In north america, i have photographed cactus plants from mexico to canada, and i think arizona cacti are the most beautiful.
which capitalized word is used as an adjective?

"Arizona" is the adjective in the sentence.

Explanation:

Adjectives are those words that add to, modify or describe a noun in a more specified way. They give more meaning and description to the nouns or pronouns they are associated to. In the following sentence-

"In North America, I have photographed cactus plants from Mexico to Canada, and I think Arizona cacti are the most beautiful."

the writer is talking of the various cactus plants that he/she had photographed. And among those, he finds the Arizona cacti the most beautiful. By naming the cacti as a specific being, 'Arizona' is used as an adjective in this case as it gives the description of the particular cactus that the narrator finds most beautiful.

are you asking true or false

the sentence does not violate the phrase structure second rule (introduced by noam chomsky) because noun phrases consist of a determiner such as a, the or every, and a noun. in the sentence, the noun phrase the cake includes a determiner (the) and a noun (cake).

on the other hand, the first rule indicates that a sentence encloses a noun phrase, followed by a verb phrase. the example sentence can be analysed as follows:

john (n) + ate (v) + the (det) + cake (n).