select the correct answer.

the value of $m$ varies inversely as the square of $n$. when $n = 3$, $m = 6$. what is the positive value of $n$ when $m = 13.5$?

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$\bigcirc 4$
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Question

select the correct answer.

the value of $m$ varies inversely as the square of $n$. when $n = 3$, $m = 6$. what is the positive value of $n$ when $m = 13.5$?

$\bigcirc 9$
$\bigcirc 4$
$\bigcirc 18$
$\bigcirc 2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Inverse Variation" ], "new_concepts": [], "current_concepts": [ "Inverse Variation" ] } ## Set up the inverse variation equation $$ m = \frac{k}{n^2} $$ ## Solve for the constant of variation k $$ \begin{aligned} 6 &= \frac{k}{3^2} \ 6 &= \frac{k}{9} \ k &= 54 \end{aligned} $$ ## Find the positive value of n when m = 13.5 $$ \begin{aligned} 13.5 &= \frac{54}{n^2} \ n^2 &= \frac{54}{13.5} \ n^2 &= 4 \ n &= 2 \quad (n > 0) \end{aligned} $$

9

4

18

2

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Inverse Variation" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the inverse variation equation

Solve for the constant of variation k

Find the positive value of n when m = 13.5

Answer: