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Home » Convert 0.48 mg to grams: 0.48 × 10⁻³ = 4.8 × 10⁻⁴ g - Aurero

Convert 0.48 mg to grams: 0.48 × 10⁻³ = 4.8 × 10⁻⁴ g - Aurero

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 Un recipiente cilíndrico con un radio de 2 metros está lleno de agua hasta una altura de 3 metros. Si el agua se vierte en un cubo con un área de base de 8 metros cuadrados, ¿cuál será la altura del agua en el cubo?

📌 Volumen del cilindro = \(\pi r^2 h = \pi \times 2^2 \times 3 = 12\pi\) metros cúbicos

📌 Volumen de agua en el cubo = \(8 \times \text{altura}\)

📌 Igualar volúmenes: \(12\pi = 8 \times \text{altura}\)

📌 Altura = \(\frac{12\pi}{8} = \frac{3\pi}{2} \approx 4.71\) metros

📌 #### 4.71 metrosQuestion: A data scientist models user engagement on a platform with the function $ f(t) = t^2 - \frac{t^4}{4} $, where $ t $ represents time in hours. Find the maximum value of $ f(t) $.

📌 Solution: To find the maximum value of $ f(t) = t^2 - \frac{t^4}{4} $, take the derivative $ f'(t) = 2t - t^3 $. Set $ f'(t) = 0 $: $ 2t - t^3 = 0 \Rightarrow t(2 - t^2) = 0 $. Critical points at $ t = 0 $ and $ t = \pm\sqrt{2} $. Evaluate $ f(\sqrt{2}) = (\sqrt{2})^2 - \frac{(\sqrt{2})^4}{4} = 2 - \frac{4}{4} = 1 $. The maximum value is $ \boxed{1} $.

📌 Question: A bioinformatician analyzes gene expression levels modeled by $ g(n) = \frac{3n^2 + 5n}{n^2 + 1} $, where $ n $ is the number of samples. Determine the limit of $ g(n) $ as $ n \to \infty $.

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