greg is in a car at the top of a roller-coaster ride. the distance \$d\$ of the car from the ground as the car descends is determined by the equation \$d = 144 - 16t^2\$, where \$t\$ is the number of seconds it takes the car to travel down to each point on the ride. for which interval of time is gregs car moving in the air?

\$0 < t \le 3\$
\$-3 < t \le 3\$
\$t > 3\$
\$0 < t < 3\$

Question

greg is in a car at the top of a roller-coaster ride. the distance \$d\$ of the car from the ground as the car descends is determined by the equation \$d = 144 - 16t^2\$, where \$t\$ is the number of seconds it takes the car to travel down to each point on the ride. for which interval of time is gregs car moving in the air?

\$0 < t \le 3\$
\$-3 < t \le 3\$
\$t > 3\$
\$0 < t < 3\$

$0 < t \le 3$
$-3 < t \le 3$
$t > 3$
$0 < t < 3$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Solving Quadratic Equations", "Quadratic Inequalities" ], "new_concepts": [], "current_concepts": [ "Solving Quadratic Equations", "Quadratic Inequalities", "Quadratic Modeling Interpretation" ] } ## Find the time when the car reaches the ground $$ \begin{aligned} d &= 0 \ 144 - 16t^2 &= 0 \ 16t^2 &= 144 \ t^2 &= 9 \ t &= 3 \quad (t > 0) \end{aligned} $$ ## Determine the interval of time in the air $$ \begin{aligned} d &> 0 \ 144 - 16t^2 &> 0 \ t^2 &< 9 \ -3 < &t < 3 \end{aligned} $$ Since time $t$ must be positive as the ride starts at $t = 0$: $$ 0 < t < 3 $$

(A) $0 < t \le 3$

(B) $-3 < t \le 3$

(C) $t > 3$

(D) $0 < t < 3$

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

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QUESTION IMAGE

Question

Explanation:

Find the time when the car reaches the ground

Determine the interval of time in the air

Answer: