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Home » \Rightarrow \gcd(12345, 125) = \gcd(125, 95) - DNSFLEX

\Rightarrow \gcd(12345, 125) = \gcd(125, 95) - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 \Rightarrow a + 2b = 3, \quad c + 2d = 4

📌 Apply the second condition:

📌 \begin{pmatrix} a & b \\ c & d \end{pmatrix} \begin{pmatrix} 0 \\ 1 \end{pmQuestion: A space explorer makes 25 voyages through a wormhole, 60% of which are successful. After 10 more voyages, her success rate increases to 68%. How many additional successful voyages did she achieve?

📌 Solution: Initially, the explorer has $ 25 \times 0.60 = 15 $ successful voyages. After 10 more attempts, the total voyages are $ 25 + 10 = 35 $. With a 68% success rate, total successful voyages become $ 35 \times 0.68 = 23.8 $, which rounds to 24 (since successes are whole numbers). The additional successful voyages are $ 24 - 15 = 9 $.

📌 Question: An epidemiologist models the spread of a virus in a population with the equation $ p(t) = -t^2 + 14t + 30 $, where $ p(t) $ represents the number of infected individuals at time $ t $. What is the maximum number of infected individuals?

📌 Solution: The quadratic $ p(t) = -t^2 + 14t + 30 $ opens downward. The vertex occurs at $ t = -\frac{b}{2a} = -\frac{14}{2(-1)} = 7 $. Substituting $ t = 7 $, $ p(7) = -(7)^2 + 14(7) + 30 = -49 + 98 + 30 = 79 $.

📌 \boxed{79}

📌 Question: A museum curator arranges two exhibit pathways modeled by the lines $ y = 4x - 5 $ and $ 2y + 3x = 10 $. Find their intersection point.

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r^2 = 25
بحل المعادلة لإيجاد \( r \):
r = 5
دائرة محاطة بمربع. إذا كانت مساحة المربع 64 وحدة مربعة، فما محيط الدائ...
طول ضلع المربع هو \( \sqrt{64} = 8 \) وحدات.
يساوي قطر الدائرة المحاطة طول ضلع المربع، إذن القطر هو 8 وحدات.
نصف القطر \( r \) للدائرة هو:
r = \frac{8}{2} = 4
المحيط \( C \) يُعطى بالصيغة:
C = 2\pi r = 2\pi \times 4 = 8\pi

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