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# Filling a Weather Balloon

The height (h km) that a weather balloon can reach is related to the volume (v m₃) of helium in it at sea level by the equation:

$h = \frac{8v^{2}}{5} – \frac{32v^{3}}{255}\ ,\ v \leq 12$

a) Find the volume of helium required to achieve the maximum height and state this height.

[5 marks]

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