"The woman studies and writes."
Translation:Femina studet et scribit.
Studet (he/she/it studies) is the third person singular present of studere which is a second conjugation verb. We use this form since femina is singular and tells us it is third person.
Studeo -> I study
Studes -> You (singular) study
Studemus -> We study
Studetis -> You (plural) study
Student -> They study
Sed "studeo" "i'm trying hard/ I work hard" est, non "study". "Study" descire est.
"studere" is most literally "to be eager", but it also means "to apply oneself" and is the usual word for "to study" in the academic sense, and is used thus by Quintilian, Cicero, and others.