complete the table that shows the length of the chain formed when rings are liked in a staright line

1)number of rings 1
length of chain 16mm
2)number of rings 2
length of chain 30m
3)number of rings 3
length of chain 44m
4)number of rings 6
length of chain ( )
5)number of rings ( )
length of chain 170mm

To complete the table, we need to find the pattern or relationship between the number of rings and the length of the chain. Let's analyze the given data:

1) When there is 1 ring, the length of the chain is 16mm.
2) When there are 2 rings, the length of the chain is 30mm.
3) When there are 3 rings, the length of the chain is 44mm.

From the given data, we can observe that each additional ring adds 14mm to the length of the chain. So, we can determine that there is a linear relationship between the number of rings and the length of the chain.

Using this pattern, we can determine the missing values:

4) When there are 6 rings:
To find the length of the chain with 6 rings, we need to know the base length. Based on the pattern, the base length should be 16mm because it is the length when there is 1 ring.
Now, to calculate the total length of the chain, we can multiply the number of additional rings (6-1=5) by the added length per ring (14mm).
Length of chain with 6 rings = Base length + (Number of additional rings * Added length per ring)
Length of chain with 6 rings = 16mm + (5 * 14mm)
Length of chain with 6 rings = 16mm + 70mm
Length of chain with 6 rings = 86mm

5) When the length of the chain is 170mm:
To find the number of rings required to achieve a chain length of 170mm, we again need to know the base length. We know that the base length is 16mm because it is the length with 1 ring.
First, we need to subtract the base length from the given total length to get the additional length added by the additional rings.
Additional length = Total length - Base length
Additional length = 170mm - 16mm
Additional length = 154mm
Now, we can divide the additional length by the added length per ring (14mm) to find the number of additional rings.
Number of additional rings = Additional length / Added length per ring
Number of additional rings = 154mm / 14mm
Number of additional rings ≈ 11.
Since we already had 1 ring, the total number of rings required to achieve a chain length of 170mm is the number of additional rings + 1.
Total number of rings = Number of additional rings + 1
Total number of rings ≈ 11 + 1
Total number of rings ≈ 12

So, the completed table would look like this:

1) Number of rings: 1
Length of chain: 16mm

2) Number of rings: 2
Length of chain: 30mm

3) Number of rings: 3
Length of chain: 44mm

4) Number of rings: 6
Length of chain: 86mm

5) Number of rings: 12
Length of chain: 170mm