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Home » One root near \( x \approx 0.542 \) - Get link 4share

One root near \( x \approx 0.542 \) - Get link 4share

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 \[ s = \frac{25 + 30 + 35}{2} = 45 \, \text{ft} \]

📌 \[ \text{Área} = \sqrt{45(45-25)(45-30)(45-35)} = \sqrt{45 \times 20 \times 15 \times 10} = \sqrt{135000} \approx 367.42 \, \text{ft}^2 \]

📌 La altitud más corta es desde el vértice opuesto al lado más largo (35 pies):

📌 \[ \text{Altitud} = \frac{2 \times \text{Área}}{35} = \frac{2 \times 367.42}{35} \approx 21.02 \, \text{ft} \]

📌 La altitud más corta es aproximadamente \(\boxed{21.02}\) pies.

📌 Pregunta: Un geógrafo estudia una zona costera triangular donde el mar retira su línea de costa, formando un triángulo con lados de 10 km, 17 km y 21 km. ¿Cuál es el radio del círculo inscrito en esta forma retráctil?

📌 Solución: Primero, calcula el semiperímetro:

📌 \[ s = \frac{10 + 17 + 21}{2} = 24 \, \text{km} \]

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But total is \(S = a / (1 - r) = a / (1 - 1/2) = 2a\)
Set \(2a = 729\) → \(a = 364.5\)
Then bottles: 364.5, 182.25, 91.125, 45.5625, 22.78125, 11.390625, 5.6...
Sum after n terms: \(S_n = a(1 - (1/2)^n)/(1 - 1/2) = 2a(1 - 2^{-n})\)
Set \(2a = 729\), so \(S_n = 729(1 - 2^{-n})\)
We want to fill 729 ml, so \(729(1 - 2^{-n}) \geq 729\) → only when n→...
Not helpful.
Instead, question is: How many bottles are needed until the *sum of ca...
Given context, likely intended:
A sequence where each bottle holds half the previous, starting with 72...

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