Lethargic means "sluggish", kind of inactive
Vital means full of energy, lively
So, they are antonyms
So, for the 2nd part of the analogy, you are looking for a antonym to trite
Trite means lacking originality or freshness. Overused. Kind of like a cliche
So, an antonym could be original, unique, innovative
The answer is: directional research hypothesis
directional research hypothesis is a form of prediction that initiated in order to guess whether two variables would experience some sort of positive or negative changes. In the example above, boys and girls are the variables and whether they agree or disagree with school rules are the changes.
Answer:

Explanation:
The volume of a rectangular box is given by;

It was given that, the volume of the box is V=8 cubic inches.
The length of the box is l=2 inches.
Let the width of the box be x inches.
The height of the box is 3 inches more than the width. That is

We now substitute all values into the formula to get:

Therefore the required equation is
