SOLUTION: QUESTION: a ball is throw downward from a window in a tall building. the distance traveled by the ball in t seconds is {{{s= 16t^2+32t}}},where s is in feet. how long (to the ne

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: QUESTION: a ball is throw downward from a window in a tall building. the distance traveled by the ball in t seconds is {{{s= 16t^2+32t}}},where s is in feet. how long (to the ne      Log On


   

Question 336007: QUESTION:
a ball is throw downward from a window in a tall building. the distance traveled by the ball in t seconds is s=+16t%5E2%2B32t,where s is in feet. how long (to the nearest tenth) will it take the ball to fall 97 feet? show your work.
I could really use some help with this problem
Thank you
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
a ball is throw downward from a window in a tall building. the distance traveled by the ball in t seconds is s=+16t%5E2%2B32t,where s is in feet. how long (to the nearest tenth) will it take the ball to fall 97 feet?
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s=+16t%5E2%2B32t+=+97
16t%5E2%2B32t+=+97
16t%5E2%2B32t+-+97+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 16x%5E2%2B32x%2B-97+=+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=%2832%29%5E2-4%2A16%2A-97=7232.

Discriminant d=7232 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-32%2B-sqrt%28+7232+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2832%29%2Bsqrt%28+7232+%29%29%2F2%5C16+=+1.65753645318366
x%5B2%5D+=+%28-%2832%29-sqrt%28+7232+%29%29%2F2%5C16+=+-3.65753645318366

Quadratic expression 16x%5E2%2B32x%2B-97 can be factored:
16x%5E2%2B32x%2B-97+=+%28x-1.65753645318366%29%2A%28x--3.65753645318366%29
Again, the answer is: 1.65753645318366, -3.65753645318366. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+16%2Ax%5E2%2B32%2Ax%2B-97+%29

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Use the positive number.