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📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 Transformation : \( x' = 2(x + 5) = 2x + 10 \).

📌 Nouvelle moyenne : \( \mu' = 2\mu + 10 = 2 imes 50 + 10 = 110 \).

📌 Nouvelle variance : \( \sigma'^2 = 2^2 \sigma^2 = 4 imes 100 = 400 \).

📌 Nouvelle Ã©cart type : \( \sigma' = \sqrt{400} = 20 \).

📌 #### Nouvelle moyenne = 110, Nouveau Ã©cart type = 20

📌 Le bÃ©nÃ©fice \( P(x) \) d'une entreprise de fabrication de \( x \) unitÃ©s est modÃ©lisÃ© par \( P(x) = -2x^2 + 120x - 1000 \). Trouver le nombre d'unitÃ©s qui maximise le bÃ©nÃ©fice et le bÃ©nÃ©fice maximal.

📌 Fonction quadratique \( P(x) = -2x^2 + 120x - 1000 \).

📌 Maximum Ã \( x = -rac{b}{2a} = -rac{120}{2(-2)} = 30 \).

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c = \sqrt{9^2 + 12^2} = \sqrt{81 + 144} = \sqrt{225} = 15 \text{ cm}
The area \(A\) of the triangle is:
A = \frac{1}{2} \times 9 \times 12 = 54 \text{ cm}^2
The semi-perimeter \(s\) of the triangle is:
s = \frac{9 + 12 + 15}{2} = 18 \text{ cm}
The radius \(r\) of the inscribed circle is given by:
r = \frac{A}{s} = \frac{54}{18} = 3 \text{ cm}
Thus, the radius of the inscribed circle is \(\boxed{3}\).
A circle is inscribed in a triangle with sides measuring 7 cm, 24 cm,...
First, verify that the triangle is a right triangle using the Pythagor...

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This is a well-known inequality in symmetric form. By the **Nesbitt’s...
\frac{a}{b + c} + \frac{b}{a + c} + \frac{c}{a + b} \geq \frac{3}{2}
with equality if and only if \( a = b = c \). Since \( a + b + c = 1 \...
\frac{\frac{1}{3}}{1 - \frac{1}{3}} = \frac{\frac{1}{3}}{\frac{2}{3}}...
So the sum is \( 3 \cdot \frac{1}{2} = \frac{3}{2} \).
Thus, the minimum value is \( \boxed{\frac{3}{2}} \).
Question: Compute \( \sum_{n=1}^{50} \frac{1}{\sqrt{n} + \sqrt{n+1}} \...
Solution: Consider the general term:
\frac{1}{\sqrt{n} + \sqrt{n+1}}
Rationalize the denominator by multiplying numerator and denominator b...

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