MIP1502 ASSIGNMENT 4 2024

MIP1502
ASSIGNMENT 4
ANSWERS 2024




MIP1502 ASSIGNMENT 4 ANSWERS 2024
Due date: 16 August 2024

,MIP1502

Assignment 4: Compulsory

Contributes 25% to the final pass mark

Unique number: 397869

Due date: 16 August 2024




Question 1

1.1 A tiling pattern is made by arranging black and red squares, as shown below:\

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

complete the table below for tile numbers 5 and 6 (6 points):




To find the missing values for tile numbers 5 and 6, let's first check the patterns in

the given data:




- The number of red squares \( R \) follows an arithmetic sequence with a common

difference of 2:

- 4, 6, 8, 10 ...

, - It appears to be \( R = 2n + 2 \).




- The number of black squares \( B \):

- 5, 10, 17, 26...

- The difference progresses as follows:

- Difference: 5, 7, 9 (which increases by 2 each time)

- Therefore, it appears to follow a quadratic sequence. We can express this as a

polynomial equation.




To calculate the total squares \( S \) for tile numbers 5 and 6:

- The total number of squares seems to be the square of the tile length \( l \).

- The relationship \( S = l^2 \); where \( l \) is 3 (for tile number 1), so it is likely that

each tile length is \( n + 2 \).




Assuming tile number \( n \):

- For \( n = 5 \), \( l \) would equal 5, and for tile \( n = 6 \), \( l \) would equal 6.

Hence, squares will be:

- \( 5^2 = 25 \)

- \( 6^2 = 36 \)