Answer :

Final answer:

The student's question about the life cycle of the trachea mite seems to confuse the trachea with the digestive system. Trachea is actually part of the respiratory system in many arthropods, facilitating gas exchange via a network of tubules and spiracles. While the specific life cycle of trachea mites depends on the species, it typically involves several developmental stages from egg to adult.

Explanation:

The student has asked about the life cycle of the trachea mite, which is closely related to the respiratory tracheae found in some arthropods. However, to clarify, the question seems to be based on a misunderstanding since the trachea is not part of the digestive system. In insects and some other arthropods, it is a part of the respiratory system. Let's address the life cycle of a generic arthropod pest as it relates to the tracheal system.

While the question mentions trachea mites, there is insufficient context about which specific mite species is being referred to. Generally, mites have a basic life cycle that includes stages such as egg, larva, protonymph, deutonymph, and adult. During their lifecycle, specific mites known as tracheal mites may infest the tracheae of insects, particularly the honeybee, through the spiracles.

It is important that we understand that the tracheal system is designed for breathing in terrestrial arthropods and operates through a network of tubules and spiracles which take air directly to tissues for gas exchange.