when a baseball is hit by a batter, the height of the ball, $h(t)$, at time $t$, $t \ge 0$, is determined by the equation $h(t) = -16t^2 + 64t + 4$. if $t$ is in seconds, for which interval of time is the height of the ball greater than or equal to 52 feet?

$1

Question

when a baseball is hit by a batter, the height of the ball, \$h(t)\$, at time \$t\$, \$t \ge 0\$, is determined by the equation \$h(t) = -16t^2 + 64t + 4\$. if \$t\$ is in seconds, for which interval of time is the height of the ball greater than or equal to 52 feet?

\$1 < t < 3\$
\$t \le 1\$
\$0 < t < 1\$
\$1 \le t \le 3\$

$1 < t < 3$
$t \le 1$
$0 < t < 1$
$1 \le t \le 3$

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 quadratic inequality $$ -16t^2 + 64t + 4 \ge 52 $$ ## Rearrange and simplify the inequality $$ \begin{aligned} -16t^2 + 64t - 48 &\ge 0 \ t^2 - 4t + 3 &\le 0 \end{aligned} $$ ## Solve the factored inequality $$ \begin{aligned} (t - 1)(t - 3) &\le 0 \ 1 \le t &\le 3 \end{aligned} $$

(A) $1 < t < 3$

(B) $t \le 1$

(C) $0 < t < 1$

(D) $1 \le t \le 3$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Set up the quadratic inequality

Rearrange and simplify the inequality

Solve the factored inequality

Answer: