To find the formula connecting the values of w and x, we need to determine the relationship between them based on the given information.
Let's break down the problem into two parts:
Part 1: The quantity is partly constant:
When w=1, x=11
When w=2, x=5
Here, we notice that as w increases from 1 to 2, x decreases from 11 to 5. This means that there is no direct relationship between w and x when the quantity is constant.
Part 2: The quantity varies inversely as the square of x:
Let's assume the formula connecting w and x is:
w = k / (x^2)
where k is a constant.
Using the given data:
When w=1, x=11:
1 = k / (11^2)
1 = k / 121
Solving for k:
k = 121
Therefore, the formula connecting w and x is:
w = 121 / (x^2)
To find w when x=4, substitute the value of x into the equation:
w = 121 / (4^2)
w = 121 / 16
w ≈ 7.5625
So, when x=4, the value of w is approximately 7.5625.