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In the $xy$-plane, line $k$ has equation $3x - 2y = 0$. Compare:
Quantity A: The $x$-intercept of line $k$
Quantity B: The $y$-intercept of line $k$
Find the intercepts of $3x - 2y = 0$:
x-intercept (set $y = 0$): $3x = 0 \Rightarrow x = 0$.
y-intercept (set $x = 0$): $-2y = 0 \Rightarrow y = 0$.
Both intercepts are $0$ (the line passes through the origin).
Quantity A $= 0 =$ Quantity B. The two quantities are equal.
Persistent Occiput Posterior (POP) position is a common cause of prolonged second stage and arrest of descent. In OP position:
- The fetal head presents with a larger diameter to the pelvis: occipito-frontal diameter \(\approx 11.5\,\text{cm}\) vs. sub-occipito-bregmatic \(9.5\,\text{cm}\) in OA
- Internal rotation from OP to OA requires \(135°\) rotation (vs. \(90°\) from OT, \(45°\) from OA)
- Causes: anthropoid/android pelvis, deflexed head
Management options:
- Manual rotation to OA (Barton's maneuver)
- Expectant management if maternal/fetal condition good
- Instrumental delivery: forceps (Kielland's rotational forceps) or rotational vacuum
- Cesarean section if rotation fails or fetal distress
CPD is less likely in a multigravida who delivered previously without CPD. Hypotonic labor would show weak contractions on partograph/CTG.
Given that $x \neq 0$, compare the two quantities below.
Column A: $\dfrac{x}{|x|}$
Column B: $1$
The expression $\dfrac{x}{|x|}$ is the sign function of $x$:
- If $x > 0$: $\dfrac{x}{|x|} = \dfrac{x}{x} = 1$ → equal to Column B
- If $x < 0$: $\dfrac{x}{|x|} = \dfrac{x}{-x} = -1$ → less than Column B
Since $x$ can be positive or negative, and we get different results, the relationship cannot be determined from the information given.
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