document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120311>Question 1120311</A>: <I><SPAN STYLE=\"word-break: break-all;\"> DURING A MANUFACTURING PROCESS A METAL PART IN A MACHINE IS EXPOSED TO VARYING TEMPERATURE CONDITION.THE MANUFACTURER OF THE MACHINE RECOMMENDS THAT THE TEMPERATURE OF THE MACHINE PART REMAIN BELOW 135F. THE TEMPERATURE,T IN DEGREE FAHRENHEIT X MINUTES AFTER THE MACHINE IS PUT INTO OPERATION IS MODELED BY THE EQUATION. T=-0.005X SQUARE + 0.45x + 125.\r<BR>\n" );
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document.write( "a. Tell whether the temperature of the part will ever reach or exceed 135 Fahrenheit. Using discriminant quadratic equation<BR>\n" );
document.write( "b. If the machine is in operation for 90 minutes before being turned off, how many will the temperature of the part be 134 fahrenheit </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #735972 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=735972\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the equation is T = -0.005 * x^2 + .45 * x + 125.\r<BR>\n" );
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document.write( "the equation is in standard form of ax^2 + bx + c\r<BR>\n" );
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document.write( "a = -.005<BR>\n" );
document.write( "b = .45<BR>\n" );
document.write( "c = 125\r<BR>\n" );
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document.write( "the maximum value of T is when x = -b/2a.\r<BR>\n" );
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document.write( "that would be when x = -.45 / (2*-.005)\r<BR>\n" );
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document.write( "simplify to get x = -.45 / -.01\r<BR>\n" );
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document.write( "solve for x to get x = 45\r<BR>\n" );
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document.write( "when x = 45, T = -.005 * x^2 + .45 * x + 125 = 135.125 degrees.\r<BR>\n" );
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document.write( "yes, the part will reach or exceed 135 degrees.\r<BR>\n" );
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document.write( "if the part is in operation for 90 minutes, the part will have reached 134 degrees two times.\r<BR>\n" );
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document.write( "you can replace T with y and graph the equation of y = -.005 * x^2 + .45 * x + 125.\r<BR>\n" );
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document.write( "the graph looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/072304.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "from the graph, you can see that the part will reach or exceeed 134 degrees when x = 30 through x = 60.\r<BR>\n" );
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document.write( "that's a period of 30 minutes.\r<BR>\n" );
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document.write( "from the graph, you can also see that the maximum value of the temperature is 135 degrees.\r<BR>\n" );
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document.write( "the part will be 125 degrees when x = 0 and when x = 90, according to the formula.\r<BR>\n" );
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document.write( "the points at which the temperature reaches 134 degrees was found by taking the equation of y = -.005 * x^2 + .45 * x + 125 and replacing y with 134.\r<BR>\n" );
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document.write( "you get 134 = -.005 * x^2 + .45 * x + 125.\r<BR>\n" );
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document.write( "subtract 134 from both sides of this equation to get -.005 * x^2 + .45 * x - 9 = 0\r<BR>\n" );
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document.write( "factor this equation to get x = 30 or x = 60.\r<BR>\n" );
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document.write( "i used an online quadratic equation solver at <a  rel=nofollow HREF= \"https://www.mathsisfun.com/quadratic-equation-solver.html\" target = \"_blank\">https://www.mathsisfun.com/quadratic-equation-solver.html</a>\r<BR>\n" );
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document.write( "the results from that quadratic equation solver are shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/072303.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "if the quadratic equation solver is unavailable, you would solve using the quadratic formula.\r<BR>\n" );
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document.write( "that formula is referenced below:\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.purplemath.com/modules/quadform.htm\" target = \"_blank\">http://www.purplemath.com/modules/quadform.htm</a>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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