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In Diabetic Ketoacidosis (DKA), insulin deficiency leads to:
- Excess fat breakdown → ketone body production
- Accumulation of ketoacids → metabolic acidosis
- Compensatory hyperventilation (Kussmaul breathing) → \\text{PaCO}_2 falls (respiratory compensation)
Expected ABG in DKA:
| Parameter | Value | Interpretation |
|---|---|---|
| pH | < 7.35 | Acidosis |
| \\text{PaCO}_2 | < 35 mmHg | Respiratory compensation (hyperventilation) |
| \\text{HCO}_3^- | < 18 mEq/L | Primary metabolic loss |
Option B (pH 7.28, PaCO₂ 28, HCO₃ 10) fits perfectly — metabolic acidosis with respiratory compensation.
A body is projected at such an angle that the horizontal range is three times the maximum height. The angle of projection is:
Range: $R = \dfrac{u^2\sin2\theta}{g}$, Max height: $H = \dfrac{u^2\sin^2\theta}{2g}$
Given $R = 3H$: $\dfrac{\sin2\theta}{1} = 3\cdot\dfrac{\sin^2\theta}{2} \Rightarrow 2\sin\theta\cos\theta = \dfrac{3}{2}\sin^2\theta$
$\Rightarrow \tan\theta = \dfrac{4}{3} \Rightarrow \theta = \tan^{-1}\!\left(\dfrac{4}{3}\right) \approx \mathbf{53°}$
J Limited makes furniture with a mark-up of 40%. A job 10 km away involves: Materials $400; Labour $240; Travel $2 per km each part of journey. What price will the company quote?
Option D ($952) is correct.
Travel = 10 km each way = 20 km × $2 = $40
Total cost = $400 + $240 + $40 = $680
Quoted price = $680 × 1.40 = $952
An employee works 40 hours/week at $8/hour. Bonus: 30% of hourly rate per hour of time saved. Standard time: 30 minutes per unit. Last week: 40 hours worked, 90 units produced. What were her total earnings?
Option B ($332) is correct.
Basic pay: 40 × $8 = $320
Allowed time for 90 units = 45 hours; Actual = 40 hours; Time saved = 5 hours
Bonus = 5 × (30% × $8) = 5 × $2.40 = $12
Total = $320 + $12 = $332
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