If Y varies inversely as X^2, determine what Y would be if X = 2 and another point on the equation is (1,8).
The answer I got was y=1/2^2=1/4
I'm not sure I worked this out correctly, is this correct?
no.
y=k/x^2 then consider the point 1,8
8=k/1^2 k=8
y=8/x^2
if x is 2, then y=2
another way to think this out: y is 8 when x is one, so if you double x, then y must be changed by 1/4, or y=2
Thank you!
To determine the value of Y when X = 2, you can use the concept of inverse variation. Inverse variation means that as one variable (X) increases or decreases, the other variable (Y) will decrease or increase respectively, but in an inverse proportion.
The equation for inverse variation can be written as Y = k / X^2, where k is a constant.
To find the value of k, we can use the other point on the equation, (1, 8). Substituting this point into the equation, we get 8 = k / 1^2, which simplifies to 8 = k.
So, the equation becomes Y = 8 / X^2.
Now, we can substitute X = 2 into the equation:
Y = 8 / (2^2)
Y = 8 / 4
Y = 2
Therefore, when X = 2, Y is equal to 2.
It seems that there was an error in the answer you obtained. Y should be equal to 2 when X = 2, not 1/4.