document.write( "Question 1209414: Xavier shoots a basketball in which the height, in feet, is modeled by the following equation:
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\n" ); document.write( "\n" ); document.write( "What is the maximum height of the basketball in feet? Round your answer to the nearest hundredth.
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Algebra.Com's Answer #848767 by ikleyn(52788) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "Xavier shoots a basketball in which the height, in feet, is modeled by the following equation:
\n" ); document.write( "h(t)= −4t2+10t+18
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\n" ); document.write( "\n" ); document.write( "What is the maximum height of the basketball in feet? Round your answer to the nearest hundredth.
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\n" ); document.write( "\n" ); document.write( " As it is written, this formula does not work.\r
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\n" ); document.write( "\n" ); document.write( "The formula in your post is written incorrectly. FATALLY INCORRECTLY, it is what I want to say.\r
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\n" ); document.write( "\n" ); document.write( "I observed it many times in this forum that the students / (the visitors) write this formula incorrectly.\r
\n" ); document.write( "\n" ); document.write( "because they do not understand the meaning of its terms.\r
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\n" ); document.write( "\n" ); document.write( "So I prepared this text below as a standard introduction to the subject for such students / visitors.\r
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\n" ); document.write( "\n" ); document.write( "Be calm, you are in good hands, and read my post to the very end.\r
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document.write( "If you have the formula for a height given to you as a function of time in the form\r\n" );
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document.write( "    h(t) = -at^2 + bt + c,    (1)\r\n" );
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document.write( "where \"a\", \"b\" and \"c\" are real numbers, a > 0, then in this formula\r\n" );
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document.write( "    (a)  the initial height is equal to the coefficient \"c\" value;\r\n" );
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document.write( "    (b)  the initial velocity is the coefficient  \"b\" in the formula;\r\n" );
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document.write( "    (c)  the coefficient \"a\" value is half of the gravity acceleration.\r\n" );
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document.write( "         For the Earth conditions, the gravity acceleration is g = 9.81 m/s^2, or 32 ft/s^2.\r\n" );
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document.write( "         THEREFORE, if you use meters for height, you should use the approximate value of g = 10 m/s^2.\r\n" );
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document.write( "         So, in this case  a =  = 5  (the numerical value).\r\n" );
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document.write( "         ALTERNATIVELY, if you use feet for height, you should use the approximate value of g = 32 ft/s^2.\r\n" );
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document.write( "         So, in this case  a =  = 16  (the numerical value).\r\n" );
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document.write( "    (d)  To find the height at the time moment \"t\", simply substitute the value of \"t\" into the formula (1) and calculate.\r\n" );
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document.write( "    (e)  To find the time \"t\" when the height has a given value h = , substitute  h =  into equation (1)\r\n" );
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document.write( "         and solve equation  \r\n" );
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document.write( "             h(t) = -at^2 + bt + c = .    (2)\r\n" );
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document.write( "    (f)  To find the time when the height is maximal, use the formula\r\n" );
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document.write( "              = .      (3)\r\n" );
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document.write( "    (g)  To find the maximal height, substitute the time value  t=   of the formula (3)  into the formula (1).\r\n" );
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\n" ); document.write( "\n" ); document.write( "        After my explanations, you can solve the problem on YOUR OWN now, \r
\n" ); document.write( "\n" ); document.write( "        but for it, you should have your governing equation written correctly.\r
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\n" ); document.write( "\n" ); document.write( "To see numerous examples of solved problems, look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Problem on a projectile moving vertically up and down\r
\n" ); document.write( "\n" ); document.write( "    - Problem on an arrow shot vertically upward\r
\n" ); document.write( "\n" ); document.write( "    - Problem on a ball thrown vertically up from the top of a tower \r
\n" ); document.write( "\n" ); document.write( "    - Problem on a toy rocket launched vertically up from a tall platform\r
\n" ); document.write( "\n" ); document.write( "    - A flare is launched from a life raft vertically up \r
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\n" ); document.write( "\n" ); document.write( "Consider these lessons as your textbook, handbook, tutorials and (free of charge) home teacher.
\n" ); document.write( "Read them attentively and learn how to solve this type of problems once and for all.\r
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