SOLUTION: determine how long the cannon ball was in the air. using h=-5t(squared)+ 40t+ 3

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Question 240171: determine how long the cannon ball was in the air.
using h=-5t(squared)+ 40t+ 3
Answer by philline_palana(20) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation at%5E2%2Bbt%2Bc=0 (in our case -5t%5E2%2B40t%2B3+=+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=%2840%29%5E2-4%2A-5%2A3=1660.

Discriminant d=1660 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-40%2B-sqrt%28+1660+%29%29%2F2%5Ca.

t%5B1%5D+=+%28-%2840%29%2Bsqrt%28+1660+%29%29%2F2%5C-5+=+-0.0743097574926722
t%5B2%5D+=+%28-%2840%29-sqrt%28+1660+%29%29%2F2%5C-5+=+8.07430975749267

Quadratic expression -5t%5E2%2B40t%2B3 can be factored:
-5t%5E2%2B40t%2B3+=+-5%28t--0.0743097574926722%29%2A%28t-8.07430975749267%29
Again, the answer is: -0.0743097574926722, 8.07430975749267. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-5%2Ax%5E2%2B40%2Ax%2B3+%29