SOLUTION: A ball is thrown downward from a window in a tall building. The distance, d, fallen after t seconds is d=16t^2 + 32t, where d is in feet. How long (to the nearest tenth) will it ta

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Question 260373: A ball is thrown downward from a window in a tall building. The distance, d, fallen after t seconds is d=16t^2 + 32t, where d is in feet. How long (to the nearest tenth) will it take the ball to fall 110 feet?
I tried dividing 110 by the equation and I get .382, for distance divided by rate. I'm not sure if this is an answer, and if it is is that 3.82 seconds?
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
plug in 110 for d in the equation and solve for t
t=1.69258
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B8x%2B-25+=+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=%288%29%5E2-4%2A4%2A-25=464.

Discriminant d=464 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-8%2B-sqrt%28+464+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%288%29%2Bsqrt%28+464+%29%29%2F2%5C4+=+1.69258240356725
x%5B2%5D+=+%28-%288%29-sqrt%28+464+%29%29%2F2%5C4+=+-3.69258240356725

Quadratic expression 4x%5E2%2B8x%2B-25 can be factored:
4x%5E2%2B8x%2B-25+=+4%28x-1.69258240356725%29%2A%28x--3.69258240356725%29
Again, the answer is: 1.69258240356725, -3.69258240356725. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B8%2Ax%2B-25+%29


Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 16x%5E2%2B32x%2B-100+=+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-100=7424.

Discriminant d=7424 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-32%2B-sqrt%28+7424+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2832%29%2Bsqrt%28+7424+%29%29%2F2%5C16+=+1.69258240356725
x%5B2%5D+=+%28-%2832%29-sqrt%28+7424+%29%29%2F2%5C16+=+-3.69258240356725

Quadratic expression 16x%5E2%2B32x%2B-100 can be factored:
16x%5E2%2B32x%2B-100+=+16%28x-1.69258240356725%29%2A%28x--3.69258240356725%29
Again, the answer is: 1.69258240356725, -3.69258240356725. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+16%2Ax%5E2%2B32%2Ax%2B-100+%29