Question 476276
You have completed the problem correctly. Your equation:
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You need to recognize that in solving the equation by using the quadratic formula as you did, you are solving for t. In other words you got as far as:
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{{{t = (-32 +-sqrt(14912))/32}}}
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and that is correct up to that point.  Good job!!!
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Now let's finish up the problem.  Note that if you use the - sign in front of the radical that you will have two negatives in the numerator ... namely negative 32 and negative the radical. This means that the answer for t will be negative.  But that's meaningless. Negative time doesn't make sense. You need to get a positive answer. That means that you should forget about the negative sign that precedes the radical and just use the positive sign. So let's do that. The equation becomes:
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{{{t = (-32+sqrt(14912))/32}}}
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Use a calculator to find the square root of 14912. You will find that it is 122.1147 and this makes the equation become:
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{{{ t = (-32+122.1147)/32}}}
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Add the two terms in the numerator:
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{{{t = 90.1147/32}}}
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Now do the division using a calculator and you get:
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{{{t = 2.816}}}
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This rounds off to {{{t = 2.8}}}
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And that's the answer in seconds that you were given by the answer key.
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You were so close because you worked the problem correctly down to the final stage. Job well done on a difficult problem!!!