To find the value of y when w = 2, we need to follow these steps:
1. Find the value of x when w = 2 using the inverse proportionality relationship between x and w:
- Given that x = 2 when w = 0.2, x is inversely proportional to w. This means that as w increases, x decreases, and vice versa.
- Using the inverse proportionality formula, we can set up the equation: x₁ * w₁ = x₂ * w₂, where x₁ = 2, w₁ = 0.2, w₂ = 2, and x₂ is what we need to find.
- Plugging in the values and solving for x₂: 2 * 0.2 = x₂ * 2. Simplifying gives us x₂ = 0.2.
2. Now that we have x = 0.2, we can use the proportionality relationship between 14y and x² to find y:
- Given that 14y is proportional to x², this means that as x² increases, 14y will also increase proportionally.
- We know that y = 3 when x = 0.5. We can use this information to find the proportionality constant between 14y and x².
- Setting up the equation: 14y₁ = k * x₁², where y₁ = 3, x₁ = 0.5, and k is the proportionality constant. Solving for k: 14 * 3 = k * (0.5)². This gives us k = 168.
- Now that we have the proportionality constant, we can find y when x = 0.2: 14y = 168 * (0.2)². Calculating this gives us y = 1.344.
Therefore, when w = 2, the value of y is 1.344.
