If Y varies inversely as X^2, determine what Y would be if X = 2 and another point on the equation is (1,8).
To determine the value of Y when X = 2 and another point on the equation is (1, 8), we need to use the inverse variation formula.
Inverse variation is represented by the relationship: Y = k/X^2, where k is the constant of variation.
To find k, we can substitute the values of X and Y from the second point (1, 8) into the formula:
8 = k/1^2
Simplifying, we have:
8 = k/1
Multiply both sides by 1:
k = 8
Now that we have the value of k, we can use it to find the value of Y when X = 2.
Y = k/X^2
Substituting the known values:
Y = 8/2^2
Simplifying:
Y = 8/4
Y = 2
Therefore, when X = 2, Y equals 2.