If f(x) varies directly with x2, and f(x) = 40 when x = 2, find the value of f(6). 36 60 120 360

The answer is 360.
f(x) varies directly with x^2 and f(2) = 40. What does that mean?
It means this f(x) = k* x^2. We need to find k.
For x=2, f(x) = 40, this means k* x^2 = 40. BUT, x=2.
This means p* 2^2 = 40. => k = 40 / 4 = 10.
We just found what f(x) is: f(x) = 10x^2.
Now, what is the value of f(6)?
Just replace the value of k by 10. => f(6) = 10* 6^2 = 10*36 = 360

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