Question

Tim throws a stick straight up in the air from the ground. The function h = -16t^2+ 48t models the height, h, in feet, of

the stick above the ground after t seconds. Which inequality can be used to find the interval of time in which the stick
reaches a height of more than 8 feet?

Answer 1

you want more than 8 feet so the answer would be -16t^2+48t>8

Explanation:

h=-16t^2+48t

-16t62+48t>8

-16t^2+48t=8

divide both sides of the equal sighn by 8

-2t^2+6t=1

put the symbol back in

-2t^2+6t>1

substitute a random mumber for t

-2(5)^2+6(5)>1

-10^2+30>1

subtract 30 from both sides

100>-29

state is true so -16t62+48t>8 is the correct answer

Answer 2

`-2t^2+ 6t -1 > 0`

Explanation:

Function Modeling

The height h in feet of the stick threw by Tim is modeled by the function:

`h = -16t^2+ 48t`

where t is the time in seconds.

It's required to write an inequality that can be used to find the interval of time in which the stick reaches a height of more than 8 feet, i.e. h > 8.

Using the given model, we write the inequality:

`-16t^2+ 48t > 8`

Dividing by 8

`-2t^2+ 6t > 1`

Subtracting 1, we get the required inequality:

`\mathbf{-2t^2+ 6t -1 > 0}`