Question

Y is inversely proportional to the square of x.

A table of values for x and y is shown.

X 1 2 3 4
Y 4 1 4/9 1/4
a, Express y in terms of x.
b, work out the positive value of x when y = 25

Answer 1

Part a

y is inversely proportional to the square of x.

That means there's some proportionality constant k such that

y = k/x²

We have points (1,4), (2,1), (3,4/9), (4,1/4)

4 = k/1² = k

y = f(x) = 4/x²

We check the other points, f(2)=1, good, f(3)=4/9 good, f(4)=1/4 good

Answer: y=4/x²

Part b, y=25

25 = 4/x²

x² = 4/25

x = 2/5

Answer: 2/5