document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=196647>Question 196647</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I keep getting the incorrect answer to the following problem, I'm not sure where my error was, can you help me? \r<BR>\n" );
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document.write( "One method for determining the depth of a well is to drop a stone into it and then measure the time it takes until the splash is heard. If d is the depth of the well (in feet) and t1 the time (in seconds) it takes for the stone to fall, then d = 16t1^2, so t1 = &#8730;d/4. Now if t2 is the time it takes for the sound to travel back up, then d = 1090t2 because the speed of sound is 1090 ft/s. So t2 = d/1090. Thus, the total time elapsed between dropping the stone and hearing the splash is given by the following equation.<BR>\n" );
document.write( "t1 + t2 = &#8730;d/4 + d/1090<BR>\n" );
document.write( "How deep is the well if this total time is 2.3 s? (Round the answer to the nearest whole number.)\r<BR>\n" );
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document.write( "thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #147391 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=147391\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> t1 + t2 = &#8730;d/4 + d/1090<BR>\n" );
document.write( "How deep is the well if this total time is 2.3 s? (Round the answer to the nearest whole number.) <BR>\n" );
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document.write( "2.3 = sqrt(d)/4 + d/1090<BR>\n" );
document.write( "sqrt(d)/4 = 2.3 - d/1090<BR>\n" );
document.write( "d/16 = 5.29 - 4.6d/1090 + d^2/1090^2<BR>\n" );
document.write( "d^2 + 5.29*1090^2 - 4.6d*1090 - d*1090^2/16 = 0<BR>\n" );
document.write( "d^2 - d*(5014 + 74256.25) + 6285049 = 0<BR>\n" );
document.write( "d^2 - 79270.25d + 6280549 = 0<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
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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=1x%5E2%2B-79270.25x%2B6280549+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-79270.25x%2B6280549+=+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=%28-79270.25%29%5E2-4%2A1%2A6280549=6258650339.0625 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-79270.25%29%5E2-4%2A1%2A6280549=6258650339.0625\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=6258650339.0625 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--79270.25%2B-sqrt%28+6258650339.0625+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--79270.25%2B-sqrt%28+6258650339.0625+%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-%28-79270.25%29%2Bsqrt%28+6258650339.0625+%29%29%2F2%5C1+=+79190.9410674966 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-79270.25%29%2Bsqrt%28+6258650339.0625+%29%29%2F2%5C1+=+79190.9410674966\"   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-%28-79270.25%29-sqrt%28+6258650339.0625+%29%29%2F2%5C1+=+79.3089325033652 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-79270.25%29-sqrt%28+6258650339.0625+%29%29%2F2%5C1+=+79.3089325033652\"   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=1x%5E2%2B-79270.25x%2B6280549 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-79270.25x%2B6280549\"   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=1x%5E2%2B-79270.25x%2B6280549+=+%28x-79190.9410674966%29%2A%28x-79.3089325033652%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-79270.25x%2B6280549+=+%28x-79190.9410674966%29%2A%28x-79.3089325033652%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 79190.9410674966, 79.3089325033652.\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+1%2Ax%5E2%2B-79270.25%2Ax%2B6280549+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-79270.25%2Ax%2B6280549+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "79 feet looks right.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );