The tides in Ulladulla Harbour can be modelled to the equation

where is the height of the tide in metres and is the time in hours after midnight.

Large fishing vessels can only enter or leave the harbour when the tide is at least 2 meters high.

Determine the first time after midnight that large shipping vessels can no longer enter or exit the harbour and when access is again possible, giving your answers to the nearest minute?   (4 marks)

A particular energy wave can be modelled by the function

1. Express this function in the form  .  (2 marks)
   

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2. Find the time the wave first attains its maximum value. Give your answer to one decimal place.  (2 marks)
   

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The current flowing through an electrical circuit can be modelled by the function

1.  Express the function in the form  .  (2 marks)
   

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2.  Find the time at which the current first obtains it maximum value.   (1 mark)
   

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3.  Sketch the graph of  . Clearly show its range and label the coordinates of its first maximum value. Do not label -intercepts.   (1 mark)
   

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