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

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

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

The sum of the squares of all the roots of the equation $x^{2}+|x+4|+|x-4|-35=0$ is

The number of pairs $(x, y)$ of integers satisfying the inequality $|x - 5| + |y - 5| \leq 6$ is:

The minimum value of $f(x)=|3-x|+|2+x|+|5-x|$ is equal to __________.