document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=151691>Question 151691</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I can't figure out where I went wrong,  please help<BR>\n" );
document.write( "104 <BR>\n" );
document.write( "worker efficiency  In a study of worker efficiency at Wong Laboratories. it was found that the number of components assembled per hour by the average worker t hours after starting work could be modeled after the formula<BR>\n" );
document.write( "       N(t) = - 3t^2 + 23t^2 + 8t<BR>\n" );
document.write( "a. rewrite the formula by factoring the right hand side completely. <BR>\n" );
document.write( "b. Use the factored version of the formula to find N(3).<BR>\n" );
document.write( "c.  Use the graph to estimate the time at which the workers are most efficient.<BR>\n" );
document.write( "d. Use the accompanying graph to estimate the maximum number of components assembled per hour during an 8 hour period.\r<BR>\n" );
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document.write( "a. -t (3t^2 - 24 t - 8 )\r<BR>\n" );
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document.write( "   -t (3t + 1 )(t - 8)\r<BR>\n" );
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document.write( "b.<BR>\n" );
document.write( "if t = 3 \r<BR>\n" );
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document.write( "3N = -3 (3(3)+1)(3-8)\r<BR>\n" );
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document.write( "3N= -3(10)(-5)\r<BR>\n" );
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document.write( "3N= -3(-50)\r<BR>\n" );
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document.write( "3N= 150\r<BR>\n" );
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document.write( "N = 50\r<BR>\n" );
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document.write( "now the only problem i see is that according to the graph this<BR>\n" );
document.write( "should be 5 not 50  can you tell what I have done wrong?<BR>\n" );
document.write( "c. at 5 hours<BR>\n" );
document.write( "d. estimate 235-240 components during the 5th hour<BR>\n" );
document.write( "the total for the day is around 1275\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #111507 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=111507\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Well, you factoring is ok, except your initial formula is in error:<BR>\n" );
document.write( "You wrote:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%28t%29+=+-3highlight%28t%5E2%29%2B23t%5E2%2B8t ALIGN=MIDDLE  ALT=\"N%28t%29+=+-3highlight%28t%5E2%29%2B23t%5E2%2B8t\"   DISABLED_style= \"max-width:90%; height:auto;\" > but you did correct it later on by writing:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%28t%29+=+-3highlight%28t%5E3%29%2B23t%5E2%2B8t ALIGN=MIDDLE  ALT=\"N%28t%29+=+-3highlight%28t%5E3%29%2B23t%5E2%2B8t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If you factor this, you get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%28t%29+=+-t%283t%2B1%29%28t-8%29 ALIGN=MIDDLE  ALT=\"N%28t%29+=+-t%283t%2B1%29%28t-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is precisely what you got!<BR>\n" );
document.write( "Now you are asked to find N(3), so, setting t=3, we get...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%283%29+=+-3%283%2A3%2B1%29%283-8%29 ALIGN=MIDDLE  ALT=\"N%283%29+=+-3%283%2A3%2B1%29%283-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%283%29+=+-3%2810%29%28-5%29 ALIGN=MIDDLE  ALT=\"N%283%29+=+-3%2810%29%28-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%283%29+=+150 ALIGN=MIDDLE  ALT=\"N%283%29+=+150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You did err in this because you calculated 3*N, which was not asked for, and is not the same as N(3).<BR>\n" );
document.write( "Now let's see what the graph of the given function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%28t%29+=+-3t%5E3%2B23t%5E2%2B8t ALIGN=MIDDLE  ALT=\"N%28t%29+=+-3t%5E3%2B23t%5E2%2B8t\"   DISABLED_style= \"max-width:90%; height:auto;\" > shows: (In the graph, N(t) is the vertical axis while t is the horizontal axis.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C10%2C-50%2C300%2C-3x%5E3%2B23x%5E2%2B8x%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C10%2C-50%2C300%2C-3x%5E3%2B23x%5E2%2B8x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can see that at t = 3, N(t) = 150.<BR>\n" );
document.write( "And, at t = 5, N(t) = 240. </SPAN>\n" );
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