MIP1502 ASSIGNMENT 4 2024 (SEMESTER 2)

PREVIEW

1.2.4 The caterer has to cook the beef stew for 40
guests. Each guest is expected to consume 200
g of stew. How long will it take to cook the stew?

First, we need to calculate the total mass of beef
needed for 40 guests. Each guest consumes 200
grams, so for 40 guests:

Total mass=40×200 grams=8000 grams=8 kilograms

Now, using the formula t=45m+40 with m=8kg:

t=45(8)+40=360+40=400

So, it will take 400 minutes to cook the stew for 40
guests.

MIP1502 Natalie Foxx
ASSIGNMENT 4
SEMESTER 2
2024

, 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)