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A-CED.3 Warmup M3-010-A06-V02

Represent constraints and systems, then interpret viable and non-viable solutions in modeling contexts.

Interpret a modeling boundary with equality, inclusion, and feasible side

Problem

An increasing design volume \(V(x)\) must satisfy \(V(x)~\le~500~\text{cubic}~\text{units}\), with \(V(5)~=~500\) and positive \(x\) in centimeters. State the boundary, inclusion, feasible side, and meaning.

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At x=5 centimeters, V(5)=500 cubic units, so the boundary is included. Positive feasible designs have x≤5 because 5 is the largest allowed parameter.

At x=5 centimeters, V(5)=500 cubic units, and designs with x≥5 remain within capacity.

V(5)=500 does not identify a capacity boundary.

At x=5 centimeters, V(5)=500 cubic units, but only 0<x<5 is feasible.

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Curriculum context

Course: Math III
Standard: A-CED.3
Category: Algebra
Domain: Creating Equations
Objective: Represent constraints and systems, then interpret viable and non-viable solutions in modeling contexts.
Problem type: Interpret a modeling boundary with equality, inclusion, and feasible side