Question

An object is dropped from a small plane. As the object falls, its distance, d, above the ground after t seconds, is given by the

formula d = -162 + 1,000. Which inequality can be used to find the interval of time taken by the object to reach the height
greater than 300 feet above the ground?
O -166 +1,000 < 300
0 -1672 +1,000 3 300
O-166 +1,000 300
O -166 +1,000 > 300
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Answer 1

`-16t^2 + 1,000>300`

`t<6.61\ s`

Explanation:

We know that the distance of the object while falling is given by the equation:

`d = -16t^2 + 1,000`

To find the time interval in which the object is at a height greater than 300 ft, we must do

`d> 300`

So

`-16t^2 + 1,000>300`

`-16t^2>-700`

`16t^2<700`

`t^2<(700)/(16)`

`t<\sqrt{(700)/(16)}`

`t<6.61\ s`

The interval is

t ∈ (0, 6.61)

And the inequality used is:
`-16t^2 + 1,000>300`