The average speed from 1 to 3 seconds = 169 ft/s
Since the fireworks height is given by h(t) = 16t² + 105t + 10 and we require its average speed from 1 to 3 seconds, which is total distance/total time.
The distance it moves from 1 to 3 seconds is d = h(3) - h(1) which is the difference it its height from 1 to 3 seconds respectively.
So, h(1) = 16(1)² + 105(1) + 10
h(1) = 16 + 105 + 10
h(1) = 131 ft
h(3) = 16(3)² + 105(3) + 10
h(3) = 16(9) + 315 + 10
h(3) = 144 + 325
h(3) = 469 ft
d = h(3) - h(1)
d = 469 ft - 131 ft
d = 338 ft
The total time t = 3 s - 1 s = 2 s
So, average speed = total distance/total time
= d/t
= 338 ft/2 s
= 169 ft/s
The average speed from 1 to 3 seconds = 169 ft/s
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