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📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 Now, to evaluate $ \lim_{t o -1} E(t) $, we use the simplified expression:

📌 \lim_{t o -1} E(t) = \lim_{t o -1} (t + 3) = -1 + 3 = 2

📌 Although $ E(t) $ is undefined at $ t = -1 $, the limit exists.

📌 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

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