What is the purpose of the paean?
to honor the gods
to entertain the audience
to create conflict
to provide exposition

The purpose of the paean is to honor the gods. (First option).

According to Greek mythology, they honored and respect God so much. Greeks have a strongly believed in god or goddesses, they used stories about it to tell and explain the unknown things that happened around them such as the moon, the sun, and stars.

That being said, the Paean is a song or a hymn used to be thankful about anything, it is used to show appreciation/ adulation. The song was sung by the Greek population to any Grek god or goddesses.

The answer is to honor the gods.  The paean was a song of thanks giving usually sung by a chorus.  It was sung to any Greek God.  Apart from honoring the gods, it also was sung to avert misfortune and protection from disease.  

the federal government of the united states was established by the constitution. us is a presidential republic. the president is head of state, head of government and of a two party legislative and electoral system. the supreme court balances the powers of the federal and the state government. yhe executive branch is headed by the oresident. there are two chambers of congress, the senate and the house of representatives. judicial power is exercised by the judicial branch (or judiciary), comprised of the supreme court and lower federal courts. the judiciary's function is to interpret the   constitution as well as the federal laws and regulations.

i think it is the third one.