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Find the circle passing through the foci of the ellipse $\dfrac{x^2}{16}+\dfrac{y^2}{9}=1$ and having its centre at $(0,3)$.
For the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$: $a^2=16, b^2=9$, so $c^2=16-9=7$, giving foci at $(\pm\sqrt{7},0)$.
The circle has centre $(0,3)$. Radius $r=$ distance from $(0,3)$ to $(\sqrt{7},0)$:
$r^2=(\sqrt{7}-0)^2+(0-3)^2=7+9=16\Rightarrow r=4$
Equation: $x^2+(y-3)^2=16\Rightarrow x^2+y^2-6y+9=16\Rightarrow x^2+y^2-6y-7=0$
Option A ($10,000) is correct.
Variable cost per unit = ($130,000 + $15,000) ÷ 5,000 = $29
Variable cost of sales (4,000 units) = $116,000
Contribution = $180,000 − $116,000 = $64,000
Profit = $64,000 − $25,000 (fixed overheads) − $29,000 (closing inventory adjustment) = $10,000
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