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Home » Solution: The volume of a hemisphere is $ V_\texthemisphere = \frac23 \pi r^3 $. - Abu Waleed Tea

Solution: The volume of a hemisphere is $ V_\texthemisphere = \frac23 \pi r^3 $. - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Let’s simplify the left-hand side. Let $ x = \frac{a + 2b}{a - 2b} $. Then the expression becomes:

📌 x + \frac{1}{x} = 2 \Rightarrow x^2 - 2x + 1 = 0 \Rightarrow (x - 1)^2 = 0 \Rightarrow x = 1.

📌 \frac{a + 2b}{a - 2b} = 1.

📌 Cross-multiplying:

📌 a + 2b = a - 2b \Rightarrow 2b = -2b \Rightarrow 4b = 0 \Rightarrow b = 0.

📌 Now substitute $ b = 0 $ into the expression we are to evaluate:

📌 \frac{a^2 + 4b^2}{a^2 - 4b^2} = \frac{a^2 + 0}{a^2 - 0} = \frac{a^2}{a^2} = 1.

📌 Question: A fish population in a polluted lake is modeled by the function

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