W = Fd cosθ; max when θ=0° (cos0=1).

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.

This is a frequently misunderstood historical fact. According to the textbook, the first printing press in Muslim territory was established in Andalusia (Muslim-ruled Spain) in the 1480s. Crucially, it was operated not by Muslim scholars but by a family of Jewish merchants, who used it to print texts in the Hebrew script. After the fall of Granada to Catholic Spain in the 1490s (completing the Reconquista), this press was relocated — the textbook notes it moved to Istanbul, which had become a major destination for the Sephardic Jewish community expelled from Spain. Islamic calligraphic traditions were highly valued, and there was cultural resistance to the printing press in many parts of the Muslim world, which partly explains why the technology spread more slowly there than in Christian Europe despite the Muslim world's earlier familiarity with papermaking.

Apply the addition formula: $\tan^{-1}(2x)+\tan^{-1}(3x)=\tan^{-1}\!\left(\dfrac{5x}{1-6x^2}\right)$ when $6x^2<1$.

Setting equal to $\pi/4$: $\dfrac{5x}{1-6x^2}=1 \Rightarrow 5x=1-6x^2 \Rightarrow 6x^2+5x-1=0$

$x=\dfrac{-5\pm\sqrt{25+24}}{12}=\dfrac{-5\pm7}{12}$

$x=\dfrac{2}{12}=\dfrac{1}{6}$ or $x=\dfrac{-12}{12}=-1$.

Since $x\geq0$, only $x=\dfrac{1}{6}$ is valid. Check: $6\cdot(1/6)^2=1/6<1$ ✓. So $A=\{1/6\}$ — a singleton.