two sentence of inverse variation
Answer (1)
Answer:Here are two sentences about inverse variation: 1. As the number of workers on a project increases, the time it takes to complete the project decreases, assuming their work rate stays constant.2. The volume of a gas decreases proportionally as the pressure applied to it increases, at a constant temperature.Step-by-step explanation:Here's a step-by-step explanation of inverse variation, using the examples from the previous response: 1. Understanding Inverse Variation - Inverse variation describes a relationship between two variables where an increase in one variable leads to a proportional decrease in the other variable.- This means that the product of the two variables remains constant. 2. Example 1: Workers and Time - Variables:- Number of workers (x)- Time to complete the project (y)- Relationship: As the number of workers (x) increases, the time to complete the project (y) decreases.- Constant Product: If you multiply the number of workers by the time, you get a constant value. For example, if 2 workers take 10 hours, then 4 workers would take 5 hours (2 * 10 = 4 * 5 = 20). 3. Example 2: Gas Volume and Pressure - Variables:- Volume of gas (V)- Pressure applied (P)- Relationship: As the pressure applied (P) increases, the volume of gas (V) decreases.- Constant Product: The product of volume and pressure remains constant (at a constant temperature). This is represented by Boyle's Law: P₁V₁ = P₂V₂. 4. Key Points - Inverse Proportionality: Inverse variation is also known as inverse proportionality.- Equation: The general equation for inverse variation is y = k/x, where k is a constant.- Graph: The graph of an inverse variation is a hyperbola. In essence, inverse variation describes a relationship where an increase in one variable causes a reciprocal decrease in the other, keeping their product constant.
