sol mat haeussler bypriale
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!"#$% '( )'*+%*+,)-".+%/ 0 1
)-".+%/ 1 23
)-".+%/ 4 35
)-".+%/ 2 67
)-".+%/ 5 124
)-".+%/ 3 180
)-".+%/ 8 199
)-".+%/ 9 421
)-".+%/ 6 473
)-".+%/ 7 222
)-".+%/ 10 239
)-".+%/ 11 296
)-".+%/ 14 542
)-".+%/ 12 587
)-".+%/ 15 327
)-".+%/ 13 815
)-".+%/ 18 836
)-".+%/ 19 890
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!
"#$%&'( )
*(+,-'./ )01
10 "#$%& '() *+ , -%.,/*0% *-/%.%#120 "#$%2 3%4,$+%5 ,-6 7 ,#% *-/%.%#+ ,-6 7 81
30 9,:+%2 3%4,$+% /;% -,/$#,: -$ 7 *+7 3%4,$+%7 D E7F G 81
40 9,:+%& 5E) H IF G 5E(5F G 5I2 3$/E5 H )FE5 H IF G J H K G IK1
50 9,:+%& ' ! D " G " D E' ! F G " ' ! 1
60 "#$%& E ! D 5FEIF G E ! FEIF D E5FEIF G I ! D K1
70 "#$%&2 2
1.2 2 2 2
x x x+ = + = +
80 "#$%2 3%4,$+% .b ab
ac c =
90 9,:+%& /;% :%>/ +*6% *+ L !" 2 3$/ /;% #*.;/ +*6% *+25 . x y
1)0 "#$%& 3B /;% ,++=4*,/*0% ,-6 4=
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!"#$%&' )* "#$%#& '( )*+#,-. /012 !"#$%&'(#%$) +,#-./,#0(,1 2",1)303
"
270 ! E " ' D ( F G ! ME " ' F D( N G ! E " ' F D ! E( FG ! M " D E ' FN D !( G ! E "F D ! E ' F D !( G !" !' D !(
280 '5 D E'IF G 'J
290 'J D 5 G 'I
3)0 J D E'IF G 5
310 7 ' 5 G L
320 7 ' E'IF G 7 D I G ((
330 L E()F G L D () G K
340 $ E%F G$ D %
350 E'5FEOF G 'E5 H OF G '(K
360 7E'OF G 'E7 H OF G 'J)
370 E'5FE'(5F G 5E(5F G 5I
380 (OE(F G E(F(O G E( H (OF G(O
390 19
1 91 9
1 = =
4)0 'E'J D ! F G 'E'JF ' ! G J ' !
410 '7E ! F G 'E7 ! F G '7 !
420 '(5E ! ' "F G E'(5F ! ' E'(5FE "F G '(5 ! D (5 " E=# (5 " ' (5 ! F
430 'M'J D E' "FN G 'E'JF ' E' "F G J D "
440 3 3 1 3 1
3 1515 15 5 3 5 = = = =
450 9 9 9 1 1
9 ( 27)27 27 9 3 3 = = = =
460 ( ) ( )
a a
a b b b
= =
470 5E'J D 5F G 5E'IF G 'K
480 )M'5E)F D JE5FN G )M'J D (5N G )MJN G (K
490 E'5FE'IFE'(F G KE'(F G 'K
5)0 E(5FE(5F G E(5FE(5F G (II
510 ) E(F G )
520 )E ! ' IF G )E ! F ' )EIF G ) ! ' (5
530 IEL D ! F G IELF D IE ! F G 58 D I !
540 'E ! ' 5F G ' ! D 5
550 8E' ! F G 8
560 1 8 1 8
811 11 11
= =
570 5
51
=
580 14 2 7 221 3 7 3
x x x y y y
= =
590 3 3 32 (2 ) 2 x x x
= =
6)0 2 1 2 1 23 3 3 x x x
= =
610 (3 ) 3
(3 )a a b ab
bc c c
= =
620 7
(5 ) 75
aa
=
630 aby a by byax a x x
= =
640 7 1 7 1 7 y x y x xy
= =
650 2 5 2 5 10 x y x y xy
= =
660 1 1 3 2 3 2 5
2 3 6 6 6 6
++ = + = =
670 5 3 5 9 5 9 14 2 7 7
12 4 12 12 12 12 2 6 6+ + = + = = = =
680 3 7 9 14 9 14 5 5 1 1
10 15 30 30 30 30 5 6 6 = = = = =
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/012 !"#$%&'(#%$) +,#-./,#0(,1 2",1)303 +&,%-./ )01
#
690 4 6 4 6 10
25 5 5 5
++ = = =
7)0
5 5 5
X Y X Y =
710 3 1 1 18 3 2 18 3 2 172 4 6 12 12 12 12 12
+ + = + = =
720 2 3 16 15 16 15 15 8 40 40 40 40
= = =
730 6 6
6 6 x y
x y y y x x
= = =
740 31
3 1 3 3
l l m l l
m m m= = =
750 2 2
2 2
x y z
xy
x z x xy x xy z yz y y
= = =
760 70
*+ -=/ 6%>*-%6 EA% 4,--=/ 6*0*6% 3B 8F1
770 0
07
=
780 00
*+ -=/ 6%>*-%6 EA% 4,--=/ 6*0*6% 3B 8F1
790 8 H 8 G 8
*(+,-'./ )03
10 3 2 3 2 5(2 )(2 ) 2 2 ( 32)+= = =
20 6 9 6 9 15 x x x x+= =
30 4 8 4 8 12w w w w+= =
40 3 2 3 1 2 6 z zz z z + += =
50 3 5 3 5 8
9 5 9 5 14 x x x x
y y y y
+
+= =
60 12 4 12 4 48( ) x x x= =
70 3 7 3 7 21
4 5 4 5 20( )
( )
a a a
b b b
= =
80
52 2 5 2 5 10
3 3 5 3 5 15( )
( )
x x x x
y y y y
= = =
90 2 3 3 3 2 3 3 3 2 3 3 3 6 9(2 ) 2 ( ) ( ) 8 8 x y x y x y x y = = =
1)0
22 3 2 3 2 2 2 3 2 2 2 3 2
2 2 2 2 2 4( ) ( ) ( )
( )
w s w s w s w s
y y y y
= = =
4 6
4w s
y=
110 9
9 5 45 x
x x x
= =
120
64 4 6
5 5 6
6 4 6
6 5 6
4 6
5 6
24
30
2 (2 )
7 (7 )
2 ( )
7 ( )
64
117,649
64
117,649
a a
b b
a
b
a
b
a
b
=
=
=
=
130 3 6 3 6 18
18 4 143 1 3 4
( )
( )
x x x x x
x x x x
+= = = =
140 2 3 3 2 2 3 3 2 6 6 12
3 4 3 4 12 12
12 12 0
( ) ( )
( )
1
x x x x x x x
x x x x
x x
= = =
= =
150 25 5=
160 4
81 3= 170 7 128 2 =
180 0.04 0.2=
190 4
44
1 1 116 216
= =
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!"#$%&' )* "#$%#& '( )*+#,-. /012 !"#$%&'(#%$) +,#-./,#0(,1 2",1)303
$
2)0 3
33
8 8 2 227 3 327
= = =
210 1/ 2(49) 49 7= =
220 1/ 3 3(64) 64 4= =
230 ( )33/ 2 39 9 (3) 27= = =
240
( )5 / 2
5 / 2 5 51 1 1 1
(9)243(9) 39
= = = =
250
( )
2 / 52 / 5 2 25
1 1 1 1(32)
4(32) (2)32= = = =
260 1/ 21/ 2
1 1 1(0.09)
0.30.09(0.09)= = =
310
1 103
= =
270 44 / 5 4
51 1 1 132 32 2 16
= = =
280
22 / 3 2
364 64 4 1627 27 3 9
= = =
290 50 25 2 25 2 5 2= = =
3)0 3 33 3 354 27 2 27 2 3 2= = =
310 3 33 33 32 2 2 x x x= =
320 4 4 2 x x x= =
330 4 4 2
16 16 4 x x x= =
340 4 4
4416 216
x x x= =
350 3 3
3
3
2 8 5 27 128 2 4 2 5 9 3 64 2
2 2 2 5 3 3 4 2
4 2 15 3 4 2
+ = + = += +
360 2 2
3 3 13 39 39 3913 13 13 1313 13
= = = =
370 4 1/ 2 4 2 2 2 2 2 2(9 ) 9 3 ( ) 3 ( ) z z z z = = = 23 z =
380 3 3
8 3/ 4 8 2 4 2 34 4(16 ) 16 (2 ) (2 ) y y y y = = =
68 y=
390
2 / 32 / 3 3 23 227 3 3 98 2 2 4t t t t
= = =
4)0
3/ 43/ 4 4 3 3
12 3 3 3 3
3 9 9
9 3
256 4 4 4( )
4644
x x x x
x x
x
= = =
= = =
410 5 3 5
5 3 52 2 3 2 3 2
1 1 1a b aa b a
c c b c b c
= = =
420 2 / 5 3/ 5
2 3 10 2 / 5 3/ 5 10 / 552
x y x y z x y z
z = =
430 2 7 2 ( 7) 99
55 5 5m m m mm
+ = = =
440 11
x y x y
+ = +
450 22 2
1 1(3 )
(3 ) 9t
t t = =
460 44
1(3 )
(3 ) z
z =
470 5 2 2 1/ 5 1/ 5 2 1/ 5 1/ 5 2 / 55 (5 ) 5 ( ) 5 x x x x= = =
480 3 3 3 3 3 3 3
9 9
9
9
( ) ( ) ( ) X Y X Y
X Y
Y
X
==
=
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/012 !"#$%&'(#%$) +,#-./,#0(,1 2",1)303 +&,%-./ )01
%
490 1/ 2 1/ 2 x y x y =
5)0 2 6 3 3 ( 5) 8
5 2 1 ( 6) 2 7u v w w w
vw u v u v
= =
510 2 2 3 2 2 3 1/ 4 2 1/ 4 2 / 4 3 / 44 ( ) x xy z x xy z x x y z = = 9 / 4 3/ 4
1/ 2 x z
y=
520 4 3 2 5 4 3 2 1/ 4 5 4
3/ 4 1/ 2 5 4
17 / 4 9 / 2
17/4
9 / 2
( )a b a b a b a b
a b a b
a b
a
b
===
=
530 2 / 3 23(2 ) (2 )a b c a b c + = +
540 42 3 3/ 4 2 3 3 3 6 94( ) ( )ab c ab c a b c= =
550 4 / 54 / 5 5 4
1 1 x
x x= =
560 1/ 2 1/ 22 (2 ) 2 2 x y x y =
570 3/ 5 3/ 5
3/ 5 3/ 5
5 5 53 3 3 35
3 13 (3 ) (3 )
3 1 3 1
(3 ) 27
w w w w
w w w w
=
= =
580 4 1/ 5 1/ 6 4 / 5 1/ 6 4 / 30 2 /15[( ) ] [ ] x x x x= = =
2/15 15 2
1 1
x x= =
590 1/ 2
1/ 2 1/ 2 1/ 26 6 6 5 6 5
55 5 5 5
= = =
6)0 1/ 4 4 4
4 1/ 4 1/ 4 1/ 4 43 3 3 2 3 2 3 2
28 168 8 2
= = = =
610 1/ 2
1/ 2 1/ 2 1/ 24 4 4(2 ) 4 2
22 (2 ) (2 ) (2 )
x x x x x x x
= = =
2 2 x x
=
620 1/ 2
1/ 2 1/ 2 1/ 2
2(2 )22 (2 ) (2 ) (2 )
y y y y y y y y y y y
= = =
2
2
y=
630 232 / 3
3 1/ 3 1/ 3 2 / 3
(3 )1 1 1(3 )33 (3 ) (3 ) (3 )
x x x x x x x
= = =
3 293 x x
=
640 1/ 3 1/ 3 3
2 / 3 2 / 3 1/ 323
22 2 2 23 33 33
y y y y y y y y y
= = = =
650 12 12
4 233
= = =
660 18
9 32
= =
670
1/ 2 3 / 45 5 5
2 / 4 1/ 4 1/ 2 1/ 4 1/ 2 3 / 44 2
1/ 5 1/ 2 3/ 4 4 / 20 10 / 20 15/ 20
204 10 15 1/ 20 10 15
2 2 2
2 2
(2 ) 16
a b
a b a b a ba ba b a bab ab
a b a bab ab
= =
= =
= =
680 1/ 2 2 / 3 3/ 6 4 / 6
3 1/ 3 1/ 3 2 / 32 2 2 3 2 3
33 3 3 3
= = =
3 4 1/ 6 6(2 3 ) 6483 3
= =
690 6
2 3 4 6 33
22 2
x x y x x y
y= =
7)0 1/ 2 1/ 2 1/ 2 1/ 2
5 / 2 1/ 2 5 / 2 1/ 2 1/ 2 1/ 2 33 3 3u v u v
u v u v u v u v
= =
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!"#$%&' )* "#$%#& '( )*+#,-. /012 !"#$%&'(#%$) +,#-./,#0(,1 2",1)303
&
710 243 243
81 933
= = =
720 3 2 5 2 2 6 5 2
10 30 2
20 60
{[(3 ) ] } {[3 ] }
{3 }
3
a a
a
a
===
730 0 6 6
2 1/ 2 2 3 6 3/ 2 6 3/ 22 1 2
(2 ) 2
y
x y x y x= =
6 1/ 2 6 1/ 2
3/ 2 1/ 2 264 64 y x y x
x x x
= =
740 5 5 / 2 15 / 6
11/62 / 3 4 / 63 2
s s s s
s s s= = =
750 2 3 2 2 3 2 3 3 33 3 3 3( )( ) x yz xy x yz xy x y z = = xyz =
760 ( )8 1/ 4 8 8 / 4 24 3 (3 ) 3 3 9= = = =
770 2 2 / 5 2 5 2 / 5
2 2
22
3 (32) 3 (2 )
3 (2 )1
32
94
==
=
=
780 2 / 5
2 2 1/ 5 2 / 5 2 2 / 255 [( ) ] ( ) x y x y x y = =
4 / 25 2 /25 x y=
790 4
1 2 2 2 2 42
4(2 ) 2
y x y x y
x= =
8)0 2 / 3 3/ 4
4 1/ 3 1/ 4 1/ 3 1/ 4 2 / 3 3/ 43
3 3 3 y x
y x y x y x y x
= =
3 / 4 2 / 33 x y xy
=
810 2 3 2 1/ 2 2 3 1/ 2 2 1/ 2( ) ( ) x x y xy x x y xy= 1/ 2 3/ 2 1/ 2 2 5 / 2( )( ) x xy x y x y= =
820 4 4 1/ 2 4 1/ 275 (75 ) [(25 )(3)]k k k = = 2 2 1/ 2 2 1/ 2[(5 ) 3] 5 3k k = =
830 3 8 8 24 8 5 14
1 2 3 3 6 24( )
( )
ab c a b c a c
a c a c b
= =
840 3 32 33 7(49) 7 7 7 7= = =
850
22 3 3 6 3 2
4 3 2 4 6 2( ) ( )
( ) ( )
x x x x
x x x x
=
62 2 6 12 2 6
12 x
x x x x x x
= = =
2 2 6 86
1 x x x x
x
= = =
860 (6)(6) 36 6= =
P=/% /;,/ 2(6) 6 +*-4% 'J Q 81
870 2
3 3 2 58 4 4
2
s
s s s s = =
880 ( )35 3 5 3 3 3 1/ 2 3
15 9 3/ 2
15 3/ 2
9
( ) ( ) ( )a b c a b c
a b c
a cb
=
=
=
890
43 23 2 2 3 4
2 3
43 3
3 3 4
4
4 12 12
4
12 12
3(3 2 )
2
32
(3 )
(2)
3
281
16
x y x y y z
y z
x z
x z
x z
x z
=
=
=
=
=
9)0
( ) ( )2 41/ 2 2 2 2
1063 1/ 2 2 3 2
102 122 ( )2 81616 (16 ) ( )
1 1 1 18
x x x x x x x
x= = = =
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/012 !"#$%&'(#%$) +,#-./,#0(,1 2",1)303 +&,%-./ )02
'
*(+,-'./ )04
10 K ! ' I " D 5 D ) ! D 5 " ' L G (( ! ' 5 " ' )
20 26 10 2 2 4 x xy z xy + + + 26 11 2 6 x xy z = + +
30 2 2 2 2 2 28 6 4 2 6 6 2 6t s s t t s + + = +
40 2 3 7 x x x x x+ + + =
50 2 3 3 35 3
a b c ba b c
+ += +
60 ) $ D 7% O L$ O% 5( G 5$ 5% )8
70 2
6 10 2 2 4 x xy z xy+ + 26 9 2 2 4 x xy z = +
80 2 3 x x x x x+ =
90 2 3 2 3 x y x z y z + =
1)0 K ' ' I ( ' ) ( D J ' G (I ' ' 7 (
110 O ! D O " ' 5( ' 5I ! D J " ' J G '(L ! D (L " ' 57
120 * ) + L* I + D * ) G ) * 7+ )
130 2 2 2 2
2 25 5 3 8 28
2 33 7
x y xy x xy y
x y xy
+ =
140 5 ' M) D I , ' (5N G 5 ' MI , ' ON G 5 ' I , D OG (( ' I ,
150 2 2 22{3[3 6 2 10]} 2{3[ 16]} x x x+ + = + 2 22{3 48} 6 96 x x= + = +
160 IR) - D (L ' - M( ' - ' (NS G IR) - D (L ' - M'- NS2 24{3 15 } 4 12 60t t t t = + + = + +
170 3 2 2
3 2 2
3 2
3 2
5(8 8 2( 5 2 ))
5(8 8 2 10 4 )
5(8 6 4 10)
40 30 20 50
x x x x
x x x x
x x x
x x x
+ += + + = + += +
180 RJ $ J % D J D (8 $ D (L% $M5% D (8NSG RI$ D O% D J 5$% (8 $SG RJ $ D O% D J 5$%SG J$ O% J D 5 $%
190 2 2(4 5) 4(5) 9 20 x x x x+ + + = + +
2)0 2 2(5 2) 2(5) 7 10u u u u+ + + = + +
210 2
2( 2)( 5) ( 5 2) 2( 5)
3 10
w w w x
w w
+ = + + + =
220 2 2(7 3) (7)(3) 10 21 z z z z + + = +
230 (2 )(5 ) [(2)(2) (3)(5)] 3(2) x x x+ + + 210 19 6 x x= + +
240 E- FE5- F D ME(FE7F D ELFE5FN- D ELFE7F22 3 35t t =
250 2 2 2 22( )(2 ) (2 ) 4 4 X X Y Y X XY Y + + = + +
260 2 2 2(2 ) 2(2 )(1) 1 4 4 1 x x x x + = +
270 2 2 22(5) 5 10 25 x x x x + = +
280
( )2
(1 2) [(1)(5) (1)(2)] (1)(5) x x + + +
2 3 5 x x= +
290 ( ) ( )2 23 2 3 (5) (5)3 10 3 25
x x
x x
+ += + +
3)0 ( )2 23 9 y y =
310 2 2 2(2 ) 1 4 1 s s =
320 2 2 2 4 2( ) (3 ) 9 z w z w =
330 2 ( 4) 3( 4) x x x+ + 3 24 3 12 x x x= +
340 2 2( 3) 1( 3) x x x x x+ + + + + 3 2 23 3 x x x x x= + + + + + 3 22 4 3 x x x= + + +
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!"#$%&' )* "#$%#& '( )*+#,-. /012 !"#$%&'(#%$) +,#-./,#0(,1 2",1)303
(
350 2 2 2
4 3 2 2
4 3 2
(3 2 1) 4(3 2 1)
3 2 12 8 4
3 2 13 8 4
x x x x x
x x x x x
x x x x
+ + = + += + +
360 3 2 3 24 3 2 3 2
4 3 2
3 (4 2 3 ) 2(4 2 3 )
12 6 9 8 4 6
12 2 13 6
y y y y y y y
y y y y y y
y y y y
+ + = + += +
370 2 2
2 2
2
3 2
{2( 2 35) 4[2 12 ]}
{2 4 70 8 48 }
{10 52 70}
10 52 70
x x x x x
x x x x x
x x x
x x x
+ = + = =
380 2 2 2 2 2[(2 ) 1 ](4 1) [4 1](4 1) z z z z + = +
2 2 2 4(4 ) 1 16 1 z z = =
390 ! E) ! D 5 " ' IF D "E) ! D 5 " ' IF D 5E) ! D 5 " ' IF2 23 2 4 3 2 4 6 4 8 x xy x xy y y x y= + + + + + 2 23 2 5 2 8 x y xy x= + + +
4)0 2 2[ ( 1)] x x+ + 2 2 2 2( ) 2 ( 1) ( 1) x x x x= + + + +
4 3 2 22 2 2 1 x x x x x= + + + + + 4 3 22 3 2 1 x x x x= + + + +
410 3 2 2 3
3 2(2 ) 3(2 ) (3) 3(2 )(3) (3)
8 36 54 27
a a a
a a a
+ + += + + +
420 3 2 2 3
3 2(3 ) 3(3 ) (2) 3(3 )(2) (2)
27 54 36 8
y y y
y y y
+ = +
430 3 2 2 3(2 ) 3(2 ) (3) 3(2 )(3) 3 x x x + 3 28 36 54 27 x x x= +
440 3 2 2 33 (2 ) 3 (2 ) (2 ) x x y x y y+ + + 3 2 2 36 12 8 x x y xy y= + + +
450 2 18
18 z z
z z z
=
460 3
22 7 4 42 7 x x
x x x x x
+ = +
470 5 3
3
2 2 2 2
6 4 1 13 2
2 2 2 2
x x x x
x x x x+ = +
480 3 4 9 5
36 93
6 93 3
32
y y y
y y
y y y
y
=
=
=
490 2
25 5 3
53
x
x x x
x x
+ + +
T-+A%#U35
x x++
5)0 2
2
14 5 4
4 4
4
0
x x x x
x x x x
+
++
T-+A%#U ! ' (
510
2
3 2
3 2
2
2
3 8 172 3 2 3
3 6
8
8 1617 3
17 34
37
x x x x x x
x x
x x
x x x x
++ +
++
+
T-+A%#U 2 37
3 8 172
x x x
+ ++
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)
520
3 2
4 3 2
4 3
3 2
3 2
2
2
3 31 0 2 0 1
2
3 0
3 33 1
3 3
4
x x x x x x x x
x x
x x
x x
x x
x x x x
+ + + + + + +
+
+
+
T-+A%#U 3 24
3 31
x x x x
+ + + +
530
2
3 2
3 2
2
2
2 4
2 0 0 0
2
2 0
2 44 0
4 8
8
x x
x x x x
x x
x
x x x x
+
+ + + ++ +
++
T-+A%#U 28
2 42
x x x
+ +
540
1
22
2
3252
3
2 3 6 8 1
6 91
x
x x x
x x x x
+ + ++
+
T-+A%#U5213
2 2 3 x
x +
+
550 2
2
2
3 2 3 4 33 2
6 3
6 4 7
x
x x x x x
x x
+ +++
T-+A%#U7
23 2
x x
++
560 2 3 2
3 2
2
2
21
2 2 2 2 2 2
z z z z z z
z z z
z
z z z
+ + + +
+
+
T-+A%#U22 2
21
z z
z z
+ + +
*(+,-'./ )05
10 5E$! D %F
20 5 "E) " ' 5F
30 L ! E5 " D ' F
40 2 23 (1 3 ) x y xy
50 3 2 3 24 (2 3 )bc a ab d b cd +
60 2 2 4 26 ( 3 12 )u v uv w v+
70 2 27 ( 7)( 7) z z z = +
80 E ! D 5FE ! )F
90 ( 3)( 1) p p+ +
1)0 E, ' IFE , ' 5F
110 2 2(4 ) 3 (4 3)(4 3) x x x = +
120 E ! D JFE ! ' IF
130 E$ D 7FE$ D LF
140 2 2(2 ) (3 ) (2 3 )(2 3 )t s t s t s = +
150 2 2 22(3)( ) 3 ( 3) x x x+ + = +
160 E " ' (8FE " ' LF
170 25( 5 6)5( 3)( 2) x x
x x+ +
= + +
180 23( 4 5)3( 1)( 5)t t
t t +
= +
-
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!"#$%&' )* "#$%#& '( )*+#,-. /012 !"#$%&'(#%$) +,#-./,#0(,1 2",1)303
!*
190 2 23( 1 ) 3( 1)( 1) x x x = +
2)0 E) " IFE) " 5F
210 2
6 13 2 (6 1)( 2) y y y y+ + = + + 220 EI ! D )FE ! ' (F
230 22 (6 5 4) 2 (3 4)(2 1) s s s s s s+ = +
240 2 2 2(3 ) 2(3 )(5) 5 (3 5) z z z + + = +
250 3/ 5 2 2 3/ 5( 4 ) ( 2 )( 2 )u v u v u v u v u v = +
260 2 / 7 2 2 2 / 7 2 / 7(3 ) 1 (3 1)(3 1) x x x = +
270 22 ( 6) 2 ( 3)( 2) x x x x x x+ = +
280 2 2 2( ) 2( )(2) 2 ( 2) xy xy xy + =
290 2 2 2[2(2 1)] 2 (2 1) x x+ = + 24(2 1) x= +
3)0 2 2
2 2 2
2 2 2
4 2
2 [2 (1 2 )]
2 (2 ) (1 2 )
2 (4 )(1 2 )
8 (1 2 )
x x x
x x x
x x x
x x
= =
=
310 2 2 2 2( 14 49) [( ) 2( )(7) 7 ] x x y xy x xy xy + = + 2( 7) x xy=
320 ! EL ! D 5F D 5EL ! D 5F G EL ! D 5FE ! D 5F
330 2 2( 4) 2(4 ) x x x + 2 2( 4) 2( 4) x x x=
2( 4)( 2) x x= G E ! D 5FE ! ' 5FE ! ' 5F
2( 2)( 2) x x= +
340 E ! D (FE ! ' (F D E ! ' 5FE ! D (FG E ! D (FME ! ' (F D E ! ' 5FNG E ! D (FE5 ! ' )F
350 2 2 2( 8 16) ( 8 16) y y y y y+ + + + 2 2( 8 16)( 1) y y y= + +
2( 4) ( 1)( 1) y y y= + +
360 2 2 2 2 2( 4) ( 4) ( 4)( ) xy x z x x xy z + = + 2( 2)( 2)( ) x x xy z = + +
370 3 3 2 2
24 ( 4)( 4( ) 4 )
( 4)( 4 16)
b b b b
b b b
+ = + += + +
380 3 3 2 21 ( 1)[ 1( ) 1 ] x x x x = + + 2( 1)( 1) x x x= + +
390 3 2 2 3 3( ) 1 ( 1)( 1) x x x = + 2 2( 1)( 1)( 1)( 1) x x x x x x= + + + +
4)0 3 3 2 23 (2 ) (3 2 )[3 3(2 ) (2 ) ] x x x x+ = + + 2(3 2 )(9 6 4 ) x x x= + +
410 2( 3) ( 1)[( 3) ( 1)] x x x x+ + + 2( 3) ( 1)[2 2] x x x= + + 2( 3) ( 1)[2( 1)] x x x= + +
22( 3) ( 1)( 1) x x x= + +
420 2 2
2 2
2 2
( 5) ( 1) [( 5) ( 1)]
( 5) ( 1) (2 6)
2( 5) ( 1) ( 3)
a a a a
a a a
a a a
+ + + + += + + += + + +
430 M. E( D / FN D M. E( D / FN/ G M. E( D / FNE( D/ F2(1 ) P r = +
440 (3 5 )[( 3 ) ( 2 )] (3 5 )( 5 )5 (3 5 )
X I X I X I X I I I X I
+ + = + = +
450 2 2 2 2 2
( ) 4 ( 4)( 4) x x x = + 2( 4)( 2)( 2) x x x= + +
460 2 2 2 2 2 2 2 2(9 ) ( ) (9 )(9 ) x y x y x y = + 2 2(9 )(3 )(3 ) x y x y x y= + +
-
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/012 !"#$%&'(#%$) +,#-./,#0(,1 2",1)303 +&,%-./ )04
!!
470 4 2 2 4 4( ) 1 ( 1)( 1) y y y = + 4 2 2( 1)( 1)( 1) y y y= + + 4 2( 1)( 1)( 1)( 1) y y y y= + + +
480 2 2 2 2 2( ) 2 ( 2)( 2)t t t = +
( )22 2( 2) 2t t = +
( )( )2( 2) 2 2t t t = + +
490 2 2 2( 5)( 1) ( 5)( 1)( 1) X X X X X + = + +
5)0 2 2( 9)( 1) ( 3)( 3)( 1)( 1) x x x x x x = + +
510 4 2 2 2 2( 2 1) ( 1) [( 1)( 1)] y x x y x y x x + = = + 2 2( 1) ( 1) y x x= +
520 22 (2 3 2) 2 (2 1)( 2) x x x x x x = +
*(+,-'./ )06
10 2
29 ( 3)( 3) 3
( 3)3
a a a aa a aa a
+ += =
20 2
23 10 ( 2)( 5) 5
( 2)( 2) 24
x x x x x x x x x
+ = =+
30 2
29 20 ( 5)( 4) 5
( 5)( 4) 520
x x x x x x x x x x
+ = =+ ++
40 2
3 23 27 24 3( 8)( 1)
2 ( 7)( 1)2 16 14
x x x x x x x x x x
+ = +
3( 8)2 ( 7)
x x x
=
50 2
26 2 (3 2)(2 1) 3 2
( 2)(2 1) 22 3 2
x x x x x x x x
x x
+ + += =+ +
+
60 2
212 19 4 (4 1)(3 4)
(2 3)(3 4)6 17 12
x x x x x x x x
+ = +
4 12 3 x x
=
70 2 2(1)
( 3)( 2) ( 3)( 2) y y
y y y y=
+ +
80 2
2( 3)( 3)
3( 3)( 3)
t t t t t t t t
+ =+
90 ( )( ) ( )( 1)( )
( )( ) ( )( )( )( 1)
ax b c x ax b x c
x c ax b x c ax bax b
ax bb axax b
= + +
=+
=+
1)0 2 2( )( )( ) ( )( )
( )( ) (1)( ) x y x y x y x y x y
x y y x x y+ + +=
+
2( ) x y= +
110 2( 1) ( 4)( 1)
( 4)( 2) ( 1)( 1)
x x x
x x x x
+ +
+ +
2( 1)( 4)( 1)( 4)( 2)( 1)( 1)
x x x x x x x
+ += + +
2( 4)( 4)( 2)
x x x
+= +
120 2( 2) ( 2)
3( 4)( 2) ( 3)( 2) x x x
x x x x+
+
2( 2)( 2)3( 4)( 2)( 3)( 2)
x x x x x x x
+ = +
( 2)3( 4)( 3) x x x x=
130 2 24 4
8 8 2 X X X
X X = =
140 23 14 3 14 3(14)
67 7 7 x x x x x x x = = =
150 3 3
2 22 2
6 36
m n mn nmn mn = =
160 2 2 ( ) 2( )( )
c d c c c d c d c c d c c d c d + + + = =
170 4 4 1 4 2
23 3 2 6 3 x x x
x x x
= = =
180 24 2 4 (2 ) 8
1 3 3 3 x x x x x = =
-
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!"#$%&' )* "#$%#& '( )*+#,-. /012 !"#$%&'(#%$) +,#-./,#0(,1 2",1)303
!"
190 3 3
2 9 3 27 271 x x
x x x = =
2)0 4 3 3
312 12 1 124 31 4 4
Y Y Y Y
Y
= = =
210 3 4 3 1 3
11 ( 3)( 4) 1 3 3
x x x x x x x x
= = =
220 2 2
2
( 3) ( 3) 1( 3)
3( 3) 3
( 3)
x x x
x x x x x
x x x
+ + + = +
+ += =+
230 3 3 210 1 10 ( 1) 2
( 1)( 1) 5 5 ( 1)( 1) 1
x x x x x
x x x x x x x
+ + = =
+ +
240 ( 3)( 2) ( 3)( 1)( 3)( 3) ( 2)( 2)
2 ( 3)( 1)3 ( 2)( 2)
( 2)( 3)( 1)( 3)( 2)( 2)
12
x x x x x x x x x x x x x x x x x x x x
x x
+ +
+ + + + = + + + + =+ + =
250 ( 2)( 5) ( 4)( 1)
( 5)( 1) ( 4)( 2)2 11 2
( 2)( 1)( 1)( 2)1
x x x x
x x x x x x x x x x x x
+ + +
+ + ++ += + ++ +=+ +
=
260 2
2
( 3) (3 4 )(3 4 )4 3 7( 3)
( 3) (3 4 )(3 4 )7(4 3)( 3)
( 3)(3 4 )( 1)(4 3)7(4 3)
( 3)(3 4 )7
x x x x x
x x x x x
x x x x
x x
+ +
++ + =
++ +
= + +=
270 (2 3)(2 3) (1 )(1 )
( 4)( 1) 2 3 x x x x x x x
+ +
+
(2 3)(2 3)(1 )(1 )( 4)( 1)(2 3)
x x x x x x x+ + =
+
(2 3)(1 )(1)( 1)( 4)( 1)
x x x x x
+ + =+
(2 3)(1 )4
x x x+ +=
+
280 2
2(6 7 3) ( 1) 4( 1)
( 1) 5( 1) ( 4)
y x x x y y x y y x y x
+ +
+ +
2(3 1)(2 3)( 1)( 4)
( 1)( 5) ( 4)
y x x y x
y x x y x
+ += + +
2
(3 1)(2 3)
( 5)
x x
x x
+=+
290 2 5 6
3 x x
x+ +
+( 3)( 2)
23
x x x
x+ += = +
+
3)0 2 2
12 2 x x
x x+ += =+ +
310 VWX G )-2 1 6 1 6 1 7
3 3 3 3 3t t t t t t ++ = + = =
320 3LCD X =
3 2 3 3 39 1 9 9 X X
X X X X X
= =
330 3LCD 1 x= 3 3 3
3 3 3
3 3
3
3
3
11
1 1 11
11
11
1
x x x
x x x x x
x
x
x
=
=
=
=
340 VWX G, D I4 4 ( 4) 4 ( 4)
4 4 4 4 s s s s
s s s s s
+ + ++ = + =+ + + +
2 24 4 ( 2)4 4
s s s s s+ + += =
+ +
-
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/012 !"#$%&'(#%$) +,#-./,#0(,1 2",1)303 +&,%-./ )04
!#
350 VWX G E5 ! ' (FE ! D )F4 4( 3) (2 1)
2 1 3 (2 1)( 3) ( 3)(2 1) x x x x
x x x x x x+ + = +
+ + +
24( 3) (2 1) 2 3 12
(2 1)( 3) (2 1)( 3)
x x x x x
x x x x
+ + + += = + +
360 VWX G E ! ' (FE ! D (F1 1 ( 1)( 1) ( 1)( 1)1 1 ( 1)( 1) ( 1)( 1)
x x x x x x x x x x x x
+ + + = + + +
2 2( 1) ( 1)( 1)( 1)
x x x x+ =
+
2 22 1 ( 2 1) 4( 1)( 1) ( 1)( 1)
x x x x x x x x x
+ + += =+ +
370 LCD ( 3)( 1)( 3) x x x= + + 1 1
( 3)( 1) ( 3)( 3)3 1
( 3)( 1)( 3) ( 3)( 1)( 3)( 3) ( 1)
( 3)( 1)( 3)2 4
( 3)( 1)( 3)2( 2)
( 3)( 1)( 3)
x x x x x x
x x x x x x x x
x x x x
x x x x
x x x
+ + +
+ += + + + + +
+ + += + +
+= + +
+= + +
380 VWX G E ! IFE5 ! D (FE5 ! (F
2
4( 4)(2 1) ( 4)(2 1)
4(2 1) (2 1)( 4)(2 1)(2 1) ( 4)(2 1)(2 1)4(2 1) (2 1)
( 4)(2 1)(2 1)
2 7 4( 4)(2 1)(2 1)
x x x x x
x x x x x x x x x
x x x x x x
x x x x x
+
+= + +
+= + + =
+
390 VWX G E ! ' (FE ! D LF24 3
31 ( 1)( 5)
x x x x
+ +
24( 5) 3( 1)( 5) 3( 1)( 5) ( 1)( 5) ( 1)( 5)
x x x x x x x x x x
+ += + + + +
2 24 20 3( 4 5) 3( 1)( 5)
x x x x x x
+ + += +
35 8( 1)( 5)
x x x
= +
4)0 VWX G E5 ! ' (FE ! D JFE) ! ' 5F2 3 3 1 1
(2 1)( 6) (3 2)( 6) 3 2 x x
x x x x x + +
+ +
(2 3)(3 2) (3 1)(2 1) (2 1)( 6)
(2 1)( 6)(3 2)
x x x x x x
x x x
+ + +=
+ 2 2 26 13 6 (6 1) 2 11 6(2 1)( 6)(3 2)
x x x x x x x x x
+ + + = +
22 1(2 1)( 6)(3 2)
x x x x x
+= +
410 2 2 21 1 1
1 x x
x x x x+ + = + =
2
22 1 x x
x
+ +=
420 2 2 2
1 1 y x y x x y xy xy xy
++ = + =
2 2
2 22 y xy x
x y
+ +=
430 1 1 11 1 1
`1
xy xy x y
x x x x xy = = =
440 2 2 2
2 2
2
1 1 1
2 1
ab aba
b b b b
a b ab
b
+ + = + =
+ +=
450 Y$:/*C:B*-. /;% -$#,4/*=- 3B ! .*0%+7 1
.5 x
x+
460 Y$:/*C:B*-. -$
-
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!$
470 Y$:/*C:B*-. -$
-
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!"#$ !"#$%&'(#%$) +,#-./,#0(,1 2",1)303 !"#$%&' )*+
!"
!"#$%&'( *+,
-+ 29 0 x x = "#$ ! % &'
2
9(1) (1) 09 1 08 0
"#$ ! % ('29(0) (0) 0
( ) ( (( % (*+,-. ( -/$0-10#- $+# #2,/$034. 5,$ & 63#- 43$7
.+ 212 7 ; x x = 8. 9"#$ ! % 8'
212 7(4) (4)
12 28 1616 16
= "#$ ! % 9'
212 7(3) (3)12 21 9
9 9
=
*+,-. 8 /46 9 -/$0-1: $+# #2,/$0347
/+ 17
3( 4) 5; , 44
z z + =
"#$17
:4
z =
17 173 4 54 4
17 5112 5
4 45 5
+
+ =
"#$ " % 8'4 3(4 4) 54 0 54 5
+ +
*+,-.174
-/$0-10#- $+# #2,/$034. 5,$ 8 63#- 43$7
0+ 2
2 8 0 x x+ = "#$ ! % ;'22 2 2 8 0 +
8 < 8 ) = (( % (
"#$ ! % )8'22(4) (4) 8 0+
)= < &> ) = (( % (*+,-. ; /46 )8 -/$0-1: $+# #2,/$0347
1+ ! ?> < ! @ ) ;? ! < &@ ) A ! % 8"#$ ! % );'?);@?> ) ;@ ) ;?); < &@ ) A?);@ 8);?8@ ) ;?)&@ < &( 8)= < ; < &( 88 % 8"#$ ! % ('(?>@ ) ;?&@ ) A?(@ 8); 8*+,-. ); -/$0-10#- $+# #2,/$034. 5,$ ( 63#- 43$7
2+ 2( 1) ( 2) 0 x x x+ + = "#$ ! % ('
20(1) (2) 0 ( % ("#$ ! % )&'
2(1)(0) (1) 0 ( % ("#$ ! % ;'
22(3) (4) 0 B; (*+,-. ( /46 )& -/$0-1: $+# #2,/$034. 5,$ ; 63#-43$7
,+ C6604D A $3 53$+ -06#-E #2,0F/G#4H# D,/I/4$##6
3+ J0F0604D 53$+ -06#- 5: =E #2,0F/G#4H#D,/I/4$##6
4+ K/0-04D 53$+ -06#- $3 $+# $+0I6 L3M#IE#2,0F/G#4H# 43$ D,/I/4$##67
-*+ J0F0604D 53$+ -06#- 5: ;E #2,0F/G#4H#D,/I/4$##6
--+ J0F0604D 53$+ -06#- 5: ! E #2,0F/G#4H# 43$D,/I/4$##6
-.+ N,G$0LG:04D 53$+ -06#- 5: ! ) ;E #2,0F/G#4H# 43$D,/I/4$##6
-/+ N,G$0LG:04D 53$+ -06#- 5: ! ) &E #2,0F/G#4H# 43$D,/I/4$##6
-0+ J0F0604D 53$+ -06#- 5: ? ! < 9@E #2,0F/G#4H# 43$D,/I/4$##67
-
7/25/2019 Sol Mat Haeussler ByPriale
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,-./$"0 )1 &'()'* +, -./'012 !"#$ !"#$%&'(#%$) +,#-./,#0(,1 2",1)303
!#
-1+ N,G$0LG:04D 53$+ -06#- 5:2 3
;2
x x
#2,0F/G#4H#
43$ D,/I/4$##6
-2+ C6604D O ) ! $3 53$+ -06#- /46 $+#4 60F0604D53$+ -06#- 5: ;E #2,0F/G#4H# D,/I/4$##6
-,+ 8 ! % &(10 54 2
x = =
-3+ (7; ! % B7
350.2
x = =
-4+ 9 # % (0
03
y = =
.*+ ; ! ) 8 ! % )A); ! % )A
5 5 2 2
x = =
.-+ 8 12 208 8 x x
= =
81
8 x
= =
..+ 4 7 37 1
1 17 7
x x
x
= =
= =
./+ A ! ) 9 % OA ! % &;
125
x =
.0+ 2 3 8 x+ = 2 5 x =
5 5 2 or 22 x
=
.1+ B ! < B % ;? ! < &@B ! < B % ; ! < ;A ! < B % ;A ! % )A
51
5 x = =
.2+ 4 3 1 417 1 417 42
426
7
s s s s
s
+ = ==
= =
.,+ 5( 7) 2(3 4) 35 35 6 8 3
27 327 4
274
p p p p p p
p p p
p
= + =
= =
=
.3+ $ % ; ) ;P; $ ) 9?& ) $ @Q$ % ; ) ;P; $ ) 9 < 9 $ Q$ % ; ) ;PA $ ) 9Q$ % ; ) &( $ < >
&&$ % =811
t =
.4+ 2 65 x
x=
! % A?; ! ) >@ ! % &( ! ) 9(9( % O !
30 109 3
x = =
/*+ 5 6
2 47 7 y
y = A # ) > % &8 ) ;= # 99 # % ;(
2033
y =
/-+ 4
79 2 x x+ =
N,G$0LG:04D 53$+ -06#- 5: O R ; D0F#-O R ; R B < ;?8 ! @ % O? ! @&;> < = ! % O !
! % &;>
/.+ 43 5 x x =
A ! ) >( % 9 ! ; ! % >(
! % 9(
-
7/25/2019 Sol Mat Haeussler ByPriale
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!"#$ !"#$%&'(#%$) +,#-./,#0(,1 2",1)303 !"#$%&' )*+
!$
//+ 4
53
r r =
N,G$0LG:04D 53$+ -06#- 5: 9 D0F#-3 4 15
1515
r r
r r
=
= =
/0+ 3 5
95 3
9 25 13534 135
13534
x x
x x x
x
+ =+ =
=
=
/1+ 1
3 5 55 5 x
x x+ = +
N,G$0LG:04D 53$+ -06#- 5: A D0F#-&A ! < ! ) ;A % & < ;A ! &> ! ) ;A % & < ;A ! )O ! % ;>
269
x =
/2+ 2 3 4 5 y y y y
y + =
>( # ) 9( # < ;( # ) &A # % &; # 9A # % &; # ;9 # % (
# % (
/,+ 2 3 6 7
4 3 y y +=
N,G$0LG:04D 53$+ -06#- 5: &; D0F#-9?; # ) 9@ % 8?> # < B@> # ) O % ;8 # < ;=)&= # % 9B
3718
y =
/3+ 5 7
( 1)4 3 2t
t t + =
N,G$0LG:04D 53$+ -06#- 5: &; D0F#-3 20 42( 1)23 42 4242 19
4219
t t t t t
t
t
+ = =
=
=
/4+ 1202 6 24w w w
w + =
N,G$0LG:04D 53$+ -06#- 5: ;8 D0F#-24 12 4 2880
15 28802880192
15
w w w w
ww
+ =
== =
0*+ 7 2( 1) 6
3 5 x x+ + =
9A < &(? ! < &@ % &= ! 9A < &( ! < &( % &= ! 8A % = !
458
x =
0-+ 2 2
23 6
x x x
+ =
N,G$0LG:04D 53$+ -06#- 5: > D0F#-;? ! < ;@ ) ?; ) ! @ % >? ! ) ;@; ! < 8 ) ; < ! % > ! ) &;9 ! < ; % > ! ) &;; % 9 ! ) &;&8 % 9 !
143
x =
0.+ 2( 4)
75 10 x x+ =
; ! < ;? ! ) 8@ % B(; ! < ; ! ) = % B(8 ! % B=
78 394 2
x = =
0/+ 9 3
(3 ) ( 3)5 4
x x =
N,G$0LG:04D 53$+ -06#- 5: ;( D0F#-9>?9 ) ! @ % &A? ! ) 9@&(= ) 9> ! % &A ! ) 8A&A9 % A& !
! % 9
00+ 2 7 8 9 3 53 14 21
y y y + =
&8?; # ) B@ < 9?= # ) O@ % ;?9 # ) A@;= # ) O= < ;8 # ) ;B % > # ) &(8> # % &&A
115 546 2
y = =
-
7/25/2019 Sol Mat Haeussler ByPriale
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,-./$"0 )1 &'()'* +, -./'012 !"#$ !"#$%&'(#%$) +,#-./,#0(,1 2",1)303
!%
01+ 4
(5 2) 7[ (5 2)]34(5 2) 21( 5 2)20 8 84 42104 50
50 25104 52
x x x
x x x x x x
x
= = +
= +=
= =
02+ 2 2 2
2 2 2
2 2
(2 5) (3 3) 13 5 7
4 20 25 9 18 9 13 5 7
13 38 34 13 5 733 27
27 933 11
x x x x
x x x x x x
x x x x x
x
+ = + + + + = +
+ = + =
= =
0,+ 5
25 x
=
N,G$0LG:04D 53$+ -06#- 5: ! D0F#-A % ;A !
525
x =
15
x =
03+ 4
21 x
=
8 % ;? ! ) &@8 % ; ! ) ;> % ; !
! % 9
04+ N,G$0LG:04D 53$+ -06#- 5: 9 ) ! D0F#- B % (.M+0H+ 0- 1/G-#7 *+,- $+#I# 0- 43 -3G,$034. -3 $+#-3G,$034 -#$ 0- 7
1*+ 3 5
03
3 5 03 5
53
x x x x
x
= ==
=
1-+ 3 7
5 2 23(2) 7(5 2 )
6 35 1414 29
2914
x x x
x
x
=
= = =
=
1.+ 3 2
5 x
x+ =
A? ! < 9@ % ; ! A ! < &A % ; ! 9 ! % )&A
! % )A
1/+ 1
5 4 3q
q=
9% % A% ) 8); % % )8% % ;
10+ 4
17
p p
=
8 & % B ) & A & % B
75
p =
11+ 1 2
1 2 p p=
& ) ; % ;? & ) &@ & ) ; % ; & ) ; & % (
12+ 2 3
64 5 x x
=
; ! ) 9 % ;8 ! ) 9(
;B % ;; ! 2722
x =
1,+ 1 1 3
7 71 3 1
7 71 2
772
x
x
x
x
+ =
=
=
=
13+ 2 3
1 22( 2) 3( 1)
2 4 3 31
1
x x x x x x
x x
=
= = =
=
-
7/25/2019 Sol Mat Haeussler ByPriale
20/717
!"#$ !"#$%&'(#%$) +,#-./,#0(,1 2",1)303 !"#$%&' )*+
!&
14+ 3 2 3 12 3 2 1 x x x x
=+ +
?9 ! ) ;@?; ! < &@ % ?9 ! ) &@?; ! < 9@2 26 2 6 7 3 x x x x = +
& % = ! 18
x =
2*+ 2 1
01 3
x x x x
+ ++ =
? ! < ;@?9 ) ! @ < ? ! < &@? ! ) &@ % (2 23 6 2 1 0 x x x x + + =
! < A % ( ! % )A
2-+ 6 6 6
6
y y
y y y
+ =
N,G$0LG:04D 53$+ -06#- 5: #? # >@ D0F#-2( 6) 6( 6) ( 6) y y y y = +
2 212 36 6 36 6 y y y y y + + = + 2 218 72 6 y y y y + = +
B; % ;8 # # % 9
2.+ 2 22 3
y y y y
=+ +
? # ;@? # < 9@ % ? # ;@? # < ;@2 26 4 y y y+ =
# % ;
2/+ 5 7 11
2 3 3 2 3 5 x x x = + +
N,G$0LG:04D 53$+ -06#- 5: ?; ! 9@?9 ! < A@ D0F#-5(3 5) 7(3 5) 11(2 3)15 25 21 35 22 3315 25 68
16 434316
x x x x x x x x
x
x
+ = + + = + =
=
=
20+ 1 3 4
3 2 1 2 x x x =
? ! ) ;@?& ) ; ! @ ) 9? ! ) 9@?& ) ; ! @% 8? ! ) 9@? ! ) ;@
2 2 22 5 2 3(2 7 3) 4( 5 6) x x x x x x + + = +
2 24 16 7 4 20 24 x x x x + = + 8 ! % &B
174
x =
21+ 9 3
3 3 x
x x=
O % 9 ! ! % 9S,$ $+# D0F#4 #2,/$034 0- 43$ 6#104#6 13I ! % 9.-3 $+#I# 0- 43 -3G,$0347 *+# -3G,$034 -#$ 0-7
22+ 2
3 43 3 9
x x x x x x
=+
! ? ! ) 9@ ) ! ? ! < 9@ % 9 ! ) 82 23 3 3 4 x x x x x =
)> ! % 9 ! ) 8)O ! % )8
49
x =
2,+ 5 4 x+ =
( )2 25 4 x+ =
! < A % &> ! % &&
23+ 2 3 z =
( )2 22 3 z = " ) ; % O " % &&
24+
( )2 2
3 4 8 0
3 4 8
3 4 (8)3 4 643 68
683
x x
x x x
x
= =
= ==
=
-
7/25/2019 Sol Mat Haeussler ByPriale
21/717
,-./$"0 )1 &'()'* +, -./'012 !"#$ !"#$%&'(#%$) +,#-./,#0(,1 2",1)303
'(
,*+
( )22
4 3 1 0
4 3 1
4 3 1
16 3 115 35
x x
x
x x x
+ == +
= +
= +==
,-+ 2
12 3 x + =
2 221
2 3 x + =
41
2 9 x + =
5
2 9
x =
5 102
9 9 x
= =
,.+ 1/ 2( 6) 7 x+ = 1/ 2 2 2[( 6) ] 7 x + =
! < > % 8O ! % 89
,/+ 4 6 x x =
( ) ( )2 24 6 x x = 8 ! ) > % ! 9 ! % >
! % ;
,0+
( ) ( )2 24 3 2 5
4 3 2 5
4 3 2 51
x x
x x
x x x
+ = +
+ = ++ = +=
,1+ 3/ 4
3/ 4 4 / 3 4 / 3( 5) 27
[( 5) ] 27
5 8186
x
x
x x
= =
==
,2+ 2 9 9 y y = 2
2 29 (9 ) y y =
2 29 81 18 y y y = + &= # % O(
905
18 y = =
,,+ 2 3 y y+ + = 2 3 y y+ =
( ) ( )2 22 3 y y+ = 2 9 6 y y y+ = +
6 7 y =
( )2 26 7 y = 9> # % 8O
4936
y =
,3+ 1 1 x x + = 1 1 x x= + +
( ) ( )2 21 1 x x= + + 1 2 1 1 x x x= + + + +
2 2 1 x = + 1 1 x = + . M+0H+ 0- 0TL3--05G# 5#H/,-#
0a 13I /GG' 7 *+,- $+#I# 0- 43 -3G,$0347*+# -3G,$034 -#$ 0- 7
,4+ 2 2 3 z z z + = + 2
2 22 (3 ) z z z + = +
2 22 9 6 z z z z + = + + )O % 8 "
94
z =
-
7/25/2019 Sol Mat Haeussler ByPriale
22/717
!"#$ !"#$%&'(#%$) +,#-./,#0(,1 2",1)303 !"#$%&' )*+
'!
3*+ 1 2
05 2w w
=
1 25 2w w
=
2 21 2
5 2w w
=
1 25 2w w
=
A( ) ; % ; ( 9( % ;
23
w =
3-+ ) %*+$ I
r Pt =
3.+
100
1 0100
1100
1 p
p P R
p P R
R P
+ = + =
=+
3/+ & % =% ) & & < & % =%
18 pq +=
30+ & % )9% < > & ) > % )9 %
6 63 3
p pq
= =
31+ , %* ?&
-
7/25/2019 Sol Mat Haeussler ByPriale
23/717
,-./$"0 )1 &'()'* +, -./'012 !"#$ !"#$%&'(#%$) +,#-./,#0(,1 2",1)303
''
4.+ 1 1 1 p q f
+ =
1 1 1q f p
=
1 p f q pf
=
pf q
p f =
4/+ 2 2660 2 2(160)660 2 320340 2
340170
2
P l wl l l
l
= += += +=
= =
*+# G#4D$+ 31 $+# I#H$/4DG# 0- &B( T7
40+ 2
2355 (2)355 4
3554
V r h
hh
h
= = =
=
*+# +#0D+$ 31 $+# H/4 0-355
28.254
H#4$0T#$#I-7
41+ / % ! < (7(=;A ! % &7(=;A !
42+ K#F#4,# #2,/G- H3-$ M+#4 8A( ! % 9=( ! < 9A((78A( ! % 9=( ! < 9A((B( ! % 9A((
! % A(A( $366G#I- 4##6 $3 5# #4I3GG#67
4,+ 1 n
V C N
=
2000 3200 18n =
;((( % 9;(( ) 8(( 0 8(( 0 % &;((0 % 9*+# 1,I40$,I# M0GG +/F# / F/G,# 31 U;(((/1$#I 9 :#/I-7
43+ 334.8
(2500)495
334.8165, 726 2500
165,72666.2904
2500
vf F
v
v
v
=
==
= =
"04H# $+# H/I 0- $I/F#G04D /$ >>7;O(8 T0V+ 34 />A T0V+ +0D+M/:. $+# 3110H#I H/4 HG/0T $+/$ :3,M#I# -L##604D7
44+ SI34M:4W- M##XG: -/G/I: 13I M3IX04D1 +3,I- 0-;B1 < &=7 "$#F#W- M##XG: -/G/I: 13I M3IX04D1 +3,I- 0- 9A 171
(27 18 35 ) 5505
62 18 2750
62 2732273244.1
62
h h
h
hh
+ + =+ =
==
*+#: T,-$ #/H+ M3IX 88 +3,I- #/H+ M##X7
-**+ # %' ?& ) .# @ ! # %'! ?& ) .# @ # %'! ) '.!# # < '.!# %'! #?& @ % &(? ! O;@= ! 9>= % &( ! O;(AA; % ; !
! % ;B>*+# T/[0T,T 4,T5#I 31 H,-$3T#I- 0- ;B>7
-
7/25/2019 Sol Mat Haeussler ByPriale
24/717
!"#$ !"#$%&'(#%$) +,#-./,#0(,1 2",1)303 !"#$%&' )*2
')
-*/+ d
t r c
=
$ ?+ ) / @ %- $+ ) $/ %- $+ - %$/
tr d d c r
t t = =
-*0+ Z#$ ! % $+# +3I0\34$/G 60-$/4H# 1I3T $+# 5/-# 31$+# $3M#I $3 $+# +3,-#7 S: $+# ]:$+/D3I#/4$+#3I#T. 2 2 2100 ( 1) . x x+ = +
2 210, 000 2 110, 000 2 1
9999 29999
4999.52
x x x x x
x
+ = + += +=
= =
*+# 60-$/4H# 1I3T $+# $3L 31 $+# $3M#I $3 $+#+3,-# 0- ! < & % 8OOO7A < & % A(((7A T#$#I-7
-*1+ 30 s fd = "#$ 2 % 8A /46 ?13I 6I: H34HI#$#@ 3 % (7=7
( )22
45 30(0.8)
45 24
(45) 24
2025 242025 675 3
84 84 ft24 8 8
d
d
d
d
d
==
==
= = =
-*2+ Z#$* 5# $+# /T3,4$ 04 $+# /HH3,4$ 34# :#/I /D37*+#4 $+# 04$#I#-$ #/I4#6 0- (7(B9* /46* < (7(B9* % &;AB71.073 1257
12571171.48
1.073
P
P
=
=
*+# /T3,4$ 04 $+# /HH3,4$ 34# :#/I /D3 M/-U&&B&78=. /46 $+# 04$#I#-$ #/I4#6 0-U&&B&78=?(7(B9@ % U=A7A;7
-*,+ Z#$4 5# *3TW- #[L#4-#- 04 ^3F/ "H3$0/ 5#13I#$+# _"* $/[7 *+#4 $+# _"* $/[ 0- (7&A 4 /46 $+#$3$/G I#H#0L$- /I#4 < (7&A4 % &7&A47 *+#L#IH#4$/D# 31 $+# $3$/G $+/$ 0- _"* 0-0.15 0.15 15 31.15 1.15 115 23
ee
= = = 3I /LLI3[0T/$#G:
&9`7
-*3+ 1 1
and8 14
/I# I33$-7
-*4+ 12
0- / I33$7
--*+ 14
61
0- / I33$7
---+ ( 0- / I33$7
!"#$%&'( *+3
-+ 2 4 4 0 x x + = 2( 2) 0 x =
! ) ; % ( ! % ;
.+ ?$ < &@?$ < ;@ % ($ < & % ( 3I $ < ; % (
$ % )& 3I $ % );
/+ 2 8 15 0( 3)( 5) 0t t t t
+ = =
$ 9 % ( 3I $ A % ($ % 9 3I $ % A
0+ ? ! ) ;@? ! < A@ % ( ! ) ; % ( 3I ! < A % ( ! % ; 3I ! % )A
1+ 2 2 3 0 x x = ? ! ) 9@? ! < &@ % (
! ) 9 % ( 3I ! < & % ( ! % 9 3I ! % )&
2+ ? ! ) 8@? ! < 8@ % ( ! ) 8 % ( 3I ! < 8 % ( ! % 8 3I ! % )8
,+ 2 13 36u u = 2 13 36 0u u + =
( 4)( 9) 0u u = 5 ) 8 % ( 3I 5 ) O % (5 % 8 3I 5 % O
3+ 23( 4 4) 0w w + = 23( 2) 0w =
( ) ; % (( % ;
-
7/25/2019 Sol Mat Haeussler ByPriale
25/717
,-./$"0 )1 &'()'* +, -./'012 !"#$ !"#$%&'(#%$) +,#-./,#0(,1 2",1)303
'*
4+ 2 4 0 x = ? ! ) ;@? ! < ;@ % (
! ) ; % ( 3I ! < ; % ( ! % ; 3I ! % );
-*+ 3 ( 2) 0u u = 5 % ( 3I 5 ; % (5 % ( 3I 5 % ;
--+ 2 5 0( 5) 0t t t t
= =
$ % ( 3I $ ) A % ($ % ( 3I $ % A
-.+ 2 9 14 0 x x+ + = ? ! < B@? ! < ;@ % (
! < B % ( 3I ! < ; % (
! % )B 3I ! % );-/+ 24 1 4 x x+ =
24 4 1 0 x x + = 2(2 1) 0 x =
; ! ) & % (12
x =
-0+ 22 9 5 0 z z + = ?; " ) &@? " < A@ % (; " ) & % ( 3I " < A % (
12
z = 3I " % )A
-1+ 2
2
(3 5) 2
3 5 2
3 5 2 0(3 2)( 1) 0
v v
v v
v vv v
= = + = =
96 ) ; % ( 3I 6 & % (23
v = 3I 6 % &
-2+ 2
2
6 2 0
6 2 0(2 1)(3 2) 0
x x
x x x x
+ + = =
+ =
2 1 0 or 3 2 01 2
or 2 3
x x
x x
+ = =
= =
-,+ 2 3 10 0 x x + + = 2 3 10 0 x x =
? ! ) A@? ! < ;@ % ( ! ) A % ( 3I ! < ; % (
! % A 3I ! % );
-3+ 21 3
07 7
y y =
1( 3) 0
7 y y =
# % ( 3I # ) 9 % ( # % ( 3I # % 9
-4+ 22 3 p p= 22 3 0 p p =
&?; & ) 9@ % (
& % ( 3I ; & ) 9 % ( & % ( 3I
32
p =
.*+ 2 12 0r r + = ?+ ) 9@?+ < 8@ % (+ ) 9 % ( 3I + < 8 % (+ % 9 3I + % )8
.-+ ! ? ! < 8@? ! ) &@ % ( ! % ( 3I ! < 8 % ( 3I ! ) & % ( ! % ( 3I ! % )8 3I ! % &
..+ 2 2( 3) ( 1) 0w w + = ( 9 % ( 3I ( < & % (( % 9 3I ( % &
./+ 3
249 0
( 49) 0( 7)( 7) 0
t t
t t t t t
= =
+ =
0 or 7 0 or 7 00 or 7 or 7
t t t t t t
= + = == = =
.0+ 2( 4 5) 0 x x x =
! ? ! ) A@? ! < &@ % ( ! % ( 3I ! ) A % ( 3I ! < & % ( ! % ( 3I ! % A 3I ! % )&
.1+ 3 26 5 4 0 x x x+ = 2(6 5 4) 0 x x x+ =
! ?; ! ) &@?9 ! < 8@ % (
-
7/25/2019 Sol Mat Haeussler ByPriale
26/717
!"#$ !"#$%&'(#%$) +,#-./,#0(,1 2",1)303 !"#$%&' )*2
'"
! % ( 3I ; ! ) & % ( 3I 9 ! < 8 % (
! % ( 3I12
x = 3I 43
x =
.2+ 2
2 1 5 1 0 x x x+ + + = 2 3 2 0 x x + = ? ! ) &@? ! ) ;@ % (
! ) & % ( 3I ! ) ; % ( ! % & 3I ! % ;
.,+ 2( 3)( 4) 0( 3)( 2)( 2) 0
x x x x x
= + =
! 9 % ( 3I ! ; % ( 3I ! < ; % ( ! % 9 3I ! % ; 3I ! % ;
.3+ A? ! < 8@? ! 9@? ! =@ % (4 0 or 3 0 or 8 0
4 or 3 or 8 x x x
x x x+ = = =
= = =
.4+ 2 3( 3) 4( 3) 0 p p p = 2( 3) [ 4( 3)] 0 p p p = 2( 3) (12 3 ) 0 p p =
23( 3) (4 ) 0 p p = & ) 9 % ( 3I 8 ) & % ( & % 9 3I & % 8
/*+ 2 2( 1)( 2) 0 x x =
( )( )( 1)( 1) 2 2 0 x x x x+ + = ! < & % ( 3I ! & % (
3I 2 0 x+ = 3I 2 0 x = ! %& 3I ! % &
3I 2 x = 3I 2 x =
/-+ 2 2 24 0 x x+ = ' % &.. % ;. / % );8
2 42
b b ac x
a =
2 4 4(1)(24)
2(1)
=
2 1002
=
2 102
=
2 104
2 x
+= = 3I 2 10 62
x = =
/.+ 2 2 15 0 x x = ' % &.. % );. / % )&A
2 42
b b ac x
a =
(2) 4 4(1)(15)
2(1)
=
2 642
=
2 82
=
2 85
2 x
+= = 3I 2 8 32
x = =
//+ 24 12 9 0 x x + = ' % 8. . % )&;. / % O
2 42
b b ac x
a =
( 12) 144 4(4)(9)
2(4)
=
12 08
=
12 08
=
32
=
/0+ 2 5 0q q = ' % &.. % A. / % (
2 42
5 25 4(1)(0)
2(1)5 25
25 5
2
b b acq
a =
=
=
=
5 5 52
q += = 3I 5 5 02
q = =
-
7/25/2019 Sol Mat Haeussler ByPriale
27/717
,-./$"0 )1 &'()'* +, -./'012 !"#$ !"#$%&'(#%$) +,#-./,#0(,1 2",1)303
'#
/1+ 2 2 7 0 p p = ' % &.. %;. / %B
2
2
42
( 2) ( 2) 4(1)( 7)
2(1)2 32
21 2 2
b b ac p
a =
=
=
=
1 2 2 p = + 3I 1 2 2 p =
/2+ 22 2 0 x x + = 2 2 2 0 x x + =
' % &.. % );. / % ;
(2) 4 4(1)(2)2(1)
x =
2 42 =
43 I#/G I33$-
/,+ 24 2 0n n + = 2 2 4 0n n + =
' % &.. % );. / % 82 4
2b b ac
na
=
( 2) 4 4(1)(4)
2(1) =
2 122 =
43 I#/G I33$-
/3+ 22 5 x x+ = 22 5 0 x x+ =
' % ;. . % &./ % )A2 4
2b b ac
xa
=
1 1 4(2)(5)
2(2)
=
1 414
=
1 414
x += 3I 1 41
4 x
=
/4+ 24 5 2 0 x x+ = ' % 8. . % A./ % );
2 42
5 25 4(4)( 2)2(4)
5 578
b b ac x
a =
=
=
5 578
x += 3I 5 57
8 x
=
0*+ 2 2 1 0w w + = ' % &.. %;. / % &
2
2
42
( 2) ( 2) 4(1)(1)
2(1)2 0
21
b b acw
a =
=
==
0-+ 20.02 0.3 20w w = 20.02 0.3 20 0w w =
' % (7(;. . % )(79. / % );(2 4
2
b b acw
a
=
(0.3) 0.09 4(0.02)(20)
2(0.02)
=
0.3 1.690.04
=
0.3 1.30.04
=
0.3 1.3 1.640
0.04 0.04w
+= = = 3I
0.3 1.3 1.025
0.04 0.04w
= = =
-
7/25/2019 Sol Mat Haeussler ByPriale
28/717
!"#$ !"#$%&'(#%$) +,#-./,#0(,1 2",1)303 !"#$%&' )*2
'$
0.+ 20.01 0.2 0.6 0 x x+ = ' % (7(&.. % (7;. / % )(7>
2 42
b b ac x
a =
0.2 0.04 4(0.01)(0.6)
2(0.01)
=
0.2 0.0640.02
=
0.2 (0.0064)(10)
0.02=
0.2 0.08 100.02
=
10 4 10= 10 4 10 x = + 3I 10 4 10 x =
0/+ 22 4 5 x x+ = 22 4 5 0 x x+ =
' % ;. . % 8./ % )A2 4
2b b ac
xa
=
4 16 4(2)(5)
2(2)
=
4 564
=
4 2 144
=
2 142
=
2 142
x += 3I 2 14
2 x
=
00+ 22 6 5 0 x x + = ' % );. . % )>. / % A
2 42
b b ac x
a =
(6) 36 4(2)(5)
2( 2)
=
6 764
=
6 2 194
=
3 192
=
3 192
x += 3I 3 19
2 x
=
01+ 2 2 2( ) 5( ) 6 0 x x + = Z#$ 2 .w x= *+#4
2 5 6 0w w + = ?( ) 9@?( ) ;@ % (( % 9. ;*+,- 2 3 x = 3I 2 2, x = -3 3, 2 x = 7
02+ 2 2 2( ) 3( ) 10 0 X X = Z#$ 2 .w X = *+#4
2 3 10 0( 5)( 2) 0
w ww w
= + =
( % A. ;*+,- 2 5 X = 3I 2 2, X = -3 $+# I#/G -3G,$034-/I# 5. X =
0,+ 21 1
3 7 2 0 x x + =
Z#$1
.w x
= *+#4
23 7 2 0
(3 1)( 2) 01
, 23
w w
w ww
+ =
==
*+,-.1
3, .2
x =
-
7/25/2019 Sol Mat Haeussler ByPriale
29/717
,-./$"0 )1 &'()'* +, -./'012 !"#$ !"#$%&'(#%$) +,#-./,#0(,1 2",1)303
'%
03+ 1 2 1( ) 12 0 x x + = Z#$ 1 .w x= *+#4
2 12 0w w+ = ?( < 8@?( ) 9@ % (( % )8. 9
*+,-.1 1
, .4 3
x =
04+ 2 2 2( ) 9( ) 20 0 x x + = Z#$ 2 .w x= *+#4
2 9 20 0w w + = ?( ) A@?( ) 8@ % (( % A. 8
*+,-.2
15
x= 3I
21
4, x
= -3 2 15
x = 3I 2 1 .4
x =
5 1, .
5 2 x =
1*+ 2
2 21 1
9 8 0 x x
+ =
Z#$2
1.w
x= *+#4
2 9 8 0w w + = ?( ) =@?( ) &@ % (( % =. &
*+,-. 21
8 x = 3I 21
1, x = -32 1
8 x = 3I2
1. x =
2, 1.
4 x =
1-+ 2( 5) 7( 5) 10 0 X X + + = Z#$( % 8 A7 *+#4
2 7 10 0( 2)( 5) 0w ww w
+ + =+ + =
( % ;. A*+,-. 8 A %; 3I 8 A %A. -3 8 % 9. (7
1.+ 2(3 2) 5(3 2) 0 x x+ + = Z#$( % 9 ! < ;7 *+#4
2 5 0( 5) 0
0, 5
w ww w
w
= =
=
*+,- 9 ! < ; % ( 3I 9 ! < ; % A. -32
, 1.3
x =
1/+ 21 1
12 35 02 2 x x
+ =
Z#$1
,2
w x
=
$+#4
2 12 35 0w w + = ?( ) B@?( ) A@ % (( % B. A
*+,-.1
72 x
=
3I1
5.2 x
=
15 11, .
7 5 x =
10+ 21 1
2 7 3 04 4 x x
+ + = + +
Z#$1
4w
x=
+ 7 *+#4
22 7 3 0w w+ + = ?; ( < &@?( < 9@ % (
1, 3
2w =
*+,-.1 1
4 2 x=
+ 3I
13
4 x=
+ 7
136,
3 x =
11+ 2 3
2
x x
+= 22 3 x x= + 22 3 0 x x =
?; ! ) 9@? ! < &@ % (
*+,-.3
, 1.2
x =
12+ 7 5
2 2 x
x=
N,G$0LG:04D 53$+ -06#- 5: $+# ZaJ. ; ! . D0F#-2 14 5 x x= 2
5 14 0 x x+ = ? ! ) ;@? ! < B@ % (*+,-. ! % ;. )B7
-
7/25/2019 Sol Mat Haeussler ByPriale
30/717
!"#$ !"#$%&'(#%$) +,#-./,#0(,1 2",1)303 !"#$%&' )*2
'&
1,+ 3 3
24
x x x
+ =
N,G$0LG:04D 53$+ -06#- 5: $+# ZaJ. ! ? ! ) 8@.D0F#-9 ! < ? ! ) 9@? ! ) 8@ % ; ! ? ! ) 8@
2 23 7 12 2 8 x x x x x+ + = 2 24 12 2 8 x x x x + =
20 4 12 x x= ( % ? ! ) >@? ! < ;@*+,-. ! % >. );7
13+ 2 6
52 1 1 x x
=+
N,G$0LG:04D 53$+ -06#- 5: $+# ZaJ.?; ! < &@? ! &@. D0F#-
2
2
2( 1) 6(2 1) 5(2 1)( 1)
10 8 10 5 50 10 5 3
x x x x
x x x x x
+ = +
= = + +
' % &(.. % A./ % 92 4 25 4(10)(3) 95 0,b ac = = $+,- $+#I#
/I# 43 I#/G I33$-7
14+ 3 2 2 1
11 2
x x x x
+ + =+
N,G$0LG:04D 53$+ -06#- 5: $+# ZaJ. ; ! ? ! < &@.D0F#-
2 2 2
2 2
2
2 (3 2) (2 1)( 1) 2 ( 1)
6 4 (2 3 1) 2 2
4 1 2 2
2 1 0(2 1)( 1) 0
x x x x x x
x x x x x x
x x x x
x x x x
+ + + = ++ + + = +
+ = + =
+ =
*+,-.1
, 1.2
x =
2*+ 6( 1)
32 1w w
w w+ + =
N,G$0LG:04D 53$+ -06#- 5: $+# ZaJ.?; ) ( @?( ) &@. D0F#->?( < &@?( ) &@
-
7/25/2019 Sol Mat Haeussler ByPriale
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,-./$"0 )1 &'()'* +, -./'012 !"#$ !"#$%&'(#%$) +,#-./,#0(,1 2",1)303
)(
20+ 2 3 4
1 2 x x x+ =
+ +
N,G$0LG:04D 53$+ -06#- 5: $+# ZaJ. ! ? ! < &@? ! < ;@. D0F#-
2 2 2
2 2
2
2 ( 2) 3( 1)( 2) 4 ( 1)
2 4 3 9 6 4 4
5 13 6 4 4
9 6 0
x x x x x x
x x x x x x
x x x x
x x
+ + + + = ++ + + + = +
+ + = ++ + =
' % &.. % O./ % >2
2
42
9 9 4(1)(6)
2(1)9 57
2
b b ac x
a =
=
=
*+,-.9 57 9 57
, .2 2
x + =
21+ 2 22 1 2
( 1)1 x x x x =
N,G$0LG:04D 53$+ -06#- 5: $+# ZaJ.2 ( 1)( 1), x x x+ D0F#-
22 ( 1) 2( 1)( 1) x x x x x + = + 2 2 22 2 2 x x x x =
2 22 2 x x x = 20 2 x x= +
( % ? ! < ;@? ! &@ ! % ); 3I ! % &S,$ ! % & 63#- 43$ H+#HX7 *+# -3G,$034 0- );7
22+ b1 ! )9. $+# #2,/$034 0-3 1
5 . x
x x =
N,G$0LG:04D 53$+ -06#- 5: ! D0F#-A ! ) 9 % & ) ! > ! % 8
23
x =
2,+ ( )2 22 3 ( 3) x x = 22 3 6 9 x x x = +
20 8 12 x x= + ( % ? ! ) >@? ! ) ;@
! % > 3I ! % ;c4G: ! % > H+#HX-7
23+ ( )2 23 4 ( 6) x x+ = 29 36 12 36 x x x+ = +
20 21 x x= ( % ! ? ! ) ;&@
! % ( 3I ! % ;&c4G: ! % ;& H+#HX-7
24+ ( )22( 2) 2 4 7q q+ = 2 4 4 16 28q q q+ + = 2 12 32 0q q + =
?% ) 8@?% ) =@ % (*+,-. % % 8. =7
,*+ ( ) ( )2 2 5 0 x x+ = Z#$ ,w x= $+#4 2 2 5 0w w+ = ' % &.. % ;. / %A
2 42
b b acw
a =
2 4 4(1)( 5)
2(1)2 24
22 2 6
21 6
w =
=
=
=
"04H# w x= /46 1 6 0, 1 6w = 63#- 43$ H+#HX7 *+,- 1 6,w = + -3
( )21 6 7 2 6. x = + =
,-+
( ) ( )
( )
2 2
22
2
2
3 3 1
3 3 1
3 3 2 3 1
2 2 2 3
1 3( 1) 3
2 1 3
5 1 0
z z
z z
z z z z z
z z z z
z z z
z z
+ = +
+ = ++ = + +
+ =
+ = + =
+ = + =
' % &.. %A. / % &
-
7/25/2019 Sol Mat Haeussler ByPriale
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!"#$ !"#$%&'(#%$) +,#-./,#0(,1 2",1)303 !"#$%&' )*2
)!
2
2
42
( 5) ( 5) 4(1)(1)
2(1)5 21
2
b b ac z
a =
=
=
c4G:5 21
2 z
= H+#HX-7
,.+ 2 2 8 x x =
( ) ( )2 22 2 8 x x = 4 4 2 8 x x x + =
4 12 x x =
( )2 24 ( 12) x x = 216 24 144 x x x= +
20 40 144 x x= + ( % ? ! ) 8@? ! ) 9>@
! % 8 3I ! % 9>c4G: ! % 8 H+#HX-7
,/+ 1 2 1 x x+ = +
( ) ( )2 21 2 1 x x+ = + 2 1 2 1 x x x+ + = +
2 x x=
( )2 22 x x= 24 x x=
20 4 x x= ( % ! ? ! ) 8@*+,-. ! % (. 87
,0+ ( ) ( )2 22 2 2 3 y y + = + 2 4 2 4 2 3 y y y + + = +
4 2 1 y y = +
( )2 2
4 2 ( 1) y y = + 216 32 2 1 y y y = + +
20 14 33 y y= + ( % ? # ) &&@? # ) 9@*+,-. # % &&. 97
,1+ ( ) ( )
( )
2 2
2 2
2
2
3 1 3
3 2 3 1 9
2 3 8 4
3 4 23 (4 2)
3 16 16 4
0 16 17 10 (16 1)( 1)
x x
x x x x x
x x x x
x x x
x x x x
+ + =+ + + + =
+ =
+ = + =
+ = += +=
116
x = 3I ! % &
c4G: ! % & H+#HX-7
,2+ ( ) ( )
( )
2 2
2 2
2
2
2 3 1
2 3 13 1
(3 1)
9 6 1
0 9 7 1
t t
t t t t
t t
t t t
t t
+ = +
+ = +=
=
= += +
' % O.. %B. / % &2
2
42
( 7) ( 7) 4(9)(1)
2(9)7 13
18
b b act
a =
=
=
c4G:7 13
18+
H+#HX-7
,,+ 2 ( 2.7) ( 2.7) 4(0.04)(8.6)
2(0.04) x
=
>87&A 3I 979A
,3+ 2 0.2 (0.2) 4(0.01)(0.6)
2(0.01)
x =
;7>A 3I );;7>A
-
7/25/2019 Sol Mat Haeussler ByPriale
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,-./$"0 )1 &'()'* +, -./'012 !"#$ !"#$%&'(#%$) +,#-./,#0(,1 2",1)303
)'
,4+ Z#$9 5# $+# G#4D$+ 31 $+# L0H$,I#. $+#4 0$- M06$+ 0-9 ) ;79?9 ) ;@ % 8=
2 2 48 0l l = ?9 ) =@?9 < >@ % (9 ) = % ( 3I 9 < > % (9 % = 3I 9 % )>"04H# G#4D$+ H/443$ 5# 4#D/$0F#.9 % =7 *+# M06$+31 $+# L0H$,I# 0-9 ) ; % = ) ; % > 04H+#-7*+# 60T#4-034- 31 $+# L0H$,I# /I# > 04H+#- 5:= 04H+#-7
3*+ *+# /T3,4$ $+/$ $+# $#TL#I/$,I# +/- I0-#4 3F#I$+# 8 6/:- 0-? 8 6#DI##- L#I 6/:@? 8 6/:-@ % 2 X 6#DI##-7
2 15 51 X + = 2 36 X =
36 X = 8 % > 3I 8 % )>*+# $#TL#I/$,I# +/- 5##4 I0-04D > 6#DI##- L#I6/: 13I > 6/:-7
3-+ ( 10)
44Q Q
M +=
244 10Q Q= + 20 10 44Q Q M = +
dI3T $+# 2,/6I/$0H 13IT,G/ M0$+ ' % &.. % &(.44 ,c M =
10 100 4(1)(44 )2(1)
Q =
10 2 25 442
+ +=
5 25 44= + *+,-. 5 25 44 + + 0- / I33$7
3.+ 2200 200 20 g P P = + + "#$ : % >(7
2
2
2
60 200 200 20
200 200 40 0
5 5 1 0
P P
P P
P P
= + + + =
+ =
dI3T $+# 2,/6I/$0H 13IT,G/ M0$+ ' % A.. %A./ % &.
5 25 4(5)(1) 5 52(5) 10
P = =
* (7;= 3I * (7B;;=` /46 B;` 31 :#/-$ D/F# /4 /F#I/D# M#0D+$D/04 31 >( DI/T-7
3/+ 1
.12 24
A Ad d
A+=
+
J0F0604D 53$+ -06#- 5:- /46 $+#4 T,G$0LG:04D53$+ -06#- 5: ;8? ; < &;@ D0F#-;8 ; % ? ; < &;@? ; < &@
224 13 12 A A A= + + 20 11 12 A A= +
dI3T $+# 2,/6I/$0H 13IT,G/.11 121 48 11 73
.2 2
A = =
11 7310
2 A
+= 3I 11 73 1.2
A =
*+# 63-#- /I# $+# -/T# /$ & :#/I /46 &( :#/I-7
/ %- 04 a3MG04DW- I,G# M+#41
1,24
A+ = M+0H+
3HH,I- M+#4 ; % ;97 *+,-. /6,G$+336 0- /H+0#F#6/$ /D# ;9 /HH3I604D $3 a3MG04DW- I,G#7
/ %- 04 e3,4DW- I,G# M+#4 1,12
A A
=+
M+0H+ 0-
4#F#I $I,#7 *+,-. /6,G$+336 0- 4#F#I I#/H+#6/HH3I604D $3 e3,4DW- I,G#7
00 25
1
e3,4DW- I,G# LI#-HI05#- G#-- $+/4 a3MG04DW- 13I/D#- G#-- $+/4 34# :#/I /46 DI#/$#I $+/4 &( :#/I-7a3MG04DW- I,G# LI#-HI05#- G#-- 13I /D#- 5#$M##4
& /46 &(7
30+ 5+ 2(2 1) 2 1 0n v nv + = dI3T $+# 2,/6I/$0H 13IT,G/ M0$+ ' % ;0 ) &.. % ); 0. / % &.
2 (2 ) 4 4(2 1)(1)
2(2 1)
n n nv
n
=
22 4 8 42(2 1)
n n nv
n +=
22 ( 1)2 2 2 1
2(2 1) 2 1
n nn n nv
n n
+= =
S#H/,-# 31 $+# H3460$034 $+/$0 &. 0$13GG3M- $+/$0 ) & 0- 4344#D/$0F#7 *+,-.
2( 1) 1n n = /46 M# +/F#( 1)
.2 1
n nv
n =
6 % & 3I1
.2 1
vn
=
-
7/25/2019 Sol Mat Haeussler ByPriale
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!"#$ !"#$%&'(#%$) +,#-./,#0(,1 2",1)303 3.$-"4.$%#.5 !'./6-&$ ,-./$"0 )
))
$+ 2 (2 1) 1 0nv n v + + = dI3T $+# 2,/6I/$0H 13IT,G/ M0$+ ' %0.. % )?; 0 < &@. /46/ % &.
2[ (2 1)] [ (2 1)] 4( )(1)
2
n n nv n
+ + =
22 1 4 12
n nv
n+ +=
S#H/,-# 24 1n + 0- DI#/$#I $+/4 ;0.H+33-04D $+# LG,- -0D4 D0F#- / 4,T#I/$3IDI#/$#I $+/4 ;0 < & < ;0. 3I 80 < &. -3 6 0-
DI#/$#I $+/44 1 1
2 .2 2n
n n+ = + *+,- 6 0-
DI#/$#I $+/4 ;7 *+0- H34$I/60H$- $+#I#-$I0H$034 3467 c4 $+# 3$+#I +/46. 5#H/,-#
24 1n + 0- DI#/$#I $+/4 &. H+33-04D $+#T04,- -0D4 D0F#- / 4,T#I/$3I G#-- $+/4 ; 0.
-3 6 0- G#-- $+/42
1.2
nn
= *+0- T##$- $+#
H3460$034 3467 *+,- M# H+33-#22 1 4 1
.2
n nv
n+ +=
31+ 5+ Y+#4 $+# 35f#H$ -$I0X#- $+# DI3,46.1 T,-$5# (. -3
20 39.2 4.9 4.9 (8 )t t t t = = $ % ( 3I $ % =
*+# 35f#H$ M0GG -$I0X# $+# DI3,46 = - /1$#I5#04D $+I3M47
$+ "#$$04D1 % >=7; D0F#-2
268.2 39.2 4.9
4.9 39.2 68.2 0
t t
t t
= + =
239.2 ( 39.2) 4(4.9)(68.2)
2(4.9)39.2 14.1
9.8
t =
$ A78 - 3I$ ;7> -7
32+ S: / LI3DI/T. I33$- /I# 87A /46 )97CGD#5I/0H/GG:'
22 3 27 0 x x = ?; ! ) O@? ! < 9@ % (*+,-. ; ! ) O % ( 3I ! < 9 % (
"39
4.52
x = = 3I ! % )97
3,+ S: / LI3DI/T. I33$- /I# &7A /46 (7BA7CGD#5I/0H/GG:'
28 18 9 0 x x + = ?; ! ) 9@?8 ! ) 9@ % (*+,-. ; ! ) 9 % ( 3I 8 ! ) 9 % (7
"33
1.52
x = = 3I 3 0.75.4
x = =
33+ S: / LI3DI/T. I33$- /I# (7B>; /46 (7;>;7
34+ S: / LI3DI/T. $+#I# /I# 43 I#/G I33$-7
4*+ 29
6.3 (1.1 7 )2 3
z z z =
2 29 1.1 76.32 3 3
z z z =
29 7 1.16.3 02 3 3 z z
+ =
K33$-' (7O=B. )(7O98
4-+ 2( 4) 4.1 3t t = 2 2 8 16 4.1 3t t t + = 2 2 (8 4.1) 19 0t t + + =
K33$-' &7OOO. (7O>9
6578&'579:5% ;85=7&" *
-+
.+ *+# LI3H#6,I# M3IX- 5#H/,-# T,G$0LG:04D / G0-$5: / 4,T5#I 0- $+# -/T# /- T,G$0LG:04D #/H+#G#T#4$ 04 $+# G0-$ 5: $+# 4,T5#I. /6604D /4,T5#I $3 / G0-$ +/- $+# #11#H$ 31 /6604D $+#4,T5#I $3 #/H+ #G#T#4$ 31 $+# G0-$. /46-,5$I/H$04D 34# G0-$ 1I3T /43$+#I 0- $+# -/T# /--,5$I/H$04D H3II#-L34604D #G#T#4$-7 *+# LG3$-T/$H+7
/+
*+# I#-,G$- /DI##7
-
7/25/2019 Sol Mat Haeussler ByPriale
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,-./$"0 )1 &'()'* +, -./'012 !"#$ !"#$%&'(#%$) +,#-./,#0(,1 2",1)303
)*
0+ *+# -T/GG#I 2,/6I/$0H I#-06,/G- 0460H/$# / 5#$$#I10$7 *+# 1/0IG: I/463T L/$$#I4 -,DD#-$- $+/$ $+#T36#G H/443$ 5# 0TLI3F#6 /4: 1,I$+#I7 *+#-G0D+$ 6#F0/$034- 1I3T $+# 2,/6I/$0H T36#G /I#LI#-,T/5G: 6,# $3 I/463T T#/-,I#T#4$ #II3I-7
-
7/25/2019 Sol Mat Haeussler ByPriale
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!"
"#$%&'( )
*(+,-'./ )0)
)0 "#$ ! %# $ '()$& *+) ,! %# $ -#+.$& /0 $-/$2
! !
, !
, ! 3+ *4#* 5 67728, ! 9! 5 677
22 800w = 2 400w =
! 5 ,7 0$3&:; $ -#+.$& (; /:+$ /0 0#+?(+.+##)#) (; ,8#+;(/+; *4# D7 0$ %E A77 0$2
20 "#$ $ 5 +:>%#4 /0 /:+?#; (+ #*?& 1*4$2 3+ '#&*F#%#4 /0 /:+?#; (+ #*?& 1*4$2 3+ '#&*F#
, $ @ A$ 5 ABC$ 5 AB163
n =
3&:; $ $:41#+$(+# +##)#) (;16 1
(1) 53 3
n = = /:+?#;2
50 "#$ ! 5 '()$& 8(+ >(-#;9 /0 ;$4(1 $/ %# ?:$2 3+$ 4#>*(+(+. 0/4#;$ &*; )(>#+;(/+; , I , ! %EA I , ! 2
!
!
! ! A
, I , !
,
A I , !
J/+;()#4(+. $ *4#* /0 $ 4#>*(+(+. 0/4#;$= '#&*F#
3(2 2 )(1 2 )
4w w =
2 32 6 44
w w + =
28 24 16 3w w + = 216 24 5 0w w + =
8
K#+?#1 5
, .4 4
w = L:$ 54
w = (; (>1/;;(%-# ;(+?#
/+# )(>#+;(/+ /0 /4(.(+*- 0/4#;$ (; A >(2 3&:;
$ '()$& /0 $ ;$4(1 ;&/:-) %#14
>(2
60 "#$ ! 5 '()$& 8(+ >#$#4;9 /0 1*F#>#+$2 3#>*(+(+. 1-/$ 0/4 0-/'#4; &*; )(>#+;(/+;6 I , ! %E < I , ! 2
!
!
! ! #+$ ;&/:-) %# A >2
70 M(+?# )(*>#$#4 /0 ?(4?:-*4 #+) (; A>= $
4*)(:; (; H7 >>2 N4#* /0 ?(4?:-*4 #+) (;2 2( radius) (70) . = N4#* /0 ;O:*4# #+) (; 2 . x PO:*$(+. *4#*;= '# &*F# 2 2(70) . x =
3&:; 2(70) 70 . x = = M(+?# ' >:;$ %#1/;($(F#= 70 124 x = >>2
80 "#$ ( 5 +:>%#4 /0 $/+; 0/4 QDB7=777 14/0($2R4/0($ 5 3/$*- S#F#+:# I 3/$*- J/;$560,000 134 (82 120,000)560,000 52 120,000680,000 52
680,00052
13,076.9 13, 077 tons.
q qqq
q
q
= += =
=
)90 "#$ ( 5 4#O:(4#) +:>%#4 /0 :+($;2R4/0($ 5 3/$*- S#F#+:# I 3/$*- J/;$150,000 50 (25 500,000)150,000 25 500,000650,000 25 , from which
26,000
q qqq
q
= += ==
))0 "#$ ' 5 *>/:+$ *$ BT *+)
,7=777 I ' 5 *>/:+$ *$1
7 %.2
' 8727B9 @ 8,7=777 I ' 98727HD9 5 A/:+$ '(-- %# 21, 000,000(1 )r + 1-:; $(+$#4#;$ /+ $&(;= '&(?& (; 21,000,000(1 ) .r r + 3&:; $ $/$*- F*-:# *$ $ #+) /0 $ $&(4) E#*4'(-- %# 2 2
31,000,000(1 ) 1,000,000(1 )
1,000,000(1 ) .
r r r
r
+ + += +
3&(; >:;$ #O:*- QA=A,D=67723
3
1,000,000(1 ) 1,125,8001,125,800
(1 ) 1.12581,000,000
1 1.040290.04029
r
r
r r
+ =
+ = =
+
3&:; * 727
-
7/25/2019 Sol Mat Haeussler ByPriale
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23-4 !"#$%&'(#%$) +,#-./,#0(,1 2",1)303 +&,%-./ )0)
!$
)60 "#$ $ 5 +:>%#4 /0 4//> *11-(?*$(/+; ;#+$ /:$272GD$ 5 HB
7680
0.95n = =
)70 "#$ $ 5 +:>%#4 /0 1#/1-# 1/--#)272,7 ) 5 H77
7003500
0.20 p = =
)80 "#$ + 5 >/+$&-E ;*-*4E /0 )#1:$E ;(00272C7+ 5 ,77
2000.30
s =
200Yearly salary 12 12 $8000
0.30 s
= = =
190 X#*4-E ;*-*4E %#0/4# ;$4(Y# 5 8H2D798698,B795 QAD=B77"/;$ '*.#; 5 8H2D798698*-92" 8AD=B779 5 ,HB7
27600.177 17.7%
15,600 P = =
1)0 "#$ ( 5 +:>%#4 /0 ?*4$4().#; ;/-) $/ %4#*Y #F#+2$/$*- 4#F#+:# 5 $/$*- ?/;$21.95 14.92 8500
7.03 85001209.10
q qqq
= +=
A,7G ?*4$4().#; >:;$ %# ;/-) $/ *114/V(>*$#-E%4#*Y #F#+2
110 "#$ $ 5 +:>%#4 /0 ;&*4#; /0 ;$/?Y $/ %# %/:.&$2$/$*- (+F#;$>#+$ 5 #= $+ . 5 "*/ 2 3/ $4(1-# *+ (+F#;$>#+$ /0" *$ $ #+) /0/ E#*4;= $ (+$#4#;$ #*4+#) ):4(+.$&*$ $(># >:;$ #O:*- ," 2 3&:;, " 5 " 8727
-
7/25/2019 Sol Mat Haeussler ByPriale
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!"#$%&' )* "##$%&'(%)*+ '*, -)./ "$0/1.' 23-4 !"#$%&'(#%$) +,#-./,#0(,1 2",1)303
!%
3&:;8A,7 @! 9867 @! 9 5 ,86798A,79
29600 200 19, 200w w+ + = 2 200 9600 0w w+ =
8! @ ,/:4 ;$/?Y;2 3+ $ ?:44#+$
F*-:# /0 $ %-:#Z?&(1 ;$/?Y (;1
,10
x x+ /4 11 .10
x
U/4 $ .-*>/:4 ;$/?Y; $ ?:44#+$ F*-:# (;1
(3,100,000 ) (3,100,000 ),
10
x x '&(?&
;(>1-(0(#; $/9
(3,100,000 ).10
x
3&:; 0/4 $ ?:44#+$ F*-:# /0 $ 1/4$0/-(/=11 9
(3,100,000 ) 3, 240,00010 10
x x+ =
AA ' @ ,H=G77=777 I G ' 5 C,=#+$ (;11
(2,250,000)10
/4 Q,=
-
7/25/2019 Sol Mat Haeussler ByPriale
40/717
23-4 !"#$%&'(#%$) +,#-./,#0(,1 2",1)303 +&,%-./ )0)
!&
!!
AD7
R"N]3
NSPN
C77 I , !
3&:;! 8C77 I , ! 9 5 AA=,77, ! 8AD7 I! 9 5 AA=,77! 8AD7 I! 9 5 DB77
20 150 5600w w= + 7 5 8! I 6798! I H79K#+?# ! 5 67= H72 [0! 5 H7= $+ -#+.$& (;C77 I , ! 5 C77 I ,8H79 5 AB72 M(+?# $%:(-)(+. &*; -#+.$& /0 /+-E AD7 0$= '# 4#^#?$! 5H72 [0! 5 67= $+ -#+.$& (;C77 I , ! 5 C77 I ,8679 5 A#+;(/+; *4# 67 0$ %E A# /0 $ +#' ;$E-#?*+)E= '# &*F#
2 22
2
(7.1) (2.1) (2.1) 0.78(97.461 )29.84142 2.1
14.21023.7696
r r
r r
= = =
M(+?#* (; * 4*)(:;= '# ?&//;# * 5 C2HH >>2
280 "#$ ' 5 *>/:+$ /0 -/*+2 3+ $ *>/:+$*?$:*--E 4#?#(F#) (; ' 72AB ' 2 K#+?#=
0.16 195,0000.84 195,000
232,142.86
x x x x
==
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0.6(0.9) if 0.9 30, 000Revenue
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q qq q q
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46 56 66 76 86 96 106532
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7.540q =
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1;0 2( ) 5 3 H s s= 2(4) 5(4) 3 80 3 77 H = = =
( ) ( )22 5 2 3 10 3 7 H = = = 22 2 20 7
5 3 33 3 9 9
H = = =
1
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,-./$"0 )1 &'()*+,(- .(/ 01.23- !"#$ !"#$%&'(#%$) +,#-./,#0(,1 2",1)303
!#
)40 2( ) 2 1 f x x x= + + 2(1) 1 2(1) 1 1 2 1 4 f = + + = + + =
2(1) (1) 2(1) 1 1 2 1 0 f = + + = + =
22 2
( ) ( ) 2( ) 12 2 2 1
f x h x h x h x xh h x h
+ = + + + += + + + + +
)70 2( ) ( 4) H x x= + 2(0) (0 4) 16 H = + = 2 2(2) (2 4) 6 36 H = + = =
2 2( 4) [( 4) 4] H t t t = + =
)80 27
( )2
xk x
x
=+
25 7 2(5)
275 2k = =
+
2 23 7 3 7
(3 )(3 ) 2 9 2
x xk x
x x
= =+ +
2 2 2( ) 7 7
( )( ) 2 2 2
x h x hk x h
x h x xh h
+ + + = =+ + + + +
)90 ( ) 3k x x= (4) 4 3 1 1k = = = (3) 3 3 0 0k = = =
( 1) ( ) ( 1) 3 32 3
k x k x x x x x
+ = + =
):0 4 / 3( ) f x x= 4 / 3(0) 0 0 f = =
( )44 / 3 43(64) 64 64 (4) 256 f = = = = 44 / 3 4
31 1 1 1 18 8 8 2 16
f = = = =
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( )22 / 5 25(32) 32 32 (2) 4 g = = = =
( )22 / 5 5
( 64) ( 64) 64 g = =
( ) ( )2 25 5 55 32 2 2 2 4 4= = =
10 10 2 / 5 4( ) ( ) g t t t = =
)
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2
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6 3 2
6 3 2
f x h f x x xh h x h x xh h
xh h hh
x h
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+ =
= +
440 2( ) 3 2 4 f x x x= +
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( ) 3 2( ) 4( )
3 2 2 4( 2 )
f x h x h x h
x h x xh h
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2
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2 8 4
2 8 4
f x h f x x h x xh h x xh h
h xh hh
x h
+ + + + +=
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470 3( ) f x x=
$0 3 3 2 2 3( ) ( ) 3 3 f x h x h x x h xh h+ = + = + + +
20 ( ) ( ) f x h f x
h+ 3 2 2 3 3( 3 3 ) x x h xh h x
h+ + + =
2 2 33 3 x h xh hh
+ += 2 23 3 x xh h= + +
480 1
( ) f x x
=
$0 1( ) f x h x h
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20 ( )1 1
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x x h x x h x h x f x h f x h
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+ +
490 8
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f x x+=
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+ +
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h h
+ + ++ + = ( )
8 8( )
( )
x h x x h x x x h
x x h h
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+( 8) ( )( 8)
( ) x x h x h x
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+
2 28 8 8( )
x xh x x hx x h x x h h
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8 8( ) ( )
h x x h h x x h
= = + +
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5
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f h f hh h
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=
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4;0 2
2
2
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2 1 72
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f x f x x x x
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