SOLUTION: The height h in feet of an object after t seconds is given by the function h = –16t2 + 90t + 7. How long will it take the object to hit the ground? Round your answer to th

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The height h in feet of an object after t seconds is given by the function h = –16t2 + 90t + 7. How long will it take the object to hit the ground? Round your answer to th      Log On


   

Question 46784: The height h in feet of an object after t seconds is given by the function h = –16t2 + 90t + 7. How long will it take the object to hit the ground? Round your answer to the nearest thousandth.
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
h+=+-16t%5E2+%2B+90t+%2B+7
0+=+-16t%5E2+%2B+90t+%2B+7
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation at%5E2%2Bbt%2Bc=0 (in our case -16t%5E2%2B90t%2B7+=+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=%2890%29%5E2-4%2A-16%2A7=8548.

Discriminant d=8548 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-90%2B-sqrt%28+8548+%29%29%2F2%5Ca.

t%5B1%5D+=+%28-%2890%29%2Bsqrt%28+8548+%29%29%2F2%5C-16+=+-0.0767310828315551
t%5B2%5D+=+%28-%2890%29-sqrt%28+8548+%29%29%2F2%5C-16+=+5.70173108283156

Quadratic expression -16t%5E2%2B90t%2B7 can be factored:
-16t%5E2%2B90t%2B7+=+-16%28t--0.0767310828315551%29%2A%28t-5.70173108283156%29
Again, the answer is: -0.0767310828315551, 5.70173108283156. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B90%2Ax%2B7+%29