document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=106902>Question 106902</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I was wondering if you could help me with this question! I dont even know where to start! Thank you!<BR>\n" );
document.write( "It is estimated that the average diameter of peeled logs coming into your sawmill is 14 inches.<BR>\n" );
document.write( "a) What is the thickness of the largest square timber that can be cut from the average log?<BR>\n" );
document.write( "b)If the rest of the log is made into mulch, what percent of the original log is the square timber? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #77773 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=77773\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In other words, you have a 14\" circle, what is the largest square that can fit inside of your circle. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+300%2C+300%2C+-1.2%2C+1.2%2C+-1.2%2C+1.2%2Cgrid%28+1+%29%2Ccircle%28+0%2C+0%2C+1+%29%2C%0D%0A++red%28line%28+0%2C+0%2C+.707%2C+.707%29%29%2C%0D%0Alocate%28.1%2C.55%2C7+in%29%2C%0D%0Alocate%28.5%2C-.2%2Cs%29%2C%0D%0Agreen%28line%28+-.707%2C+.707%2C+.707%2C+.707%29%29%2C%0D%0Agreen%28line%28++.707%2C+.707%2C+.707%2C-.707%29%29%2C%0D%0Agreen%28line%28++.707%2C-.707%2C-.707%2C-.707%29%29%2C%0D%0Agreen%28line%28+-.707%2C-.707%2C-.707%2C+.707%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The diagonal line is also the radius of the circle (7 inches). <BR>\n" );
document.write( "The diagonal line is also the hypotenuse of the right, isoceles triangle with sides s,s, and 7 inches. <BR>\n" );
document.write( "Since it's a right triangle, you can use the Pythagorean theorem. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2%2Bs%5E2=7%5E2 ALIGN=MIDDLE  ALT=\"s%5E2%2Bs%5E2=7%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2s%5E2=7%5E2 ALIGN=MIDDLE  ALT=\"2s%5E2=7%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=7%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"s=7%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The side of the square is 2s long, so the largest square that can be cut from the circle will be <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=2s=14%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"t=2s=14%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t=9.9 inches<BR>\n" );
document.write( "b) The area of the circle equals the area of the square plus the leftover(mulch). <BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bc%5D=A%5Bs%5D%2BA%5Bm%5D ALIGN=MIDDLE  ALT=\"A%5Bc%5D=A%5Bs%5D%2BA%5Bm%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Percentage of mulch area to total area is equal to <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bm%5D%2FA%5Bc%5D ALIGN=MIDDLE  ALT=\"A%5Bm%5D%2FA%5Bc%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide equation 1. by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bc%5D ALIGN=MIDDLE  ALT=\"A%5Bc%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bc%5D%2FA%5Bc%5D=A%5Bs%5D%2FA%5Bc%5D%2BA%5Bm%5D%2FA%5Bc%5D ALIGN=MIDDLE  ALT=\"A%5Bc%5D%2FA%5Bc%5D=A%5Bs%5D%2FA%5Bc%5D%2BA%5Bm%5D%2FA%5Bc%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=t%5E2%2F%28pi%29R%5E2%2BA%5Bm%5D%2FA%5Bc%5D ALIGN=MIDDLE  ALT=\"1=t%5E2%2F%28pi%29R%5E2%2BA%5Bm%5D%2FA%5Bc%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bm%5D%2FA%5Bc%5D=1-t%5E2%2F%28pi%29R%5E2 ALIGN=MIDDLE  ALT=\"A%5Bm%5D%2FA%5Bc%5D=1-t%5E2%2F%28pi%29R%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bm%5D%2FA%5Bc%5D=1-%2814%5E2%2F2%29%2F%28%28pi%29%2A7%5E2%29 ALIGN=MIDDLE  ALT=\"A%5Bm%5D%2FA%5Bc%5D=1-%2814%5E2%2F2%29%2F%28%28pi%29%2A7%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bm%5D%2FA%5Bc%5D=1-%28128%29%2F%28153.9%29 ALIGN=MIDDLE  ALT=\"A%5Bm%5D%2FA%5Bc%5D=1-%28128%29%2F%28153.9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bm%5D%2FA%5Bc%5D=.168 ALIGN=MIDDLE  ALT=\"A%5Bm%5D%2FA%5Bc%5D=.168\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "16.8% of the tree ends up as mulch. <BR>\n" );
document.write( "83.2% of the tree ends up as the square.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );