The domain of the function h(x) = sqrt(81-x^2) + sqrt(-(x-10)) is an interval of what width?
sqrt (81 - x^2) + sqrt (-(x - 10)) we can write
sqrt (81 - x^2) + sqrt ( 10 - x)
As long as the values for x under each radical don't produce a negative value for the expression in the radical, they will be in the domain
Considering the first radical x can take on the vaues [ -9, 9]
Considering the second radical, x can take on the values (-inf, 10 ]
We need to take this most restrictive interval.....this is the first = [ -9, 9]
[the interval width = 18 ]
The graph here confirms this : https://www.desmos.com/calculator/nvq8fnqsun