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 $P \mathrm{~cm}$. (iv) Find the value of $\theta$ at this stationary value.
Explanation
To find the value of $\\theta$ at the stationary value, we can use the fact that the derivative of $P$ with respect to $\\theta$ is equal to zero at the stationary value. We can use the chain rule to find the derivative of $P$ with respect to $\\theta$. Then, we can set the derivative equal to zero and solve for $\\theta$. This will give us the value of $\\theta$ at the stationary value.
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