A circle, centre $O$ and radius $r \mathrm{~cm}$, has a sector $O A B$ of fixed area $10 \mathrm{~cm}^{2}$. Angle $A O B$ is $\theta$ radians and the perimeter of the sector is $P \mathrm{~cm}$. (ii) Find the value of $r$ for which $P$ has a stationary value.
Explanation
To find the value of $r$ for which $P$ has a stationary value, we need to find the value of $r$ that makes the derivative of $P$ with respect to $r$ equal to zero. We can use the chain rule to find the derivative of $P$ with respect to $r$. Then, we can set the derivative equal to zero and solve for $r$. This will give us the value of $r$ for which $P$ has a stationary value.
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