document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=956644>Question 956644</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A computer can sort x objects in t seconds, as modeled by the function below:<BR>\n" );
document.write( "t = 0.003x^2 + 0.001x<BR>\n" );
document.write( "How many objects are required to keep the computer busy for exactly 7 seconds?<BR>\n" );
document.write( "Round to the nearest whole object.\r<BR>\n" );
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document.write( "(Please help me, 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 #584463 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=584463\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula given is t = .003x^2 + .001x\r<BR>\n" );
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document.write( "when t = 7, the formula becomes:\r<BR>\n" );
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document.write( "7 = .003x^2 + .001x \r<BR>\n" );
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document.write( "subtract 7 from both sides of the equation to get:\r<BR>\n" );
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document.write( ".003x^2 + .001x - 7 = 0\r<BR>\n" );
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document.write( "this is a quadratic equation in standard form.\r<BR>\n" );
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document.write( "a = .003<BR>\n" );
document.write( "b = .001<BR>\n" );
document.write( "c = -7\r<BR>\n" );
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document.write( "use the quadratic formula to solve for x.\r<BR>\n" );
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document.write( "that formula is x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-b+%2B-+sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"%28-b+%2B-+sqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "replace b with .001<BR>\n" );
document.write( "replace c with -7<BR>\n" );
document.write( "replace a with .003\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x1 = 48.13821001\r<BR>\n" );
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document.write( "x2 = -48.47154335\r<BR>\n" );
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document.write( "since x represents the number of objects, then x has to be greater than or equal to 0, so x2 is invalid and the only valid solution is x = 48.13821001.\r<BR>\n" );
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document.write( "round to the nearest whole number and the answer is 48.\r<BR>\n" );
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document.write( "the computer can sort 48 objects in 7 seconds.\r<BR>\n" );
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document.write( "the following graph shows the equation of y = .003x^2 + .001x and shows the equation of y = 7.\r<BR>\n" );
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document.write( "the intersection of y = .003x^2 + .001x and y = 7 tells you how many objects the computer can sort in 7 seconds.\r<BR>\n" );
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document.write( "when you subtract 7 from both sides of the equation of y = .003x^2 + .001x = 7, you get .003x^2 + .001x - 7 = 0.\r<BR>\n" );
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document.write( "the graph of the equation y = .003x^2 + .001x - 7 will show you that y = 7 when x = 48.\r<BR>\n" );
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document.write( "the graphs show you both zero crossings.\r<BR>\n" );
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document.write( "you ignore the negative value of x because that's invalid.\r<BR>\n" );
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document.write( "in other words, when you graph two separate equations of y = .003x^2 + .001x and y = 7, then the value of x when y = 7 will be the intersection of the graph of those two equations, and when you graph y = .003x^2 + .001x - 7, then the value of x when y = 7 will be the intersection of the graph of y = .003x^2 + .001x - 7 with the x-axis.\r<BR>\n" );
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document.write( "you'll see that in the following two graphs.\r<BR>\n" );
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document.write( "first graph is the two equations of y = .003x^2 + .001x and y = 7.\r<BR>\n" );
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document.write( "look for the intersection point of the graph of those two equations.\r<BR>\n" );
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document.write( "second graph is the equation of y = .003x^2 + .001x - 7.\r<BR>\n" );
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document.write( "look for the intersection of the graph of that equation with the x-axis.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/031802.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/031803.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "in the graphs, y is the vertical axis and x is the horizontal axis.\r<BR>\n" );
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document.write( "y represents the time in seconds.\r<BR>\n" );
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document.write( "x represents the number of objects.\r<BR>\n" );
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document.write( "the positive value of x is the only intersection point that's valid.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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