Six flags is working on a new concept of a rollercoaster. The traje...

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Six flags is working on a new concept of a rollercoaster. The trajectory followed by future users is given (in 10-2km) by r (t) = (4cos (6t), 5sin (12t), sin (18t)) where t ≥ 0 is expressed in minutes. 1) Calculate the function κ (t), then give its value in t = π / 8. 2) Determine the moment or moments when the curvature κ (t) of the ride's trajectory is maximum. What is the maximum value of the curvature? Show it on a graph.

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