In the final sentence of this passage we read: "The frontiers of science do not end in knowledge but are _____ to the formation of appliances for actual use." Choose the option that best completes the blank to show how scientific knowledge leads to practical applications.

Introduction / Context:
This cloze test question completes the author's argument about science. After explaining that scientific theories must be supported by tangible proof and that they yield material comforts, the passage states that the frontiers of science do not stop at knowledge itself. Instead, they reach outward into the realm of useful applications. The blank describes this reaching out, and you must select a verb that captures the idea of stretching from pure knowledge into technology.

Given Data / Assumptions:

• Sentence: The frontiers of science do not end in knowledge but are _____ to the formation of appliances for actual use.
• The passage highlights that science moves beyond theory to create tools and appliances.
• Options: implied, associated, designated, extended.
• We need a word that shows continuation or stretching beyond a limit.

Concept / Approach:
The phrase frontiers of science suggests boundaries that can be pushed outward. The contrast do not end in knowledge but are [blank] to the formation of appliances signals that the boundaries go beyond pure theory into practical production. Extended is the natural verb for this context, as it means stretched out or carried further. Implied means suggested indirectly, associated means connected, and designated means officially named or assigned. None of these alternatives clearly express the idea of boundaries pushing outwards from knowledge to application.

Step-by-Step Solution:
Step 1: Focus on the phrase do not end in knowledge. This tells you that the boundaries of science go further than simple understanding. Step 2: Consider what the boundaries go into: the formation of appliances for actual use. This means science leads to practical devices and technologies. Step 3: Examine extended. The frontiers of science are extended to the formation of appliances is a natural way to say that the reach of science continues beyond knowledge into application. Step 4: Evaluate implied. If frontiers were implied to the formation of appliances, the sentence would be unclear and unidiomatic, because frontiers themselves are not described as implied to something. Step 5: Evaluate associated. Associated suggests a loose connection, not a continuation or stretching of boundaries, so it does not match the image of frontiers moving outward. Step 6: Evaluate designated. Designated is usually used with positions and roles, such as designated leader, and does not describe the movement of frontiers. Step 7: Conclude that extended is the only option that sensibly describes how the frontiers of science reach into the world of practical appliances.

Verification / Alternative check:
Insert extended and read the sentence with the rest of the passage: The frontiers of science do not end in knowledge but are extended to the formation of appliances for actual use. This clearly summarises the idea that scientific investigation leads not just to understanding but also to practical devices that improve everyday life. Substituting implied, associated, or designated makes the sentence confusing or ungrammatical, because these words do not match the metaphor of frontiers.

Why Other Options Are Wrong:
Implied would normally require a subject such as meaning or intention and does not pair with frontiers in this way. Associated implies a link without direction or movement and fails to show that the boundaries of science move from one area to another. Designated is used to label people or places and therefore does not fit with the description of scientific progress.

Common Pitfalls:
In cloze tests, some students pick associated because it feels comfortably vague and often appears in academic writing. However, the best strategy is to pay attention to metaphors in the sentence. The metaphor of frontiers suggests movement, expansion, and extension, all of which align with extended. Once you recognise this, it becomes much easier to eliminate options that do not support the image of science pushing its boundaries into new domains.

Final Answer:
The correct completion is extended, so the sentence reads: The frontiers of science do not end in knowledge but are extended to the formation of appliances for actual use.