document.write( "Question 1192920: \"+h%28t%29+=+c+-+%28d-4t%29%5E2+\"\r
\n" ); document.write( "\n" ); document.write( "At time t=0, a ball was thrown upward from an initial height of 4 feet. The ball's height, in feet, after t seconds is given by the function h above, in which both c and d are positive constants. If the ball reached its maximum height of 104 feet at time t=3, what is the height, in feet, of the ball at time t=1.5? \n" ); document.write( "
Algebra.Com's Answer #824852 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "At time t=0, a ball was thrown upward from an initial height of 4 feet.
\n" ); document.write( "The ball's height, in feet, after t seconds is given by the function h above,
\n" ); document.write( "in which both c and d are positive constants. If the ball reached its maximum height
\n" ); document.write( "of 104 feet at time t=3, what is the height, in feet, of the ball at time t=1.5?
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document.write( "In this problem, the standard quadratic function of height, h(t) = -16t^2 + ut + h0,  is presented\r\n" );
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document.write( "in vertex form, and your first task is to identify the parameters of this vertex form.\r\n" );
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document.write( "    I will help you to identify these parameters.\r\n" );
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document.write( "First, the term \"c\" represents the highest position of the ball, which is given in the problem as 104 feet.\r\n" );
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document.write( "So, c = 104 feet.\r\n" );
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document.write( "Second, d - 4t = 0  determines the time \"t\", when the highest position is reached.\r\n" );
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document.write( "The problem says that the maximum height is reached at t= 3 seconds;  hence, d= 4t = 4*3 = 12 seconds.\r\n" );
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document.write( "    Now you know everything about your function: it is  h(t) = 104 - (12-4t)^2.\r\n" );
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document.write( "Now to answer the problem's question, you simply substitute t= 1.5 seconds in the last formula.\r\n" );
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document.write( "You get then\r\n" );
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document.write( "    h(1.5) = 104 - (12 - 4*1.5)^2 = 68 feet.    ANSWER\r\n" );
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document.write( "Thus, the solution of this tangled problem is completed.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, explained and completed.\r
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\n" ); document.write( "\n" ); document.write( "In this site,  there is a bunch of lessons on a projectile thrown/shot/launched vertically up\r
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\n" ); document.write( "\n" ); document.write( "    - Introductory lesson on a projectile thrown-shot-launched vertically up \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
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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 on how to solve this type of problems once and for all.\r
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this textbook under the topic \"Projectiles launched/thrown and moving vertically up and dawn\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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Post-solution notes at the end:

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\n" ); document.write( "\n" ); document.write( "        (a)   the initial condition  \"at  time t=0,  a ball was thrown upward from an initial height of  4  feet\" \r
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\n" ); document.write( "                 is not used in the solution.  So,  this condition is  EXCESSIVE  and  UNNECESSARY.\r
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\n" ); document.write( "\n" ); document.write( "                By the way,  this condition is  INCONSISTENT  with the rest of the problem, \r
\n" ); document.write( "\n" ); document.write( "                so  IT  MUST  BE  EXCLUDED  from the problem,  for clarity.\r
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\n" ); document.write( "\n" ); document.write( "        (b)   To solve the problem,  it is assumed that the reader/(the student) firmly knows the prerequisites\r
\n" ); document.write( "\n" ); document.write( "                 that are given in the lessons listed in my post.\r
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\n" ); document.write( "\n" ); document.write( "                 This knowledge is a  NECESSARY  condition to solve the problem.\r
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\n" ); document.write( "\n" ); document.write( "                 If you know these prerequisites,  you are able to solve the problem and to understand the solution.\r
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\n" ); document.write( "\n" ); document.write( "                 If you do not know them,  you will find yourselves in difficult position.\r
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