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King's Conceptual System (1981) consists of three open, dynamic interacting systems:
- Personal System: The individual — includes concepts of body image, growth, development, perception, self, space, and time
- Interpersonal System: Two or more individuals interacting — includes communication, interaction, role, stress, and transaction
- Social System: Larger groups — includes authority, decision-making, organization, power, and status
Key equation: Perception → Judgment → Action → Reaction → Interaction → Transaction → Goal Attainment
Substituting into \(xy^2 = 8\): \(\dfrac{2}{y} \times y^2 = 8 \Rightarrow 2y = 8 \Rightarrow y = 4\)
Then \(x = \dfrac{2}{4} = 0.5\)
Draft loss for year: $320. Adjustments needed: (1) Irrecoverable debts of $930 recovered; (2) Existing allowance $520, required allowance = 5% of trade receivables $9,600. What is the revised profit or loss?
Option D (Profit of $650) is correct.
Recovery of debt: +$930
Required allowance = 5% × $9,600 = $480; Reduction = $520 − $480 = +$40
Revised = −$320 + $930 + $40 = +$650 profit
For each $t\in\mathbb{R}$, let $[t]$ denote the greatest integer $\leq t$. Evaluate: $\displaystyle\lim_{x\to0^+} x\left(\left[\dfrac{1}{x}\right]+\left[\dfrac{2}{x}\right]+\cdots+\left[\dfrac{15}{x}\right]\right)$
For large $N=1/x$, $[k/x]\approx kN$ with error at most 1.
$x\sum_{k=1}^{15}\left[\dfrac{k}{x}\right] \approx x\sum_{k=1}^{15}\dfrac{k}{x} = \sum_{k=1}^{15}k = \dfrac{15\cdot16}{2} = 120$
More rigorously: $[k/x] = k/x - \{k/x\}$ where $0\leq\{k/x\}<1$. Then $x\cdot\{k/x\}
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