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Property purchased 1 January 2010 for $100,000, useful life 50 years. On 1 January 2024, revalued to $119,000. Total useful life remains 50 years from 2010. What is the depreciation charge for year ended 31 December 2024?
Option D ($3,306) is correct.
Years elapsed by 1 Jan 2024 = 14 years; Remaining life = 50 − 14 = 36 years
Annual depreciation = $119,000 ÷ 36 = $3,305.56 ≈ $3,306
The standard hydrogen electrode (SHE) is assigned a potential of:
By convention, SHE potential is defined as 0 V at all temperatures, with H⁺ (1 M) | H₂ (1 atm) | Pt.
The solution of the differential equation $\dfrac{dy}{dx} = (x-y)^2$, subject to $y(1)=1$, is:
Let $v = x - y$, so $\frac{dv}{dx} = 1 - \frac{dy}{dx} = 1 - v^2$.
Separate: $\frac{dv}{1-v^2} = dx \Rightarrow \frac{1}{2}\ln\left|\frac{1+v}{1-v}\right| = x + C$
i.e. $\ln\left|\frac{1+x-y}{1-x+y}\right| = 2x + C'$
At $(1,1)$: $v=0$, $\ln(1)=2+C' \Rightarrow C'=-2$
Final: $-\ln\left|\dfrac{1-x+y}{1+x-y}\right| = 2(x-1)$ which matches option B.
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