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Question
If the mass m(x) (in kilograms) of a thin rod of length x (in metres) is given by, m(x) = `sqrt(3x)` then what is the rate of change of mass with respect to the length when it is x = 3 and x = 27 metres
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Solution
Mass m (x) = `sqrt(3x) = sqrt(3) sqrt(x)`
Ratre of change `"dm"/("d"x) = "m'"(x) = sqrt(3) 1/(2sqrt(x))`
When x = 3, m'(x) = `sqrt(3)/2 1/sqrt(3) = 1/2` kg/m
When x = 27, m'(x) = `sqrt(3)/2 1/sqrt(27)`
= `sqrt(3)/2 1/(3sqrt(3)`
= `1/6` kg/m
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