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If the determinant $\begin{vmatrix}x-4&2x&2x\\2x&x-4&2x\\2x&2x&x-4\end{vmatrix} = (A+Bx)(x-A)^2$, find the ordered pair $(A,B)$.
Apply $R_1\to R_1+R_2+R_3$: each element in row 1 becomes $5x-4$.
Factor out $(5x-4)$: $\Delta = (5x-4)\begin{vmatrix}1&1&1\\2x&x-4&2x\\2x&2x&x-4\end{vmatrix}$
Apply $C_2-C_1, C_3-C_1$: $= (5x-4)\begin{vmatrix}1&0&0\\2x&-x-4&0\\2x&0&-x-4\end{vmatrix} = (5x-4)(x+4)^2$
Comparing with $(A+Bx)(x-A)^2$: $A=-4$, $B=5$. So $(A,B)=\mathbf{(-4,5)}$.
The genetic information inherited from your parents for a specific trait like hair color is called your:
Genotype refers to the actual alleles present (e.g., BB, Bb, bb). Phenotype is the physical expression. Karyotype is the chromosome set.
Elongation $\Delta L = \frac{FL}{AY} = \frac{FL}{\pi(d/2)^2 Y} \propto \frac{L}{d^2}$.
- New elongation $\Delta L' \propto \frac{2L}{(2d)^2} = \frac{2L}{4d^2} = \frac{1}{2} \Delta L$
- $\Delta L' = \frac{1}{2} \times 0.04 = 0.02\text{ m}$.
KCl must NEVER be administered via IV push — it can cause fatal cardiac arrest. During KCl infusion, the critical monitoring parameter is urine output (renal function).
Safe KCl infusion requires:
- Urine output \\geq 30 \\text{ mL/hr} — confirms kidneys can excrete excess potassium
- Urine output < 25–30 mL/hr indicates oliguria → STOP infusion immediately (risk of fatal hyperkalemia)
- Maximum peripheral infusion rate: 10 \\text{ mEq/hr}
- Maximum concentration peripherally: 40 mEq/L
- Never administer undiluted KCl
Signs of KCl toxicity/hyperkalemia: peaked T-waves, widened QRS, bradycardia, cardiac arrest. As a Charge Nurse, monitoring IV KCl infusions is a major patient safety responsibility.
Information for a period:
- Sales: $1,500,000
- Purchases: $1,000,000
- Closing Inventory: $50,000
Inventory turnover was 12 times and the gross profit margin was 40%. There were also returns and carriage inwards. Calculate opening inventory.
1. Gross Profit = $1,500,000 $\times$ 40% = $600,000.
2. Cost of Sales (COS) = $1,500,000 - $600,000 = $900,000.
3. Average Inventory = COS / Turnover = $900,000 / 12 = $75,000.
4. Average Inv = (Opening + Closing) / 2 $\Rightarrow$ $75,000 = (Opening + $50,000) / 2.
5. Opening Inventory = $150,000 - $50,000 = $100,000.
Total power: $P = 15 \times 40 + 5 \times 100 + 5 \times 80 + 1 \times 1000 = 600 + 500 + 400 + 1000 = 2500\,\text{W}$
Total current: $I = \frac{P}{V} = \frac{2500}{220} \approx 11.36\,\text{A}$
The fuse must safely carry this current. The smallest standard value that is greater than or equal to 11.36 A from the options is 12 A. Answer: A.
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