Answer:
[tex]-16t^2 + 1,000>300[/tex]
[tex]t<6.61\ s[/tex]
Step-by-step explanation:
We know that the distance of the object while falling is given by the equation:
[tex]d = -16t^2 + 1,000[/tex]
To find the time interval in which the object is at a height greater than 300 ft, we must do
[tex]d> 300[/tex]
So
[tex]-16t^2 + 1,000>300[/tex]
[tex]-16t^2>-700[/tex]
[tex]16t^2<700[/tex]
[tex]t^2<\frac{700}{16}[/tex]
[tex]t<\sqrt{\frac{700}{16}}[/tex]
[tex]t<6.61\ s[/tex]
The interval is
t ∈ (0, 6.61)
And the inequality used  is: [tex]-16t^2 + 1,000>300[/tex]
