A swimmer dives into a pool. Her position, p m, underwater can be modelled in relation to

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A swimmer dives into a pool. Her position, p m, underwater can be modelled in relation to her horizontal distance, x m, from the point she entered the water as a quadratic equation p = 1/2x2 – 3x.


The position of the bottom of the pool can be modelled by the linear equation p = 0.3x – 6.


Determine whether this model predicts that the swimmer will touch the bottom of the pool.


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