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The domain of the function h(x) = sqrt(81-x^2) + sqrt(-(x-10)) is an interval of what width?

 Nov 19, 2020
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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

 

 

cool cool cool

 Nov 19, 2020

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