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**1)**

X-3|2 2|+4|5 2 |+3|5 2|= -24

| -4 6-x| |2 6-x| |2 -4|

X-3(12-2x+8)+4(30-5x-4)+3(-20-4) = -24

X-3(20-2x)+4(26-5x)+3(-24)= -24

20x - 2x² - 60 + 6x + 104 - 20x - 72 = -24

-2x² + 6x - 60+104-72+24 = 0

-2x² + 6x - 4 = 0

Divide through by -2

X² - 3X + 2 = 0

X² - 2X - X + 2= 0

X(X-2)-1(X-2)=0

(X - 1)(X - 2)=0

X=1 OR X=2X-3|2 2|+4|5 2 |+3|5 2|= -24

| -4 6-x| |2 6-x| |2 -4|

X-3(12-2x+8)+4(30-5x-4)+3(-20-4) = -24

X-3(20-2x)+4(26-5x)+3(-24)= -24

20x - 2x² - 60 + 6x + 104 - 20x - 72 = -24

-2x² + 6x - 60+104-72+24 = 0

-2x² + 6x - 4 = 0

Divide through by -2

X² - 3X + 2 = 0

X² - 2X - X + 2= 0

X(X-2)-1(X-2)=0

(X - 1)(X - 2)=0

X=1 OR X=2

**
**

U=x-2 hence x=u+2

therefore

x^2+5/(x-2)^4

=(u+2)^3+5/(u+2-2)^2

=(u+2)^3+5/u^4

3b)

(u+2)^3+5/u^4

=(u+2)^3/u^4+5/u^4

==============================

**2)**

Log 3x - 3logx³+ 2 = 0

Log 3x - 3log3³/log3x + 2 = 0

Log3x - 3/log3x + 2 = 0

P - 3/p + 2 = 0 where P = log3x

P² - 3 + 2p = 0

P² + 2p - 3 = 0

(p + 3) ( p - 1) = 0

P = -3 OR p = 1

But log3x = p

when p = -3

Log3x = -3

X = 3-³ = 1/27

And when P = 1

Log3x = 1

X = 3¹ = 3

And X = 1/27Log 3x - 3logx³+ 2 = 0

Log 3x - 3log3³/log3x + 2 = 0

Log3x - 3/log3x + 2 = 0

P - 3/p + 2 = 0 where P = log3x

P² - 3 + 2p = 0

P² + 2p - 3 = 0

(p + 3) ( p - 1) = 0

P = -3 OR p = 1

But log3x = p

when p = -3

Log3x = -3

X = 3-³ = 1/27

And when P = 1

Log3x = 1

X = 3¹ = 3

And X = 1/27

==============================

3a)U=x-2 hence x=u+2

therefore

x^2+5/(x-2)^4

=(u+2)^3+5/(u+2-2)^2

=(u+2)^3+5/u^4

3b)

(u+2)^3+5/u^4

=(u+2)^3/u^4+5/u^4

====================================

No 4

Sn = n/2[2a+(n-1)d]

S12 = 12/6[2a + 11d]

S12= 6[2a + 11d] = 168

2a + 11d = 28-------(1)

Also

T3 = a + 2d = 7---------(2)

Multiplying 1 by 2

2a + 4d = 14

Eqn 1 minus Eqn 3 gives

7d = 14

d = 2

Putting this in eqn 2

a + 2(2) = 7

a + (4) = 7

a = 7 - 4

a = 3

Common difference = 2

First term = 3

===============================

====================================

No 4

Sn = n/2[2a+(n-1)d]

S12 = 12/6[2a + 11d]

S12= 6[2a + 11d] = 168

2a + 11d = 28-------(1)

Also

T3 = a + 2d = 7---------(2)

Multiplying 1 by 2

2a + 4d = 14

Eqn 1 minus Eqn 3 gives

7d = 14

d = 2

Putting this in eqn 2

a + 2(2) = 7

a + (4) = 7

a = 7 - 4

a = 3

Common difference = 2

First term = 3

===============================

**5)**

tabulate

X,y,d,d^2

A 8,6,2,4

B 5,3,2,4

C 1,4,-3,9

D 7,8,-1,1

E 2,5,-3,9

F 6,7,-1,1

G 3,1,2,4

H 4,2,2,4

Ed^2 =4+4+9+1+9+1+4+4

=36

r=1-6£d^2/n(n^2-1)

=1-6*36/8(8^2-1)=1-216/504

=1-0.43

=0.57tabulate

X,y,d,d^2

A 8,6,2,4

B 5,3,2,4

C 1,4,-3,9

D 7,8,-1,1

E 2,5,-3,9

F 6,7,-1,1

G 3,1,2,4

H 4,2,2,4

Ed^2 =4+4+9+1+9+1+4+4

=36

r=1-6£d^2/n(n^2-1)

=1-6*36/8(8^2-1)=1-216/504

=1-0.43

=0.57

**(6)**

**It follow that:**

P(n) = 1/3 and p(k)¹ = 1 - 1/3 = 2/3

P(T) = 1/5 and P(T)¹ = 1- 1/5 = 4/5

Hence,

probability that only one if the them will be solve the questions will be:

= (1/3 × 4/5) + (1/5 × 2/3)

= 4/15 + 2/15

= 6/15

= 2/5

====================================

(7)

m = 3i - 2j ; n = 2i + 3j ; p = i + 6j

Therefore:

4(3i - 2j) +2(2i +3j) -3(-i + 6j)

12i - 8j + 4i + 6j + 3i - 18j

12i + 4i + 3i - 8j + 6j - 18j

19i = 20j

====================================

(8a)

m1 = 20kg

u1 = 8ms-1

m2 = 30kg

u2 = 50ms-1

(a) in same direction

m1u1 + m2u2 = (m1+m2)v

20 × 80 + 30 × 50 = (20+30)v

1600+1500 = 50v

3100/50 = 50/50

V = 62ms-1

(b)

In opposite direction

m1u1 - m2u2 = (m1 + u2)V

20×30 - 30×50 = (20+30)V

1600 - 1500 = 50V

100/50 = 50V/50

V = 2m/s

KEEP REFRESHING PAGE.P(n) = 1/3 and p(k)¹ = 1 - 1/3 = 2/3

P(T) = 1/5 and P(T)¹ = 1- 1/5 = 4/5

Hence,

probability that only one if the them will be solve the questions will be:

= (1/3 × 4/5) + (1/5 × 2/3)

= 4/15 + 2/15

= 6/15

= 2/5

====================================

(7)

m = 3i - 2j ; n = 2i + 3j ; p = i + 6j

Therefore:

4(3i - 2j) +2(2i +3j) -3(-i + 6j)

12i - 8j + 4i + 6j + 3i - 18j

12i + 4i + 3i - 8j + 6j - 18j

19i = 20j

====================================

(8a)

m1 = 20kg

u1 = 8ms-1

m2 = 30kg

u2 = 50ms-1

(a) in same direction

m1u1 + m2u2 = (m1+m2)v

20 × 80 + 30 × 50 = (20+30)v

1600+1500 = 50v

3100/50 = 50/50

V = 62ms-1

(b)

In opposite direction

m1u1 - m2u2 = (m1 + u2)V

20×30 - 30×50 = (20+30)V

1600 - 1500 = 50V

100/50 = 50V/50

V = 2m/s

KEEP REFRESHING PAGE.

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