document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=364992>Question 364992</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have worked this problem before and got it wrong and so I'm trying to fix it to get second chance credit but I just dont understand it. Can someone please help?\r<BR>\n" );
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document.write( "Let X[cm] be the diameter of bolts in a production. Assume that X has the density f(x)=k(x-0.9)(1.1-x) if 0.9< x <1.1 and 0 otherwise. Determine k. graph f(x), and the mean and variance. \r<BR>\n" );
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document.write( "I dont know if there is any way to put graphs on here but if not can you please try and help as much as possible. I would so appreciate it.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #260232 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=260232\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The integral of the density function from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.9 ALIGN=MIDDLE  ALT=\"x=0.9\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1.1 ALIGN=MIDDLE  ALT=\"x=1.1\"   DISABLED_style= \"max-width:90%; height:auto;\" > must equal <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28k%28x-0.9%29%281.1-x%29%2Cdx%2C0.9%2C1.1%29=1 ALIGN=MIDDLE  ALT=\"int%28k%28x-0.9%29%281.1-x%29%2Cdx%2C0.9%2C1.1%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%2Aint%28%28-x%5E2%2B2x-%2899%2F100%29%29%2Cdx%2C0.9%2C1.1%29=1 ALIGN=MIDDLE  ALT=\"k%2Aint%28%28-x%5E2%2B2x-%2899%2F100%29%29%2Cdx%2C0.9%2C1.1%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28%281.1%29%5E3-%280.9%29%5E3%29%2F3%2B%281.1%29%5E2-%280.9%29%5E2-%2899%2F100%29%281.1-0.9%29=1%2Fk ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28%281.1%29%5E3-%280.9%29%5E3%29%2F3%2B%281.1%29%5E2-%280.9%29%5E2-%2899%2F100%29%281.1-0.9%29=1%2Fk ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-602%2F3000%2B1200%2F3000-594%2F3000=1%2Fk ALIGN=MIDDLE  ALT=\"-602%2F3000%2B1200%2F3000-594%2F3000=1%2Fk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fk=4%2F3000 ALIGN=MIDDLE  ALT=\"1%2Fk=4%2F3000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28k=750%29 ALIGN=MIDDLE  ALT=\"highlight%28k=750%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C0.9%2C1.1%2C-1%2C8%2C750%28x-0.9%29%281.1-x%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C0.9%2C1.1%2C-1%2C8%2C750%28x-0.9%29%281.1-x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The left endpoint is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.9 ALIGN=MIDDLE  ALT=\"x=0.9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the right endpoint is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1.1 ALIGN=MIDDLE  ALT=\"x=1.1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The peak of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.5 ALIGN=MIDDLE  ALT=\"7.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > occurs when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Now that you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > you can solve for the mean and the variance.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu=int%28x%2Ap%28x%29%2Cdx%29=k%2Aint%28%28-x%5E3%2B2x%5E2-%2899%2F100%29x%29%2Cdx%2C0.9%2C1.1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu%2Fk=-0.25%28%281.1%29%5E4-0.9%5E4%29%2B%282%2F3%29%28%281.1%29%5E3-0.9%5E3%29-%2899%2F2000%29%281.1-0.9%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28mu=1%29 ALIGN=MIDDLE  ALT=\"highlight%28mu=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=int%28%28x-1%29%5E2%2Ap%28x%29%2Cdx%29=k%2Aint%28%28-x%5E4%2B4x%5E3-%28599%2F100%29x%5E2%2B%28398%2F100%29x-99%2F100%29%2Cdx%2C0.9%2C1.1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%2Fk=-%281%2F5%29%28%281.1%29%5E5-0.9%5E5%29%2B%28599%2F300%29%28%281.1%29%5E3-0.9%5E3%29%2B%28199%2F100%29%281.1%5E2-0.9%5E2%29-0.99%281.1-0.9%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%2Fk=8%2F3000000 ALIGN=MIDDLE  ALT=\"V%2Fk=8%2F3000000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28V=1%2F500%29 ALIGN=MIDDLE  ALT=\"highlight%28V=1%2F500%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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