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Cardiac Tamponade: Beck's Triad
- Hypotension β reduced cardiac output due to compression
- Muffled (distant) heart sounds β fluid surrounding the heart dampens sounds
- Jugular venous distension (JVD) β elevated venous pressure as blood cannot enter compressed heart
- Pulsus paradoxus \(> 10 \text{ mmHg}\): Exaggerated fall in systolic BP during inspiration
- Tachycardia (compensatory)
- Electrical alternans on ECG (alternating QRS amplitude)
- Enlarged cardiac silhouette on CXR ('water bottle' heart)
If $0 < st < 1$, then which of the following can be true?
I. $s < -1$ and $t > 0$
II. $s < -1$ and $t < -1$
III. $s > -1$ and $t < -1$
We need $0 < st < 1$, which means $st$ is positive and less than 1.
Check each statement:
I. $s < -1$ and $t > 0$: If $s < -1$ (negative) and $t > 0$ (positive), then $st < 0$ (negative). This violates $st > 0$. β
II. $s < -1$ and $t < -1$: Both negative means $st > 0$ β. If $s = -2$ and $t = -0.4$, then $st = 0.8$, which satisfies $0 < st < 1$ β
Actually, wait. Let's reconsider: if $s < -1$ and $t < -1$, then both are less than $-1$, so both magnitudes are greater than 1. The product would be greater than 1, violating $st < 1$. Let me recalculate: if $s = -1.5$ and $t = -0.5$, then $st = 0.75$, which works. But $t = -0.5$ does not satisfy $t < -1$. If both $s < -1$ and $t < -1$, then $|s| > 1$ and $|t| > 1$, so $|st| > 1$, meaning $st > 1$ since both are negative (making product positive). This violates $st < 1$. β
III. $s > -1$ and $t < -1$: This gives us $-1 < s$ and $t < -1$. If $s$ is positive (satisfies $s > -1$) and $t$ is negative with $|t| > 1$, then $st < 0$. β If $s$ is negative with $|s| < 1$ (like $s = -0.5$) and $t < -1$ (like $t = -1.5$), then $st = (-0.5)(-1.5) = 0.75 > 0$ and $< 1$ β
Actually, I need to reconsider option I more carefully...
The maximum horizontal range of a projectile is 16 km ($g = 10\text{ m/s}^2$). The minimum muzzle velocity required is:
Maximum range occurs at $45Β°$: $R_{\max} = \dfrac{u^2}{g}$
$u^2 = R_{\max}\times g = 16000 \times 10 = 160000$
$u = \sqrt{160000} = \mathbf{400\text{ m/s}}$
A business uses marginal costing. Which formula correctly calculates contribution?
Option C is correct.
Contribution = Sales Revenue − All Variable Costs (variable production costs + variable selling expenses).
Fixed costs are period costs deducted after contribution β they are not part of the contribution formula.
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