formulated

Formulated is the past participle of the verb formulate and is used as both a verb form and an adjective. As an adjective, it describes something that has been devised, developed, or stated according to a plan, formula, or method. This can apply to ideas and theories that have been articulated clearly, as well as to products or compounds prepared according to a specific formulation.

Etymology and related forms: Formulate comes from Latin formulare, from forma meaning form or shape. The related noun formulation refers to the act or process of creating a formulation, and to the actual mixture or recipe of ingredients in a product. The term is common in scientific, technical, and policy contexts.

Usage and contexts: In science and industry, formulated products are those prepared according to a defined recipe or composition, such as formulated drugs, cosmetics, or cleaners. In research, a hypothesis or theory may be formulated, meaning it has been developed and presented in precise terms. In mathematics or logic, a problem or proposition can be formulated to express it clearly and unambiguously.

Examples: The researchers formulated a new hypothesis based on the observed data. The vaccine was formulated to balance efficacy with stability. The company markets a formulated shampoo designed to deliver specific active ingredients. The theorem was carefully formulated to avoid ambiguity.

Overall, formulated emphasizes deliberate construction, specification, and documentation of a plan, theory, or composition, often with an emphasis on repeatability and clarity.