\y^3 = -512,000\
\
^3 = -1,000,000\

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Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Cube Roots", "Solving Cubic Equations" ], "current_concepts": [ "Cube Roots", "Solving Cubic Equations" ] } ## Solve the first cubic equation $$ \begin{aligned} y^3 &= -512,000 \ y &= \sqrt[3]{-512,000} \ y &= \sqrt[3]{-1 \times 512 \times 1000} \ y &= -1 \times 8 \times 10 \ y &= -80 \end{aligned} $$ ## Solve the second cubic equation $$ \begin{aligned} r^3 &= -1,000,000 \ r &= \sqrt[3]{-1,000,000} \ r &= \sqrt[3]{-1 \times 100^3} \ r &= -100 \end{aligned} $$ | No. | Problem | Answer | |---|---|---| | 1 | $y^3 = -512,000$ | $y = -80$ | | 2 | $r^3 = -1,000,000$ | $r = -100$ | { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Solving Cubic Equations" ] }

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Explanation:

Solve the first cubic equation

Solve the second cubic equation

Answer: