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Home » Try $ m = 0 $: $ x = 8 $ (not two-digit) - Groen Casting

Try $ m = 0 $: $ x = 8 $ (not two-digit) - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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

📌 Substituez \( x = 30 \) : \( P(30) = -2(900) + 120(30) - 1000 = -1800 + 3600 - 1000 = 800 \).

📌 #### UnitÃ©s = 30, BÃ©nÃ©fice maximal = 800

📌 Une balle est lancÃ©e verticalement vers le haut avec une vitesse initiale \( v_0 = 20 \) m/s. Sa hauteur \( h(t) \) aprÃ¨s \( t \) secondes est \( h(t) = 20t - 5t^2 \). Trouver le temps pour atteindre la hauteur maximale et la hauteur maximale.

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\mathbf{r}(t) = \mathbf{A} + t(\mathbf{B} - \mathbf{A}) = \langle 1, 3...
angle + t\langle 3, -2, 3
angle = \langle 1 + 3t, 3 - 2t, -2 + 3t
Let $P = \mathbf{r}(t)$. The vector $\overrightarrow{CP} = \mathbf{r}(...
angle = \langle -1 + 3t, 4 - 2t, -5 + 3t
To minimize the distance, minimize $\|\overrightarrow{CP}\|^2$:
D^2 = (-1 + 3t)^2 + (4 - 2t)^2 + (-5 + 3t)^2
= (1 - 6t + 9t^2) + (16 - 16t + 4t^2) + (25 - 30t + 9t^2) \
= 42 - 52t + 22t^2
Take derivative and set to zero:

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