document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=409077>Question 409077</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When mineral deposits formed a coating 1mm thick on the inside of a pipe the area through wich fluid can flow was reduced by 20%. Find the original inside diameter of the pipe.<BR>\n" );
document.write( "(Remeber: area of circle = pi(r^2) and diameter = 2r)<BR>\n" );
document.write( "Thanks for the help =) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #288050 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=288050\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I think they are saying that the area of the pipe opening has been<BR>\n" );
document.write( "reduced by 20%.<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > = original area<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > = original radius<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "If the diameter is reduced by 1 mm, then the <BR>\n" );
document.write( "radius is reduced by .5 mm.<BR>\n" );
document.write( "given:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"A+=+pi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+-+.2A+=+pi%2A%28r+-+.5%29%5E2 ALIGN=MIDDLE  ALT=\"A+-+.2A+=+pi%2A%28r+-+.5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.8A+=+pi%2A%28r+-+.5%29%5E2 ALIGN=MIDDLE  ALT=\".8A+=+pi%2A%28r+-+.5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "substituting from (1):<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.8%2Api%2Ar%5E2+=+pi%2A%28r%5E2+-+r+%2B+.25%29 ALIGN=MIDDLE  ALT=\".8%2Api%2Ar%5E2+=+pi%2A%28r%5E2+-+r+%2B+.25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.8%2Ar%5E2+=+r%5E2+-+r+%2B+.25 ALIGN=MIDDLE  ALT=\".8%2Ar%5E2+=+r%5E2+-+r+%2B+.25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.2r%5E2+-+r+%2B+.25+=+0 ALIGN=MIDDLE  ALT=\".2r%5E2+-+r+%2B+.25+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20r%5E2+-+100r+%2B+25+=+0 ALIGN=MIDDLE  ALT=\"20r%5E2+-+100r+%2B+25+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4r%5E2+-+20r+%2B+5+=+0 ALIGN=MIDDLE  ALT=\"4r%5E2+-+20r+%2B+5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"r+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%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+=+4 ALIGN=MIDDLE  ALT=\"a+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+-20 ALIGN=MIDDLE  ALT=\"b+=+-20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+5 ALIGN=MIDDLE  ALT=\"c+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28-%28-20%29+%2B-+sqrt%28+%28-20%29%5E2-4%2A4%2A5+%29%29%2F%282%2A4%29+ ALIGN=MIDDLE  ALT=\"r+=+%28-%28-20%29+%2B-+sqrt%28+%28-20%29%5E2-4%2A4%2A5+%29%29%2F%282%2A4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%2820+%2B-+sqrt%28+400+-+80+%29%29%2F8+ ALIGN=MIDDLE  ALT=\"r+=+%2820+%2B-+sqrt%28+400+-+80+%29%29%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%2820+%2B-+sqrt%28+320+%29%29%2F8+ ALIGN=MIDDLE  ALT=\"r+=+%2820+%2B-+sqrt%28+320+%29%29%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%2820+%2B+8%2Asqrt%285%29%29%2F8 ALIGN=MIDDLE  ALT=\"r+=+%2820+%2B+8%2Asqrt%285%29%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+5%2F2+%2B+sqrt%285%29 ALIGN=MIDDLE  ALT=\"r+=+5%2F2+%2B+sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+4.736 ALIGN=MIDDLE  ALT=\"r+=+4.736\"   DISABLED_style= \"max-width:90%; height:auto;\" > mm<BR>\n" );
document.write( "The original diameter = 2r, or 9.472 mm<BR>\n" );
document.write( "check answer:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+-+.2A+=+pi%2A%28r+-+.5%29%5E2 ALIGN=MIDDLE  ALT=\"A+-+.2A+=+pi%2A%28r+-+.5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.8A+=+pi%2A%284.736+-+.5%29%5E2 ALIGN=MIDDLE  ALT=\".8A+=+pi%2A%284.736+-+.5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.8A+=+pi%2A4.236%5E2 ALIGN=MIDDLE  ALT=\".8A+=+pi%2A4.236%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.8A+=+3.141%2A17.944 ALIGN=MIDDLE  ALT=\".8A+=+3.141%2A17.944\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.8A+=+56.361 ALIGN=MIDDLE  ALT=\".8A+=+56.361\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+70.451 ALIGN=MIDDLE  ALT=\"A+=+70.451\"   DISABLED_style= \"max-width:90%; height:auto;\" > mm2<BR>\n" );
document.write( "and<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"A+=+pi%2Ar%5E2\"   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+=+3.141%2A4.736%5E2 ALIGN=MIDDLE  ALT=\"A+=+3.141%2A4.736%5E2\"   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+=+70.451 ALIGN=MIDDLE  ALT=\"A+=+70.451\"   DISABLED_style= \"max-width:90%; height:auto;\" > mm2<BR>\n" );
document.write( "OK<BR>\n" );
document.write( "Hope I got it\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );