1) The document presents a series of mathematical equations relating various variables represented by letters A through k.
2) A table is provided that gives values for each variable in terms of other variables based on 12 different scenarios labeled A through L.
3) The purpose seems to be demonstrating relationships between unknown variables and solving for their values using a system of interconnected equations.
14. . 8 . ,*
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7
: _$
`
A AAD = D × a × ` =
: : F# ()
A
A b_b S0E 0
15. 5
QE
) ( % × × A =
S 19V /P
A
A Z7T 7 R . cE
US R
=
% × × A × YYYYY ( – ) ( % – ) =
% × × A × B × C = : _$
C
% –
= (A)
B × C = C = : _$
A B
C
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44. 3 7 : C =
`% = –
– %Y
%Y : : 2b () B
`% k
A +
× ( A + ) = : : : 2b
(%A)
+
: : 2b (%B)
B
:
–
B +
B
A –
B
%
A – :
45. 3 c]q r 1 7 =
ka
BY :
kD
A
= : : 2b (%C) BY ( ak × YYY × C × A × % )
BY `Y
= ÷ : : 2b (%D) CY ( kk × YYY × C × A × % )
: :
1 (%a)
CY %YY
+
A 8 CYB =
–
B :
59. ! 0E #
1 *
{ a 8 C 8 B } 8 { a 8 C 8 A } 8 { a 8 B 8 A } 8 { C 8 B 8 A } : :0E
{ B 8 A 8 C }9q
N*# ({ C 8 A 8 B }9q
N*# ({ C 8 B 8 A }9q
: : x
_ i
+E 5
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)
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I
1 x#
: : F#
( Z + )
=
Z + Z +
A
( Z + ) 8
A
=
Z A + Z
A +
A
Z +
B
( Z + ) 8
B
=
A
B +
D + Z
Z
A
Z B +
B
Z +
: 5( 9@
‚0*
107. _ :
_# 7
= %
B
Y = B 8
B
% = D 8
B
= B 8
B
A = % 8
B
B
: I
1 x#
: :;6 Q wI[ ) 8
) Z 8 : :
1
=
( Z + )
Y
+
%
% –
+ Z
% –
Z
+ YYYYY +
–
Z
+ YYYYY +
Z
: W
% + = ‚0*
111. ! :0 : WI.
: E
a
( p + ) ‚0* 7 (%)
„
3 QN
''''''''''''I
a
=
( p + )
a
Y a
+
D
a
%
+ p
a
C
p
+
a
A B
A
p
+
a
B A
B
+
p
a
C
C
+
p
D
+
a
D p
a
a
a p
a
= a
p + +
112. C
( p + A ) ‚0* 7 ()
„
3 QN
''''''''''''I
: c}# 7 _x
_
( Z – ) [%]
=
–
%
% –
+ Z
% –
Z
–
A
A
A –
Z
YYYYY
+
–
( Z –)
( Z –) + YYYYY +
#$
#$
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:
( Z + ) ‚0* 56
I
: : F#
=
( Z + )
Y
+
%
% –
+ Z
% –
Z
+ YYYYY +
–
Z
+ YYYYY +
Z
: : !# 5 . 7
B =
A
A
A –
Z
=
A
A Z
A –
8 a =
D
D Z
D –
8 AC =
AB
AB Z
AB –
8 % + =
Z
–
( Z + ) ‚0* 56
I
( 7
8 YYYY 8 B 8 A 8 8 % = : W
: : % + =
( 5#$
)
( ?7@
)
–
: E
A ) ‚0* 56 oN
I
7 (%)
A
( –
k
''''''''''''I
D =
C ( 5#$
)
C
( ?7@
)
C –
=
A
k
C ( –)
C
A )
(
C – k
129. =
) ‚0* 56 i]
I
:
1 ()
–
–
(
%%
I
F3 7 %DC 7N
''''''''''''I
A k B %DC =
%%
` –)
–
(
`
)
(
A
%DC =
B
%%
A ×
%D –
×
D
130. B %DC =
( + ) ‚0* 56 (A)
:
1 )z
3 QN
C 7N k 7
:
1 8
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a_shantory2007@yahoo.com
: I
1 ‚0* 56 P t.N
I
7
. N
% + –
× =
: x
_
% +
. ,*
€ (%)
:
5#$
?7@
% – 8 % + : : W
=
% –
173. 6
k :
% + –
` k = : :0E k : ` ` = : :0E
: 5( I
1 ‚0* 56
5 . N
()
% + –
× =
: E
%Y
% +
( p B – A ) ‚0* 56 (%)
7 C : B
''''''''''''I
5#$
?7@
% + B – %Y
p B –
A
174. = × =
C
B
B
( A + % ) ‚0* 56 ()
. N
2#
1 a 5 C C : %` N
175. 3 7
''''''''''''I
a
D
D
C
!* = × =
a
C
% + D –
% + C –
!* = A × × A × B
D
= ( B – ) ( C – ) B
B
–
C
B
275. 6
: :
1
% 8 B + A = D + C =
: :;6
% A` + k – = ( + %` ) + ( – %C ) = ( D + C )( B + A ) =
B
% A` – k – =
8
% A` + k – = ( D – C )( B – A ) =
B
% =
%
#$
#$
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: : 7 g : :
1 (C)
: F3 7 Y = –
'''''''''''''''I
= : : h*#
= B p +
p –
) B
( p +
) –
Y = ( p –
B
p – p +
=
p –
B
p –
() p – = p 8 (%) =
Y = p + p ()
Y = ( % + ) p B
401. !
=
6L
i.. p +
= / ] – B
p – p +
B
p –
() / ] – = p 8 (%) =
: c (%) i..
B
–
p
B
p +
(A) B =
B : c () i.. 8
p
(B) =
: c (B) 8 (A) i
402. !.
B
+
p
B
p +
%D =
) :
p +
(
B %D =
p +
(C) B =
: c (C) 8 (%) i
403. !.
B D =
/ ] = B A =
p : c (C) 8 (%) OL.
p B =
% = B % =
Pq
56 :*+ p 8 B ]
562. r6 :7. (%)
''''''''''''I
%
%
p : /
;. p = p – % p 8 A p = A p – %
? ? %
( ? – ) ( ? – ) = = B
? – Y
? – Y
p : /
;. A p = p – A
? –
? –
? ? %
? + % Y
% Y
? +
? ? %
? + % Y
( – ) ( ? – ) ( ? – ) = ( ? – ) ( ? – ) = B
Y Y
–
I
578. !
-
+];. 7 ()
8 B = ƒ A+ p B + C 8 8 % = ƒ + p + A 8 %Y = ƒ – p +
'''''''''''I
– %
A
A B C
– % %Y
%
A B B
a – = ( %Y – ) – ( %Y – k ) % – ( ` – D ) = =
– %Y
% A
A B C
% 8 a – = = %B – = =
%Y %
% A
B B C
A = =
A – = ƒ 8 = p 8 % = B
{ A – 8 8 % } = I
)
584. 3 7 ()
: W
'(
'(
'(
'(
–
%
: W
8 % – =
A
% =
+% Y %
% Y
% – –%
: : 2b I
585. r6 :7. (A)
% %
%
% ƒ p
% ƒ p
( – ƒ ) ( ƒ – p ) ( p – ) = (%
ƒ
% p
% % %
p
p –
= (
p –
Z
Z
( Z + + ) ( Z – ) ( – ) = (A
Z
A
A %
p
*[ = (B
A –
A – % p
A
A % ƒ
ƒ
– B C
A – %
a % – A
– B C
B C – %
a % – A
– D – C
% C A
a ` A
*[ = + + (C
#$
#$
594. I
- +] (`)
a = ƒ + p – A 8 % = ƒ + p + (%
Y = A + ƒ + p
Y = ƒ + p – 8 A = ƒ + p + (
a = – ƒ B + p A
= ƒ + p 8 % = ƒ + p – (A
Y = ƒ – p +
Y = % + ƒ + p A – 8 C = ƒ + p – (B
aB = ƒ + p C +
#$
#$