The 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 is:
[tex]d = -16t^2 + 1000[/tex]
Solution:
The object falls, its distance, d, above the ground after t seconds, is given by the formula:
[tex]d = -16t^2 + 1000[/tex]
To find the time interval in which the object is at a height greater than 300 ft
Frame a inequality,
[tex]-16t^2 + 1000 > 300[/tex]
Solve the inequality
Subtract 1000 from both sides
[tex]-16t^2 + 1000 - 1000 > 300 - 1000\\\\-16t^2 > -700[/tex]
[tex]16t^2 < 700\\\\Divide\ both\ sides\ by\ 16\\\\t^2 < \frac{700}{16}\\\\Take\ square\ root\ on\ both\ sides\\\\t < \sqrt{\frac{700}{16}}\\\\t < \pm 6.61[/tex]
Time cannot be negative
Therefore,
t < 6.61
And the inequality used is: [tex]-16t^2 + 1000>300[/tex]
