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Home » Solution: Let’s plug in $ a = b = 1 $ into the functional equation: - Red Crowns

Solution: Let’s plug in $ a = b = 1 $ into the functional equation: - Red Crowns

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Use the Pythagorean theorem: \( \text{base}^2 + 8^2 = 10^2 \).

📌 \( \text{base}^2 = 100 - 64 = 36 \).

📌 Base = \( \sqrt{36} = 6 \) meters.

📌 The sum of the first 10 terms of an arithmetic sequence is 155. If the first term is 5, find the common difference.

📌 The sum formula for an arithmetic sequence is \( S_n = \frac{n}{2} (2a + (n-1)d) \).

📌 Substituting known values: \( 155 = \frac{10}{2} (2 \times 5 + 9d) \).

📌 Simplifying: \( 155 = 5 (10 + 9d) \) → \( 155 = 50 + 45d \) → \( 105 = 45d \) → \( d = \frac{105}{45} = \frac{7}{3} \).

📌 #### \(\frac{7}{3}\)1. A laboratory experiment requires a solution with 150 mL of a 20% saline solution. The technician has a 30% saline solution and a 10% saline solution available. How many mL of each solution should be mixed to achieve the desired concentration?

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