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Stress is defined as $\frac{\text{Force}}{\text{Area}}$.
- Force (Weight) $\propto \text{Volume} \propto L^3$
- Area $\propto L^2$
- $\text{Stress} \propto \frac{L^3}{L^2} \propto L$
- Since $L$ increases by factor $9$, stress increases by factor $9$.
Iga suspects that some credit notes received from suppliers have not been recorded. Which of the following actions should she take to verify this?
- Compare purchases ledger balances against supplier statements
- Extract a trial balance of individual purchases ledger accounts
- Prepare a purchases ledger control account
Comparing the business's records with the supplier's statement is the most effective way to find missing credit notes, as the supplier will have recorded the credit note even if the business forgot to. A trial balance or control account only checks internal consistency.
Key measurement concepts:
| Concept | Definition |
|---|---|
| Reliability | Consistency and stability of measurements over repeated testing |
| Validity | Accuracy โ does the tool measure what it claims to measure? |
| Sensitivity | Ability to correctly identify true positives |
| Specificity | Ability to correctly identify true negatives |
If $\cos^{-1}x - \cos^{-1}\!\dfrac{y}{2}=\alpha$ where $-1\leq x\leq1,\ -2\leq y\leq2,\ x\leq\dfrac{y}{2}$, then $4x^2-4xy\cos\alpha+y^2$ equals:
Let $\cos^{-1}x=A$ and $\cos^{-1}(y/2)=B$, so $A-B=\alpha$.
Then $\cos A=x,\ \cos B=y/2,\ \sin A=\sqrt{1-x^2},\ \sin B=\sqrt{1-y^2/4}$.
Using $\cos\alpha=\cos(A-B)=\cos A\cos B+\sin A\sin B=\dfrac{xy}{2}+\sqrt{1-x^2}\sqrt{1-\frac{y^2}{4}}$
$4x^2-4xy\cos\alpha+y^2 = (2x-y\cos\alpha)^2+y^2(1-\cos^2\alpha)$... expanding directly: $= 4x^2+y^2-4xy\cos\alpha$.
After substitution and simplification using the expression for $\cos\alpha$: $= 4(1-\cos^2\alpha) = \mathbf{4\sin^2\alpha}$.
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