SOLUTION: I need to understand each step in the procedure to show and explain EACH step in setting up and solving the following application problems. Give answers to the nearest thousandth.

Algebra ->  Square-cubic-other-roots -> SOLUTION: I need to understand each step in the procedure to show and explain EACH step in setting up and solving the following application problems. Give answers to the nearest thousandth.       Log On


   

Question 41055: I need to understand each step in the procedure to show and explain EACH step in setting up and solving the following application problems. Give answers to the nearest thousandth.
a. The equation h = -16t^2 - 32t + 320 gives the height of a ball, thrown downward from the top of a 320-ft building with an initial velocity of 32ft/s. Find the time it takes for the ball to reach a height of 64ft.
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
h = -16t^2 - 32t + 320
64 = -16t^2 - 32t + 320
0 = -t^2 - 2t + 16
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation at%5E2%2Bbt%2Bc=0 (in our case -1t%5E2%2B-2t%2B16+=+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=%28-2%29%5E2-4%2A-1%2A16=68.

Discriminant d=68 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+68+%29%29%2F2%5Ca.

t%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+68+%29%29%2F2%5C-1+=+-5.12310562561766
t%5B2%5D+=+%28-%28-2%29-sqrt%28+68+%29%29%2F2%5C-1+=+3.12310562561766

Quadratic expression -1t%5E2%2B-2t%2B16 can be factored:
-1t%5E2%2B-2t%2B16+=+-1%28t--5.12310562561766%29%2A%28t-3.12310562561766%29
Again, the answer is: -5.12310562561766, 3.12310562561766. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B-2%2Ax%2B16+%29

About 3.123 seconds
Pretty Self-Explanatory