the time, in seconds, that it takes a pendulum to swing back and forth is modeled by the equation below.

$f(l) = 2\pi \sqrt{\frac{l}{32}}$, where $l$ is the length of the pendulum in feet

what is the approximate length of a pendulum that takes $2.4\pi$ seconds to swing back and forth?

1.72 ft
3.05 ft
38.40 ft
46.08 ft

Question

the time, in seconds, that it takes a pendulum to swing back and forth is modeled by the equation below.

$f(l) = 2\pi \sqrt{\frac{l}{32}}$, where $l$ is the length of the pendulum in feet

what is the approximate length of a pendulum that takes $2.4\pi$ seconds to swing back and forth?

1.72 ft
3.05 ft
38.40 ft
46.08 ft

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Radical Equation Solving" ], "new_concepts": [], "current_concepts": [ "Radical Equation Solving", "Radical Modeling" ] } ## Set up the equation with the given time $$ 2.4\pi = 2\pi \sqrt{\frac{l}{32}} $$ ## Solve for the square root term $$ \begin{aligned} \frac{2.4\pi}{2\pi} &= \sqrt{\frac{l}{32}} \ 1.2 &= \sqrt{\frac{l}{32}} \end{aligned} $$ ## Square both sides and solve for l $$ \begin{aligned} (1.2)^2 &= \frac{l}{32} \ 1.44 &= \frac{l}{32} \ l &= 1.44 \times 32 \ l &= 46.08 \end{aligned} $$

(A) 1.72 ft

(B) 3.05 ft

(C) 38.40 ft

(D) 46.08 ft

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Radical Equation Solving" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the equation with the given time

Solve for the square root term

Square both sides and solve for l

Answer: