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Home » Thus, the value of \(b\) is: - Dyverse

Thus, the value of \(b\) is: - Dyverse

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Pregunta: Un modelo climático utiliza un patrón hexagonal de celdas para estudiar variaciones regionales de temperatura. Cada celda es un hexágono regular con longitud de lado $ s $. Si la densidad de datos depende del área de la celda, ¿cuál es la relación entre el área de un hexágono regular y el área de un círculo inscrito de radio $ r $?

📌 A) $ \frac{2\sqrt{3}}{3} \cdot \frac{r^2}{\text{Area}} = 1 $ → Area ratios: $ \frac{2\sqrt{3} s^2}{6\sqrt{3} r^2} = \frac{s^2}{3r^2} $, and since $ s = \sqrt{3}r $, this becomes $ \frac{3r^2}{3r^2} = 1 $? Corrección: Pentatexto A) $ \frac{2\sqrt{3}}{3} \cdot \frac{r^2}{\text{Area}} $ — but correct derivation: Area of hexagon = $ \frac{3\sqrt{3}}{2} s^2 $, inscribed circle radius $ r = \frac{\sqrt{3}}{2}s \Rightarrow s = \frac{2r}{\sqrt{3}} $. Then Area $ = \frac{3\sqrt{3}}{2} \cdot \frac{4r^2}{3} = 2\sqrt{3} r^2 $. Circle area: $ \pi r^2 $. Ratio: $ \frac{\pi r^2}{2\sqrt{3} r^2} = \frac{\pi}{2\sqrt{3}} $. But question asks for "ratio of area of circle to hexagon" or vice? Question says: area of circle over area of hexagon → $ \frac{\pi r^2}{2\sqrt{3} r^2} = \frac{\pi}{2\sqrt{3}} $. But none match. Recheck options. Actually, $ s = \frac{2r}{\sqrt{3}} $, so $ s^2 = \frac{4r^2}{3} $. Hexagon area: $ \frac{3\sqrt{3}}{2} \cdot \frac{4r^2}{3} = 2\sqrt{3} r^2 $. So $ \frac{\pi r^2}{2\sqrt{3} r^2} = \frac{\pi}{2\sqrt{3}} $. Approx: $ \frac{3.14}{3.464} \approx 0.907 $. None of options match. Adjust: Perhaps question should have option: $ \frac{\pi}{2\sqrt{3}} $, but since not, revise model. Instead—correct, more accurate: After calculation, the ratio is $ \frac{\pi}{2\sqrt{3}} $, but among given:

📌 A) $ \frac{\pi}{2\sqrt{3}} $ — yes, if interpreted correctly.

📌 But actually, $ \frac{\pi r^2}{2\sqrt{3} r^2} = \frac{\pi}{2\sqrt{3}} $, so A is correct.

📌 But in original list, no such. So revise:

📌 Pregunta: In a hexagonal climate grid with side $ s $, the area is $ \frac{3\sqrt{3}}{2}s^2 $. If an inscribed circle has radius $ r $, and $ r = \frac{\sqrt{3}}{2}s $, what is $ \frac{\pi r^2}{\text{Area}} $?

📌 But to match format, best:

📌 Corrected:

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rac{(3v+2) + (5v-4) + (4v+7)}{3} = rac{3v + 5v + 4v + 2 - 4 + 7}{3} =...
Set this equal to 15:
rac{12v + 5}{3} = 15.
12v + 5 = 45.
Subtract 5:
12v = 40.
Divide by 12:
v = rac{40}{12} = rac{10}{3}.
Thus, the value of $v$ is $oxed{\dfrac{10}{3}}$.Question: What two-di...
Solution: To find the number, compute the least common multiple (LCM)...

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