The area enclosed by the curve $2|x| + 3|y| = 6$ is

If $|x+1| + (y+2)^2 = 0$ and $ax - 3ay = 1$, then the value of $a$ is

The length of the line segment joining the two intersection points of the curves $y = 4970 - |x|$ and $y = x ^ 2$ is

If $a, b, c$ are three distinct natural numbers, all less than $100$, such that $|a - b| + |b - c| = |c - a|$, then the maximum possible value of $b$ is ______

If $n$ is an integer such that $\frac{|n+6|-|n-3|}{\sqrt{100-n^3}} \geq 0$, then the number of possible values of $n$ is ___

For $a > b > c > 0$, the minimum value of the function $f(x) = |x - a| + |x - b| + |x - c|$ is

Given that $f(x)=|x|+2|x-1|+|x-2|+|x-4|+|x-6|+2|x-10|, x \in(-\infty, \infty)$ the minimum value of $f(x)$ is _________.