document.write( "Question 85825: HELP!!!\r
\n" ); document.write( "\n" ); document.write( "tonisha hit a ball into the air with an initial velocity of 48 feet per second. the height h in feet of the ball above the ground can be modeled by h=-16t squared+48t+2, where t is the time in seconds after tonisha hit the ball. find the time it takes the ball to reach 38 feet above the ground. \n" ); document.write( "
Algebra.Com's Answer #62027 by bucky(2189)\"\" \"About 
You can put this solution on YOUR website!
The problem tells you that the equation for the height of the ball is:
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\n" ); document.write( "\"h+=+-16t%5E2+%2B+48t+%2B+2\"
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\n" ); document.write( "It asks you to find the time that the ball reaches a height of 38 feet.
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\n" ); document.write( "Substitute 38 feet into the equation. Since 38 feet is the height, it replaces h in the
\n" ); document.write( "equation, and the equation becomes:
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\n" ); document.write( "\"38+=+-16t%5E2+%2B+48t+%2B+2\"
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\n" ); document.write( "The standard form for solving equations of this type is:
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\n" ); document.write( "\"at%5E2+%2B+bt+%2B+c+=+0\"
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\n" ); document.write( "in which a, b, and c are integers.
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\n" ); document.write( "You can work the height equation into this form. Begin by transposing (switching sides) of
\n" ); document.write( "the height equation to get:
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\n" ); document.write( "\"-16t%5E2+%2B+48t+%2B+2+=+38\"
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\n" ); document.write( "Next subtract 38 from both sides of the equation:
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\n" ); document.write( "\"-16t%5E2+%2B+48t+%2B+2+-+38+=+0\"
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\n" ); document.write( "and after the subtraction the left side becomes:
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\n" ); document.write( "\"+-16t%5E2+%2B+48t+-36+=+0\"
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\n" ); document.write( "Notice that this equation now matches the standard form ... in which a = -16, b = +48, and
\n" ); document.write( "c = -36.
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\n" ); document.write( "You can simplify this a little by noting that 4 is a factor of all the terms. So divide
\n" ); document.write( "all the terms in this equation by 4 to get:
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\n" ); document.write( "\"-4t%5E2+%2B+12t+-+9+=+0\"
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\n" ); document.write( "You can further simplify this by multiplying all the terms on both sides by -1 to get:
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\n" ); document.write( "\"4t%5E2+-+12t+%2B+9+=+0\"
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\n" ); document.write( "This can be solved by using the quadratic formula, or you might notice that the left side
\n" ); document.write( "of this equation factors to give:
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\n" ); document.write( "\"%282t+-3%29%5E2+=++0\"
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\n" ); document.write( "The equation will be true when the left side equals zero. Therefore, it will be true if
\n" ); document.write( "\"2t+-+3+=+0\"
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\n" ); document.write( "Solve this equation by adding 3 to both sides to get:
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\n" ); document.write( "\"+2t+=+3\"
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\n" ); document.write( "and solve for t by dividing both sides by 2 to get:
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\n" ); document.write( "\"t+=+3%2F2+=+1.5+\" seconds.
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\n" ); document.write( "So the ball reaches a height of 38 feet 1.5 seconds after Tonisha hits it.
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\n" ); document.write( "Hope this helps you to understand the problem.
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