document.write( "Question 83815: An professor finds that the number of students enrolling in his class is approximated by s(t) = -tsquared + 20t + 80 where t is the number of tests given in one semester.\r
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Algebra.Com's Answer #60288 by Edwin McCravy(20060)\"\" \"About 
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document.write( "An professor finds that the number of students enrolling \r\n" );
document.write( "in his class is approximated by s(t) = -tｲ + 20t + 80 \r\n" );
document.write( "where t is the number of tests given in one semester. \r\n" );
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document.write( "Here is the graph. t, the number of tests is on the \r\n" );
document.write( "x-axis and the number of students is on the y-axis.\r\n" );
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document.write( "(a) How many tests should the professor give so that the \r\n" );
document.write( "number of students enrolling in the class is a maximum? \r\n" );
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document.write( "That will be the highest point, the vertex, of the graph.\r\n" );
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document.write( "The vertex is the point (h,k) where h = \"-b%2F%282a%29\",\r\n" );
document.write( "and k = s(h)\r\n" );
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document.write( "s(t) = -tｲ + 20t + 80\r\n" );
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document.write( "a = -1 (the coefficient of tｲ\r\n" );
document.write( "b = 20 (the coefficient of t)\r\n" );
document.write( "c = 80 (the constant)\r\n" );
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document.write( "h = \"-b%2F%282a%29\" = \"-%28-20%29%2F%282%28-1%29%29\" = 10\r\n" );
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document.write( "k = s(h) = -10ｲ + 20(10) + 80 = -100 + 200 + 80 = 180\r\n" );
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document.write( "The vertex (10,180) at the top of the graph is \r\n" );
document.write( "interpreted as \"when the professor gives 10 tests,\r\n" );
document.write( "there will be 180 students.\r\n" );
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document.write( "(b) If the professor does not want students to enroll, \r\n" );
document.write( "how many tests should he give?\r\n" );
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document.write( "We substitute 0 students for s(t) and solve for t:\r\n" );
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document.write( "            s(t) = -tｲ + 20t + 80 \r\n" );
document.write( "               0 = -tｲ + 20t + 80\r\n" );
document.write( "   tｲ - 20t - 80 = 0 \r\n" );
document.write( "  \r\n" );
document.write( "That doesn't factor so we have to use the quadratic\r\n" );
document.write( "formula:\r\n" );
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document.write( "                  ______ \r\n" );
document.write( "            -b ｱ ﾖbｲ-4ac\r\n" );
document.write( "        t = 覧覧覧覧覧覧予r\n" );
document.write( "                2a \r\n" );
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document.write( "where a = 1; b = -20; c = -80\r\n" );
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document.write( "                       ________________\r\n" );
document.write( "             -(-20) ｱ ﾖ(-20)ｲ-4(1)(-80)\r\n" );
document.write( "        x = 覧覧覧覧覧覧覧覧覧覧覧覧覧覧予r\n" );
document.write( "                       2(1) \r\n" );
document.write( "                   _______ \r\n" );
document.write( "             20 ｱ ﾖ400+320\r\n" );
document.write( "        x = 覧覧覧覧覧覧覧覧\r\n" );
document.write( "                   2\r\n" );
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document.write( "                   ___ \r\n" );
document.write( "             20 ｱ ﾖ720\r\n" );
document.write( "        x = 覧覧覧覧覧覧\r\n" );
document.write( "                 2 \r\n" );
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document.write( "                   _____ \r\n" );
document.write( "             20 ｱ ﾖ144ｷ5\r\n" );
document.write( "        x = 覧覧覧覧覧覧予r\n" );
document.write( "                  2 \r\n" );
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document.write( "                     _ \r\n" );
document.write( "             20 ｱ 12ﾖ5\r\n" );
document.write( "        x = 覧覧覧覧覧予r\n" );
document.write( "                 2 \r\n" );
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document.write( "                       _\r\n" );
document.write( "             20     12ﾖ7\r\n" );
document.write( "        x = 覧覧 ｱ 覧覧覧\r\n" );
document.write( "              2       2\r\n" );
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document.write( "        x = 10 ｱ 6ﾖ7 \r\n" );
document.write( "                        _\r\n" );
document.write( "Using the +, x = 10 + 6ﾖ5, which\r\n" );
document.write( "is one solution and equals about 23.41640786\r\n" );
document.write( "                        _ \r\n" );
document.write( "Using the -, x = 10 - 6ﾖ5, which\r\n" );
document.write( "is the other solution and equals about -3.416407865. This is\r\n" );
document.write( "meaningless for this problem, since it's negative, so we\r\n" );
document.write( "disregard it.\r\n" );
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document.write( "Therefore the point where the graph crosses the horizontal\r\n" );
document.write( "axis is (23.4, 0) which means that if the professor gives \r\n" );
document.write( "more than 23 tests, he will have no students.\r\n" );
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document.write( "Edwin
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