jerald jumped from a bungee tower. if the equation that models his height, in feet, is \$h = -16t^2 + 729\$, where \$t\$ is the time in seconds, for which interval of time is he less than 104 feet above the ground?

\$t > 6.25\$
\$-6.25 < t < 6.25\$
\$t < 6.25\$
\$0 \le t \le 6.25\$

Question

jerald jumped from a bungee tower. if the equation that models his height, in feet, is \$h = -16t^2 + 729\$, where \$t\$ is the time in seconds, for which interval of time is he less than 104 feet above the ground?

\$t > 6.25\$
\$-6.25 < t < 6.25\$
\$t < 6.25\$
\$0 \le t \le 6.25\$

$t > 6.25$
$-6.25 < t < 6.25$
$t < 6.25$
$0 \le t \le 6.25$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Inequalities" ], "new_concepts": [], "current_concepts": [ "Quadratic Inequalities", "Projectile Motion Modeling" ] } ## Set up the inequality for height $$ -16t^2 + 729 < 104 $$ ## Solve the quadratic inequality for t $$ \begin{aligned} -16t^2 &< -625 \ t^2 &> 39.0625 \ t > 6.25 &\quad \text{or} \quad t < -6.25 \end{aligned} $$ ## Apply physical constraints $$ \begin{aligned} t &\ge 0 \ t &> 6.25 \end{aligned} $$

(A) $t > 6.25$

(B) $-6.25 < t < 6.25$

(C) $t < 6.25$

(D) $0 \le t \le 6.25$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Inequalities" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the inequality for height

Solve the quadratic inequality for t

Apply physical constraints

Answer: