Which of the following explains the purpose of the federalist essays?

a. the essays outlined the strengths of the constitution.
b. the essays outlined the weaknesses of the constitution.
c. the essays supported keeping the colonies independent from one another.
d. the essays asked the government to abolish slavery.

The essays outlined the strengths of the Constitution, is the right answer.

The Federalist Papers are a series of 85 articles, which gave assistance to the Constitution of the United States.  These 85 articles were drafted by Alexander Hamilton, John Jay, and James Madison under the pen name Publius. These articles act as the description of the newly proposed laws under the constitution to the people of U.S, in the hope of encouraging them to sanction the new constitution in the upcoming convention. These papers are considered as the most important source for translating and understanding the original purpose of the Constitution.

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to act quickly in times of danger to the united states

because you have to act quickly if you want to live/survive.