Given that y = 3 for x = 1 and x varies inversely as , then find the value of x for y =12.

Given that y = 3 for x = 1 and x varies inversely as y, we can use the inverse variation formula to find the value of x for y = 12.

The inverse variation formula states that if two variables, x and y, vary inversely, then their product remains constant. Mathematically, this can be represented as xy = k, where k is the constant of variation.

In this case, we know that y = 3 when x = 1. So, we can substitute these values into the formula to find the value of k:

(1)(3) = k 3 = k

Now that we have the value of k, we can use it to find the value of x when y = 12. Again, we substitute the values into the formula:

x(12) = 3 12x = 3 x = 3/12 x = 1/4

Therefore, when y = 12, the value of x is 1/4.