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Math Help - Optimizations... Clueless

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    Optimizations... Clueless

    Optimizations... Clueless-untitled.jpg
    Consider a symmetric cross inscribed in a circle of radius r:

    A. Write the area A of the cross as a function of x and find the value of x that maximizes the area.
    B. Write the area A of the cross as a function of θ and find the value of θ that maximizes the area.
    C. Show that the critical numbers of parts (a) and (b) yield the same maximum area. What is that area?


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  2. #2
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    Quote Originally Posted by ursapine View Post
    Consider a symmetric cross inscribed in a circle of radius r:

    A. Write the area A of the cross as a function of x and find the value of x that maximizes the area.
    B. Write the area A of the cross as a function of θ and find the value of θ that maximizes the area.
    C. Show that the critical numbers of parts (a) and (b) yield the same maximum area. What is that area?
    A = 6x\sqrt{r^2-x^2} , 0 < x < r

    A = 3r^2\sin(2\theta) , 0 < 2\theta < \frac{\pi}{2}
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    Last edited by ursapine; November 10th 2010 at 05:15 AM.
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