a square base.<BR>\n" );
document.write( "a. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%28x%29=%2830-2x%29%2830-2x%29%2Ax ALIGN=MIDDLE  ALT=\"V%28x%29=%2830-2x%29%2830-2x%29%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%28x%29=%2830-2x%29%5E2%2Ax ALIGN=MIDDLE  ALT=\"V%28x%29=%2830-2x%29%5E2%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b.Each dimension has to be greater than 0.<BR>\n" );
document.write( "x>0 and 30-2x>0<BR>\n" );
document.write( "30-2x>0<BR>\n" );
document.write( "-30+30-2x>0-30<BR>\n" );
document.write( "-2x>-30<BR>\n" );
document.write( "-2x/-2<-30/-2<BR>\n" );
document.write( "x<15in<BR>\n" );
document.write( "Therefore <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3Cx%3C15in ALIGN=MIDDLE  ALT=\"0%3Cx%3C15in\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the domain.<BR>\n" );
document.write( "Interval notation: (0,15in)<BR>\n" );
document.write( "Happy Calculating!!!  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );