Question
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TIME REMAINING
55:32
The path of a flying fish as it made its approach to the surface of the ocean and flew out of the water is represented by the quadratic function h(t) = -t2 + 6t - 5, where t represents the time, in seconds, and h(t) represents the fish's height and depth, in feet. Graph the function using the graphing calculator. To the nearest second, how long was the fish out of the water?
1 second
3 seconds
4 seconds
5 seconds
TIME REMAINING
55:32
The path of a flying fish as it made its approach to the surface of the ocean and flew out of the water is represented by the quadratic function h(t) = -t2 + 6t - 5, where t represents the time, in seconds, and h(t) represents the fish's height and depth, in feet. Graph the function using the graphing calculator. To the nearest second, how long was the fish out of the water?
1 second
3 seconds
4 seconds
5 seconds
Answers
GPT 3.5
To find out how long the fish was out of the water, we need to find when h(t) = 0, as this represents the fish being at the surface of the water.
Setting h(t) = 0:
0 = -t^2 + 6t - 5
Solving for t using the quadratic formula:
t = (-6 ± √(6^2 - 4(-1)(-5))) / 2(-1)
t = (-6 ± √(36 - 20)) / -2
t = (-6 ± √16) / -2
t = (-6 ± 4) / -2
So, t = (-6 + 4) / -2 = -2 / -2 = 1 second
t = (-6 - 4) / -2 = -10 / -2 = 5 seconds
Since the fish cannot be out of the water for -2 seconds, we take the positive value of t, which is 5 seconds.
Therefore, the fish was out of the water for 5 seconds.
Setting h(t) = 0:
0 = -t^2 + 6t - 5
Solving for t using the quadratic formula:
t = (-6 ± √(6^2 - 4(-1)(-5))) / 2(-1)
t = (-6 ± √(36 - 20)) / -2
t = (-6 ± √16) / -2
t = (-6 ± 4) / -2
So, t = (-6 + 4) / -2 = -2 / -2 = 1 second
t = (-6 - 4) / -2 = -10 / -2 = 5 seconds
Since the fish cannot be out of the water for -2 seconds, we take the positive value of t, which is 5 seconds.
Therefore, the fish was out of the water for 5 seconds.