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Home » Thus, the radius of the inscribed circle is \(\boxed3\). - ToelettAPP

Thus, the radius of the inscribed circle is \(\boxed3\). - ToelettAPP

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Question: An astronomer models the orbital period $ T $ of a planet around a star as $ T = k \cdot r^{3/2} $, where $ r $ is the semi-major axis and $ k $ is a constant. If $ T = 8 $ when $ r = 4 $, find $ T $ when $ r = 9 $.

📌 Solution: First, find the constant $ k $ using the given values:

📌 = k \cdot 4^{3/2}

📌 Since $ 4^{3/2} = (2^2)^{3/2} = 2^3 = 8 $, we have:

📌 = k \cdot 8 \Rightarrow k = 1

📌 Thus, the formula becomes $ T = r^{3/2} $.

📌 Now substitute $ r = 9 $:

📌 T = 9^{3/2} = (9^{1/2})^3 = 3^3 = 27

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