document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=817600>Question 817600</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A duck drives under water and its path is describe by the equation y= 2x^2 - 4x, where y represent position of duck in meters and x represent time in seconds. <BR>\n" );
document.write( "a) how long was the duck under water?<BR>\n" );
document.write( "b) how long was the duck under water at least 0.5 meters below water surface?\r<BR>\n" );
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document.write( "- thank you.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #492140 by </B><A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><B>TimothyLamb(4379)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><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=TimothyLamb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=492140\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y = 2x^2 - 4x<BR>\n" );
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document.write( "part a:<BR>\n" );
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document.write( "0 = 2x^2 - 4x<BR>\n" );
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document.write( "the above quadratic equation is in standard form, with a=2, b=-4, and c=0<BR>\n" );
document.write( "---<BR>\n" );
document.write( "to solve the quadratic equation, plug this:<BR>\n" );
document.write( "2 -4 0<BR>\n" );
document.write( "into this: https://sooeet.com/math/quadratic-equation-solver.php<BR>\n" );
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document.write( "the roots of the quadratic are:<BR>\n" );
document.write( "x = 2<BR>\n" );
document.write( "x = 0<BR>\n" );
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document.write( "Answer a: <BR>\n" );
document.write( "the duck was underwater (y <= 0 meter ) for 2 seconds<BR>\n" );
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document.write( "part b:<BR>\n" );
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document.write( "0.5 = 2x^2 - 4x<BR>\n" );
document.write( "0 = 2x^2 - 4x - 0.5<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the above quadratic equation is in standard form, with a=2, b=-4, and c=0.5<BR>\n" );
document.write( "---<BR>\n" );
document.write( "to solve the quadratic equation, plug this:<BR>\n" );
document.write( "2 -4 0.5<BR>\n" );
document.write( "into this: https://sooeet.com/math/quadratic-equation-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the roots of the quadratic are:<BR>\n" );
document.write( "x = 0.133974596<BR>\n" );
document.write( "x = 1.8660254<BR>\n" );
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document.write( "Answer b:<BR>\n" );
document.write( "dt = 1.8660254 - 0.133974596 = 1.7320509<BR>\n" );
document.write( "the duck was underwater below half a meter depth (y <= 0.5 meter ) for 1.73 seconds<BR>\n" );
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document.write( "Solve and graph linear equations:<BR>\n" );
document.write( "https://sooeet.com/math/linear-equation-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve quadratic equations, quadratic formula:<BR>\n" );
document.write( "https://sooeet.com/math/quadratic-formula-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Convert fractions, decimals, and percents:<BR>\n" );
document.write( "https://sooeet.com/math/fraction-decimal-percent.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Calculate and graph the linear regression of any data set:<BR>\n" );
document.write( "https://sooeet.com/math/linear-regression.php </SPAN>\n" );
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