# Science:Math Exam Resources/Courses/MATH103/April 2009/Question 05 (c)

MATH103 April 2009
Other MATH103 Exams

### Question 05 (c)

A carrot has the shape formed by revolving the region under the graph of

$f(x)={\sqrt {14-x}}$ for $0\leq x\leq 12$ cm about the x axis. The concentration of vitamin A is found to vary in the carrot with x according to

$c(x)={\frac {1}{12}}e^{-x/12}{\frac {\text{mg}}{{\text{cm}}^{3}}}$ You want to cut the carrot at a certain value of x, obtaining two pieces of equal volume. How many centimeters from x = 0 do you have to cut?

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