Tim throws a stick straight up in the air from the ground. The function [tex]h = -16 t^2 + 48 t[/tex] models the height, [tex]h[/tex], in feet, of the stick above the ground after [tex]t[/tex] seconds. Which inequality can be used to find the interval of time in which the stick reaches a height of more than 8 feet?

A. [tex]-16 t^2 + 48 t \ \textgreater \ 8[/tex]
B. [tex]-16 t^2 + 48 t \ \textless \ 8[/tex]
C. [tex]-16 t^2 + 48 t^3 8[/tex]
D. [tex]-16 t^2 + 48 t \le 8[/tex]

Question

27-06-2024
Mathematics

Answered

Tim throws a stick straight up in the air from the ground. The function [tex]h = -16 t^2 + 48 t[/tex] models the height, [tex]h[/tex], in feet, of the stick above the ground after [tex]t[/tex] seconds. Which inequality can be used to find the interval of time in which the stick reaches a height of more than 8 feet?

A. [tex]-16 t^2 + 48 t \ \textgreater \ 8[/tex]
B. [tex]-16 t^2 + 48 t \ \textless \ 8[/tex]
C. [tex]-16 t^2 + 48 t^3 8[/tex]
D. [tex]-16 t^2 + 48 t \le 8[/tex]

Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-06-27T14:42:09-04:00

To determine the interval of time during which the stick's height is more than 8 feet, we need to set up an inequality with the given height function \( h(t) = -16t^2 + 48t \).

Given function:
[tex]\[ h(t) = -16t^2 + 48t \][/tex]

We are looking for the values of \( t \) where \( h(t) > 8 \).

First, set up the inequality:
[tex]\[ -16t^2 + 48t > 8 \][/tex]

This inequality describes the time intervals where the height of the stick is greater than 8 feet. Hence, the inequality that can be used to find this interval is:
[tex]\[ -16t^2 + 48t > 8 \][/tex]

Therefore, the correct inequality is:
[tex]\[ -16t^2 + 48t > 8 \][/tex]

Among the provided options, the correct one is:
[tex]\[ -16 t^2 + 48 t > 8 \][/tex]