Learn Hardcore Latin: Servus in culina manet, ut cenam finire possit. - The servant stays in the kitchen so that he can finish the dinner.

Servus is the subject of the main verb manet (stays/remains). In Latin, the subject of a finite verb is typically in the nominative case, so servus is nominative singular: the slave.

What case is in culina, and why?

In culina uses in + ablative to express location (in/inside/on in the sense of “where?”).

culina is ablative singular of culina, -ae (f.) kitchen.
If Latin wanted motion toward (the question “where to?”), it would often use in + accusative instead.

How can I tell whether in takes the ablative or the accusative?

A common rule:

in + ablative = location (where?) → in culina = in the kitchen
in + accusative = motion toward (where to?) → in culinam = into the kitchen
This sentence is about staying in a place, so it uses the ablative.

What tense and meaning does manet have?

Manet is of ().So it means .