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Given that $st = \sqrt{10}$, compare:
Quantity A: $s^2$
Quantity B: $\dfrac{10}{t^2}$
From $st = \sqrt{10}$, squaring both sides: $(st)^2 = 10$, so $s^2 t^2 = 10$.
Therefore $s^2 = \dfrac{10}{t^2}$.
Quantity A $= s^2 = \dfrac{10}{t^2} =$ Quantity B.
The two quantities are equal.
- Orthophosphorous acid ($H_{3}PO_{3}$): $+3$
- Pyrophosphorous acid ($H_{4}P_{2}O_{5}$): $+3$
- Hypophosphoric acid ($H_{4}P_{2}O_{6}$): $+4$
- Pyrophosphoric acid ($H_{4}P_{2}O_{7}$): $+5$
Overlap occurs when $n_1 \lambda_1 = n_2 \lambda_2$.
$n_1(650) = n_2(520) \implies \frac{n_1}{n_2} = \frac{520}{650} = \frac{4}{5}$.
Distance $y = \frac{n_1 \lambda_1 D}{d} = \frac{4 \times 650 \times 10^{-9} \times 1.5}{0.5 \times 10^{-3}} = 7.8 \times 10^{-3} \text{ m} = 7.8 \text{ mm}$.
Bi Sheng invented movable clay type in China around 1041 AD โ nearly four centuries before Gutenberg. However, the Chinese writing system contains thousands of characters (Mandarin has over 50,000, with several thousand in common use), compared to the 26-letter Latin alphabet used in European languages. Setting up movable type for Chinese therefore required an enormous number of individual pieces, making it cumbersome and time-consuming โ often slower than traditional block printing for short or medium runs. By contrast, a European printer needed only a small set of metal type for the entire alphabet, making Gutenberg's press extraordinarily efficient for European languages. This alphabetic advantage is a key reason the printing press became a revolutionary mass communication tool in Europe but remained a marginal improvement in China. Interestingly, Gutenberg also used durable oil-based ink and rag paper introduced to Europe via Muslim trade routes, further improving output quality.
This is a classic presentation of Neonatal Respiratory Distress Syndrome (RDS), also called Hyaline Membrane Disease:
- Prematurity (36 weeks โ late preterm)
- Grunting, retractions, nasal flaring, tachypnea
- Ground glass appearance + air bronchograms on CXR = pathognomonic of RDS
Pathophysiology: Deficiency of surfactant (produced by Type II pneumocytes from ~24 weeks, mature by ~35 weeks). Surfactant reduces alveolar surface tension. Without it:
\[\text{Surface tension} \uparrow \Rightarrow \text{Alveolar collapse} \Rightarrow \text{V/Q mismatch} \Rightarrow \text{Hypoxia}\]
- Treatment: Exogenous surfactant (beractant, poractant alfa) via endotracheal tube + respiratory support (CPAP/mechanical ventilation)
- Prevention: Antenatal corticosteroids (betamethasone 12 mg IM ร 2 doses, 24 hrs apart) if delivery expected before 34 weeks โ accelerates fetal lung maturity
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