10. The platform of a theme park ride oscillates vertically. For the first 75 seconds of the ride, $$\frac { \mathrm { d } x } { \mathrm {~d} t } = \frac { t \cos \left( \frac { \pi } { 4 } t \right) } { 32 x }$$ where \(x\) metres is the height of the platform above the ground after time \(t\) seconds.
At \(t = 0\), the height of the platform above the ground is 4 metres.
Find the height of the platform after 45 seconds, giving your answer to the nearest centimetre.
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