document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1087689>Question 1087689</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help, I'm stuck!\r<BR>\n" );
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document.write( "A machinist is to manufacture a circular metal disk with area 900&#120587; cm2\r<BR>\n" );
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document.write( "a) What is the ideal radius of such a disk? (gives exactly 900&#120587; cm2<BR>\n" );
document.write( "area)\r<BR>\n" );
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document.write( "b) If the machinist is allowed a tolerance of ± 10 &#119888;&#119898;2<BR>\n" );
document.write( "in producing such a disk, by how much can the radius vary from the ideal radius found in part a)?\r<BR>\n" );
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document.write( "c) In terms of the &#120576;, &#120575; definition of lim&#119909;&#8594;&#119886; &#119891;(&#119909;) = &#119871;, what is x? What is &#119891;(&#119909;)? What is &#119886;? What is &#119871;? What value of &#120576; is given and what is the corresponding value of &#120575;? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #702112 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=702112\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Area+=+pi%2Ar%5E2+ ALIGN=MIDDLE  ALT=\"+Area+=+pi%2Ar%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+900pi+=+pi%2Ar%5E2+ ALIGN=MIDDLE  ALT=\"+900pi+=+pi%2Ar%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > —> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+900+=+r%5E2+ ALIGN=MIDDLE  ALT=\"+900+=+r%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > —> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%28r+=+30cm%29+ ALIGN=MIDDLE  ALT=\"+highlight%28r+=+30cm%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b)  For a tolerance of +/- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10cm%5E2+ ALIGN=MIDDLE  ALT=\"+10cm%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the Area A can fall in this range: (approx) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+896.8%28pi%29cm%5E2+%3C=+A+%3C=+903.2%28pi%29cm%5E2 ALIGN=MIDDLE  ALT=\"+896.8%28pi%29cm%5E2+%3C=+A+%3C=+903.2%28pi%29cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > so the radius can vary over the range <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28896.2%29+%3C=+r+%3C=+sqrt%28903.2%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28896.2%29+%3C=+r+%3C=+sqrt%28903.2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >cm<BR>\n" );
document.write( "or approx. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+29.937+%3C=+r+%3C=+30.053+ ALIGN=MIDDLE  ALT=\"+29.937+%3C=+r+%3C=+30.053+\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm so that means the radius can vary approx.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-0.063+%3C=+v+%3C=+0.053+ ALIGN=MIDDLE  ALT=\"+-0.063+%3C=+v+%3C=+0.053+\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm from the ideal (v = variation from ideal).\r<BR>\n" );
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document.write( "c)  <BR>\n" );
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document.write( "           x is the independent variable, I'd say it corresponds to 'r' in the above.\r\n" );
document.write( "         f(x) is a function of x,  and it corresponds to Area in the above.\r\n" );
document.write( "           a  is a constant that x approaches, (30cm)\r\n" );
document.write( "           L  is the limit,   ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+900%28pi%29cm%5E2+ ALIGN=MIDDLE  ALT=\"+900%28pi%29cm%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > )\r\n" );
document.write( "          The limit is defined such that for 0<|x-p|<<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=delta ALIGN=MIDDLE  ALT=\"delta\"   DISABLED_style= \"max-width:90%; height:auto;\" >,   |f(x) - L| < <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+epsilon+ ALIGN=MIDDLE  ALT=\"+epsilon+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  for real <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=epsilon%3E0 ALIGN=MIDDLE  ALT=\"epsilon%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and real <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+delta+%3E+0 ALIGN=MIDDLE  ALT=\"+delta+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.   My guess is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+%3C+delta+%3C=+0.053cm+ ALIGN=MIDDLE  ALT=\"+0+%3C+delta+%3C=+0.053cm+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0%3Cepsilon%3C=10cm%5E2+ ALIGN=MIDDLE  ALT=\"+0%3Cepsilon%3C=10cm%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r\n" );
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document.write( " </PRE>          \r<BR>\n" );
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