SOLUTION: a ball is thrown downward from a window in a tall building. the distance, d, fallen after t seconds is d=16t2(squared) + 32t where d is in feet. how long (to the nearest tenth) w

Algebra ->  Coordinate-system -> SOLUTION: a ball is thrown downward from a window in a tall building. the distance, d, fallen after t seconds is d=16t2(squared) + 32t where d is in feet. how long (to the nearest tenth) w      Log On


   

Question 260445: a ball is thrown downward from a window in a tall building. the distance, d, fallen after t seconds is d=16t2(squared) + 32t where d is in feet. how long (to the nearest tenth) will it take the ball to fall 110 feet?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
a ball is thrown downward from a window in a tall building. the distance, d, fallen after t seconds is d=16t2(squared) + 32t where d is in feet. how long (to the nearest tenth) will it take the ball to fall 110 feet?
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16t^2 + 32t = 110
8t^2 + 16t - 55 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 8x%5E2%2B16x%2B-55+=+0) has the following solutons:

x%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=%2816%29%5E2-4%2A8%2A-55=2016.

Discriminant d=2016 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-16%2B-sqrt%28+2016+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2816%29%2Bsqrt%28+2016+%29%29%2F2%5C8+=+1.80624304008046
x%5B2%5D+=+%28-%2816%29-sqrt%28+2016+%29%29%2F2%5C8+=+-3.80624304008046

Quadratic expression 8x%5E2%2B16x%2B-55 can be factored:
8x%5E2%2B16x%2B-55+=+%28x-1.80624304008046%29%2A%28x--3.80624304008046%29
Again, the answer is: 1.80624304008046, -3.80624304008046. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B16%2Ax%2B-55+%29

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Ignore the negative number
1.8 seconds