Chapter Test
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What is inductive reasoning? How are the given equivalences related? Do they follow a pattern?
40°C= 104 °F
Temperature in °C | Temperature in ° F |
---|---|
10 | 50 |
20 | 68 |
30 | 86 |
40 | ? |
We can see that there is a clear pattern. Each time the temperature in °C rises by 10, the equivalent in °F rises by 18.
Temperature in ° C | Temperature in ° F |
---|---|
10 | 50 |
10 + 10 = 20 | 50 + 18 = 68 |
20 + 10 = 30 | 68 + 18 = 86 |
30 + 10 = 40 | 86 + 18 = 104 |
Furthermore, following the same rule, if we start from 10 ° C = 50 ° F and move backwards, we can see that these two expressions are equivalent. 10- 10 &= 0 ° C 50- 18 &= 32 ° F We can use this to create a general formula. Starting from 0 ° C = 32 ° F, and considering that each time the temperature in ° C rises by 10, the equivalent in ° F rises by 18. We can write the equation. ° F = 18/10° C + 32