document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=662171>Question 662171</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sailboat Races	The speed that a sailboat is capable of sailing is determined by three factors: its total length L, the surface area A of its sails, and its displacement V (the volume of water it displaces), as shown in the sketch.<BR>\n" );
document.write( "	In general, a sailboat is capable of greater speed if it is longer, has a larger sail area, or displaces less water. To make sailing races fair, only boats in the same “class” can qualify to race together. For certain race, a boat is considered to qualify if<BR>\n" );
document.write( "0.30L	+	0.38A1/2		-	3V1/3	&#8804;	16<BR>\n" );
document.write( "Where L is measured in feet, A in square feet , and V in cubic feet. Use this inequality to answer the following questions.<BR>\n" );
document.write( "(a)	A sailboat has length 60ft, a sail area 3400ft2, and displacement 650ft3. Does this boat qualify for the race?<BR>\n" );
document.write( "(b)	A sailboat has length 65ft and displaces 600ft3. What is the largest possible sail area that could be used and still allow the boat to qualify for this race? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #412115 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=412115\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sailboat Races The speed that a sailboat is capable of sailing is determined by three factors: its total length L, the surface area A of its sails, and its displacement V (the volume of water it displaces), as shown in the sketch.<BR>\n" );
document.write( "In general, a sailboat is capable of greater speed if it is longer, has a larger sail area, or displaces less water. To make sailing races fair, only boats in the same “class” can qualify to race together. For certain race, a boat is considered to qualify if<BR>\n" );
document.write( "0.30L + 0.38A1/2 - 3V1/3 &#8804; 16<BR>\n" );
document.write( "Where L is measured in feet, A in square feet , and V in cubic feet. Use this inequality to answer the following questions.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The formula: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.30L+%2B+0.38A%5E%281%2F2%29+-+3V%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"0.30L+%2B+0.38A%5E%281%2F2%29+-+3V%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > =< 16<BR>\n" );
document.write( ":<BR>\n" );
document.write( "(a) A sailboat has length 60ft, a sail area 3400ft2, and displacement 650ft3. Does this boat qualify for the race?<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.30%2860%29+%2B+0.38%283400%5E%281%2F2%29%29+-+3%28650%5E%281%2F3%29%29 ALIGN=MIDDLE  ALT=\"0.30%2860%29+%2B+0.38%283400%5E%281%2F2%29%29+-+3%28650%5E%281%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > =< 16<BR>\n" );
document.write( "do the math<BR>\n" );
document.write( " 18 + 22.2 - 26 = 14.2, less than 16, would qualify<BR>\n" );
document.write( ":<BR>\n" );
document.write( "(b) A sailboat has length 65ft and displaces 600ft3. What is the largest possible sail area that could be used and still allow the boat to qualify for this race?<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.30%2865%29+%2B+0.38A%5E%281%2F2%29+-+3%28600%5E%281%2F3%29%29 ALIGN=MIDDLE  ALT=\"0.30%2865%29+%2B+0.38A%5E%281%2F2%29+-+3%28600%5E%281%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > =< 16<BR>\n" );
document.write( "19.5 + .38A^(1/2) - 25.3 =< 16<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.38A%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\".38A%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - 5.8 =<16<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.38A%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\".38A%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > =< 16 + 5.8<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.38A%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\".38A%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > =< 21.8<BR>\n" );
document.write( "Divide both sides by .38<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"A%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 57.4<BR>\n" );
document.write( "Find the square of both sides<BR>\n" );
document.write( "A = 3291 sq/ft of sail area should qualify<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check that<BR>\n" );
document.write( ".3(65) + .38(3291^(1/2)) - 3(600^(1/3) =< 16<BR>\n" );
document.write( "19.5 + 21.8 - 25.3 = 16; just qualifies<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );