Question

May someone help me with this HW problem?

The depth (D metres) of water in a harbour at a time (t hours) after midnight on a particular day can be modelled by the function
D = 2 sin(0.51t - 0.4) +5, t <=15,
where radians have been used.

Select the two options which are correct statements about the predictions based on this model.

Select one or more:
a) The smallest depth is 5 metres. 
b) At midday, the depth is approximately 7 metres. 
c) The model can be used to predict the tide for up to 15 days. 
d) The largest depth is 7 metres.
e) At midnight the depth is approximately 4.2 metres.
f) The time between the two high tides is exactly 12 hours. 
g) The depth of water in the harbour falls after midnight. 

Answer 1

not a, shallow = -2+5 = 3
check b, 2 sin (.51*12 -.4) + 5 = 2 sin (around 2 pi) +5 around 5, no
t is HOURS </= 15, not days] so not c
YES d, because 2+5 = 7
e. when t = 0 D = 2 sin (-.4 ) + 5 = - 2(.4)+5 = 5-.8 =4.2 YES
f. .51*12 = which is close but not exactly 2 pi. In fact nothing but 2 pi is exactly 2 pi
g. well, it goes up and down