document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=885774>Question 885774</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A stream of water in steady flow from a kitchen faucet. At the faucet the diameter of stream is 0.96 cm. The stream fills a 125 cm^3 in 16.3 seconds. Find the diameter of the stream 13 cm below the opening of the faucet. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #535417 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=535417\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A stream of water in steady flow from a kitchen faucet. At the faucet the diameter of stream is 0.96 cm. The stream fills a 125 cm^3 in 16.3 seconds. Find the diameter of the stream 13 cm below the opening of the faucet.<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Find the speed of the stream at the faucet:<BR>\n" );
document.write( "Flow rate = Vol/sec = area*speed = 125/16.3 cc/sec<BR>\n" );
document.write( "area*speed = 125/16.3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=area+=+pi%2Ar%5E2+=+0.48%5E2%2Api+=+0.2304pi ALIGN=MIDDLE  ALT=\"area+=+pi%2Ar%5E2+=+0.48%5E2%2Api+=+0.2304pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > (area at the faucet)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=speed+=+%28125%2F16.3%29%2F%280.2304pi%29 ALIGN=MIDDLE  ALT=\"speed+=+%28125%2F16.3%29%2F%280.2304pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "speed =~ 10.595 cm/sec (speed at the faucet)<BR>\n" );
document.write( "------<BR>\n" );
document.write( "Use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-4.9t%5E2+-+10.595t ALIGN=MIDDLE  ALT=\"h%28t%29+=+-4.9t%5E2+-+10.595t\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find the time it takes to fall 13 cm<BR>\n" );
document.write( "13 cm = 0.13 meters<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-4.9t%5E2+-+10.595t+=+-0.13 ALIGN=MIDDLE  ALT=\"h%28t%29+=+-4.9t%5E2+-+10.595t+=+-0.13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4.9t%5E2+-+10.595t+%2B+0.13+=+0 ALIGN=MIDDLE  ALT=\"-4.9t%5E2+-+10.595t+%2B+0.13+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4.9x%5E2%2B-10.595x%2B0.13+=+0 ALIGN=MIDDLE  ALT=\"-4.9x%5E2%2B-10.595x%2B0.13+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-10.595%29%5E2-4%2A-4.9%2A0.13=114.802025 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-10.595%29%5E2-4%2A-4.9%2A0.13=114.802025\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=114.802025 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--10.595%2B-sqrt%28+114.802025+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--10.595%2B-sqrt%28+114.802025+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-10.595%29%2Bsqrt%28+114.802025+%29%29%2F2%5C-4.9+=+-2.17444598843739 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-10.595%29%2Bsqrt%28+114.802025+%29%29%2F2%5C-4.9+=+-2.17444598843739\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-10.595%29-sqrt%28+114.802025+%29%29%2F2%5C-4.9+=+0.0122010904782066 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-10.595%29-sqrt%28+114.802025+%29%29%2F2%5C-4.9+=+0.0122010904782066\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4.9x%5E2%2B-10.595x%2B0.13 ALIGN=MIDDLE  ALT=\"-4.9x%5E2%2B-10.595x%2B0.13\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4.9x%5E2%2B-10.595x%2B0.13+=+%28x--2.17444598843739%29%2A%28x-0.0122010904782066%29 ALIGN=MIDDLE  ALT=\"-4.9x%5E2%2B-10.595x%2B0.13+=+%28x--2.17444598843739%29%2A%28x-0.0122010904782066%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -2.17444598843739, 0.0122010904782066.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4.9%2Ax%5E2%2B-10.595%2Ax%2B0.13+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4.9%2Ax%5E2%2B-10.595%2Ax%2B0.13+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "====================<BR>\n" );
document.write( "t = 0.0122 seconds<BR>\n" );
document.write( "The water is accelerated at 9.8m/sec/sec<BR>\n" );
document.write( "Its speed after 0.0122 seconds is 0.10595 m/sec + 9.8*0.0122<BR>\n" );
document.write( "= 0.22551 m/sec<BR>\n" );
document.write( "= 22.551 cm/sec<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Area at that speed = (125/16.3)/22.551 sq cm<BR>\n" );
document.write( "Area =~ 0.3400608 sq cm = pi*r^2<BR>\n" );
document.write( "r = 0.329 cm<BR>\n" );
document.write( "d = 0.658 cm<BR>\n" );
document.write( "=======================<BR>\n" );
document.write( "So you have 2 answers that don't agree.<BR>\n" );
document.write( "You can see how it's done.<BR>\n" );
document.write( "Check the work, pick the one you like.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );