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An arch of a bridge is semi-elliptical with major axis horizontal. If the length the base is 9 meter and the highest part of the bridge is 3 meter from the horizontal; the best approximation of the height of the arch. 2 meter from the centre of the base is
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The correct answer is:
$8 / 3 \mathrm{~m}$
The equation of the ellipse is
$$
\frac{x^{2}}{\left(\frac{9}{2}\right)^{2}}+\frac{y^{2}}{9}=1
$$
Where centre is assumed as origin and base as $x$ -axis. Put $x=2,$ we get
$$
\frac{16}{81}+\frac{\mathrm{y}^{2}}{9}=1 \Rightarrow \mathrm{y}=\frac{\sqrt{65}}{3} \approx \frac{8}{3} \mathrm{~m}
$$
(approximately)
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