document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=466674>Question 466674</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help...spent two nights on these and cannot solve. <BR>\n" );
document.write( "A) During the first part of a trip, a canoeist travels 63 miles at a certain speed. The canoeist travels 10 miles on the second part of a trip at a speed of 5 mph slower. The total time for the trip is 4 hours. What was the speed on each part of the trip?<BR>\n" );
document.write( "B) Write a quadratic equation having the given numbers as a solution; -6,-2.<BR>\n" );
document.write( "C) Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form ax^2+bx+c=0; -sqrt 5, 3 sqrt 5.<BR>\n" );
document.write( "Thank you so much for your help!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #319955 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=319955\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A) During the first part of a trip, a canoeist travels 63 miles at a certain speed. The canoeist travels 10 miles on the second part of a trip at a speed of 5 mph slower. The total time for the trip is 4 hours. What was the speed on each part of the trip?<BR>\n" );
document.write( "r = the \"certain speed\"<BR>\n" );
document.write( "t = d/r = 63/r + 10/(r-5) = 4<BR>\n" );
document.write( "Multiply thru by r*(r-5)<BR>\n" );
document.write( "63(r-5) + 10r = 4r(r-5) = 4r^2 - 20r<BR>\n" );
document.write( "63r-315 + 10r = 4r^2 - 20r<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4r%5E2+-+93r+%2B+315+=+0 ALIGN=MIDDLE  ALT=\"4r%5E2+-+93r+%2B+315+=+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=4x%5E2%2B-93x%2B315+=+0 ALIGN=MIDDLE  ALT=\"4x%5E2%2B-93x%2B315+=+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=%28-93%29%5E2-4%2A4%2A315=3609 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-93%29%5E2-4%2A4%2A315=3609\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=3609 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--93%2B-sqrt%28+3609+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--93%2B-sqrt%28+3609+%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-%28-93%29%2Bsqrt%28+3609+%29%29%2F2%5C4+=+19.1343691479378 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-93%29%2Bsqrt%28+3609+%29%29%2F2%5C4+=+19.1343691479378\"   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-%28-93%29-sqrt%28+3609+%29%29%2F2%5C4+=+4.11563085206221 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-93%29-sqrt%28+3609+%29%29%2F2%5C4+=+4.11563085206221\"   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=4x%5E2%2B-93x%2B315 ALIGN=MIDDLE  ALT=\"4x%5E2%2B-93x%2B315\"   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=4x%5E2%2B-93x%2B315+=+%28x-19.1343691479378%29%2A%28x-4.11563085206221%29 ALIGN=MIDDLE  ALT=\"4x%5E2%2B-93x%2B315+=+%28x-19.1343691479378%29%2A%28x-4.11563085206221%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 19.1343691479378, 4.11563085206221.\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%2Ax%5E2%2B-93%2Ax%2B315+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-93%2Ax%2B315+%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( "r = x<BR>\n" );
document.write( "Ignore the answer that's less than 5.<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "B) Write a quadratic equation having the given numbers as a solution; -6,-2.<BR>\n" );
document.write( "(x+6)*(x+2) = 0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+8x+%2B+16+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+8x+%2B+16+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "C) Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form ax^2+bx+c=0; -sqrt 5, 3 sqrt 5.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+sqrt%285%29%29%2A%28x+-+3sqrt%285%29%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+%2B+sqrt%285%29%29%2A%28x+-+3sqrt%285%29%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+2x%2Asqrt%285%29+-+15+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+2x%2Asqrt%285%29+-+15+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );