Final answer:
In mathematics dealing with inverse proportionality, with the given values y=250 when x=0.2, the constant of proportionality is found to be 2. Using this, the value of y when x=0.5 is calculated to be 16.
Step-by-step explanation:
The relationship described in the student's question indicates that y is inversely proportional to the cube of x. This means that y can be described by the equation y = k/x^3, where k is a constant of proportionality. When y=250 and x=0.2, we can find the constant k by plugging in these values:
- 250 = k / 0.2^3
- k = 250 * (0.2)^3
- k = 250 * 0.008
- k = 2
With the constant k found, we can now determine the value of y when x=0.5:
- y = k / 0.5^3
- y = 2 / (0.5)^3
- y = 2 / 0.125
- y = 16
Therefore, when x is 0.5, the value of y is 16.