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Home » \Rightarrow \cos\theta = 1 \Rightarrow \theta = 0^\circ - AMAZONAWS

\Rightarrow \cos\theta = 1 \Rightarrow \theta = 0^\circ - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 \gcd(2028, 2025) = \gcd(2025, 2028 - 2025) = \gcd(2025, 3)

📌 Now check divisibility: \( 2025 \div 3 = 675 \), remainder 0. Thus:

📌 \gcd(2025, 3) = 3

📌 Hence, the greatest common divisor is \(oxed{3}\).

📌 A community nutrition educator is organizing a cooking workshop. If the number of participants on two consecutive days are \( p \) and \( q \), and it is known that \( p + q = 150 \), what is the greatest possible value of \(\gcd(p, q)\)?

📌 Let \( d = \gcd(p, q) \). Then \( p = dk \), \( q = dl \) with \(\gcd(k, l) = 1\), and:

📌 dk + dl = 150 \implies d(k + l) = 150

📌 To maximize \( d \), minimize \( k + l \). Since \(\gcd(k, l) = 1\), the smallest sum is 2 (when \( k = 1 \), \( l = 1 \)). Then:

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Differentiate:
f'(x) = 3x^2 - 8x + 5
Substitute \(x = 2\):
f'(2) = 3(2)^2 - 8(2) + 5 = 12 - 16 + 5 = 1
Solve the logarithmic equation \(\log_2(x+3) + \log_2(x-1) = 3\).
Combine logs:
\log_2[(x+3)(x-1)] = 3
Convert to exponential form:
Expand and solve:
x^2 + 2x - 3 = 8

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