Question

Jerald jumped from a bungee tower. If the equation that models his height, in feet, is h = –16t2 + 729, where t is the time in seconds, for which interval of time is he within 104 feet above the ground? A t > 6.25

B –6.25 < t < 6.25
C t < 6.25
D, 0

Answer 1

t >6.25

Explanation:

Given :
`h = -16t^(2) +729`

To Find: for which interval of time is he within 104 feet above the ground?

Solution ;

`h = -16t^(2) +729`

Since we are required to find for which interval of time is he within 104 feet above the ground

So,

`-16t^(2) +729<104`

`-16t^(2) <104-729`

`-16t^(2) < -625`

`16t^(2)>625`

`t^(2) >(625)/(16)`

`t >√(39.0625)`

`t >6.25`

Thus for t >6.25 he is within 104 feet above the ground

Answer 2

Answer :- t > 6.25 would be the interval of time is he within 104 feet above the ground.

Explanation:-

Given equation:-
`h=-16t^2+729`, where t is the time in seconds.

For the interval that he is at height within 104 feet above the ground.
`0<-16t^2+729<104`

`-16t^2+729<104\\\Rightarrow\ -16t^2<104-729........[\text{subtract 729 both sides}]\\\Rightarrow-16t^2<-625\\\Rightarrow\ 16t^2>625....[\text{multiply -1 on both sides}]\\\Rightarrow\ 4t>25\text{ or }4t<-25....[\text{take square root on both sides}]\\\Rightarrow\ t>6.25\text{ or }t>-6.25..[\text{divide 4 on both sides}]`

And time cannot be negative

Thus at t>6.25 seconds,for height= 104 feet above the ground.

⇒The interval of time is he within 104 feet above the ground

would be t > 6.25 .