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is coffee good for your liver - Deep Underground Poetry

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 f(2) + 0 = 4 \Rightarrow f(2) = \boxed{4}

📌 Question: Find the area enclosed by the graph of $ |x| + |y| = 4 $.

📌 Solution: The equation $ |x| + |y| = 4 $ represents a diamond (rhombus) centered at the origin. In the first quadrant, it becomes $ x + y = 4 $, with intercepts at $ (4, 0) $ and $ (0, 4) $. The full figure is symmetric across both axes.

📌 The diamond has diagonals of length 8 (horizontal) and 8 (vertical), so the area is:

📌 \text{Area} = \frac{1}{2} \times \text{diagonal}_1 \times \text{diagonal}_2 = \frac{1}{2} \times 8 \times 8 = \boxed{32}

📌 ---**Question:** An ornithologist is studying a flock of 8 distinct bird species migrating together. In how many ways can the ornithologist label these species with unique tags numbered 1 through 8?

📌 To solve this problem, we need to determine the number of permutations of 8 distinct bird species, as each species is assigned a unique tag. The number of permutations of \( n \) distinct objects is given by \( n! \) (n factorial).

📌 For 8 species, the number of permutations is calculated as:

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