Taiyee Homepage by Huadong Li

ï¿½ï¿½

ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½ï¿½]

ï¿½Õ¿ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½Ï¿ï¿½ï¿½ï¿½

3 ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ï¿½Ï´ï¿½. ï¿½×·ï¿½ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½. ï¿½×·ï¿½ï¿½Ù¸ï¿½

ï¿½î¶»ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½Ï¸ï¿½ ï¿½É±ï¿½?

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½Ø¼ï¿½ ï¿½Ýµï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ ï¿½Ò¸ï¿½ï¿½ï¿½ ï¿½ï¿½È²ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½Ö¸ï¿½ ï¿½ï¿½ï¿½Ï¿ï¿½

28 TIMES 18

ï¿½ï¿½

36 TIMES 24 ï¿½ï¿½

ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½Ï±ï¿½:

ï¿½ï¿½

55.5 TIMES 375=20812.5

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½ï¿½]: 336

ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½]: 145

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½]: 81.5

ï¿½Õ°ï¿½: 21275.0 ï¿½ï¿½ ï¿½Ì´ï¿½.

ï¿½ï¿½

M= { Pl} over {4 }= { 1} over {4 } TIMES 21275 TIMES 300=1595670 ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½

Ç¥ 29ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½

Z=5184

ï¿½ï¿½

, ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½:

ï¿½ï¿½

sigma = { M} over {Z }= { 1595670} over {5184 } =307.8 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }<645 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½ï¿½

(Ç¥ 30) ï¿½Ì´ï¿½.

J=93312

ï¿½ï¿½

)

ï¿½ï¿½

f= { P { l}^{3 } } over {48EJ }= { 21275 TIMES { 300}^{3 } } over {48 TIMES 4.96 TIMES { 10}^{5 } TIMES 93312 } =0.25 ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ç¿¬ï¿½ï¿½[ï¿½ï¿½ï¿½Ë¿ï¿½]ï¿½Ü¸ï¿½ï¿½ï¿½

45 TIMES 30

ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½:

P=24415 ï¿½ï¿½

ï¿½ï¿½ï¿½îµ¥ ï¿½ï¿½ ï¿½ï¿½ï¿½Æ®:

{ M}_{1 }=3662365 ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½

{ M}_{2 }=255150 ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½Ï±ï¿½:

Ç¥29 ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½

Z=10125

ï¿½ï¿½

{ sigma }_{1 }= { 3662365} over {10125 } =362ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½ï¿½

{ sigma }_{ 2}= { 255150} over {10125 } =25.2 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½Õ°ï¿½:

sigma =362+25.2=387.2 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }<645 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

f= 1.0 ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

100 TIMES 40

ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½:

P=39405.7 ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½ï¿½îµ¥ ï¿½ï¿½ ï¿½ï¿½ï¿½Æ®ï¿½ï¿½

{ M}_{1 }=5910855 ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½

{ M}_{2 }=1020600 ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½

{ M}_{ 1} ï¿½ï¿½ { M}_{2 }

ï¿½ï¿½

ï¿½ï¿½ ï¿½ï¿½ï¿½Ï¸ï¿½:

ï¿½ï¿½

M= { M}_{ 1}+ { M}_{2 }=6931455 ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½:

ï¿½ï¿½

sigma = { 6931455} over {24000 } =288.8 ï¿½ï¿½/ { ï¿½ï¿½}^{ 2}

ï¿½ï¿½

ï¿½Ì´ï¿½.

(Ç¥ 29ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½

Z=24000

ï¿½ï¿½

)

ï¿½ï¿½ï¿½îµ¥ ï¿½Ö´ï¿½ Ã³ï¿½ï¿½ï¿½ï¿½

f=1.8 ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½È¿ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½Ë¿ï¿½]: ï¿½Ü¸ï¿½

60 TIMES 40

ï¿½ï¿½

ï¿½ï¿½, ï¿½ï¿½ï¿½ï¿½ 1200 ï¿½ï¿½:(ï¿½×¸ï¿½ 7-7)

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½:

P=57004.6 ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½ï¿½îµ¥ ï¿½ï¿½ ï¿½ï¿½ï¿½Æ®;

{ M}_{ 1}=8530690 ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½

{ M}_{2 }=1814400 ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½Ö´ï¿½ ï¿½ï¿½ ï¿½ï¿½ï¿½Æ®ï¿½ï¿½:

ï¿½ï¿½

M= { M}_{1 }+ { M}_{2 }=10365090 ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½ï¿½îµ¥ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½:

ï¿½ï¿½

sigma =432 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }<645 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½ï¿½ï¿½îµ¥ Ã³ï¿½ï¿½ï¿½ï¿½:

f=4.8

ï¿½ï¿½

ï¿½ï¿½ ï¿½Ì´ï¿½.

42 TIMES 28

ï¿½ï¿½

ï¿½ï¿½, ï¿½ï¿½ï¿½ï¿½ 375 ï¿½ï¿½(ï¿½×¸ï¿½ 7-8)

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½:

P=69328

ï¿½ï¿½

ï¿½ï¿½ ï¿½Ì´ï¿½.

ï¿½ï¿½

a=150 ï¿½ï¿½, { }_{ } b=255 ï¿½ï¿½

ï¿½ï¿½

ï¿½ï¿½

M= { Pab} over {a+b }= { 69328 TIMES 150 TIMES 225 } over {150+225 } =6230520 ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

Ç¥ 29 ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½

Z=8232

ï¿½ï¿½

ï¿½ï¿½

sigma = { 6230520} over {8232 } =757

ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

>645

ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½ï¿½

45 TIMES 30

ï¿½ï¿½

ï¿½ï¿½, ï¿½ï¿½ï¿½ï¿½ 750ï¿½ï¿½:( ï¿½×¸ï¿½ 7-9):

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½:

P=69328

ï¿½ï¿½

ï¿½ï¿½ ï¿½Ì´ï¿½.

ï¿½ï¿½ï¿½îµ¥ ï¿½ï¿½ ï¿½ï¿½ï¿½Æ®ï¿½ï¿½:

ï¿½ï¿½

M=8307360 ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

Ç¥29 ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½

Z=10125

ï¿½ï¿½

ï¿½ï¿½

sigma = { 8307360} over { 10125}=820 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }>645 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½ï¿½

45 TIMES 30

ï¿½ï¿½

ï¿½ï¿½, ï¿½ï¿½ï¿½ï¿½ 375 ï¿½ï¿½(ï¿½×¸ï¿½7-10):

ï¿½ï¿½ï¿½ï¿½:

P=50117 ï¿½ï¿½

ï¿½ï¿½

ï¿½ï¿½ï¿½îµ¥ ï¿½ï¿½ ï¿½ï¿½ï¿½Æ®:

M=5706656 ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½:

sigma =563 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }<645 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

30 TIMES 20

ï¿½ï¿½

42 TIMES 28

ï¿½ï¿½

ï¿½ï¿½ï¿½Ì´ï¿½. ï¿½ï¿½ï¿½â¼ï¿½ï¿½

42 TIMES 28

ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½:

P=50117 ï¿½ï¿½

ï¿½ï¿½

ï¿½ï¿½ï¿½îµ¥ ï¿½ï¿½ ï¿½ï¿½ï¿½Æ®:

ï¿½ï¿½

M=4396931 ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½

ï¿½ï¿½ï¿½îµ¥ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½:

ï¿½ï¿½

sigma =534 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½ï¿½

ï¿½ï¿½

{ l}_{0 }=375-60=315 ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½ï¿½îµ¥ ï¿½ï¿½ ï¿½ï¿½ï¿½Æ®ï¿½ï¿½:(

a=150ï¿½ï¿½, b=185ï¿½ï¿½, c=45ï¿½ï¿½

ï¿½ï¿½

)

ï¿½ï¿½

M= { Pab} over { { l}_{0 } }(1- { c} over {2 { l}_{ 0} })= { 69228 TIMES 150 TIMES 165} over { 315}(1- { 40} over {2 TIMES 315 } )=5058588 ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½

ï¿½ï¿½ï¿½îµ¥ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½: (

Z=8232

ï¿½ï¿½

)

ï¿½ï¿½

sigma = { 5058588} over {8232 } =614.5 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }<645 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½ï¿½

ï¿½Ì°ï¿½, ï¿½ï¿½ï¿½ï¿½ï¿½Ï´ï¿½.

ï¿½ï¿½

{ l}_{ 0}=300-60=240ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½

M= { P { l}_{0 } } over { 4} = { 69228 TIMES 240} over {4 }=4153680 ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½

sigma =499 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }<645 ï¿½ï¿½ / { ï¿½ï¿½}^{2 }

ï¿½×¸ï¿½ 7-11. ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½

ï¿½ï¿½

{ a}_{1 }= { b}_{ 2}=140, { l}_{ 1} =610, { l}_{2 }=235

ï¿½ï¿½

{ P}_{1 }= { P}_{2 }=P=39405.7, { M}_{A } = { M}_{C }=0

ï¿½ï¿½

2 { M}_{B }( { l}_{1 }+ { l}_{ 2})=- { { P}_{1 } { a}_{1 }( { l}`_{1 } ^{2 }- { a}`_{1 } ^{2 }) } over { { l}_{1 } }- { { P}_{2 } { b}_{ 2}( { l}`_{2 } ^{2 }- { b}`_{2 } ^{2 }) } over { { l}_{2 } }

ï¿½ï¿½

2 { M}_{B }(610+235)=-P { a}_{1 }( { { 610}^{2 }- { 140}^{2 } } over {610 }+ { { 235}^{ 2}- { 140}^{2 } } over {235 })

ï¿½ï¿½

1690 { M}_{B }=-P { a}_{1 }(577.9+151.6)=-39405.7 TIMES 140 TIMES 729.5

ï¿½ï¿½

{ M}_{B } =-2381363 ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½

{ Q}_{A }=30361.8+ { -2381363} over {610 } =26458 ï¿½ï¿½

ï¿½ï¿½

{ Q}`_{B } ^{' }=-9044+ { -2381363} over {610 }=-12947.8 ï¿½ï¿½

ï¿½ï¿½

{ Q}`_{B } ^{'' }=23475.7+ { { M}_{C }- { M}_{ B} } over { { l}_{2 } }=23475.7+ { 2381363} over {235 }=33609ï¿½ï¿½

ï¿½ï¿½

{ Q}_{C }=-15930+10133.5=5796.5ï¿½ï¿½

ï¿½ï¿½

{ N}`_{A } ^{ }=26458 ï¿½ï¿½

ï¿½ï¿½

{ N}_{B }= { Q}`_{B } ^{'' }- { Q}`_{B } ^{' }=33609-(-12947.8)=46557 ï¿½ï¿½

ï¿½ï¿½

{ N}_{C }=5796.5 ï¿½ï¿½

ï¿½ï¿½

{ N}_{A }, { }^{ } { N}_{C }

ï¿½ï¿½

ï¿½ï¿½

a=b=150, { l}_{1 }= { l}_{2 }=600, { M}_{A }= { M}_{ C}, P=57004.6

(ï¿½Õ¿ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½Ï¿ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½)

ï¿½ï¿½

2 { M}_{B }( { l}_{1 }+ { l}_{2 })=- { 2Pa( { l}`_{1 } ^{2 }- { a}^{2 }) } over { { l}_{1 } }

ï¿½ï¿½

{ M}_{B }=- { Pa( { l}`_{1 } ^{2 }- { a}^{ 2} ) } over {2 { l}`_{1 } ^{2 } }

ï¿½ï¿½

=- { 57004.6 TIMES 150 TIMES ( { 600}^{2 }- { 150}^{2 }) } over {2 TIMES { 600}^{2 } }=-4008136 ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½ï¿½Ü·ï¿½ ï¿½ï¿½ï¿½Ï±ï¿½:(ï¿½×¸ï¿½ 7-14c )

ï¿½ï¿½

{ Q}_{A }=45603+ { -4008136} over {600 } =38923 ï¿½ï¿½

ï¿½ï¿½

{ Q}`_{B } ^{' }=-11401.6+ { -4008136} over {600 } =-18082 ï¿½ï¿½

ï¿½ï¿½

{ N}_{A }=38923 ï¿½ï¿½

ï¿½ï¿½

{ N}_{B }=18082-(-18082)=36146 ï¿½ï¿½

ï¿½ï¿½

a=150, { l}_{1 }=225, { l}_{2 }=750

ï¿½ï¿½

{ M}_{A }= { M}_{D }=0, { M}_{B }= { M}_{C }, P=57004.6

ï¿½ï¿½

2 { M}_{B }( { l}_{1 }+ { l}_{2 })+ { M}_{C } { l}_{2 }=- { Pa} over { { l}_{1 } }( { l}`_{1 } ^{2 }- { a}^{2 })

ï¿½ï¿½

2 { M}_{B }(225+750)+750 { M}_{C }=- { 57004.6 TIMES 150} over {225 }( { 225}^{ 2} - { 150}^{2 })

ï¿½ï¿½

2700 { M}_{B }=-1068834375

ï¿½ï¿½

{ M}_{B }=-395846.6 ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½ï¿½Ü·ï¿½ ï¿½ï¿½ï¿½Ï±ï¿½:(ï¿½×¸ï¿½7-15c)

ï¿½ï¿½

{ Q}_{A }=19001.5+ { { M}_{B }- { M}_{A } } over { { l}_{1 } }=19001.5+ { -395846.6-0} over {225 } =17242

ï¿½ï¿½

{ Q}_{B }=-38003+(-1759.4)=-39762.4

ï¿½ï¿½

{ N}_{A }=17242 ï¿½ï¿½

ï¿½ï¿½

{ N}_{B }=39762 ï¿½ï¿½

ï¿½ï¿½

{ N}_{A }ï¿½ï¿½ { N}_{B }

ï¿½ï¿½

ï¿½ï¿½

M= { 26541 TIMES 150 TIMES 225} over {375 } =2388690 ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½

Ç¥29ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½

Z=8232

ï¿½ï¿½

ï¿½ï¿½

sigma = { 2388690} over {8232 } =290 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½ï¿½

ï¿½ï¿½/ { ï¿½ï¿½}^{ 2}

ï¿½ï¿½

ï¿½ Ã»ï¿½ï¿½[ï¿½ï¿½ï¿½ï¿½]

ï¿½ï¿½

{ P}_{2 }

ï¿½ï¿½

{ P}_{1 }

ï¿½ï¿½

ï¿½ï¿½ 7184.0 ï¿½ï¿½ ï¿½Ì´ï¿½. (ï¿½×¸ï¿½ 7-19 a, b)

B ï¿½ï¿½ï¿½ï¿½ ï¿½Ý·ï¿½ï¿½ï¿½

{ Q}_{f }

ï¿½ï¿½

: (

a=90, b=120

ï¿½ï¿½

)

ï¿½ï¿½

{ Q}_{f }= { 1} over {2 }(- { 1} over {2 } TIMES 120 TIMES 30 TIMES { P}_{2 }+120 TIMES 90 TIMES { P}_{1 })

ï¿½ï¿½

= { 1} over {2 }(-1800 { P}_{2 }+10800 { P}_{1 })

ï¿½ï¿½

= { 1} over {2 }(-1800 TIMES 10709.7+10800 TIMES 7184.0)=29155410.0

ï¿½ï¿½

Ã³ï¿½ï¿½ï¿½ï¿½

{ f}_{A }

ï¿½ï¿½

ï¿½ï¿½:

ï¿½ï¿½

{ f}_{A }= { { M}_{f }} over {EJ } = { 1} over {EJ } LEFT [ 29155410.0 TIMES 90+ { 2 TIMES 90} over {3 }(90 { P}_{1 } TIMES { 1} over {2 }) RIGHT ]

ï¿½ï¿½

= { 2643383970.0} over {EJ } = { 2643383970.0} over {4.1 TIMES { 10}^{5 } TIMES 45000 } =0.14 ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

{ b}_{ 4}

ï¿½ï¿½

ï¿½ï¿½

{ b}_{4 }:1.5=390:540, { b}_{4 }=1.1ï¿½ï¿½

ï¿½ï¿½

ï¿½ï¿½

{ f}_{ 4} +1.1=0.7+1.1=1.8 ï¿½ï¿½

ï¿½ï¿½

(

{ f}_{4 }=0.7

ï¿½ï¿½

)

{ b}_{3 }

ï¿½ï¿½

ï¿½ï¿½

{ b}_{ 3}:1.8=240:390, { b}_{3 }=1.1 ï¿½ï¿½

ï¿½ï¿½

{ f}_{3 }+1.1=0.5+1.1=1.6ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.(

{ f}_{3 }=0.5

ï¿½ï¿½

)

ï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½ï¿½]:

ï¿½Ü¸ï¿½Ä¡ï¿½ï¿½ï¿½ï¿½

30 TIMES 20 ï¿½ï¿½

ï¿½ï¿½

, ï¿½È¸ï¿½Å¸ï¿½ 300ï¿½ï¿½ ï¿½Ì´ï¿½.

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½Ï¸ï¿½:

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½: 10710 ï¿½ï¿½

ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½]ï¿½ï¿½ï¿½ï¿½: 145 ï¿½ï¿½

ï¿½Õ°ï¿½: 11111.5 ï¿½ï¿½

ï¿½ï¿½ï¿½îµ¥ï¿½ï¿½ ï¿½ï¿½ ï¿½ï¿½ï¿½Æ®ï¿½ï¿½:

ï¿½ï¿½

M=833377 ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½

sigma = { 833377} over { 3000} =278 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }<532.5 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½ï¿½

(Ç¥30)

ï¿½ç¿¬ï¿½ï¿½[ï¿½ï¿½ï¿½Ë¿ï¿½]:

ï¿½Ü¸ï¿½Ä¡ï¿½ï¿½

36 TIMES 24 ï¿½ï¿½, { }_{ } ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ { }_{ } 600ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½:

P=13520.0 ï¿½ï¿½

ï¿½ï¿½ï¿½îµ¥ ï¿½Ú¸ï¿½ï¿½Æ®:

ï¿½ï¿½

M=2028000 ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½ï¿½îµ¥ ï¿½ï¿½ï¿½ï¿½:

ï¿½ï¿½

sigma = { 2028000} over {5184 } =391.0 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½ï¿½

(

Z=5184

ï¿½ï¿½

)

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½Ë¿ï¿½]:

ï¿½Ü¸ï¿½

36 TIMES 24ï¿½ï¿½, { } atop { } ï¿½ï¿½ï¿½ï¿½ { }_{ } 660ï¿½ï¿½

ï¿½ï¿½

(ï¿½×¸ï¿½ 7-21)

ï¿½ï¿½ï¿½ï¿½:

P=22009.0 ï¿½ï¿½

ï¿½ï¿½ï¿½îµ¥ ï¿½ï¿½ ï¿½ï¿½ï¿½Æ®:

ï¿½ï¿½

M=2253069.0 ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½ï¿½îµ¥ ï¿½ï¿½ï¿½ï¿½:

ï¿½ï¿½

sigma = { 2253069} over {5184 }=434.6 ï¿½ï¿½ / { ï¿½ï¿½}^{2 }

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½Ë¿ï¿½]:

ï¿½Ü¸ï¿½

42 TIMES 28ï¿½ï¿½, { } atop { } ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ { }_{ } 794ï¿½ï¿½

ï¿½ï¿½

(ï¿½×¸ï¿½ 7-22)

ï¿½ï¿½ï¿½ï¿½:

P=26715.0 ï¿½ï¿½

ï¿½ï¿½ï¿½îµ¥ ï¿½ï¿½ ï¿½ï¿½ï¿½Æ®:

ï¿½ï¿½

2998508.0

ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½

ï¿½ï¿½ï¿½îµ¥ ï¿½ï¿½ï¿½ï¿½:

ï¿½ï¿½

sigma =364 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½ï¿½

ï¿½ï¿¬ï¿½ï¿½[ß²ï¿½Ë¿ï¿½]:

ï¿½Ü¸ï¿½:

30 TIMES 20ï¿½ï¿½, { } atop { } ï¿½ï¿½ï¿½ï¿½ { }_{ } 402ï¿½ï¿½

ï¿½ï¿½

(ï¿½×¸ï¿½ 7-23)

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½Ï¸ï¿½:

ï¿½Õ°ï¿½: 7888.0 ï¿½ï¿½

ï¿½ï¿½ï¿½îµ¥ï¿½ï¿½ ï¿½ï¿½ ï¿½ï¿½ï¿½Æ®:

ï¿½ï¿½

M= { 7888.0 TIMES 150 TIMES 252} over {402 } =741707.0 ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½ï¿½îµ¥ ï¿½ï¿½ï¿½ï¿½:

ï¿½ï¿½

sigma = { 741707.0} over {3000 } =247.0 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½ï¿½

(

Z=3000

ï¿½ï¿½

)

ï¿½ï¿½ï¿½îµ¥ Ã³ï¿½ï¿½: (

E=4.1 TIMES { 10}^{5 } { }_{ } (Ç¥31), { }_{ } a=150, { }_{ } b=252

ï¿½ï¿½

)

ï¿½ï¿½

f= { P { a}^{ 2} { b}^{2 } } over {3EJl } = { 7888.0 TIMES { 150}^{2 } TIMES { 252}^{2 } } over {3 TIMES 4.1 TIMES { 10}^{5 } TIMES 402 } =0.5 ï¿½ï¿½

ï¿½ç¿¬ï¿½ï¿½[ï¿½ï¿½ï¿½Ë¿ï¿½]:

ï¿½Ü¸ï¿½:

36 TIMES 24ï¿½ï¿½, { } atop { } ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ { }_{ } 552ï¿½ï¿½

ï¿½ï¿½

(ï¿½×¸ï¿½ 7-24)

ï¿½ï¿½ï¿½ï¿½:

P=12696.0 ï¿½ï¿½

ï¿½ï¿½ï¿½îµ¥ ï¿½Ú¸ï¿½ï¿½Æ®:

M=1386911.0 ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½ï¿½îµ¥ ï¿½ï¿½ï¿½ï¿½:

sigma =267.5 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½ï¿½ï¿½îµ¥ Ã³ï¿½ï¿½:

f=0.7 ï¿½ï¿½

ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½Ë¿ï¿½]:

ï¿½Ü¸ï¿½:

36 TIMES 24ï¿½ï¿½, { } atop { } span { }_{ } 686ï¿½ï¿½

ï¿½ï¿½

(ï¿½×¸ï¿½ 7-25)

ï¿½ï¿½ï¿½ï¿½:

P=14296.0 ï¿½ï¿½

ï¿½ï¿½ï¿½îµ¥ ï¿½Ú¸ï¿½ï¿½Æ®:

M=1541467.0 ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½ï¿½îµ¥ ï¿½ï¿½ï¿½ï¿½:

sigma =297 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½ï¿½ï¿½îµ¥ Ã³ï¿½ï¿½:

f=1.5ï¿½ï¿½

ï¿½ï¿½

ï¿½×¸ï¿½ 7-25. ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½

ß² ï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½]

28 TIMES 18

ï¿½ï¿½

ï¿½Ü¸ï¿½ï¿½ï¿½ï¿½:

21 TIMES 10=210 { ï¿½ï¿½}^{2 }

È¾ï¿½ï¿½[ï¿½ï¿½Ú£]ï¿½ï¿½ï¿½ï¿½(Ëï¿½ï¿½):

327.7 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½ï¿½

327.7 TIMES 210=68817 ï¿½ï¿½

ï¿½ï¿½

16 TIMES 10=160 { ï¿½ï¿½}^{2 }

ï¿½ï¿½

149ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½ï¿½

149 TIMES 160=23840 ï¿½ï¿½ ï¿½Ì´ï¿½.

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ 1/2:

19288.0/2=9644.0

13012.5/3=4338.0

ï¿½Õ°ï¿½: 14527.0 ï¿½ï¿½ï¿½Ì´ï¿½.

ï¿½ï¿½

ï¿½ç¿¬ï¿½ï¿½[ï¿½ï¿½ï¿½Ë¿ï¿½] ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ 1/2: 3402.0/2=1701.0 ï¿½ï¿½

ï¿½Õ°ï¿½: 29461.0 ï¿½ï¿½

ï¿½ï¿½

18 TIMES 16=288 { ï¿½ï¿½}^{2 }

ï¿½ï¿½

149.0 TIMES 288=42912.0

ï¿½ï¿½

ï¿½Õ°ï¿½: 38253.7 ï¿½ï¿½

20 TIMES 14=280{ ï¿½ï¿½}^{2 }

ï¿½ï¿½

89.3 ï¿½ï¿½/ { ï¿½ï¿½}^{ 2}

ï¿½ï¿½

ï¿½ï¿½

89.3 TIMES 280=25004.0 ï¿½ï¿½<38253.7 ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

{ ï¿½ï¿½}^{2 }

ï¿½ï¿½

{ ï¿½ï¿½}^{2 }

ï¿½ï¿½

645 TIMES 280=180600 ï¿½ï¿½

ï¿½ï¿½

645 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½) ï¿½ç¿¬ï¿½ï¿½

[ï¿½ï¿½ï¿½Ë¿ï¿½] ï¿½Ó¸ï¿½ï¿½ï¿½ ï¿½ßµï¿½

ï¿½ï¿½ ï¿½Ö´ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ 35424.0

ï¿½ï¿½ï¿½Ì¾î¼ ï¿½ï¿½ï¿½ï¿½ï¿½Ï´ï¿½.

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½[ï¿½ß¿ï¿½ï¿½ï¿½] ï¿½ï¿½

ï¿½Îºï¿½[ï¿½Ý»]ï¿½ï¿½ ï¿½ßµï¿½ ï¿½ï¿½

ï¿½Ö´ï¿½ ï¿½Ö´ï¿½ ï¿½Ð·ï¿½ï¿½ï¿½

20636.0 ï¿½ï¿½ï¿½Ì¾î¼

22009 ï¿½Åºï¿½ï¿½ï¿½ ï¿½Û¾ï¿½

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½Ï´ï¿½.

Èï¿½ï¿½[ï¿½ï¿½ï¿½ï¿½]ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ 25830 ï¿½ï¿½ï¿½ï¿½

{ ï¿½ï¿½}^{2 }

ï¿½ï¿½

{ ï¿½ï¿½}^{2 }

ï¿½ï¿½

{ ï¿½ï¿½}^{2 }

ï¿½ï¿½

ï¿½ï¿½

123 TIMES 350=43050 ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½

P= { 22009 TIMES 125} over {535 } + { 2722} over {2 }=6503 ï¿½ï¿½ <43050 ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì°ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½Ï´ï¿½.

ï¿½ï¿½ ï¿½ï¿½[ï¿½ï¿½]ï¿½ï¿½ ï¿½ï¿½Ä§[ï¿½ï¿½]

ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½:

P=14296 ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

l=690 ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

È¸ï¿½ï¿½ï¿½ï¿½(ï¿½ï¿½ï¿½ï¿½ï¿½)ï¿½ï¿½:(

a=138, J=93312, E=4.1 TIMES { 10}^{5 }

ï¿½ï¿½

)

ï¿½ï¿½

theta = { P { l}^{2 } } over {6EJ } ( { a} over {l }- { { a}^{3 } } over { { l}^{3 } })= { 14296 TIMES { 690}^{2 } } over {6 TIMES 4.1 TIMES { 10}^{5 } TIMES 93312 } ( { 138} over {690 }- { { 138}^{ 3} } over { { 690}^{3 } })

ï¿½ï¿½

=- { 0.006}^{ ï¿½ï¿½}

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½

b=(30+24)tan { 0.006}^{ ï¿½ï¿½} =0.05ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

21 TIMES 10ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì°ï¿½ Ç¥29ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½

J=7717

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½

P=14206 ï¿½ï¿½

ï¿½ï¿½

{ P}^{' } = { 14206 TIMES 138} over {690 } =2859 ï¿½ï¿½

l=(96-36)/2=30

ï¿½ï¿½

ï¿½ï¿½ ï¿½Ì´ï¿½)

ï¿½ï¿½

f= { { P}^{' } { l}^{3 } } over {3EJ }= { 2859 TIMES { 30}^{3 } } over {3 TIMES 4.1 TIMES { 10}^{5 } TIMES 7717 } =0.01 ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

P=31107 ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

(

a=122, { }_{ } b=672, { }_{ } l=794, { }_{ } J=172872

ï¿½ï¿½

)

ï¿½ï¿½

theta = { 31107 TIMES { 794}^{2 } } over {6 TIMES 4.1 TIMES { 10}^{5 } TIMES 172872 } ( { 122} over {794 }- { { 672}^{3 } } over { { 794}^{3 } })= { 0.02}^{ï¿½ï¿½ }

ï¿½ï¿½

b=(30+30+36)tan{ 0.02}^{ï¿½ï¿½ } =96 TIMES 0.0004=0.038ï¿½ï¿½

ï¿½ï¿½

( 0.6mm) ï¿½Ì´ï¿½.

SQRT { 2} :1

ï¿½ï¿½

Z= { 1} over {6 }b { h}^{2 }

ï¿½ï¿½

ï¿½ï¿½

Ç¥A.

Z=24000

ï¿½ï¿½

ï¿½Ü¸ï¿½ï¿½ï¿½

ï¿½ï¿½ï¿½

24000 ï¿½Ï¶ï¿½

ï¿½Ü¸ï¿½

h TIMES b

ï¿½ï¿½ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½: ï¿½ï¿½ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½

60 TIMES 40

2400

3: 2

72.0

66 TIMES 33

2187

2: 1

74.0

52.4 TIMES 52.4

2745

1: 1

74.0

Ç¥ B.

F=2400

{ ï¿½ï¿½}^{2 }

ï¿½ï¿½

ï¿½Ü¸ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½

ï¿½ï¿½ï¿½

2400

{ ï¿½ï¿½}^{2 }

ï¿½Ï¶ï¿½

ï¿½Ü¸ï¿½

h TIMES b

ï¿½Ü¸ï¿½ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½: ï¿½ï¿½ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½

60 TIMES 40

24000

3: 2

72.0

69.2 TIMES 34.6

27615

2: 1

77.4

49 TIMES 49

19608

1: 1

69.3

Ç¥ C.

D=72ï¿½ï¿½

ï¿½ï¿½

ï¿½Ü¸ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ 72ï¿½ï¿½

ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½

ï¿½Ü¸ï¿½

h TIMES b

ï¿½Ü¸ï¿½ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½: ï¿½ï¿½ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½

60 TIMES 40

24000

3: 2

2400

64.4 TIMES 32.2

22257

2: 1

2047

51 TIMES 51

21987

1: 1

2601

ï¿½ï¿½

{ ï¿½ï¿½}^{2 }

ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ ï¿½Ü¸ï¿½ï¿½ï¿½ï¿½ï¿½

Z=24000

ï¿½ï¿½

ï¿½ï¿½

M=420P

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½

M=810 P

ï¿½ï¿½

ï¿½Ì´ï¿½. (ï¿½×¸ï¿½ 7-34)

810P -420P=390P

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½ï¿½ï¿½:

M=120P

ï¿½ç¿¬ï¿½ï¿½:

M=270P

ï¿½Õ°ï¿½:

120P+270P=390P

ï¿½ï¿½ 8 ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½ï¿½]

ï¿½ï¿½

(ï¿½ï¿½ï¿½)ï¿½Ì´ï¿½.

ï¿½ï¿½Ã·[ï¿½â®Š]ï¿½ï¿½ ï¿½Ú¸ï¿½ï¿½Ï´ï¿½

ï¿½Ñ´ï¿½.

1ï¿½ï¿½[ï¿½ï¿½Ô¯] 30ï¿½ï¿½ï¿½ï¿½ ï¿½Å¸ï¿½ï¿½ï¿½

ï¿½ï¿½ ï¿½Ï¾ï¿½[ï¿½ï¿½ï¿½ï¿½]

ï¿½ï¿½[ï¿½ï¿½]ï¿½ï¿½ ï¿½Ü¸ï¿½Ä¡ï¿½ï¿½ï¿½ï¿½

10 TIMES 15

ï¿½ï¿½

ï¿½ï¿½ï¿½Ì°ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½

ï¿½ï¿½

P=11263

ï¿½ï¿½

ï¿½ï¿½

P=11263cos 27ï¿½ï¿½=10024

ï¿½ï¿½

ï¿½ï¿½ ï¿½Ì´ï¿½.(ï¿½×¸ï¿½ 8-4ï¿½ï¿½ï¿½ï¿½

{ N}_{1 }

ï¿½ï¿½

ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½)

ï¿½ï¿½

M=10024 TIMES 26.2=262628 { }^{ } ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½Ü¸ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½:(

Z=375

ï¿½ï¿½

)

ï¿½ï¿½

sigma = { 262628} over {375 } =700 ï¿½ï¿½/ { ï¿½ï¿½}^{2 } >645 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½ï¿½

M=10024 TIMES 12=120288 ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½ï¿½ï¿½:

sigma =320 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }<645 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½ï¿½

M=Z TIMES sigma

ï¿½ï¿½

ï¿½Ì°ï¿½,

Z=375, { }_{ } sigma =645 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½ï¿½

ï¿½Ì´ï¿½. ï¿½ï¿½ï¿½ï¿½

M=645 TIMES 375 =241875 ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½

ï¿½ï¿½.

M=Pl, { }^{ } ï¿½ï¿½ï¿½ï¿½ l=M/P

ï¿½ï¿½

, ï¿½×·ï¿½ï¿½ï¿½:

ï¿½ï¿½

l=241875/9953=24.3ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

27.3 ï¿½ï¿½ TIMES cos 27=24.3

ï¿½ï¿½

ï¿½ï¿½ ï¿½Ì´ï¿½.

ï¿½ï¿½

{ P}^{' } = { 9935 TIMES 26.2} over {113.8 } =2287 ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

9935+2287=12222 ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½×·ï¿½ï¿½ï¿½ ï¿½Ö´ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½:

ï¿½ï¿½

l= { 241875} over {12222 }=19.8 ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

{ N}_{ 1}

ï¿½ï¿½

{ N}_{2 }

ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½

{ N}_{2 }

ï¿½ï¿½

ï¿½ï¿½

AB=18ï¿½ï¿½

ï¿½ï¿½

(ï¿½×¸ï¿½ 8-4)

ï¿½ï°¢ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½:

6sin27ï¿½ï¿½=2.7 ï¿½ï¿½

ï¿½ï°¢ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½:

2 TIMES { 18 TIMES 2.7} over { 2} =48.6 { ï¿½ï¿½}^{2 }

2 TIMES 18=36 { ï¿½ï¿½}^{2 }

ï¿½Õ°ï¿½: 84.6

{ ï¿½ï¿½}^{2 }

119ï¿½ï¿½/ { ï¿½ï¿½}^{ 2}

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½

119 TIMES 84.6=10067 ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½

11960 TIMES sin 27ï¿½ï¿½=5382 ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

12cos27ï¿½ï¿½=10.7 ï¿½ï¿½

ï¿½ï¿½

ï¿½ï°¢ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½:

2 TIMES { 10.7 TIMES 2.7} over {2}=28.7 { ï¿½ï¿½}^{2 }

ï¿½ï¿½

ï¿½Ì´ï¿½.

10.7 TIMES 2=21.4 { ï¿½ï¿½}^{ 2}

ï¿½Õ°ï¿½: 50

{ ï¿½ï¿½}^{2 }

ï¿½ï¿½

ï¿½Ì´ï¿½.

119 TIMES 50=5950

ï¿½ï¿½

ï¿½ï¿½ï¿½Ì´ï¿½.

ï¿½ï¿½

{ N}_{2 }

ï¿½ï¿½

ï¿½ï¿½

{ N}_{2 }

ï¿½ï¿½

{ N}_{1 }

ï¿½ï¿½

ï¿½ï¿½

{ N}_{2 }

ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½[Ê£ï¿½ï¿½ï¿½ï¿½]

ï¿½ ï¿½ï¿½ï¿½[ß¾ï¿½ï¿½]

ï¿½ï¿½

{ N}_{1 }ï¿½ï¿½ { N}_{2 }

ï¿½ï¿½

30 TIMES 2+6 TIMES 2=72ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

10 TIMES 15

ï¿½ï¿½

2 TIMES 15

ï¿½ï¿½

ï¿½ï¿½

2 TIMES 15+32=62

ï¿½ï¿½

ï¿½Ø´ï¿½.

[ï¿½ï¿½ï¿½ï¿½]ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½Ñ´ï¿½.

ï¿½Ü¸ï¿½ï¿½ï¿½ { }_{ } 10 TIMES 15

ï¿½ï¿½

TRIANGLE

ï¿½ï¿½

TRIANGLED

ï¿½ï¿½

ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½.

Èï¿½ï¿½[ï¿½ï¿½ï¿½ï¿½]

ï¿½ï¿½ ï¿½Ò·ï¿½[ï¿½ï¿½]

16 TIMES 18

ï¿½ï¿½

16 TIMES 14

ï¿½ï¿½

10 TIMES 12=120 { ï¿½ï¿½}^{ 2}

ï¿½ï¿½

ï¿½Ì´ï¿½.

119 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½ï¿½

ï¿½ï¿½

119 TIMES 120=17880

ï¿½ï¿½

ï¿½ï¿½ï¿½Ì´ï¿½.

ï¿½ï¿½ï¿½ï¿½(ï¿½ï¿½ï¿½)

sigma =+23ï¿½ï¿½26', { }_{ } ï¿½ï¿½ï¿½ï¿½(ï¿½ï¿½ï¿½) { }_{ } sigma =-23ï¿½ï¿½26' { }_{ } (ï¿½ï¿½ï¿½ï¿½)

ï¿½ï¿½

phi + sigma =39ï¿½ï¿½57'+23ï¿½ï¿½26'=63ï¿½ï¿½23'

ï¿½ï¿½

phi - sigma =39ï¿½ï¿½57'-23ï¿½ï¿½26'=16ï¿½ï¿½31'

ï¿½ï¿½ï¿½ï¿½(ï¿½ï¿½ï¿½) ï¿½ï¿½ï¿½ï¿½:

h=73ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½(ï¿½ï¿½ï¿½) ï¿½ï¿½ï¿½ï¿½:

h=27ï¿½ï¿½

ï¿½ï¿½ï¿½Ì´ï¿½ 470ï¿½ï¿½ ï¿½Ì´ï¿½. ï¿½×·ï¿½ï¿½ï¿½

ï¿½ï¿½ï¿½Ì´ï¿½ 294tan27ï¿½ï¿½=153ï¿½ï¿½ï¿½Ì´ï¿½.

ï¿½Î¿ï¿½ ï¿½Üºï¿½(Ó®Ý»)ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½Õ¸Ó¸ï¿½

ï¿½×¸ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½.

4 TIMES 21=84

ï¿½ï¿½

3 TIMES 13=39

ï¿½ï¿½

ï¿½ï¿½ 9 ï¿½ï¿½

ï¿½Öµï¿½[ï¿½ï¿½ï¿½ï¿½]

3 TIMES 15

ï¿½ï¿½

{ ï¿½ï¿½}^{ 2}

ï¿½ï¿½

ï¿½ï¿½

10(32+22)=540 { ï¿½ï¿½}^{2 }

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½

{ ({ 24} over {12 }) }^{2 } TIMES 3.14=452 { ï¿½ï¿½}^{ 2}

ï¿½ï¿½

{ ï¿½ï¿½}^{2 }

ï¿½ï¿½

ï¿½ï¿½Ã·ï¿½ï¿½[ï¿½ï¿½ï¿½]ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½:

1. ï¿½ï¿½ï¿½ï¿½ï¿½[ï¿½Ö®ï¿½Û³]ï¿½ï¿½ï¿½ï¿½: 11163

2. ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½(Ç¥20-2) 1821

{ 50117 TIMES 600} over { 750} =40761

ï¿½ï¿½

0.7ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½ï¿½

ï¿½Ì°ï¿½, ï¿½ï¿½ï¿½984ï¿½ï¿½ ï¿½Ì´ï¿½.)

ï¿½Õ°ï¿½: 68131 ï¿½ï¿½

ï¿½ï¿½Ã·ï¿½ï¿½[ï¿½ï¿½ï¿½ï¿½ï¿½]:

1. ï¿½ï¿½ï¿½ï¿½ï¿½[ï¿½Ö®ï¿½Û³]ï¿½ï¿½ï¿½ï¿½: 11163

2. ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½(Ç¥20-2) 1821

{ 50117 TIMES 235} over { 375} =31407

ï¿½ï¿½

5. Ãµï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½a]ï¿½ï¿½ï¿½ï¿½: 492

ï¿½Õ°ï¿½: 53816 ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½[Ò®ï¿½]:

50117 TIMES 2-(31407+40761)=28066

5. Ãµï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½a]ï¿½ï¿½ï¿½ï¿½:

492+984=1476

ï¿½Õ°ï¿½: 36247 ï¿½ï¿½

ï¿½ï¿½

ï¿½], ï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½ï¿½] 375ï¿½ï¿½.

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½]:

2. ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ 1821

{ 69228TIMES 225} over { 375} =41537

ï¿½ï¿½

5. Ãµï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½a]ï¿½ï¿½ï¿½ï¿½: 429

ï¿½Õ°ï¿½: 63946 ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½[Ò®ï¿½]:

{ 69228 TIMES 150} over { 375} =27691

3. Ãµï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½a]ï¿½ï¿½ï¿½ï¿½: 1470

ï¿½Õ°ï¿½: 35366 ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½]:

1. ï¿½ï¿½ï¿½ï¿½ï¿½[ï¿½Ö®ï¿½Û³]ï¿½ï¿½ï¿½ï¿½: 11163

2. ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½(Ç¥20-2) 1821

{ 69228 TIMES 600} over { 750} =55382

ï¿½ï¿½

5. Ãµï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½a]ï¿½ï¿½ï¿½ï¿½: 984

ï¿½Õ°ï¿½: 80211 ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½[Ò®ï¿½]:

2 TIMES { 69228 TIMES 15} over { 750} =27691

2. ï¿½ç¿¬ï¿½ï¿½[ï¿½ï¿½ï¿½Ë¿ï¿½]ï¿½ï¿½ï¿½ï¿½:

3402 TIMES 2=6804

ï¿½ï¿½

(ï¿½Î°ï¿½ ï¿½ï¿½ï¿½ï¿½)

3. Ãµï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½a]ï¿½ï¿½ï¿½ï¿½: 1968

ï¿½Õ°ï¿½: 37792 ï¿½ï¿½

ï¿½ï¿½Ã·ï¿½ï¿½[ï¿½ï¿½ï¿½]:

1. ï¿½ï¿½ï¿½ï¿½ï¿½[ï¿½Ö®ï¿½Û³]ï¿½ï¿½ï¿½ï¿½: 3632

{ 26715TIMES 672} over { 794} =22610

ï¿½ï¿½

ï¿½Õ°ï¿½: 29579 ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½[Ò®ï¿½]:

{ 22009 TIMES 125} over {660 }=4168

{ 26715 TIMES 122} over { 794} =4104

ï¿½ï¿½

22009

ï¿½Õ°ï¿½: 31791 ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½]:

1. ï¿½ï¿½ï¿½ï¿½ï¿½[ï¿½Ö®ï¿½Û³]ï¿½ï¿½ï¿½ï¿½: 3632

{ 14296 TIMES552} over { 686} =11503

ï¿½ï¿½

ï¿½Õ°ï¿½: 19696 ï¿½ï¿½

ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½[Ò®ï¿½]:

7071 TIMES 2=14142

ï¿½ï¿½

{ 7888.5 TIMES 150} over { 402} TIMES 2=5587

{ 12696 TIMES 150} over {552 } TIMES 2 =6900

{ 14296 TIMES 150} over {686 } TIMES 2=6200

6. Ãµï¿½ï¿½ï¿½ï¿½, 2, 3, 4, 5ï¿½ï¿½ï¿½ï¿½[ï¿½Ë¿ï¿½]ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ ï¿½Õ°ï¿½: 6149

ï¿½Õ°ï¿½: 49988 ï¿½ï¿½

ï¿½Öµï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½Ï±ï¿½:

ï¿½Ï°ÔµÈ´ï¿½.

ï¿½ï¿½

ï¿½ï¿½Ã·ï¿½ï¿½[ï¿½ï¿½ï¿½]:

1. ï¿½ï¿½ï¿½ï¿½ï¿½[ï¿½Ö®ï¿½Û³]ï¿½ï¿½ï¿½ï¿½: 11163

4. ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½: 1821

ï¿½ï¿½

{ (6175+26458) TIMES 610} over {750 }=26541

ï¿½ï¿½

ï¿½Õ°ï¿½: 51370 ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½[Ò®ï¿½]:

5. Ãµï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½a]ï¿½ï¿½ï¿½ï¿½:

492+984=1476

ï¿½Õ°ï¿½: 58196 ï¿½ï¿½

ï¿½ï¿½Ã·ï¿½ï¿½[ï¿½ï¿½ï¿½ï¿½ï¿½]:

1. ï¿½ï¿½ï¿½ï¿½ï¿½[ï¿½Ö®ï¿½Û³]ï¿½ï¿½ï¿½ï¿½: 11163

ï¿½ï¿½

{ (6175+5796) TIMES 235} over { 375} =7502

ï¿½ï¿½

7. Ãµï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½a]ï¿½ï¿½ï¿½ï¿½: 492

ï¿½Õ°ï¿½: 29911 ï¿½ï¿½

ï¿½Ï°ï¿½ ï¿½È´ï¿½:

ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½]:

1. ï¿½ï¿½ï¿½ï¿½ï¿½[ï¿½Ö®ï¿½Û³]ï¿½ï¿½ï¿½ï¿½: 11163

ï¿½ï¿½

{ (6275+17242) TIMES 225} over {375}=14110

ï¿½ï¿½

8. Ãµï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½a]ï¿½ï¿½ï¿½ï¿½: 492

ï¿½Õ°ï¿½: 39543 ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½[Ò®ï¿½]:

23517-14110=9402

ï¿½ï¿½

3. ï¿½È¿ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½Ë¿ï¿½] ï¿½ï¿½ï¿½ï¿½(1/4): 3042

7. Ãµï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½a]ï¿½ï¿½ï¿½ï¿½:

492+984=1476

ï¿½Õ°ï¿½: 59869 ï¿½ï¿½

ï¿½ï¿½Ä¡ï¿½Ï°ï¿½ ï¿½È´ï¿½:

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½]:

1. ï¿½ï¿½ï¿½ï¿½ï¿½[ï¿½Ö®ï¿½Û³]ï¿½ï¿½ï¿½ï¿½: 11163

ï¿½ï¿½

{ (38763+6275) TIMES 600} over {750}=36030

ï¿½ï¿½

8. Ãµï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½a]ï¿½ï¿½ï¿½ï¿½: 984

ï¿½Õ°ï¿½: 63883 ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½[Ò®ï¿½]:

ï¿½ï¿½

{ 150 TIMES 2 TIMES (38763+6275)} over {750 } =15500

5. ï¿½È¿ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½Ë¿ï¿½] ï¿½ï¿½ï¿½ï¿½(1/2): 6048

6. Ãµï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½a]ï¿½ï¿½ï¿½ï¿½: 1968

ï¿½Õ°ï¿½: 64748 ï¿½ï¿½

29 TIMES 375 TIMES { 3} over {4 }=8156

ï¿½ï¿½

ï¿½ï¿½ï¿½Ì´ï¿½.

ï¿½ï¿½

15+ { 0.27} over {18 } TIMES 100=16.5 ï¿½ï¿½ / {100 ï¿½ï¿½}^{ 2}

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½ï¿½Ø¸ï¿½ï¿½ï¿½ï¿½ï¿½:

ï¿½ï¿½

477 TIMES 477=227529 { ï¿½ï¿½}^{2 }

ï¿½ï¿½

, ï¿½ï¿½,

2275.9 TIMES 100 { } atop { } { ï¿½ï¿½}^{2 }

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ß·ï¿½ï¿½ï¿½:

ï¿½ï¿½

16.5 TIMES 2275.9=37542 ï¿½ï¿½

ï¿½ï¿½

(ï¿½ï¿½ 18 ton) ï¿½Ì´ï¿½.

4600 TIMES 2=9200

ï¿½ï¿½

37542-9200=28342 ï¿½ï¿½ï¿½Ì´ï¿½.

ï¿½ï¿½

600 TIMES 5=3000

ï¿½ï¿½

ï¿½ï¿½ï¿½Ì´ï¿½.

ï¿½ï¿½

20 TIMES 10=200

ï¿½ï¿½

ï¿½ï¿½ï¿½Ì´ï¿½.

4845 ï¿½ï¿½ï¿½Ì´ï¿½.

ï¿½Õ°ï¿½: 38387 ï¿½ï¿½

ï¿½Öµï¿½ï¿½ï¿½ Å©ï¿½ï¿½ï¿½

32 TIMES 32 TIMES 20

ï¿½ï¿½

{ ï¿½ï¿½}^{3 }

ï¿½ï¿½

15 TIMES 10

ï¿½ï¿½

ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½ï¿½

ï¿½ï¿½

{ 63946} over {149 } =429.2 { ï¿½ï¿½}^{2 }

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½

pi { r}^{2 }=429.2

ï¿½Öµï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½

2r ï¿½Ì°ï¿½ { }_{ } SQRT { { 429.2} over {3.14 } } =23.4 ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

{ ï¿½ï¿½}^{2 }

ï¿½ï¿½

ï¿½ï¿½

426.2/0.9=473.5 { ï¿½ï¿½}^{2 }

ï¿½ï¿½

. ï¿½ï¿½ï¿½ï¿½ ï¿½Öµï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½:

ï¿½ï¿½

{ 1} over {2 } ( { 473.5} over {10 }+10)=28.6

ï¿½ï¿½

ï¿½ï¿½ ï¿½Ì´ï¿½.

ï¿½Ä¿ï¿½ ï¿½Ü¿ï¿½ 5ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½

(ï¿½×¸ï¿½ 9-2), ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½

ï¿½Ø¼ï¿½ï¿½ï¿½ ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½.

36ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½: 25. 56ï¿½ï¿½

42ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½: 29. 82ï¿½ï¿½

45ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½: 31. 95ï¿½ï¿½ ï¿½Ì´ï¿½.

ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½

{ ï¿½ï¿½}^{2 }

ï¿½ï¿½

{ ï¿½ï¿½}^{2 }

ï¿½ï¿½

{ ï¿½ï¿½}^{2 }

ï¿½ï¿½

ï¿½ï¿½

2 TIMES SQRT { { 540} over {3.14 } } =26.2

ï¿½ï¿½

ï¿½ï¿½ï¿½Ì´ï¿½.

(32-26)/2=3

ï¿½ï¿½

ï¿½ï¿½ï¿½æº¸ï¿½ï¿½ Å«ï¿½ï¿½ ï¿½ï¿½ï¿½

ï¿½×¸ï¿½ 9-6 ï¿½Öµï¿½ ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½

ï¿½ï¿½ 10 ï¿½ï¿½

ï¿½ï¿½ï¿½[ï¿½]

A: ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½:

phi =0.9

ï¿½ï¿½

R=645 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½ï¿½

, ï¿½Ð·ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½:

F=1017 { ï¿½ï¿½}^{2 }

ï¿½ï¿½

. ï¿½Ö´ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½:

ï¿½ï¿½

N= phi RF=0.9 TIMES 645 TIMES 1017=590369 ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½

M=Pl/4, { }^{ }ï¿½Ì´ï¿½. ï¿½ï¿½ï¿½ï¿½ P=4M/l

ï¿½ï¿½

ï¿½ï¿½

sigma =M/Z

ï¿½ï¿½

ï¿½Ì´ï¿½. ï¿½ï¿½ï¿½ï¿½

M= sigma Z

ï¿½ï¿½

ï¿½Ü¸ï¿½ï¿½ï¿½ï¿½ï¿½:

Z= { pi { d}^{3 } } over {32 }

ï¿½ï¿½

ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½Ï¿ï¿½:

ï¿½ï¿½

M= { sigma pi { d}^{ 3} } over { 32}

ï¿½ï¿½

ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½Ï¿ï¿½:

ï¿½ï¿½

P= { sigma pi { d}^{3 } } over {8l }

ï¿½Ü¸ï¿½ï¿½ï¿½ ï¿½Ö´ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½

sigma

ï¿½ï¿½

ï¿½ï¿½ R(

R=645 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½ï¿½

)ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½,

ï¿½ï¿½

P= { 645 TIMES 3.14 TIMES { 36}^{3 } } over {8 TIMES 300 } =39372

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½ï¿½ï¿½:

{ N} over {P }= { 590369} over {39372 } =15

ï¿½ï¿½

ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ß´É·ï¿½

ï¿½ï¿½

mu =1

ï¿½ï¿½

mu =1

ï¿½ï¿½

È¸ï¿½ï¿½ï¿½Ý°ï¿½(ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½):

r=d/4=42/4=10.5

ï¿½ï¿½ï¿½ï¿½ï¿½(ï¿½ï¿½ï¿½ï¿½ï¿½):

lambda = { mu l} over { r} = { 1 TIMES 360} over {10.5 } =34.3

ï¿½ï¿½

ï¿½Ì´ï¿½.

lambda <75

ï¿½ï¿½

lambda

ï¿½ï¿½

phi

ï¿½ï¿½

ï¿½ï¿½ï¿½Ï±ï¿½:

ï¿½ï¿½

phi =1-0.8 { ( { lambda } over {100 } )}^{2 }=1-0.8 { ( { 34.3} over {100 }) }^{2 } =0.9

R=645 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½ï¿½

)

ï¿½ï¿½

N= phi R { pi { d}^{2 } } over {4 }=0.9 TIMES 645 TIMES { 3.14 TIMES { 42}^{2 } } over {4 } =803842

ï¿½ï¿½

ï¿½ï¿½ ï¿½Ì´ï¿½.

mu =1, { }_{ } r=9, { } atop { } lambda =33.3

ï¿½ï¿½

phi =1-0.8 { ( { lambda } over {100 } )}^{2 }=1-0.8 { ( { 33.3} over {100 }) }^{2 } =0.91

Ç¥30ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½

R=532.5 ï¿½ï¿½/ { ï¿½ï¿½}^{ 2}

ï¿½ï¿½

ï¿½Ì´ï¿½. ï¿½ï¿½ï¿½ï¿½:

ï¿½ï¿½

N= phi R { pi { d}^{2 } } over {4 }=0.91 TIMES 532.5 TIMES { 3.14 TIMES { 36}^{2 } } over {4 } =492987

ï¿½ï¿½

ï¿½ ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½

mu =1, { }_{ } r=10.5, { }_{ } lambda =23.8, { }_{ } phi =0.95

ï¿½ï¿½

ï¿½ï¿½

N=0.95 TIMES 645 TIMES { 3.14 TIMES { 42}^{ 2} } over { 4} =848499

ï¿½ï¿½

ï¿½ï¿½ ï¿½Ì´ï¿½.

phi =0.81

ï¿½ï¿½

, ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½

phi =0.95

ï¿½ï¿½

{ m}^{2 }

ï¿½ï¿½

ï¿½ï¿½

ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½]

ï¿½ï¿½ï¿½[ï¿½]

ï¿½ï¿½ï¿½ï¿½(

ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

)

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½]

ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½

ï¿½Î°ï¿½ ï¿½ï¿½ï¿½

22.5

ï¿½Î°ï¿½ ï¿½ï¿½ï¿½

ï¿½ï¿½/{ï¿½ï¿½}^{2 }

ï¿½ï¿½

ï¿½ï¿½/{ï¿½ï¿½}^{2 }

ï¿½ï¿½

, Ã¢ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ 242

ï¿½ï¿½/{ï¿½ï¿½}^{2 }

ï¿½ï¿½

ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½Ç»ï¿½[ï¿½ï¿½ß¯]

ï¿½ï¿½

y= { (D-32)(l-x)} over {2(l+3x) }

ï¿½ï¿½

ï¿½Ì´ï¿½.

x(x=0-l/3)

ï¿½ï¿½

ï¿½ï¿½

ï¿½à¼±ï¿½ï¿½ï¿½ï¿½ ï¿½Å¸ï¿½ï¿½Ì´ï¿½.

ï¿½ï¿½

y=c TIMES sin( { pi } over { l}x)

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½ ï¿½ï¿½ï¿½Ä¿ï¿½ï¿½ï¿½:

l ----- ï¿½ï¿½Õ³ï¿½ï¿½ï¿½

ï¿½ï¿½

----- 0-

ï¿½ï¿½

x=l/2

ï¿½ï¿½

y=c

ï¿½ï¿½

ï¿½ï¿½

{ { d}^{2 }y } over { { d}^{2 }x } = { M(x)} over {EJ }

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½

J= { pi { d}^{ 4} } over { 64}

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½ï¿½ï¿½:

ï¿½ï¿½

{ { d}^{2 }y } over { { d}^{2 }x } = {64 M(x)} over {E pi { d}^{4 } }

ï¿½ï¿½

ï¿½Îºï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ ï¿½Û°ï¿½ ï¿½È´Ù¸ï¿½

ï¿½Â±ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½È´ï¿½.

ï¿½ï¿½Èï¿½ï¿½ï¿½ï¿½ ï¿½Ê´Â´ï¿½.

ï¿½î¼±ï¿½ï¿½ ï¿½ï¿½ï¿½ß±ï¿½ ï¿½ï¿½ï¿½Ï¿ï¿½

ï¿½ï¿½ 11 ï¿½ï¿½

ï¿½ï¿½

{ h}_{ x} = SQRT { 7.35x}

ï¿½ï¿½

ï¿½ï¿½

{ h}_{x} = { 10x} over {4(15+x) }

ï¿½ï¿½

ï¿½ï¿½

P= { 26715.0 TIMES 134} over {134+552 } =5218.0

ï¿½ï¿½

ï¿½ï¿½

M=5218.0 TIMES 30=156551.0 { }_{ } ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½

ï¿½Ü¸ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½: (

Z=735

ï¿½ï¿½

)

ï¿½ï¿½

sigma = { 156551.0} over {735 }=213.0 ï¿½ï¿½/ { ï¿½ï¿½}^{2 } < 532.5 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½ï¿½

(Ç¥30 )

ï¿½ï¿½

P= { 26715 TIMES 134} over {134+522 } =5457.0

ï¿½ï¿½

ï¿½ï¿½ï¿½Ì´ï¿½.

ï¿½ï¿½

M=5457.0 TIMES 60=327421.6 { }_{ } ï¿½ï¿½ TIMES ï¿½ï¿½

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½Ü¸ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½:

ï¿½ï¿½

sigma = { 327421.6} over {735 } =445 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }<532.5 ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½

{ h}_{ x} = { 105x} over {4(15+x) }

ï¿½ï¿½

ï¿½Ì´ï¿½. ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ß¿ï¿½ï¿½ï¿½:

ï¿½ï¿½

{ h}_{x }

ï¿½ï¿½

ï¿½ï¿½

ï¿½ï¿½

, ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½

ï¿½ï¿½

M=Pl

{ M}_{ x} =Px

ï¿½ï¿½

ï¿½ï¿½

{ Z}_{x }= { 1} over {6 }bx {{ h}_{x }}^{ 2}

ï¿½ï¿½

ï¿½Ì´ï¿½.

ï¿½ï¿½

{ Z}_{x }= { 1} over {6 }b { { h}_{ x} }^{2 }

ï¿½ï¿½

ï¿½Ì´ï¿½. ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ ï¿½Ü¸ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½:

sigma = { { M}_{ x} } over { { Z}_{x } }

ï¿½ï¿½

ï¿½ï¿½ï¿½é¿¡ ï¿½ï¿½ï¿½ï¿½

{ h}_{x } = { 6Px} over {6 sigma }

ï¿½ï¿½

ï¿½Ì´ï¿½ ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½Ì´ï¿½.

x=60

ï¿½ï¿½

ï¿½Ì¶ï¿½ï¿½

h=21

ï¿½ï¿½

M=60P, { }_{ } P=M/60, { }_{ } W= { 1} over {6 }b { h}^{2 }, { }_{ } b=10

ï¿½ï¿½

ï¿½ï¿½

{ { h}_{ x} }^{2 }= { 6M { Z}_{x } } over {60bM } = { { Z}_{x }} over {10b }= { { h}^{2 }x } over {60 } =7.35x

ï¿½ï¿½

. ï¿½ï¿½ï¿½ï¿½:

ï¿½ï¿½

{ h}_{x }= SQRT { 7.35x}

ï¿½ï¿½ 12 ï¿½ï¿½

ï¿½ï¿½

ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½ï¿½]ï¿½ï¿½ï¿½ï¿½

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W=81485+36123=117608

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delta = { { h}^{3 } } over {3EJ } = { { 500}^{3 } } over {3 TIMES 4.96 TIMES { 10}^{ 5 }TIMES 152667 } =0.0005498

ï¿½ï¿½

ï¿½ï¿½ ï¿½Ì´ï¿½.

( h: ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½=500ï¿½ï¿½,

E=4.96 TIMES { 10}^{5 }

ï¿½ï¿½

(Ç¥ 31),

J=152667

ï¿½ï¿½

Ç¥28 )

ï¿½ß·Â°ï¿½ï¿½Óµï¿½ï¿½ï¿½

g=558 ï¿½ï¿½/ { s}^{2 }

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ï¿½ï¿½

T=2 pi SQRT { { W delta } over {g } } =2 TIMES 3.14 TIMES SQRT { { 117608 TIMES 0.0005498} over {558 } }=2.137

ï¿½ï¿½

ï¿½ï¿½ ï¿½Ì´ï¿½.

{ a}_{max } =0.45

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ï¿½Ì´ï¿½.

ï¿½ï¿½

{ a}_{max }

ï¿½ï¿½

ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½

{ a}_{1 }

ï¿½ï¿½

ï¿½ï¿½ :

ï¿½ï¿½

{ a}_{1 }= { 0.3} over {T } TIMES { a}_{max } = { 0.3} over {2.137 } TIMES 0.45=0.0063

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ï¿½Ì´ï¿½.

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½:

ï¿½ï¿½

{ Q}`_{0 } ^{' }=C { a}_{1 }W =0.25 TIMES 0.063 TIMES 117608=1852

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ï¿½ï¿½ ï¿½Ì´ï¿½.

C=0.25

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)

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delta = { { h}^{ 3} } over {3EJ } = { { 250}^{3 } } over {3 TIMES 4.96 TIMES { 10}^{5 } TIMES 152667 } =0.0000687

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ï¿½ï¿½ ï¿½Ì´ï¿½.

ï¿½ï¿½ï¿½ï¿½ ï¿½Ö±ï¿½[ï¿½ï¿½ï¿½ï¿½ï¿½Ñ¢]ï¿½ï¿½:

ï¿½ï¿½

T=2 pi SQRT { { 42000 TIMES 0.0000687} over {558 } }=0.45

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ï¿½Ì´ï¿½.

ï¿½ï¿½

{ a}_{1 }= { 0.3} over {0.45 } TIMES 0.45=0.3

ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½:

ï¿½ï¿½

{ Q}`_{0 } ^{'' } =0.25 TIMES 0.3 TIMES 42000=3150

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ï¿½ï¿½

1852cos { 85}^{ï¿½ï¿½ } { 46}^{' } =137

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ï¿½ï¿½ ï¿½Ì´ï¿½.

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3150cos { 80}^{ï¿½ï¿½ } { 1}^{' } =541

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ï¿½ï¿½ ï¿½Ì´ï¿½.

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1852+3150-137-541=4324

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ï¿½ï¿½ ï¿½Ì´ï¿½.

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{ N}_{0 } = { 1715 TIMES 500+2609 TIMES 250} over {273 }=5530

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ï¿½ï¿½ ï¿½Ì´ï¿½.

(ï¿½ï¿½ ï¿½ï¿½ï¿½Ä¿ï¿½ï¿½ï¿½ 1715=1852-137 ï¿½ï¿½, 2609=3150-541 ï¿½ï¿½ï¿½Ì´ï¿½. 273 ï¿½ï¿½ï¿½ï¿½ 2ï¿½ï¿½ï¿½ï¿½[2ï¿½ï¿½ï¿½] ï¿½Î°ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½]ï¿½Ì´ï¿½)

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{ N}_{1 } = { 5530} over {tan { 25}^{ï¿½ï¿½ } } = { 5530} over {0.466 } =11867

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ï¿½ï¿½ ï¿½Ì´ï¿½.

{ N}_{ 1}

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4 TIMES 4

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ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

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Q=327.7 TIMES 4 TIMES 4 TIMES 2=10486 ï¿½ï¿½<11867 ï¿½ï¿½

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ï¿½Ì´ï¿½.

ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

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ï¿½ï¿½

{ N}_{ 2} = { 123} over {2 } TIMES 10 TIMES 42 =25830

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ï¿½ï¿½ ï¿½Ì´ï¿½.

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{ N}_{3 }= { 5530 TIMES (273+21)} over { 28} =58065 ï¿½Å¡ï¿½51660 ï¿½ï¿½

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ï¿½Ì´ï¿½.

ï¿½ï¿½ ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½] 2ï¿½ï¿½:

69746 TIMES 2=138952

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ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½] 4ï¿½ï¿½:

81485 TIMES 4=325940

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ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½[Ò®ï¿½] 4ï¿½ï¿½:

36123 TIMES 4=125052

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ï¿½Õ°ï¿½: 694159 ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½:

W= { 1} over {4 } TIMES 694159=173540 ï¿½ï¿½

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ï¿½ï¿½Õ¸Ó¸ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½:

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delta = { { h}^{3 } } over {3EJ } = { { 320}^{3 } } over {3 TIMES 4.96 TIMES { 10}^{ 5 TIMES 152667} } =0.000144

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ï¿½ï¿½ï¿½ï¿½ ï¿½Ö±ï¿½:

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T=2 pi SQRT { { 173540 TIMES 0.0000144} over {558 } }=1.33

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{ a}_{1 }= { 0.3} over {133 } TIMES 0.45=0.1

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ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½:

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{ Q}_{ 0} =0.25 TIMES 0.1 TIMES 173540=4339

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ï¿½ï¿½ ï¿½Ì´ï¿½.

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4339 TIMES 4=17356

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ï¿½ï¿½ ï¿½Ì´ï¿½.

ï¿½ï¿½

{ 10} over {2 } TIMES 30 TIMES 2=300 { ï¿½ï¿½}^{2 }

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ï¿½Ì´ï¿½.

ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

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(Ç¥30) ï¿½Ì°ï¿½ ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½

ï¿½Ö´ï¿½ ï¿½Ö´ï¿½ ï¿½ï¿½ï¿½Ü·ï¿½ï¿½ï¿½:

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71 TIMES 300=21300

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ï¿½ï¿½ ï¿½Ì´ï¿½.

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N= { 21300 TIMES 20} over {320-30 } =1469

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1469 TIMES 6=8814

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{ 2847} over {320 } TIMES 2=18

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ï¿½ï¿½ ï¿½Ì´ï¿½.

ï¿½ï¿½Ã¼ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½

15 kg/ { cm}^{2 }

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ï¿½ï¿½ï¿½ï¿½Ï´ï¿½. ï¿½ï¿½ï¿½ï¿½

10kg/ { cm}^{2 }

ï¿½ï¿½

ï¿½ï¿½

30 TIMES 32=960 ï¿½ï¿½>18 ï¿½ï¿½

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ï¿½Ì´ï¿½.

ï¿½×¸ï¿½ 12-9 ï¿½ï¿½Å¾ï¿½ï¿½ ï¿½Ü¸éµµ

10 cm TIMES 10cm

ï¿½ï¿½

) 1800

4. ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½: 263296

5. ï¿½ï¿½ï¿½ï¿½ ï¿½ß·ï¿½: 22355

9. ï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½ï¿½](ï¿½ï¿½ 9ï¿½ï¿½) 1000

10. ï¿½ë¸¶ï¿½ï¿½ 73880

13. ï¿½ï¿½ï¿½ï¿½[Û°ï¿½ï¿½] 18270

14. ï¿½ï¿½ï¿½(ï¿½Õ°ï¿½) 250213

16. ï¿½ï¿½Ã·[é¦®ï¿½]ï¿½ï¿½ ï¿½ï¿½ ï¿½ë¸¶ï¿½ï¿½ 880688

20. ï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½ï¿½]ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½[ï¿½ï¿½](1-8 ï¿½ï¿½) 154148

21. ï¿½ë·®[ï¿½ï¿½ï¿½ï¿½] (1-8 ï¿½ï¿½) 22958

23. ï¿½ï¿½ï¿½ 5000

24. ï¿½Ò»ï¿½(ï¿½ï¿½ï¿½ï¿½) 69000

25. ï¿½ï¿½(Ú¦)ï¿½ï¿½ Ã¢(ï¿½ï¿½) 30000

ï¿½Õ°ï¿½: 2517524 ï¿½ï¿½

ï¿½ï¿½ 2518000 ï¿½ï¿½(ï¿½ï¿½ 1260 ton)

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{ Q}_{0 } =C { a}_{max } W

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ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ C=0.25,

{ a}_{max } =0.45

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( 8ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½),

W=251800/16=157375 ï¿½ï¿½

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. ï¿½ï¿½ï¿½ï¿½:

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{ Q}_{0 } =0.25 TIMES 0.45 TIMES 157375=17700

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ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½Õ°ï¿½

17700 TIMES 16=283200

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ï¿½ï¿½ï¿½Ì´ï¿½.

ï¿½ï¿½

{ 21300 TIMES 20} over {480 } =887.5

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ï¿½ï¿½ ï¿½Ì´ï¿½.

ï¿½ï¿½

887.5 TIMES 8=7100

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ï¿½ï¿½ ï¿½Ì´ï¿½.

ï¿½ï¿½

887.5 TIMES 16cos { 45}^{ï¿½ï¿½ } =10039.0

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ï¿½ï¿½ ï¿½Ì´ï¿½.

ï¿½ï¿½

{ 51660 TIMES 25} over { 273} =5646

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ï¿½ï¿½ ï¿½Ì´ï¿½.

ï¿½ï¿½

5646 TIMES 8=45168

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ï¿½ï¿½ ï¿½Ì´ï¿½.

ï¿½ï¿½

45168cos { 45}^{ï¿½ï¿½ } =31617

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ï¿½ï¿½ ï¿½Ì´ï¿½.

ï¿½ï¿½

189276/20=9463

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ï¿½ï¿½ ï¿½Ì´ï¿½.

ï¿½ï¿½

{ 9463} over {480 } TIMES 2 =39.4

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ï¿½ï¿½ ï¿½Ì´ï¿½.

ï¿½ï¿½Ã¼ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½(Ëï¿½ï¿½)ï¿½ï¿½ 10

kg/ { cm}^{2 }

ï¿½ï¿½

ï¿½ï¿½/ { ï¿½ï¿½}^{2 }

ï¿½ï¿½

ï¿½ï¿½

30 TIMES 34=1020 ï¿½Å¡ï¿½ 39.4

ï¿½ï¿½

ï¿½ï¿½ ï¿½Ì´ï¿½.

ï¿½×¸ï¿½ 12-12 ï¿½ï¿½Å¾ 1 ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½éµµ

2695 ï¿½ï¿½ TIMES 1375 ï¿½ï¿½

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