document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190623>Question 1190623</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2. A square of side length x is cut from each corner of a piece of tin that is 14 inches by 18 inches.\r<BR>\n" );
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document.write( "a)Draw a diagram for this problem, be sure to label all lengths of this piece of tin.\r<BR>\n" );
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document.write( "b)The sides of the piece of tin are then folded up to form a box whose height is x inches. Write the volume V as a function of x ( V(x) = ...).\r<BR>\n" );
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document.write( "c)There are three values of x that make the volume equal to 0, what are these values? Are all three realistic? Why or why not?\r<BR>\n" );
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document.write( "d)What is the domain of V(x)? </SPAN>\n" );
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document.write( "a) I'll let you do the drawing....<br><BR>\n" );
document.write( "b) With squares of side length x cut off each corner of the piece of tin, the dimensions of the bottom of the box are 14-2x and 18-2x.  The volume -- length times width times height -- is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%28x%29=x%2814-2x%29%2818-2x%29 ALIGN=MIDDLE  ALT=\"V%28x%29=x%2814-2x%29%2818-2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "c) The expression for the volume is equal to 0 for x=0, x=7, and x=9.<BR>\n" );
document.write( "None of them is realistic -- a box with volume 0 is of no use.<br><BR>\n" );
document.write( "d) All three dimensions should be positive numbers.  However, mathematically, in determining the domain of the function, we need to allow dimensions that make the volume 0.<BR>\n" );
document.write( "x>0<BR>\n" );
document.write( "14-2x>0 --> x<7<BR>\n" );
document.write( "18-2x>0 --> x<9<br><BR>\n" );
document.write( "The \"realistic\" domain of V(x) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3Cx%3C7 ALIGN=MIDDLE  ALT=\"0%3Cx%3C7\"   DISABLED_style= \"max-width:90%; height:auto;\" >; the mathematical domain is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3C=x%3C=7 ALIGN=MIDDLE  ALT=\"0%3C=x%3C=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
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