Page 44 - WCS - Electrical

WORKSHOP CALCULATION & SCIENCE - CITS

3x + 2y 2 n m+ n n
2
m
a m
a =
3
y 2
3x 2
2 a m
a m+
2 a x n
m+
2x - 3y m a x a a x n n a= = a m+ n n = = 3x 2 2 y 3 3 = y y2 2 2
3x2
y3
x
a
a =
y
y =
m x a = a m+ n 2 3x 3 5 = 2 3
n
y
a
y 2x 3
y 6x 5
3x −
_________________ = = − − − 6x 5 y = 2x 3
y
6x5
2x3
m
=
= y
2x
6x
y
a m
m−
a m
m−
2 =
2 m
a
=
x + 5y a m a am− n n n n a= m+ n − 6x 5 y 2x 3
n
n a
a a x
m−
m n = = m− n 3x 2 y 3 y 2
a
a a
an
n
a
a
=
_________________ = 5 = 3
a
n
3 −
26x
a 3x 3 y 2 y 2x
2

m
y
Multiplication nm a a a= m. n − n = 3x3 3 y y2 2 = 3x 2 2 y y

= = 3x
y =
m.m
3x
3x2
n
[ m
n
a ] =
a ] =
2 xy
=
3x
3
[ m
n
a nm.
=
n
n
m
[
2
a ] = n
xy
2 a ][
a
1 - 4x x 8x mnm 5 = a a n . m. = - 4 x 8x 2+5 = 3x = xy y xy = 3x 3x y
xy
y

a ] =
a
[

m
1/m = m a = -32x 7 3x 3 2 y 2 b 2 2 2 c c 2
a 1/m

45a
a
a 1/m
45a2
= m
=
b2
1/m m
a
= = 45a
c
2a
2 (3d - 2d) 3d ][ a = = a m a n a a= m. n = = 45a xy 2 b c c b 2 3x= c y
1/m
2 2
m
2 2
45a9a
a
=
9
b ca2
9a
= 9d - 6d 2 = 9a 2 c c
3
2
− − m 1 1 9a c
m 1/m
m
a
=
1
= 1 =
a ma
−
3 (5x + 3y) (5x - 3y) a = 45a 2 b 2 c
−
m
m
a
=

= m
a
1 a
m
−
am
a
a
2 =
2 a
= (5x) - (3y) m 9a 2 c
m
a
1
m
1
m 1
= 5x x 5x - 3y x 3y
a
1 −
= m
=
1
− a
am =
m
m =
m
1 a a− − 2m = a a m
2 m
= 25x - 9y a= a
−
m
a
a
m
−
a

4 5x y x 8x y n mnm / n = 1 n m m
5 3
2

m /
a
a
=n
n
am /
am
7 4 n
m /
=
a
a
a
= 40x y =m n m a=
a
−
m /
n m
n a
a = a

2
2

5 (2a+b) (a+2b)
2
2
3x +
2y

3x +
2
2y2
2
2
2y
3x +
2 +
3x
2 3y 2 n mn
2
= 2a + 4ab + ab + 2b
2x 2 m / 2y 2 2 a 2
3y2 =
2x +
2 + a
2
2y
3x +2
3y
2x +
y
_______ 32x +
2 _______
_______
= 2a + 2b + 5ab
2 3y 2
2x + 5y 2 2 2
2 _______ 22
x +
_______ 22
5y2
2
x + 2
5y
x +
_______ 23x +
y
3 5 -55yx +
2_______
6 8a b c x 3a b c
2 -5 5
2
5y___
2
____ 2
x + _______
3y
2x +
_____ 5__
= 24a_______
2
2
3 x
Division 12x 3 3 _______
2 5y+
y 2
12x3
y2
2
=
3xy
12x
3xy
12x
2 2
3
12x 4x 2 y y = = 3xy
=
y y
3xy
y
4x2
1 4x 2 y = 3xy
=
3xy
4x
y
2
4x y
1512x
15y 15 3 y 2
=
10
2 = y10 3xy
15y 15
y 10
15
15y
= 2
=
15y
10 y
15y 15y 5 4x y y 10
15 5 =
y
=
15y5
10
15y 5 y
=
15y
9c d ÷ c d
3 15y 5 5 3 2 2 = 9c d
3

3a 2 15y 15 5a y= 3 10
2
3
x
x
4a
4a
x
x
3a2
5a3
2
x
4a5
4a
x
x
3a
5a
4 15y
4 3a 3a x 6a 4a x 10ax x 5a 3
2
3
4
5a
x
10a
6a4
6a
10a
x
6a 4 x 10a
4
6a x 10a
60a x a 2 6 6 4a x 5a 3
3

60a6
=
6
= a== 60a
= = 60a 4 = = a a
a
6 5 = 10a x 6a
5
60a 60a
60a5
= 60a = 5 a
60a
60a 5

5 -25a ÷ -5a 6 -8
15
60a
− = 15 a
15 =
25a
−
= = 25a 60a
25a 15
15 5
−
25a
15 8−
= = − 5a − 8
= 25a− −
−
5a 8−
= − − 5a − 8
5a
−
4x 2 5a − 8 15
2
y
25a

4x2
=
15 8 2x=
= 4x y 2y 2 y y − 2x 2 2 2 8 23
y =
= 5a a = 5a
4x =
2x2
=
2 2y =
2x −
=
4x =
2y
6 = 2y 2y 2 = 2x − 25a
4x y ÷ 2y
4x 2 y
2
=
2x
=
=
2y
31
CITS : WCS - Electrical - Exercise 4