the ratios are inversely proportional. find the missing variable.
if $r_1 = 6$, $r_2 = 2$, and $i_1 = 8$, what is the value of $i_2$?

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Inverse Proportion Equations" ], "new_concepts": [], "current_concepts": [ "Inverse Proportion Equations", "Algebraic Substitution", "Linear Equations Solving" ] } ## Set up the inverse proportion equation $$ R_1 \cdot I_1 = R_2 \cdot I_2 $$ ## Substitute the given values $$ 6 \cdot 8 = 2 \cdot I_2 $$ ## Solve for the missing variable $$ \begin{aligned} 48 &= 2 \cdot I_2 \ I_2 &= 24 \end{aligned} $$ If $R_1 = 6$, $R_2 = 2$, and $I_1 = 8$, what is the value of $I_2$? 24 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Inverse Proportion Equations" ] }

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Question

Explanation:

Set up the inverse proportion equation

Substitute the given values

Solve for the missing variable

Answer: