document.write( "Question 966145: The cost C in pesos of operating a certain wood-cutting machine is related to the number of minutes n the machine is run by the function C(n) = 2.2n^2 - 66n + 655. For what number of minutes is the cost of running the machine a minimum? What is the minimum cost?
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Algebra.Com's Answer #590512 by Theo(13342)![]() ![]() You can put this solution on YOUR website! 2.2n^2 - 66n + 655 is a quadratic equation that opens up and points down.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "the graph of that equation looks like this:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "the minimum point on the graph of that equation is found by the formula:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "x = -b/2a\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "the quadratic formula in standard form is ax^2 + bx + c = 0\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "just replace n with x and your equation will conform to this convention.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "2.2n^2 - 66n + 655 becomes 2.2x^2 - 66x + 655.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "since this equation is in standard form, then:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "a = 2.2 \n" ); document.write( "b = -66 \n" ); document.write( "c = 655\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "x = -b/2a becomes x = 66/4.4 which becomes x = 15\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "when x = 15, 2.2x^2 - 66x + 655 becomes 2.2(15)^2 - 66(15) + 655 which becomes 160.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "the minimum point on the graph is when x = 15 and y = 160.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "that can be seen on the same graph with y = 160 added to it as shown below:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "the question is:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "For what number of minutes is the cost of running the machine a minimum? What is the minimum cost?\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "the answer is:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "the minimum cost is 160 pesos when the machine has been running for 15 minutes.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |