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📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 En résolvant l’équation quadratique, \( n = \frac{-7 \pm \sqrt{7^2 + 4 \cdot 3 \cdot 220}}{2 \cdot 3} = \frac{-7 \pm 37}{6} \).

📌 Ainsi, \( n = 5 \) (la solution positive).

📌 #### 5سؤال: يحتوي النمس أنموذجي على دودة طويلة بشكل أسي كدالة للحرارة \( T \) (بالكلفن)، مُمَثّلة بالمعادلة \( J(T) = aT^n \)، حيث \( n \) ثابت. إذا كان الجنس يتضاعف عندما ترتفع درجة الحرارة من 300 كلفن إلى 310 كلفن، فحدد قيمة \( n \).

📌 الحل: لدينا نموذج \( J(T) = aT^n \)، حيث \( J(T) \) هو عدد الأفراد و\( T \) هي درجة الحرارة. بما أن الدود يتضاعف عندما ترتفع \( T \) من 300 كلفن إلى 310 كلفن، لدينا:

📌 \frac{J(310)}{J(300)} = 2 \implies \frac{a(310)^n}{a(300)^n} = 2 \implies \left(\frac{310}{300}\right)^n = 2

📌 بأخذ الطبيع والت LOG:

📌 n \ln\left(\frac{310}{300}\right) = \ln 2 \implies n = \frac{\ln 2}{\ln\left(\frac{31}{30}\right)} \approx \frac{0.6931}{0.0324} \approx 21.42

📌 إذن، القيمة التقريبية لـ \( n \) هي:

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