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A coastal canal has a uniform cross section along its 700m length. Surveyors measure the depth, in meters, at equally spaced points across its 21 meter width. The results are summarized in the diagram below.
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Using the trapezoid rule, estimate the cross sectional area of the canal.
Hence calculate the volume of water in the canal when it is full. Give your answer in the form a×10k, where a≤1<10 and k∈Z.
The depth D meters of water in the canal t hours after midnight on a given day can be modeled by
where A>0.
Find the time at which the first low tide occurs, giving your answer in hour : minutes.
Given that the canal is full at high tide and only empty at low tide, find the value of A and the value of c.
Francesca models the volume of water in the canal with the function V(t)=700k×D(t).
Calculate the value of k that Francesca should use, and explain what it represents in this context.
Using technology and Francesca's model, estimate the maximum rate at which water enters the canal.
Explain why this estimate is unlikely to be accurate, and state for what shape of canal it would be accurate.
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