document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=900733>Question 900733</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The radius of the base of each of two right circular cones is 8 inches. The altitude of the first cone is 9 greater than that of the second cone and its slant height is 7 inches greater than that of the second. Find the altitude of the taller cone. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #546554 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=546554\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The radius of the base of each of two right circular cones is 8 inches.<BR>\n" );
document.write( " The altitude of the first cone is 9 greater than that of the second cone<BR>\n" );
document.write( " and its slant height is 7 inches greater than that of the second.<BR>\n" );
document.write( " Find the altitude of the taller cone.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "This can be done by considering two right triangles, using pythag formulas<BR>\n" );
document.write( "let x = the height of taller cone<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(x-9) = the height of the smaller cone<BR>\n" );
document.write( "The slant dimensions are the hypotenuses<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2%2B8%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2%2B8%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - 7 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x-9%29%5E2+%2B+8%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28x-9%29%5E2+%2B+8%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=sqrt%28x%5E2%2B64%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2%2B64%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - 7 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x%5E2-18x%2B81%29%2B64%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28x%5E2-18x%2B81%29%2B64%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2%2B64%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2%2B64%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - 7 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x%5E2-18x%2B145%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28x%5E2-18x%2B145%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "square both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+64+-+14sqrt%28x%5E2%2B64%29+%2B+49+=+x%5E2+-+18x+%2B+145 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+64+-+14sqrt%28x%5E2%2B64%29+%2B+49+=+x%5E2+-+18x+%2B+145\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "subtract x^2 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64+-+14sqrt%28x%5E2%2B64%29+%2B+49+=+-+18x+%2B+145 ALIGN=MIDDLE  ALT=\"64+-+14sqrt%28x%5E2%2B64%29+%2B+49+=+-+18x+%2B+145\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-14sqrt%28x%5E2%2B64%29+%2B+113+=+-+18x+%2B+145 ALIGN=MIDDLE  ALT=\"-14sqrt%28x%5E2%2B64%29+%2B+113+=+-+18x+%2B+145\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-14sqrt%28x%5E2%2B64%29+=+-+18x+%2B+145+-+113 ALIGN=MIDDLE  ALT=\"-14sqrt%28x%5E2%2B64%29+=+-+18x+%2B+145+-+113\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-14sqrt%28x%5E2%2B64%29+=+-18x+%2B+32 ALIGN=MIDDLE  ALT=\"-14sqrt%28x%5E2%2B64%29+=+-18x+%2B+32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "simplify, change the signs, divide by -2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7sqrt%28x%5E2%2B64%29+=+9x+-+16 ALIGN=MIDDLE  ALT=\"7sqrt%28x%5E2%2B64%29+=+9x+-+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "square both sides<BR>\n" );
document.write( "49(x^2 + 64) = 81x^2 - 288x + 256<BR>\n" );
document.write( "49x^2 + 3136 = 81x^2 - 288x + 256<BR>\n" );
document.write( "combine like terms on the right<BR>\n" );
document.write( "0 = 81x^2 - 49x^2 - 288x + 256 - 3136<BR>\n" );
document.write( "0 = 32x^2 - 288x - 2880<BR>\n" );
document.write( "simplify divide by 32<BR>\n" );
document.write( "x^2 - 9x - 90 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(x-15)(x+6) = <BR>\n" );
document.write( "the positive solution here<BR>\n" );
document.write( "x = 15 in is the altitude of the taller cone<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "See if that checks out the height of the smaller will be 6<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2815%5E2%2B8%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2815%5E2%2B8%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 17<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%286%5E2%2B8%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%286%5E2%2B8%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  = 10<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "slant differences 7 in </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );