Answers
Exercise 58
58.1 ( a ) ( 0 , 0 ) , ( 6,1.5 ) ( b ) ( i )
( ii ) d y ( x � 6 ) y � d x ( 3� 2 y) x dy
� 2.5
x �
d t
( iii ) |
The population of |
|
|
shark is decreasing at the beginning . |
58.2 |
( a ) |
( 0 , 0 ) , ( 8 , 0.4 ) |
( b ) ( i )
( ii )
0
d y ( x �8 ) y � d x ( 2 �5 y) x dy
3 � dx �
13 ( iii ) 0 � y � 0.4
58.3 |
( a ) |
The population of crocodile is increasing at the beginning . |
( b ) |
( i ) |
600 |
|
( ii ) |
550 |
58.4 |
( a ) |
10 x �
3
|
( b ) |
( i ) |
210 |
|
( ii ) |
270 |
Exercise 59
59.1 ( a ) ( 0 , 0 ) ( b ) t 0
2 det ( M��I
) � � �8� �12
( c ) �1 �� 6 , �2 �� 2 �1� �5�
( d ) v
1
� � � , v
2
� � �
�1� �1�
( e ) ( i ) ( ii ) ( f ) ( 1.35 , 0.268 )
x � �e � 10e
� 6t �2t y � �e � 2e
( g ) Refer to solution
� 6t �2t
59.2 ( a ) y � 3 ( b )
59.3 ( a )
2 det ( M��I
) � � �� �12
( c ) �1 �� 3 , �2 � 4 �7� �0�
( d ) v
1
� � � , v
2
� � �
�1� �1�
( e ) ( i ) ( ii ) x� 7
3t
e � y �e � e
�3t 4t
( f ) The population of horse will approach 0 .
( g ) Refer to solution �dv �3v�4x
� dt � �dx
� v
�� dt ( b ) ( i ) v1 � 1.3
( ii ) x1 � 0.1
( c ) |
( i ) |
0.23 m |
|
( ii ) |
0.403 m |
( d )
2 det ( M��I
) � � �3� � 4
( e ) �1 �� 1, �2 � 4 ��1� �4�
( f ) v
1
� � � , v
2
� � � � 1 � �1�
( g ) |
( i ) |
� x� �0.2e t �
0.2e
|
|
( ii ) |
0.516 m |
( h ) 0.113 m
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