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MIP1502 ASSIGNMENT 4 S2 2024
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MIP1502ASSIGNMENT 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):
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