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what is an a acute angle - IQnection

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 To maximize \( d \), \( m + n \) must be minimized. Since \(\gcd(m, n) = 1\), the smallest possible value for \( m + n \) is 2, achieved when \( m = 1 \) and \( n = 1 \). Thus:

📌 d imes 2 = 100 \implies d = rac{100}{2} = 50

📌 Therefore, the largest possible value of \(\gcd(x, y)\) is \(oxed{50}\).

📌 An entomologist is studying the population dynamics of a certain insect species. The population count, \( n \), is observed to be a three-digit number such that the sum of its digits is a perfect square. What is the largest possible population count?

📌 Let \( n = 100a + 10b + c \), where \( a, b, c \) are digits and \( a

📌 eq 0 \). The sum of the digits is \( a + b + c \), and we require this sum to be a perfect square. The largest three-digit number is 999, so \( a + b + c \) ranges from 1 to 27.

📌 The largest perfect square within this range is \( 25 \) (since \( 5^2 = 25 \)). We seek the largest \( n \) such that \( a + b + c = 25 \).

📌 Given \( a + b + c = 25 \), maximize \( n \) by choosing the largest possible \( a \). Start with \( a = 9 \):

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