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Home » First, factorize 180: - Deep Underground Poetry

First, factorize 180: - Deep Underground Poetry

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 30^2 = 900 < 1000

📌 Thus, the largest possible value of \( x \) is \(\boxed{30}\).

📌 Question:** A mechanical engineer is designing a component for an HVAC system. The component must fit between two points that are \( 4\pi \) and \( 10\pi \) units apart. How many whole numbers lie within this interval?

📌 Solution:** First, approximate the interval endpoints using \( \pi \approx 3.14 \):

📌 4\pi \approx 4 \times 3.14 = 12.56

📌 10\pi \approx 10 \times 3.14 = 31.4

📌 The interval of interest is \( (12.56, 31.4) \). We seek the whole numbers strictly greater than 12.56 and strictly less than 31.4. These numbers are:

📌 13, 14, 15, \ldots, 31

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