Question

1. find the c.o.p. of this table:

minutes	feet
2	24
3	36
4	44

Explanation:

Step1: Recall C.O.P formula

The Constant of Proportionality (C.O.P) for a proportional relationship is given by \( \text{C.O.P} = \frac{y}{x} \), where \( y \) is the dependent variable (Feet) and \( x \) is the independent variable (Minutes). But first, we need to check if the relationship is proportional. For a proportional relationship, the ratio \( \frac{y}{x} \) should be constant for all pairs.

Step2: Check ratios for each pair

• For \( x = 1, y = 12 \): \( \frac{12}{1} = 12 \)
• For \( x = 2, y = 24 \): \( \frac{24}{2} = 12 \)
• For \( x = 3, y = 36 \): \( \frac{36}{3} = 12 \)
• For \( x = 4, y = 44 \): \( \frac{44}{4} = 11 \)

Wait, there's a mistake here. Wait, the last pair: 4 minutes and 44 feet. But 412=48, not 44. So maybe a typo? But assuming the first three are correct (since 1-3 have consistent ratio), or maybe I miscalculated. Wait 44 divided by 4 is 11, but 124=48. So perhaps the table has an error, but if we consider the first three, the C.O.P is 12. But let's check again. Wait, maybe the problem is that the last entry is wrong, but in proportional relationships, the ratio should be constant. So for the first three, the ratio is 12. Let's proceed with the first three as they are consistent.

Step3: Determine C.O.P

Since for \( x = 1,2,3 \), \( \frac{y}{x} = 12 \), so the C.O.P is 12 (ignoring the last entry as it might be a typo, or maybe I misread). Wait, 44 feet in 4 minutes: 44/4=11, which is different. So maybe the table is not proportional? But the question says "Find the C.O.P", so maybe the last entry is a mistake. So we take the consistent ratio from the first three.

Answer:

12 (assuming the last entry is an error, and the relationship is proportional with C.O.P 12 from the first three pairs)