document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=205242>Question 205242</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0176157786/algebrahomeworkh>Advanced Functions & Introductory Calculus</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A tent has the shape of a triangular prism. The volume of the tent is (x^3+7x^2+11x+5) cubic units. The triangular face of the tent is (2x+2) units wide by (x+1) units high. How long is the tent? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #154923 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=154923\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> hand written notes and a picture can be found at the following website:<BR>\n" );
document.write( "http://theo.x10hosting.com/<BR>\n" );
document.write( "just click on 205242.1 and 205242.2<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the volume of your tent is the area of the face times the length.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the face is a triangle.<BR>\n" );
document.write( "the area of the face is (1/2)bh = (bh)/2 where:<BR>\n" );
document.write( "b = the base and<BR>\n" );
document.write( "h = the height.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the base is given as (2x+2) units wide.<BR>\n" );
document.write( "the height is given as (x+1) units high.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the area of the face is therefore:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282x%2B2%29%2A%28x%2B1%29%29 ALIGN=MIDDLE  ALT=\"%28%282x%2B2%29%2A%28x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >/2<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "this comes out to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%5E2+%2B+4x+%2B+2%29%2F2 ALIGN=MIDDLE  ALT=\"%282x%5E2+%2B+4x+%2B+2%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >k which reduces to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x%2B1 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the volume for this type of a triangular prism is:<BR>\n" );
document.write( "V = A*L<BR>\n" );
document.write( "where A is the area of the face and L is the length of the tent.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the volume is given as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+%2B+7x%5E2+%2B+11x+%2B+5 ALIGN=MIDDLE  ALT=\"x%5E3+%2B+7x%5E2+%2B+11x+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > cubic units.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "we know the area so we have to solve for L.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "L = V/A <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E3+%2B+7x%5E2+%2B+11x+%2B+5%29%2F%28x%5E2%2B2x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x%5E3+%2B+7x%5E2+%2B+11x+%2B+5%29%2F%28x%5E2%2B2x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "The division is shown on page 2 of the notes.<BR>\n" );
document.write( "The result of the division is L = x+5 units.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "That's your answer.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "to doublecheck, take (x+5) and multiply it by (x^2 + 2x + 1) and you'll get the volume of the tent.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "more information can be found at the following website:<BR>\n" );
document.write( "http://www.mathsteacher.com.au/year9/ch14_measurement/19_prism/prism.htm<BR>\n" );
document.write( "-----<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );