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moderno sombreados cortes de cabello hombres - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Find the area of a regular hexagon with side length 6 cm.

📌 A regular hexagon can be divided into 6 equilateral triangles.

📌 Area of one equilateral triangle: \(\frac{\sqrt{3}}{4} s^2 = \frac{\sqrt{3}}{4} \times 36 = 9\sqrt{3}\).

📌 Total area = \(6 \times 9\sqrt{3} = 54\sqrt{3}\) cm².

📌 #### \(54\sqrt{3}\) cm²**Question:

📌 A philosopher of science is contemplating the symmetry of natural laws and wonders: If the sum of two positive integers \(a\) and \(b\) equals 2023, what is the largest possible value of \(\gcd(a, b)\)?

📌 To maximize \(\gcd(a, b)\), we note that if \(\gcd(a, b) = d\), then \(a = dx\) and \(b = dy\) for some integers \(x\) and \(y\) with \(\gcd(x, y) = 1\). Thus, \(a + b = dx + dy = d(x + y) = 2023\). Therefore, \(d\) must divide 2023.

📌 First, we factor 2023 to find its divisors. Checking small prime numbers:

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1 block of discoveries from the 18th century (4 discoveries)
1 block of discoveries from the 19th century (2 discoveries)
First, we calculate the number of ways to arrange the three blocks. Si...
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The 3 discoveries in the 17th century block can be arranged in \(3! =...
The 4 discoveries in the 18th century block can be arranged in \(4! =...
The 2 discoveries in the 19th century block can be arranged in \(2! =...
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3! \times 3! \times 4! \times 2! \times 2! = 6 \times 6 \times 24 \tim...
Calculate step-by-step:

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