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Home » n \equiv 0 \pmod36, \quad n \equiv 3 \pmod7 - Upplift

n \equiv 0 \pmod36, \quad n \equiv 3 \pmod7 - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 Equate exponents: \( x + 1 = 4x - 4 \).

📌 Solve: \( 1 + 4 = 4x - x \rightarrow 5 = 3x \rightarrow x = \frac{5}{3} \).

📌 #### \(\frac{5}{3}\)

📌 A ladder 13 meters long leans against a wall, with its base 5 meters from the wall. How high up the wall does the ladder reach?

📌 Use the Pythagorean theorem: \( a^2 + b^2 = c^2 \).

📌 Let \( a = 5 \) (base), \( c = 13 \) (ladder), solve for \( b \) (height).

📌 \( 5^2 + b^2 = 13^2 \rightarrow 25 + b^2 = 169 \).

📌 \( b^2 = 169 - 25 = 144 \).

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