Your Practice Set – Applications and Interpretation for IBDP Mathematics SE Production Limited 338 55.1 ( a ) 2 det ( ) 8 9 � � � � � � � M I ( b ) 1 1 � �� , 2 9 � � ( c ) 1 1 1 � � � � � � � � v , 2 3 2 1 � � � � � � � � � � � v ( d ) 9 3 1 2 1 1 t t Ae Be � � � � � � � � � � � � � � � � � � � � X 55.2 ( a ) 2 det ( ) 3 28 � � � � � � � M I ( b ) 1 4 � �� , 2 7 � � ( c ) 1 5 2 1 � � � � � � � � � � � � v , 2 3 1 � � � � � � � v ( d ) ( i ) 4 7 5 3 2 t t x Ae Be � � � � ( ii ) 4 7 t t y Ae Be � � � 55.3 ( a ) 2 det ( ) 2 10 � � � � � � � M I ( b ) 1 3i � , 1 3i � ( c ) 3 i 3 i 1 2 ( ) t t t e Ae Be � � � X v v ( d ) The phase portrait is an unstable spiral . 55.4 ( a ) 2 det ( ) 10 29 � � � � � � � M I ( b ) 5 2i � � , 5 2i � � ( c ) 5 2 i 2 i 1 2 ( ) t t t e Ae Be � � � � X v v ( d ) The phase portrait is a stable spiral . 56.1 ( a ) 1 10.6 y � ( b ) ( i ) 2 11.12639 y � ( ii ) 3 11.7 y � 56.2 ( a ) 1 3.8 y � ( b ) ( i ) 2 7.084281 y � ( ii ) 3 13.050070 y � ( iii ) 4 23.9 y � 56.3 ( a ) 1 2.75 y � ( b ) ( i ) 2 3.428 y � ( ii ) 3 4.0734 y � ( iii ) 4 4.70 y � 56.4 ( a ) 1 4.2 y � ( b ) ( i ) 2 6.248 y � ( ii ) 3 9.8166 y � ( iii ) 4 16.1646 y � ( iv ) 5 27.7 y � 57.1 ( a ) ( i ) 1 6.05 x � ( ii ) 1 3.05 y � ( b ) ( i ) 2 7.48 x � ( ii ) 2 4.55 y � 57.2 ( a ) ( i ) 1 1.11 x � ( ii ) 1 1.01 y � ( b ) ( i ) 2 1.12 x � ( ii ) 2 1.02 y � ( iii ) 3 1.13 x � ( iv ) 3 1.03 y � 57.3 ( a ) d 8 15 d d d u u x t x u t � � � � � � � � �� ( b ) ( i ) 1 0.2 u � ( ii ) 1 0.1 x � ( c ) 2 0.12 x � 57.4 ( a ) d 12 36 d d d u u x t x u t � � � � � � � �� ( b ) ( i ) 1 1.2 u � ( ii ) 1 2.15 x � ( c ) 2 2.21 x � Exercise 55 Exercise 56 Exercise 57