To answer these questions thoroughly, let's proceed step-by-step.
Question 2.1.1
To determine the values of [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex]:
From the table, we know:
- 1 labourer takes 30 days.
- 2 labourers take 15 days.
- 3 labourers take 10 days.
- 10 labourers take 2 days.
From this information, we observe that as the number of labourers increases, the number of days decreases in proportion. This suggests an inverse proportionality relationship, where the product of the number of labourers and days should be constant.
Let’s denote this constant as [tex]\( k \)[/tex]:
[tex]\[ \text{Number of labourers} \times \text{Number of days} = k \][/tex]
Using the data for 1 labourer:
[tex]\[ 1 \times 30 = 30 \][/tex]
Thus, [tex]\( k = 30 \)[/tex].
Now calculate [tex]\( A \)[/tex] for 5 labourers:
[tex]\[ 5 \times A = 30 \][/tex]
[tex]\[ A = \frac{30}{5} = 6 \][/tex]
Next, calculate [tex]\( B \)[/tex] for 4 labourers:
[tex]\[ 10 \times 2 = 30\][/tex] [tex]\[ 4 \times B = 30 \][/tex]
[tex]\[ B = \frac{30}{10} = 3 \][/tex]
Lastly, we need to find [tex]\( C \)[/tex]. Given the relationship, as there are 10 labourers and they take 2 days:
[tex]\[ \text{Constant} = 30 \][/tex]
[tex]\[ C = \frac{30}{2} = 15 \][/tex]
Values are:
[tex]\[ A = 6 \][/tex]
[tex]\[ B = 3 \][/tex]
[tex]\[ C = 15 \][/tex]
Question 2.1.2
Based on the table and the calculations, the relationship between the number of labourers and the number of days is an example of "Inverse proportionality." This means that doubling the number of labourers would halve the time required, and so forth.
Question 2.1.3
The formula that correctly represents the relationship between the number of days and the number of labourers, where:
[tex]\[ \text{Number of days} \times \text{number of labourers} = 30 \][/tex]
So, the correct choice from the options given is:
[tex]\[ A \text{ Number of days} \times \text{number of labourers} = 30 \][/tex]
Answer: 1 (A)
Question 2.1.4
For the graph, you would plot the number of labourers on the horizontal axis (x-axis) and the number of days on the vertical axis (y-axis). You should label the axes as follows:
- Horizontal axis (x): Number of labourers
- Vertical axis (y): Number of days
The points you would plot based on the data would be:
- (1, 30)
- (2, 15)
- (3, 10)
- (5, 6)
- (10, 2)
The graph should be titled: "Number of Labourers vs. Number of Days to Complete the Job."
The relationship will appear as a hyperbolic curve, indicating the inverse proportional relationship between the number of labourers and the number of days taken to complete the job.
So, marking and labeling these points properly on the graph will illustrate the relationship clearly.
