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Home » Therefore, the volume of water remaining in the tank is \( 54\pi \) cubic meters. - Londonproperty

Therefore, the volume of water remaining in the tank is \( 54\pi \) cubic meters. - Londonproperty

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 Queremos la probabilidad de que $ X \leq Y - 15 $, es decir, Clara llega al menos 15 minutos antes que Daniel.

📌 Tablamos el espacio muestral como un cuadrado en el plano $ XY $, con $ 0 \leq X \leq 60 $, $ 0 \leq Y \leq 60 $. El área total es $ 60 \times 60 = 3600 $.

📌 La condición $ X \leq Y - 15 $ implica $ Y \geq X + 15 $. La región en el cuadrado que satisface esto está delimitada por la línea $ Y = X + 15 $, intersectada con $ Y \leq 60 $.

📌 Enjulga los límites:

📌 Cuando $ X = 0 $, $ Y \geq 15 $

📌 Cuando $ X = 45 $, $ Y \geq 60 $

📌 Para $ X > 45 $, $ Y \geq X + 15 > 60 $, lo cual está fuera del cuadrado

📌 Así, la región válida es un trapecio desde $ X = 0 $ hasta $ X = 45 $, con altura constante en $ Y $ desde $ X+15 $ hasta 60.

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