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A projectile is thrown at angles $(45ยฐ-\theta)$ and $(45ยฐ+\theta)$ with the horizontal. The ratio of their horizontal ranges is:
Using $R = \dfrac{u^2\sin2\alpha}{g}$:
$R_1 = \dfrac{u^2\sin(90ยฐ-2\theta)}{g} = \dfrac{u^2\cos2\theta}{g}$
$R_2 = \dfrac{u^2\sin(90ยฐ+2\theta)}{g} = \dfrac{u^2\cos2\theta}{g}$
$R_1 : R_2 = \mathbf{1:1}$
The magnitude of change in velocity is $|\Delta v| = 2v \sin(\frac{\theta}{2})$.
- $|\Delta v| = 2(10) \sin(60^{\circ}/2) = 20 \sin 30^{\circ}$
- $|\Delta v| = 20 \times \frac{1}{2} = 10\text{ m/s}$.
Propofol Infusion Syndrome (PRIS) is a rare but life-threatening complication of prolonged high-dose propofol infusion.
Risk factors:
- Dose \(> 5 \text{ mg/kg/hr}\) (or \(> 83 \text{ mcg/kg/min}\)) for \(> 48\) hours
- Concomitant use of catecholamines or corticosteroids
- Low carbohydrate intake
- Children (higher risk)
- Pink/lipemic plasma, rhabdomyolysis
- Renal failure (AKI)
- Increase in CK, triglycerides
- Severe metabolic acidosis, cardiac failure
- Immediately stop propofol infusion
- Switch to alternative sedation (midazolam, dexmedetomidine)
- Supportive care (CRRT for renal failure)
- Treat metabolic acidosis
The pK_b of n-propylamine is approximately:
n-Propylamine is a weak base with K_b ~5ร10โปโด, pK_b = -log(5ร10โปโด) โ 3.30. Closest is 3.32? Actually standard value ~3.32. But MDCAT often uses 3.28 or 3.32. Given options, 3.32 is common.
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