5
? B? 10mé¥à
ás?1 () (0.3 6)xxρ = + L H N
0≤≤10x
pà¥é
b
3
L H 'à¥é
1 L H b
10
0
(0.3 6) 75mxdx=+=
∫
? X??tLè -
yx=
2
? ≤ ≤11x
¥?B?)¥è?L
á
D??? ॠ???1 )¥
á1 q pNè -
¥9è
b
y (,)11
3
3
1
221
2
0
1
1
14 (14 ) (551)
66
Q q x x dx q x q
?
=+=+=?
∫
'Nè -
¥9è
1
1
(5 5 1)
6
q? b
à
£ o¥C
ê
^B??%0?
? 36m/ ? 24mú 16m
£
ü
?
? 4mpC
ê
?
s?¥
£a ?
£¥
á1 1000kg/m
3
b
3 [0?¥
?1 à V
?¥??<°_/1y xà?_ 5
£
/ ?
£
? ?1 )ú1 ¥B
C
êB§
?
s¥
£a ?1 x dx
3
1000 (4 ) 24 (16 )
4
dF g x x dx
? ?
=++?
? ?
? ?
?
^C
ê
?
s¥9¥
£a ?1
16
7
0
3
1000 (4 ) 24 (16 ) 5.4 10
4
Fgx xdx
??
=++?≈
??
??
∫
×(N) b
á B??T
?@??
?LZ?
xa t
ya t
zbt
=
=
=
?
?
?
?
?
cos ,
sin ,
,
0>t
0,0 >> ba
?B?)¥
áD
?? Oxyü
?¥ ???1
kp?B
247
?¥é
b
3 é
2
22 22
0
2mkbtabdtkbab
π
2
π=+=+
∫
b
? B????
£y?? 10mú 30m= μB?¥
£ p|
£??
?
?1S¥? b
3 (J) b
30
32
15
10 10 1.04 10Wxgdxπ=?? =×
∫
9
? ??1 r¥oz
à?
£?o¥
á1 ρC1|o?
£
?K
1S
?$
3 I
n
£/ ?
£
? ?1 )¨1 ¥??
?¥S?f x dx
? ??1 r¥oz ? 7
£
? 5??
?¥êM1 r2
£
?M?¥ ?1
£
M?¥ ?1x xr ?2 b
?¥
?1
2
(2 )rx x π?
!
0
ρ 1
£¥
á5|oz?
£
?à
1S¥?1
∫∫
??+??=
rr
dxxrxxgdxxrxxrgW
2
0
2
0
2
0
2
)2()()2)(2( πρρπρ
)2(
3
4
0
4
ρρπ ?= gr b
? ??1 r
á1 ¥o T[?
?ρ ω?°?è p
?¥?? b
3 ==
2
2
1
ωIW
2
2
22
0
(2 )2 2 1
2
r
rx x rx x y dx
ω
ρπ
2
′??+
∫
=
2
2
22
20
(2 )2 2
2
2
r
r
rx x rx x dx
rx x
ω
ρπ??
?
∫
2
22
0
4
(2 )
3
r
rrxxdxρω π πρω=?=
∫
4
r b
?
P?1?é1 1m¥?T
%é 2 5cm3n ? 15NC|
?V
1 1m ?à 1 2mù1S
?$
3 ? ? m
HkxF = 025.0=x 15=F N} ?¤ 600=k b?
^
?S
¥?1
248
0.2
0.1
9W kxdx==
∫
J b
? Bt8¥??
p1 s tt= ?3
3
oé¥E ?D
?¥üZ??
1pt8V t ?à
HE ?
?S¥? b =1 t T=
3
!oé¥E ?1
? 5 b?
^ F 19
2
?=′= tsv
22
)19( ?= tkF
35
2224
9
5
243
7
729
)19(
357
1
32
1
??+?=?=′=
∫∫
TTTTdttdtsFW
TT
b
? ??1 1mú1 2m ¥° ?¥?????
?
£ù???
¥B???1 1cm ¥?0a
£ 7
S
@
k?
£
?ú
?
H
WM?¥?
p ip
£??
@ b
?3¥
HW b
£
?1
£ gú
H
£
?
h
h
vg=×06 2. h b
3
!
H Y
£
?¥ú1 V
HWa
£
?¥ú??
5 t h dt dh
dtghvdtdh 26.0)01.0()01.0(1
222
×?=?= πππ
'
dtg
h
dh
2106
5?
×?= b
T
Hs?i 0=t
H 2=h ¤?
25
)1031(2 tgh
?
×?=
[ }?3¤ 0=h
5
4
10
1.06 10
3
t
g
==×
s b
è
5?¥?????1??è8? ??
P
£
@
H
£
?
ú/?
^
?¥ b
3 ? 5i o1
5¥?B??
T¥PHcμy0 h' V 9
'
H Y
£
?¥??t r?
?@
2
rkh= ? 1è
? b
?[ Vê¨ k
249
wL ? àèB?a
?¤èw
?T1?V7
P¤
£
@
4
cxy = y
H
£
?ú/?
^
?¥ b
é ?¥
?M
?D
?¥Ci
??1
! t
Hμ ? gü 1600M
?¥
h
B?p ?¥
?M?
p b
0 0
Q
3
!
H Y t ?¥Ci
1 )(tQQ = 5
kQ
dt
dQ
?=
?
T
Hs?i
H Y μ ? Q g¤? t
0 0
)(
0
0
)(
ttk
eQtQ
=?
= b
?5i ?
H1600
0
=?tt
2
)(
0
Q
tQ = }?
T ¤ ?
1600
2ln
=k
? [
1600
0
0
2
tt
QQ
?
?
= b
ê | Até?1 Bté¥?DQ?
?D Bté¥i?Q1
!Q? 7
S
Hμ B té 20%?l
Haμ B té 25%p B t
é¥i¥M??
p b
3
!
H Y t Bté¥i1 , 5 )(ty
y
k
dt
dy
=
3¤
ckty += 2 b
y1
5
1
)0( =y
4
1
)
2
1
( =y
?[
400
9
,
25
1
== kc ?
^¤?
20
1618 +
=
t
y b
?
! ?¥| g9é
D],[ dttt + p
max
? pt()??1
k?M?¥|
g? ?| gM?f ?¥¤miD Malthus? Verhulst| g
250
?F[1? b
3 ?5i V?
max
()
(()
dp t
kp pt
dt
=?
00
() p tp=
?N V3¤
0
(
max max 0
() ( )
kt t
pt p p p e
??
=? ?
)
b
ì ?Q??
H Y?0¥9F
?D?
H¥
?
??1 b
! £
ü
t Nt()
N()0 = N
0
[ ]
1
0
2
)( t
N
tN
[ ]
2
0
1
)( t
N
tN
= b
£ ?5i V?
kN
dt
dN
=
?
T
Hs?i N()0 N
0
= V3¤
251
tk
eNtN
0
)( =
?N' V¤?
2
21
1
0
1
0
2
)()(
t
ttk
t
N
tN
e
N
tN
?
?
?
?
?
?
?
?
==
?
?
?
?
?
?
?
?
b
í B? 1000m
3
¥vO?¥ b=cμ a %¥lC[ 1m
3
min
???7 b?a¥ b ?[]"¥
?
q?p
H Y b
=cμ¥liip
Plih
B?
?3¥
HW b
t
3
!
H Y t b=cμ¥li1 5 )(ty
1
()
1000
dy y t dt=? (0)
100
a
y =
3NZ?'¤?
1000
100
)(
t
e
a
ty
?
= b
? ()
200
a
yt =
Hμ
1000
2
t
e = V7¤? 1000ln 2t =
min'l
ih
B?
?3¥
HW1
min b 1000ln 2
252