SOLUTION: A rock is thrown from the top of a tall building. The distance, in feet, between the rock and the ground t seconds after it is thrown is given by d=-16t^2-2t+733. How long after th

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Question 982622: A rock is thrown from the top of a tall building. The distance, in feet, between the rock and the ground t seconds after it is thrown is given by d=-16t^2-2t+733. How long after the rock is thrown is it 400 feet from the ground?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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400=-16t^2-2t+733
0=-16t^2-2t+333
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation at%5E2%2Bbt%2Bc=0 (in our case -16t%5E2%2B-2t%2B333+=+0) has the following solutons:

t%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-2%29%5E2-4%2A-16%2A333=21316.

Discriminant d=21316 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+21316+%29%29%2F2%5Ca.

t%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+21316+%29%29%2F2%5C-16+=+-4.625
t%5B2%5D+=+%28-%28-2%29-sqrt%28+21316+%29%29%2F2%5C-16+=+4.5

Quadratic expression -16t%5E2%2B-2t%2B333 can be factored:
-16t%5E2%2B-2t%2B333+=+-16%28t--4.625%29%2A%28t-4.5%29
Again, the answer is: -4.625, 4.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B-2%2Ax%2B333+%29

The answer that makes sense here is 4.5 seconds