Apps. and Interpretation for IBDP Maths Ebook 1 | Page 151

(b) (i) p �1.2 � 2
(M1) for valid approach
p � 0.6
A1 N2
12
(ii)
360
Period � (M1) for valid approach
q
360
q � (A1) for substitution
12
q � 30
A1 N3
(iii)
2 � 0.8
r � (M1) for valid approach
2
r � 1.4
A1 N2
(c) The value of t at 00:00 on 3 March 2018
�4� 24
(M1) for valid approach
� 28
The value of t of the second low tide on 3 March 2018
�30 � 12
� 42
(A1) for correct value of t
Thus, the second low tide on 3 March 2018 occurs
at 14:00. A1 N3
[7]
[3]
Exercise 40
1. In a coast the height of the sea water in metres is modelled by the function
h( t) � psin( qt)
� r , where t is the number of hours after 23:00 hours on 7 April 2018,
for 0 �t
� 72 .
The point A (8.25, 0.4) represents the first low tide and B (13.75,1.8) represents the next
high tide.
(a) (i) How much time is there between the first low tide and the next high
tide?
(ii)
Find the difference in height between low tide and high tide.
[4]
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