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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.
The system $x+ky+3z=0$, $3x+ky-2z=0$, $2x+4y-3z=0$ has a non-zero solution $(x,y,z)$. Find the value of $\dfrac{xz}{y^2}$.
For non-zero solution, $\Delta=0$:
$\begin{vmatrix}1&k&3\\3&k&-2\\2&4&-3\end{vmatrix}=1(−3k+8)−k(−9+4)+3(12−2k)=−3k+8+5k+36−6k=44−4k=0$
So $k=11$.
With $k=11$: from equations 1 and 2: $x+11y+3z=0$ and $3x+11y-2z=0$. Subtracting: $2x-5z=0\Rightarrow x=\frac{5z}{2}$.
Substituting back: $\frac{5z}{2}+11y+3z=0\Rightarrow 11y=-\frac{11z}{2}\Rightarrow y=-\frac{z}{2}$.
$\frac{xz}{y^2}=\frac{\frac{5z}{2}\cdot z}{\frac{z^2}{4}}=\frac{\frac{5z^2}{2}}{\frac{z^2}{4}}=\frac{5}{2}\times4=\mathbf{10}$
- Moles of $CH_{4} = 6.4 / 16 = 0.4 \text{ mol}$
- Moles of $CO_{2} = 8.8 / 44 = 0.2 \text{ mol}$
- Total $n = 0.6 \text{ mol}$
- Using $P = \frac{nRT}{V}$:
- $P = \frac{0.6 \times 8.314 \times 300}{10 \times 10^{-3} \text{ m}^{3}}$
- $P \approx 149,652 \text{ Pa} \approx 150 \text{ kPa}$
The dimension of magnetic permeability $\mu_0$ is:
From the Biot-Savart law or the force between parallel conductors:
$F = \dfrac{\mu_0 I_1 I_2 L}{2\pi r}$
$[\mu_0] = \dfrac{[F][r]}{[I]^2[L]} = \dfrac{MLT^{-2} \cdot L}{A^2 \cdot L} = MLT^{-2}A^{-2}$
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