Final answer:
An inverse variation relationship exists when y varies inversely with x, and if y=a when x=a^2, then the inverse variation equation relating x and y is y = a^3 / x. As per the inverse variation formula, if any variable x is inversely proportional to another variable y, then the variables x and y are represented by the formula: xy = k or y=k/x where k is any constant value.
Step-by-step explanation:
When a student asks that 'Suppose y varies inversely with x, and y = a when x = a2. What inverse variation equation relates x and y ?', we need to establish the equation that defines an inverse relationship between two variables.
In an inverse variation, the product of the two variables is constant. Therefore, if y varies inversely as x, and y = a when x = a2, then the constant can be found by multiplying the two known values. Thus, the constant k = a * a2 = a3.
So, the inverse variation equation that relates x and y would be y = k/x, and since we know that k = a3, the equation becomes y = a3 / x.
In Maths, inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value. It states if the value of one quantity increases, then the value of the other quantity decreases.
Sometimes, we observe that the variation in values of one quantity is just opposite to the variation in the values of another quantity. If the value of one quantity increases, the value of the other quantity decreases in the same proportion and vice versa. This is termed inverse variation and the two quantities are said to be inversely proportional to each other.