SOLUTION: help me please!!!!!This is for a test!!!!! How do you get the answer!!!!! A small flare is launched off the deck of a ship. The height of the flare above the water is given b

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Question 123939: help me please!!!!!This is for a test!!!!!
How do you get the answer!!!!!

A small flare is launched off the deck of a ship. The height of the flare above the water is given by h(t)=-4.9^2+92t+9, where h(t) is measured in metres and t is time is seconds

a)When will the flare's height be 150m?
b)How long will the flare's height be about 150m?

The answer for a) should be 1.7s and 17.1s
The answer for b) should be 15.4s
But i don't know the process to get to this answer
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
a) When (at what time, t) will the flare be at 150m (h = 150).
Start with the given formula for the height (h) as a function of time (t):
h%28t%29+=+-4.9t%5E2%2B92t%2B9 Now substitute h = 150 and solve for t using the quadratic formula:t+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a
The a, b, and c, in the formula come from the standard form of the quadratic equation:ax%5E2%2Bbx%2Bc+=+0
150+=+-4.9t%5E2%2B92t%2B9 Subtract 150 from both sides.
0+=+-4.9t%5E2%2B92t%2B%289-150%29 Simplify.
-4.9t%5E2%2B92t-141+=+0 Solve this quadratic using the quadratic formula:
t+=+%28-92%2B-sqrt%2892%5E2-4%28-4.9%29%28-141%29%29%29%2F2%28-4.9%29
t+=+%28-92%2B-sqrt%288464-2763.6%29%29%2F-9.8%29
t+=+%28-92%2B-sqrt%285700.4%29%29%2F-9.8%29
t%5B1%5D+=+%28-92%2B75.5%29%2F-9.8
t%5B1%5D+=+1.68 or approx. 1.7 seconds.
t%5B2%5D+=+%28-92-75.5%29%2F-9.8
t%5B2%5D+=+17.09 or approx. 17.1 seconds.
b) To find out how long the flare was AT OR ABOVE 150m, just subtract the two times:
t%5B2%5D+-+t%5B1%5D+=+17.1+-+1.7 = 15.4seconds.