Question

A geographer proposes that the depth, d metres, of a river can be modelled by a function of the
form d = p sinqx, where x is the distance from the left bank of the river.
The river is 8 m wide and the depth halfway across the river is 2.3 m.
a Find the value of p and q.
[3]
b Calculate the depth the model predicts 2 m from the left bank.
[1]
The geographer checks the prediction by measuring the depth of the river 2 m from the left bank.
He finds the depth is 2.5 m.
c Calculate the percentage error in the model's prediction.
[2]
In view of the extra measurement, the geographer decides that a model of the form
d = ar3 + bx2 + cx would be more appropriate.
d Find, to three significant figures, the values of a, b and c.
[4]
e Sketch the function found in part d for 0 [2]
f Use this model to find
i the maximum depth of the river
ii the cross-sectional area of the river.
[4]
a

Answer 1

Answer:

0.20.2

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