MIP1502 ASSIGNMENT 4 S2 2024

MIP1502
ASSIGNMENT NO: 04
SEMESTER 2
YEAR : 2024




PREVIEW:


QUESTION 1
Complete the table below for tile numbers 5 and 6.


Tile no (n) 1 2 3 4 5 6 27
Tile length (L) 3 4 5 6 7 8
Number of red squares (R) 4 6 8 10 12 14
Number of black squares (B) 5 10 17 26 37 50
Total number of squares (S) 9 16 25 36 49 64


Length of Tile number 7

Given that the length of tile number 1 is 3, and the length increases by 1 for
each subsequent tile, the length of tile number 7 will be:

L=3+(7−1)=3+6=9

So, the length of tile number 7 is 9.

, QUESTION 1

1.1.1 Complete the table below for tile numbers 5 and 6.


Tile no (n) 1 2 3 4 5 6 27
Tile length (L) 3 4 5 6 7 8
Number of red squares (R) 4 6 8 10 12 14
Number of black squares (B) 5 10 17 26 37 50
Total number of squares (S) 9 16 25 36 49 64


1.1.2 Length of Tile number 7

Given that the length of tile number 1 is 3, and the length increases by 1 for
each subsequent tile, the length of tile number 7 will be:

L=3+(7−1)=3+6=9

So, the length of tile number 7 is 9.

1.1.3 Finding the Formula

a) Formula for red squares (R) in terms of tile length (l):

Observing the pattern: R=2L−2.
For example, for Tile 1 (L=3), R=2(3)−2=6−2=4.


b) Formula for black squares (B) in terms of tile length (l):

Observing the pattern: B=L²−L

For example, for Tile 1 (L=3L = 3L=3), B=32−3=9−3=6

1.1.4 Completing Column 27


Tile no (n) 1 2 3 4 5 6 27
Tile length (L) 3 4 5 6 7 8 29
Number of red squares (R) 4 6 8 10 12 14 56
Number of black squares (B) 5 10 17 26 37 50 812
Total number of squares (S) 9 16 25 36 49 64 841


1.1.5 Showing the Algebraic Relationship

We need to show that (L−2)(L+2)=n(n+4)

a. Expand (L−2)(L+2):