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(1)

ﻲﻨﻃﻮﻟا نﺎﺤﺘﻣ ا ﺢﻴﺤﺼﺗ ءﺎﻳﺰﻴﻔﻠﻟ

2015 ﺔﻳدﺎﻌﻟا ةروﺪﻟا

ﺔﻴﺋﺎﻳﺰﻴﻔﻟا مﻮﻠﻌﻟا ﻚﻠﺴﻣ

assilah.com -

www.svt

لو ا ﻦﻳﺮﻤﺘﻟا

مﻮﻳدﻮﺼﻟا رورﻮﻠﻛ لﻮﻠﺤﻤﻟ ﻲﺋﺎﺑﺮﻬﻜﻟا ﻞﻴﻠﺤﺘﻟا : لو ا ءﺰﺠﻟا

1 - ﻲﺒﻳﺮﺠﺘﻟا ﺐﻴﻛﺮﺘﻟا ﺔﻧﺎﻴﺒﺗ ﺐﺴﺣ ﻧوﺮﺘﻜﻟ ا روﺮﻣ ﻰﺤﻨﻣ

تﺎ

ﻦﻣ تﺎﻧوﺮﺘﻜﻟ ا ﻞﻘﺘﻨﺗ ﺚﻴﺣ ﻲﺋﺎﺑﺮﻬﻜﻟا رﺎﻴﺘﻟا ﻰﺤﻨﻣ ﺲﻜﻋ دوﺮﺘﻜﻟ ا دوﺮﺘﻜﻟ ا ﻮﺤﻧ

(ﻪﺒﻧﺎﺟ ﻞﻜﺸﻟا ﺮﻈﻧأ)

دوﺮﺘﻜﻟ ا دﻮﺛﺎﻜﻟا ﻞﺜﻤﻳ

ﻳ لاﺰﺘﺧا هاﻮﺘﺴﻣ ﻰﻠﻋ ثﺪﺤ يأ)

بﺎﺴﺘﻛا é

. (

دوﺮﺘﻜﻟ ا دﻮﻧ ا ﻞﺜﻤﻳ

يا) ةﺪﺴﻛأ هاﻮﺘﺴﻣ ﻰﻠﻋ ثﺪﺤﺗ

ناﺪﻘﻓ é . (

2 - :ءﺎﻤﻟا ﺔﺌﻳﺰﺟ لاﺰﺘﺧا ثﺪﺤﻳ دﻮﺛﺎﻜﻟا راﻮﺠﺑ

2 ( )+ 2 ⇄ ( )+ 2 ( )

ةﺪﺴﻛأ ثﺪﺤﺗ دﻮﻧ ا راﻮﺠﺑ نﻮﻳأ

رورﻮﻠﻜﻟا :

2 ( )( )+ 2

: ﺔﻠﻴﺼﺤﻟا ﺔﻟدﺎﻌﻤﻟا 2 ( )+ 2 ( )( )+ + 2 ( )

3 - : دﻮﻧ ا ﺪﻨﻋ نﻮﻜﺘﻤﻟا رﻮﻠﻜﻟا زﺎﻏ ﻢﺠﺣ بﺎﺴﺣ

: ﺔﻟدﺎﻌﻤﻟا ﻒﺼﻧ ل ﺧ ﻦﻣ

2 ( )( )+ 2

:ﺎﻨﻳﺪﻟ ( ) = ( )

:نأ ﻢﻠﻌﻧ

( ) = ( )

( ) = = ∆ ⇒ ( ) = ∆

2 ⇒ ( ) = ∆ . 2

: ع.ت ( ) =3 × 25 × 60 × 25

2 × 9,65.10 ≈ 0,58

ﺔﻠﯾﺻﺄﺑ ضرﻷا و ةﺎﯾﺣﻟا موﻠﻋ تﺎﯾدﺗﻧﻣ

(2)

لﻮﻧﺎﺜﻳ ا ﻊﻣو ءﺎﻤﻟا ﻊﻣ ﻚﻳوﺰﻨﺒﻟا ﺾﻤﺣ ﻞﻋﺎﻔﺗ ﺔﺳارد : ﻲﻧﺎﺜﻟا ءﺰﺠﻟا

1 - ءﺎﻤﻟا ﻊﻣ ﻚﻳوﺰﻨﺒﻟا ﺾﻤﺣ ﻞﻋﺎﻔﺗ ﺔﺳارد

1.1 - : ﻞﺻﺎﺤﻟا ﻞﻋﺎﻔﺘﻠﻟ ﻲﻔﺻﻮﻟا لوﺪﺠﻟا

H( ) + H O( ) ⇄ COO( ) H O( )

ﺔﻴﺋﺎﻴﻤﻴﻜﻟا ﺔﻟدﺎﻌﻤﻟا

ب ةدﺎﻤﻟا تﺎﻴﻤﻛ (mol)

مﺪﻘﺘﻟا ﺔﻋﻮﻤﺠﻤﻟا ﺔﻟﺎﺣ

0 ﺮﻴﻓو 0

0 CV

ﺔﻴﺋﺪﺒﻟا ﺔﻟﺎﺤﻟا

x ﺮﻴﻓو x

C. V − x لﻮﺤﺘﻟا ﺔﻟﺎﺣ x

xé xé

ﺮﻴﻓو C. V − xé

xé ﺔﻴﺋﺎﻬﻨﻟا ﺔﻟﺎﺤﻟا

مﺪﻘﺘﻟا ﺔﺒﺴﻧﺮﻴﺒﻌﺗ :

= é

: ﺾﻤﺤﻟا ﻮﻫ ﺪﺤﻤﻟا ﻞﻋﺎﻔﺘﻤﻟا C. V − x = 0 ⇒ x = .

: ﺔﻴﻠﺻﻮﻤﻟا ﻒﻳﺮﻌﺗ ﺐﺴﺣ

= [ ]é + [ ]é

: ﻲﻔﺻﻮﻟا لوﺪﺠﻟا ﺐﺴﺣ

= [ ]é + ( )[ ]é ⇐ [ ]é = [ ]é = é

é = .

+ ( )

⇐ = ( + ( )) é

: مﺪﻘﺘﻟا ﺔﺒﺴﻧ

= .

( + ( )). . =

( + ( )).

: ع.ت

= 2,76.10

(3,23.10 + 35.10 ) × 10⟹ = 0,072

1.2 - ﺮﻴﺒﻌﺗ : نزاﻮﺘﻟا ﺪﻨﻋ ﻞﻋﺎﻔﺘﻟا جرﺎﺧ

=[ ]é [ ]é

[ ]é

: ﻲﻔﺻﻮﻟا لوﺪﺠﻟا ﺐﺴﺣ [ ]é = [ ]é

[ ]é = . − é

= − é ⇒ [ ]é = [ ]é

[ ]é = − [ ]é ⇒ [ ]é = [ ]é = . [ ]é = − 10 = − .

(3)

= [ ]é

− [ ]é = ( . )

− . ⟹ = . 1 −

1.3 - ﺔﻤﻴﻗ جﺎﺘﻨﺘﺳا

: ﺎﻨﻳﺪﻟ

=

و

= −

= − .

1 −

= − 10.10 × 0,072

1 − 0,072 ≈ 4,25

2 - لﻮﻧﺎﺜﻳ ا ﻊﻣ ﻚﻳوﺰﻨﺒﻟا ﺾﻤﺣ ﻞﻋﺎﻔﺗ ﺔﺳارد

2.1 - رود ( زﺎﻔﺤﻟا ) ﻚﻴﺘﻳﺮﺒﻜﻟا ﺾﻤﺣ ﻞﻋﺎﻔﺘﻟا ﻊﻳ ﺗ

.

2.2 - ﻞﻋﺎﻔﺘﻟا ﺔﻟدﺎﻌﻣ : لﻮﻧﺎﺜﻳ او ﻚﻳوﺰﻨﺒﻟا ﺾﻤﺣ ﻦﻴﺑ

− + − − ⇄ − − − +

2.3 - : ﻞﻋﺎﻔﺘﻟا دودﺮﻣ ﺪﻳﺪﺤﺗ

: دوﺪﻤﻟا ﻒﻳﺮﻌﺗ ﺐﺴﺣ

= =

: ﻲﻔﺻﻮﻟا لوﺪﺠﻟا ﺐﺴﺣ

− + − − ⇄ − − − +

ﺔﻴﺋﺎﻴﻤﻴﻜﻟا ﺔﻟدﺎﻌﻤﻟا

ب ةدﺎـــــــــــــــــــــــــــــــــــــــﻤﻟا تﺎـــــــــــــــــــــــــــــﻴﻤﻛ

( )

مﺪﻘﺘﻟا

ﺔﻋﻮﻤﺠﻤﻟا ﺔﻟﺎﺣ

0 0

( ) ( )

ﺔﻴﺋﺪﺒﻟا ﺔﻟﺎﺤﻟا 0

( ) − ( ) −

ﺔﻴﻄﻴﺳﻮﻟا ﺔﻟﺎﺤﻟا

( )−

( ) − ﺔﻴﺋﺎﻬﻨﻟا ﺔﻟﺎﺤﻟا

( ) =

( )= 2,44

122 = 0,02

( ) =

( ) = .

( )=0,78 × 10

46 = 0,17

ﻗ ا مﺪﻘﺘﻟاو ﻚﻳوﺰﻨﺒﻟا ﺾﻤﺣ ﻮﻫ ﺪﺤﻤﻟا ﻞﻋﺎﻔﺘﻤﻟا

= 0,02

(4)

= ( )= 2,25

150 = 0,015

= =0,015

0,02 = 0,75 ⇒ = 75%

2.4 - ﻚﻳوﺰﻨﺒﻟا ﺾﻤﺣ ضﻮﻌﻧ ﻞﻋﺎﻔﺘﻟا دودﺮﻣ ﻦﻣ ﻊﻓﺮﻠﻟ ﻚﻳوﺰﻨﺒﻟا ﺪﻳرﺪﻧﺄﺑ

ﻐﻴﺻ ﻪﺘ

: ﻲﻫ ةرﻮﺸﻨﻤﻟا ﻒﺼﻧ

ﻲﻧﺎﺜﻟا ﻦﻳﺮﻤﺘﻟا ﺔﻳوﻮﻨﻟا ت ﻮﺤﺘﻟا و تﺎﺟﻮﻤﻟا :

ﻞﻴﻠﻌﺗ ﺎﺑﻮﻠﻄﻣ ﺲﻴﻟ ﻦﻳﺮﻤﺘﻟا اﺬﻫ ﺔﺑﻮﺟا

تﺎﺟﻮﻤﻟا

1 - ﻲﻨﻣﺰﻟا ﺮﺧﺄﺘﻟا

= 1 ﻮﻫ

ﺎﺑﻮﻠﻄﻣ ﺲﻴﻟ ﻞﻴﻠﻌﺘﻟا

: ﺎﻨﻳﺪﻟ

=0,2

× 5 = 1,0

2 - فﺎﻔﺸﻟا ﻂﺳﻮﻟا رﺎﺴﻜﻧا ﻞﻣﺎﻌﻣ n

≈ 1,6 ﻮﻫ

ﻞﻴﻠﻌﺘﻟا

= = 3.10

1,87.10 ≈ 1,6

3 - ﻮﻫ عﺎﻌﺷ ا اﺬﻫ نﻮﺗﻮﻓ ﺔﻗﺎﻃ

≈ 3,75.10

ﻞﻴﻠﻌﺘﻟا

= ℎ =ℎ

⇒ = 6,63.10 × 3.10

530.10 ≈ 3,75.10

ﺔﻳوﻮﻨﻟا ت ﻮﺤﺘﻟا

4 - ةاﻮﻨﻟا ﺖﺘﻔﺗ ﻦﻋ ﺔﺠﺗﺎﻨﻟا تﻮﻣﺰﺒﻟا ةاﻮﻧ ﻮﻫ ﺎﻫﺰﻣر

.

ﻞﻴﻠﻌﺘﻟا : ﺔﻴﻟﺎﺘﻟا ﺖﺘﻔﺘﻟا ﺔﻟدﺎﻌﻣ ﻰﻠﻋ ﻞﺼﺤﻧ يدﻮﺻ ﺎﻧﻮﻧﺎﻗ لﺎﻤﻌﺘﺳﺎﺑ

⇄ +

5 - تﺎﺘﻴﺳ ﻟ ﻒﺼﻨﻟا ﺮﻤﻋ 211

: يوﺎﺴﻳ

≈ 7,17 ℎ

ﻞﻴﻠﻌﺘﻟا

: ﻲﻋﺎﻌﺷ ا ﺺﻗﺎﻨﺘﻟا نﻮﻧﺎﻗ

= :يأ

= −

= − 2

ﺔﻟاﺪﻠﻟ ﻪﺟﻮﻤﻟا ﻞﻣﺎﻌﻤﻟا ﺔﻴﻔﻟﺂﺘﻟا

= ( )

= , , = − ﻮﻫ

= 3 2

37,94 − 37,65≈ 7,17 ℎ

ﺚﻟﺎﺜﻟا ﻦﻳﺮﻤﺘﻟا ءﺎﺑﺮﻬﻜﻟا :

(5)

ﺐﻄﻘﻟا ﻲﺋﺎﻨﺛ ﺔﺳارد : لو ا ءﺰﺠﻟا ةﺪﻋﺎﺻ ﺮﺗﻮﺗ ﺔﺒﺗﺮﻟ ﻊﺿﺎﺧ

1.1 - ﻦﻳﺮﺗﻮﺘﻟا ﻞﻴﺜﻤﺗ و

ﻞﺒﻘﺘﺴﻣ ح ﻄﺻا ﻲﻓ

1.2 - ﺮﺗﻮﺘﻟا ﺎﻬﻘﻘﺤﻳ ﻲﺘﻟا ﺔﻴﻠﺿﺎﻔﺘﻟا ﺔﻟدﺎﻌﻤﻟا تﺎﺒﺛإ

:

: تاﺮﺗﻮﺘﻟا ﺔﻴﻓﺎﺿإ نﻮﻧﺎﻗ ﺐﺴﺣ

+ =

+ =

= =

:ﻊﻣ

+ =

: ﺐﺘﻜﺗ ﺔﻴﻠﺿﺎﻔﺘﻟا ﺔﻟدﺎﻌﻤﻟا

+ =

=

ﻊﻣ 1.3 - 3 ﻦﻣ ﻞﻛ ﺮﻴﺒﻌﺗ A

و B :

: ﺎﻨﻳﺪﻟ

= +

= −

: ﺔﻴﻠﺿﺎﻔﺘﻟا ﺔﻟدﺎﻌﻤﻟا ﻲﻓ ضﻮﻌﻧ

+

+

=

⇒ −

+ (1 − 1) = 0

⇒ =

: ﺔﻴﺋﺪﺒﻟا طو ﻟا ﺐﺴﺣ

(0) = + = 0 ⇒ = − ⟹

= −

: ﺐﺘﻜﻳ ﺔﻴﻠﺿﺎﻔﺘﻟا ﺔﻟدﺎﻌﻤﻟا ﻞﺣ

( ) = (1 − )

1.4 - ﻦﻣﺰﻟا ﺔﺘﺑﺎﺛ ﺪﻳﺪﺤﺗ

ةراﺮﺤﻟا ﺔﺟرد ﺪﻨﻋ

205°C

:

ﺔﻈﺤﻠﻟا ﺪﻨﻋ

=

: ﺐﺘﻜﻧ

( )=E(1-

) = 6(1 − ) = 3,79

ﻞﻜﺸﻟا ﺮﻈﻧأ) ﺎﻴﻧﺎﻴﺒﻣ 2

: ﺪﺠﻧ (

= 0,5

(6)

ةراﺮﺤﻟا ﺔﺟرد ﺖﻌﻔﺗرا ﺎﻤﻠﻛ ﺔﻤﻴﻗ ﺖﺼﻗﺎﻨﺗ ﺎﻤﻠﻛ ،

ﻲﻟﺎﺘﻟﺎﺑو ﻦﺤﺸﻟا ةﺪﻣ ﺖﺼﻗﺎﻨﺗ

.

1.5 - ةراﺮﺤﻟا ﺔﺟرد ﺪﻳﺪﺤﺗ :

يراﺮﺤﻟا ﺲﺠﻤﻟا ﺔﻣوﺎﻘﻣ ﺪﻳﺪﺤﺗ ﺔﻤﻴﻘﻟ ﻖﻓاﻮﻤﻟا

: ﺚﻴﺣ

= .

:يأ

=

= 0,45.10

1,5.10 = 300Ω = 0,3 Ω

ﻞﻜﺸﻟا نﺎﻴﺒﻣ لﺎﻤﻌﺘﺳﺎﺑ 3

: ﺪﺠﻧ

= 210 °

ﻊﺳﻮﻟا ﻦﻴﻤﻀﺗ ﺔﺳارد : ﻲﻧﺎﺜﻟا ءﺰﺠﻟا

2.1 ﻊﺳﻮﻟا ﻦًﻤﻀﻤﻟا ﺮﺗﻮﺘﻟا ﻊﺳو ﺮﻴﺒﻌﺗ تﺎﺒﺛإ- ( )

: ﺎﻨﻳﺪﻟ ( ) = . ( ). ( ) ⇒ ( ) = [ + (2 )] (2 )

( ) = . . 1 + (2 ) (2 )

: ﻊﻀﻧ

= . .

و

=

2.2 - ددﺮﺘﻟا ﺪﻳﺪﺤﺗ و

:

روﺪﻟا ﻞﻜﺸﻟا ﺐﺴﺣ : يوﺎﺴﻳ

=

8 × 0,5 .

ددﺮﺘﻟا :

= =

× , ×

= 250

روﺪﻟا : يوﺎﺴﻳ

= 20

ددﺮﺘﻟا :

= 20 ×

:يأ

= 20 = 20 × 250 = 5.10

= 50

ﺔﻠﯾﺻﺄﺑ ضرﻷا و ةﺎﯾﺣﻟا موﻠﻋ تﺎﯾدﺗﻧﻣ

(7)

2.3 - ﻦﻴﻤﻀﺘﻟا ﺔﺒﺴﻧ بﺎﺴﺣ :

= −

+

ﻞﻜﺸﻟا ﺐﺴﺣ 5

:

= 1 ⁄ × 1 = 1

= 1 ⁄ × 5 = 5 ⇒ =5 − 1

5 + 1= 0,67

ﺑ نأ ﺎﻤ

< 1 نﺈﻓ ،

ﺪﻴﺟ ﻦﻴﻤﻀﺘﻟا .

ﻚﻴﻧﺎﻜﻴﻤﻟا : ﻊﺑاﺮﻟا ﻦﻳﺮﻤﺘﻟا

ﻢﻈﺘﻨﻤﻟا ﺔﻟﺎﻘﺜﻟا لﺎﺠﻣ ﻲﻓ ﻒﻟﻮﻐﻟا ةﺮﻛ ﺔﻛﺮﺣ ﺔﺳارد : لو ا ءﺰﺠﻟا

1 - ﻦﻴﺘﻴﻨﻣﺰﻟا ﻦﻴﺘﻟدﺎﻌﻤﻟا ( )

( ) و

: ﺔﺳورﺪﻤﻟا ﺔﻋﻮﻤﺠﻤﻟا ﻒﻟﻮﻐﻟا ةﺮﻛ

ةﺪﻴﺣو ةﻮﻘﻟ ةﺮﻜﻟا ﻊﻀﺨﺗ

ﻢﻠﻌﻤﻟا رﺎﺒﺘﻋﺎﺑ (0 , ⃗ , ⃗ )

: ﺐﺘﻜﻧ ﻦﺗﻮﻴﻨﻟ ﻲﻧﺎﺜﻟا نﻮﻧﺎﻘﻟا ﻖﺒﻄﻧ ، ﺎﻴﻠﻴﻟﺎﻏ ضر ﺎﺑ ﻂﺒﺗﺮﻤﻟا

⃗ = ⃗

:يأ

⃗ =

: ﻲﻟﺎﺘﻟﺎﺑو ⃗ = ⃗

: ﺔﻴﺋﺪﺒﻟا طو ﻟا ﺐﺴﺣ

=

= و = 0

= 0

ﻰﻠﻋ طﺎﻘﺳ ا و

:

= 0

= − ⇒

= = 0

= =ﺰﻛ ةﺮﻔﺤﻟا −

ﻞﻣﺎﻜﺗ

= =

= − + = − +

= =

= = − +

ﻞﻣﺎﻜﺗ

⎯⎯

( ) = . + ( ) = −1

2 + . +

ﻦﻴﺘﻴﻨﻣﺰﻟا ﻦﻴﺘﻟدﺎﻌﻤﻟا

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

( ) = . ( ) = −1

2 + .

: ع.ت ( ) = 10 × cos(45°) . ⇒ ( ) = 7,07

( ) = −1

2× 10. + 10 sin(45°) . ⇒ ( ) − 5 + 7,07

ﺔﻠﯾﺻﺄﺑ ضرﻷا و ةﺎﯾﺣﻟا موﻠﻋ تﺎﯾدﺗﻧﻣ

(8)

2 . - رﺎﺴﻤﻟا ﺔﻟدﺎﻌﻣ جﺎﺘﻨﺘﺳا :

: ﻦﻴﻴﺘﻴﻨﻣﺰﻟا ﻦﻴﺘﻟدﺎﻌﻤﻟا ﻦﻣ ﻦﻣﺰﻟا ءﺎﺼﻗﺈﺑ رﺎﺴﻤﻟا ﺔﻟدﺎﻌﻣ دﺪﺤﻨﻟ

= = −1

2 + . = −

2 + .

:ع.ت

= − 10

2 × 10 × (45°). + . tan(45°) ⇒ ( ) = −0,1 +

3 - ﺪﻳﺪﺤﺗ

: رﺎﺴﻤﻟا ﺔﻤﻗ لﻮﺼﻓأ

: نﻮﻜﻳ رﺎﺴﻤﻟا ﺔﻤﻗ ﺪﻨﻋ

= 0 ⇒ −2 × (0,1) + 1 = 0 ⇒ −0,2 = −1 ⇒ = = 1 0,2= 5

4 - ﺔﻄﻘﻨﻟا ﻦﻣ ﺮﻤﺗ ةﺮﻜﻟا نأ ﻦﻣ ﻖﻘﺤﺘﻟا :

ﺔﻄﻘﻨﻟا ﺖﻠﻴﺛاﺪﺣإ : ﺎﻤﻫ

= + + = 2,2 + 4 cos(24°) + 2,1 = 7,95

= = 4 sin(24°) = 1,63

ﺔﻄﻘﻨﻟا بﻮﺗرأ دﺪﺤﻧ : رﺎﺴﻤﻟا ﺔﻟدﺎﻌﻣ لﺎﻤﻌﺘﺳﺎﺑ

( ) = −0,1 × (7,95) + 7,95 ⇒ ( ) = = 1,63

ﺔﻄﻘﻨﻟا ﻦﻣ ﺮﻤﺗ ةﺮﻜﻟا نأ ﺞﺘﻨﺘﺴﻧ . ةﺮﻔﺤﻟا ﺰﻛﺮﻣ

ﻲﻘﻓأ بﺬﺑﺬﺘﻣ ﺔﺳارد : ﻲﻧﺎﺜﻟا ءﺰﺠﻟا

1 - يرود ﻪﺒﺷ تﺎﺑﺬﺑﺬﺘﻟا مﺎﻈ .

2 - ﺔﻧﺮﻤﻟا ﻊﺿﻮﻟا ﺔﻗﺎﻃ ﺮﻴﻐﺗ بﺎﺴﺣ

ﻦﻴﺘﻈﺤﻠﻟا ﻦﻴﺑ بﺬﺑﺬﺘﻤﻠﻟ

= 0 و :

: ﺎﻨﻳﺪﻟ

= ( ) − ( ) =1

2 + 1

2 + =1

2 ( )

ﺪﻨﻋ ﺎﻨﻳﺪﻟ ﺎﻴﻧﺎﻴﺒﻣ

= 1,2

= 1 = 10

ﺪﻨﻋو

= 0

= 2,5 = 2,5. 10

(9)

: ع.ت

=1

2× 20 × {[(1.10 ] − [(2,5.10 ] } = −5,25.10 ⇒ = −5,25

: داﺪﺗر ا ةﻮﻗ ﻞﻐﺷ جﺎﺘﻨﺘﺳا ( ⃗)

⃗ = −∆ = 5,25

3 - ﺪﻳﺪﺤﺗ

: ﺔﻴﻜﻴﻧﺎﻜﻴﻤﻟا ﺔﻗﺎﻄﻟاﺮﻴﻐﺗ

: ﺎﻨﻳﺪﻟ

= +

. ﺲﻜﻌﻟاو ﺔﻣﺪﻌﻨﻣ ﺔﻴﻛﺮﺤﻟا ﺔﻗﺎﻄﻟا نﻮﻜﺗ ، ﺔﻳﻮﺼﻗ ﺔﻧﺮﻤﻟا ﻊﺿﻮﻟا ﺔﻗﺎﻃ نﻮﻜﺗ ﺎﻣﺪﻨﻋ

ﺔﻈﺤﻠﻟا ﺪﻨﻋ

= 1 نﻮﻜﺗ

ﺔﻋ ﻟاو

= 0 : ﻲﻟﺎﺘﻟﺎﺑو

= 0

ﺔﻈﺤﻠﻟا ﺪﻨﻋ

= 2,5 نﻮﻜﺗ

ﺔﻋ ﻟاو

= 0 : ﻲﻟﺎﺘﻟﺎﺑو

= 0

= ∆ + ∆ = ∆ ⇒ ∆ = −5,25 < 0

ﺮﻴﺴﻔﺘﻟا نﺈﻓ) ، ﻞﻤﻬﻣ ﺮﻴﻏ دﻮﻤﺧ ﺔﻟﺎﺣ ﻲﻓ ﻆﻔﺤﻨﺗ ﺔﻴﻜﻴﻧﺎﻜﻴﻤﻟا ﺔﻗﺎﻄﻟا

ﺺﻗﺎﻨﺘﺗ ( ،

ﺔﻗﺎﻃ ﻰﻟا ﺎﻴﺠﻳرﺪﺗ ﺔﻴﻜﻴﻧﺎﻜﻴﻤﻟا ﺔﻗﺎﻄﻟا لﻮﺤﺘﺗ ﺚﻴﺣ

كﺎﻜﺘﺣ ا ىﻮﻗ ﻞﻐﺷ ﻞﻌﻔﺑ ﺔﻳراﺮﺣ

= ( ) < 0 .

ﺔﻠﯾﺻﺄﺑ ضرﻷا و ةﺎﯾﺣﻟا موﻠﻋ تﺎﯾدﺗﻧﻣ

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