The end for example cat touched the hat
There are two prepositional phrases in this sentence:
1. into the little shops
2. across the street
After we finished lunch is not a prepositional phrase, because the word after is used as a conjunction, not a preposition.
The best way to revise the sentence is <em>#2. I had to prove my identity to gain entrance to the building; I was required to fill out an impressive number of forms. </em>
Answer:
The connection between the recurrence and frequency of a wave is given by the condition: v=λf, where v is the speed of the wave, λ is the frequency and f is the recurrence. From here we see that the frequency and recurrence are contrarily relative.