document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1142489>Question 1142489</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi Please help me.<BR>\n" );
document.write( "1. The depth d of a liquid in a bottle with a hole of area 0.5 cm2 in its side can be approximated by <BR>\n" );
document.write( "d = 0.0034t2 − 0.52518t + 20,<BR>\n" );
document.write( "where t is the time since a stopper was removed from the hole. When will the depth be 1 cm? Round to the nearest tenth of a second.\r<BR>\n" );
document.write( "\n" );
document.write( "2. A small pipe can fill a tank in 9 min more time than it takes a larger pipe to fill the same tank. Working together, the pipes can fill the tank in 6 min. How long would it take each pipe, working alone, to fill the tank?\r<BR>\n" );
document.write( "\n" );
document.write( "3. A car travels 238 mi. A second car, traveling 9 mph faster than the first car, makes the same trip in 1 h less time. Find the speed of each car.\r<BR>\n" );
document.write( "\n" );
document.write( "4. A homeowner hires a mason to lay a brick border around a rectangular patio that measures 8 ft by 10 ft. If the total area of the patio and border is 168 ft2, what is the width of the border?<BR>\n" );
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 #763198 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=763198\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. The depth d of a liquid in a bottle with a hole of area 0.5 cm2 in its side can be approximated by <BR>\n" );
document.write( "d = 0.0034t^2 − 0.52518t + 20, where t is the time since a stopper was removed from the hole. When will the depth be 1 cm? Round to the nearest tenth of a second.<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "d = 0.0034t^2 − 0.52518t + 20 = 1<BR>\n" );
document.write( "0.0034t^2 − 0.52518t + 19 = 0<BR>\n" );
document.write( "---<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=0.0034x%5E2%2B-0.52518x%2B19+=+0 ALIGN=MIDDLE  ALT=\"0.0034x%5E2%2B-0.52518x%2B19+=+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=%28-0.52518%29%5E2-4%2A0.0034%2A19=0.0174140324 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-0.52518%29%5E2-4%2A0.0034%2A19=0.0174140324\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=0.0174140324 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--0.52518%2B-sqrt%28+0.0174140324+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--0.52518%2B-sqrt%28+0.0174140324+%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-%28-0.52518%29%2Bsqrt%28+0.0174140324+%29%29%2F2%5C0.0034+=+96.6385644909046 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-0.52518%29%2Bsqrt%28+0.0174140324+%29%29%2F2%5C0.0034+=+96.6385644909046\"   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-%28-0.52518%29-sqrt%28+0.0174140324+%29%29%2F2%5C0.0034+=+57.8261413914483 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-0.52518%29-sqrt%28+0.0174140324+%29%29%2F2%5C0.0034+=+57.8261413914483\"   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=0.0034x%5E2%2B-0.52518x%2B19 ALIGN=MIDDLE  ALT=\"0.0034x%5E2%2B-0.52518x%2B19\"   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=0.0034x%5E2%2B-0.52518x%2B19+=+%28x-96.6385644909046%29%2A%28x-57.8261413914483%29 ALIGN=MIDDLE  ALT=\"0.0034x%5E2%2B-0.52518x%2B19+=+%28x-96.6385644909046%29%2A%28x-57.8261413914483%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 96.6385644909046, 57.8261413914483.\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+0.0034%2Ax%5E2%2B-0.52518%2Ax%2B19+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+0.0034%2Ax%5E2%2B-0.52518%2Ax%2B19+%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 = the smaller solution.<BR>\n" );
document.write( "========<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );