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Centripetal force $F = \frac{mv^2}{R} \propto \frac{1}{R^n}$.
- $v^2 \propto \frac{1}{R^{n-1}} \implies v \propto R^{(1-n)/2}$
- $T = \frac{2\pi R}{v} \propto \frac{R}{R^{(1-n)/2}} = R^{1 - (\frac{1-n}{2})} = R^{(n+1)/2}$.
Depolarization of the postsynaptic membrane is caused by diffusion of which ion?
Depolarization occurs when Na⁺ enters the postsynaptic neuron (excitatory postsynaptic potential). Cl⁻ influx causes hyperpolarization (inhibitory). Ca²⁺ triggers neurotransmitter release, not directly depolarization.
Mary purchased a book whose price plus a 4% sales tax equaled the total amount she paid. She gave the cashier a $10 bill and received correct change of less than $3.00. Which of the following statements must be true? Select all that apply.
Let the price of the book $= p$. Total paid $= 1.04p$.
She paid $10 and received change less than $3.00, meaning total paid was more than $7.00:
$1.04p > 7.00 \Rightarrow p > 6.73$
She also received some change, so total paid $< \$10.00$:
$1.04p < 10.00 \Rightarrow p < 9.615$
So $6.73 < p < 9.615$. Now check each statement:
- Statement A: $p < \$9.50$ — Not necessarily, since $p$ can be up to $9.615$. ✗
- Statement B: $p > \$6.90$ — Not necessarily, $p$ can be $6.80$ (giving change $\approx \$2.93 < \$3.00$). ✗
- Statement C: Sales tax $= 0.04p < 0.04 \times 9.615 \approx \$0.385 < \$0.45$. This is always true within the valid range. ✓
- Statement D: Tax $> \$0.50$ would require $p > 12.50$, which is impossible here. ✗
Only Statement C must be true.
Post-term Pregnancy Management (\(\geq 42\) weeks; post-dates \(\geq 41\) weeks):
This patient:
- 41+3 weeks = post-dates (risk period begins)
- Bishop score 4 = unfavorable cervix (score \(\leq 6\))
- AFI 6 cm = borderline oligohydramnios (normal: \(8{-}24\,\text{cm}\); oligohydramnios: \(\leq 5\,\text{cm}\))
- Reactive CTG = reassuring currently
Risks of post-term pregnancy:
- Placental insufficiency, meconium aspiration
- Macrosomia, shoulder dystocia
- Oligohydramnios, cord compression
- Perinatal mortality increases after 41 weeks
Management: Most guidelines recommend induction of labor by 41–42 weeks. With unfavorable cervix (Bishop score 4), cervical ripening first (Prostaglandin E₂ gel/insert or misoprostol) then oxytocin induction.
AFI trending down is additional reason not to wait further. Conservative management is inappropriate here.
Energy flux (Intensity) is the rate of heat flow per unit area:
$J = \frac{H}{A} = \frac{k \Delta T}{L}$
$J = \frac{0.1 \times (10^3 - 10^2)}{1} = 0.1 \times 900 = 90 \text{ Wm}^{-2}$
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