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📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 Express 81 as \( 3^4 \), so equation becomes:

📌 \( 3^{2x+1} = 3^4 \cdot 3^{x-1} = 3^{4 + x - 1} = 3^{x+3} \).

📌 Since bases are equal, set exponents equal:

📌 \( 2x + 1 = x + 3 \) → \( 2x - x = 3 - 1 \) → \( x = 2 \).

📌 In a triangle, the lengths of two sides are 13 cm and 15 cm. If the angle between them is 60°, what is the length of the third side?

📌 Use the Law of Cosines: \( c^2 = a^2 + b^2 - 2ab\cos C \), where \( a = 13 \), \( b = 15 \), \( C = 60^\circ \), \( \cos 60^\circ = 0.5 \).

📌 \( c^2 = 13^2 + 15^2 - 2 \cdot 13 \cdot 15 \cdot 0.5 = 169 + 225 - 195 = 199 \).

📌 So, \( c = \sqrt{199} \approx 14.106 \), but we keep exact: \( \sqrt{199} \).

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