"A 10-meter length of wire is available for making a circle and a square. How should the wire be distributed between the two shapes to maximize the sum of the enclosed areas?"Here's what I have: A r e a c = π r 2 A r e a s = 4 r 2 So, I'm thinking that I need to find the maximized radius size to figure everything else out. A r e a c + A r e a s = 10 ( π r 2 ) + ( 4 r 2 ) = 10 d d ⁡ r [ ( π r 2 ) + ( 4 r 2 ) − 10 ] = 2 π r + 8 rBut here's my dilemma; if I take the derivative of that and solve for r, it comes out 0. So I'm not sure where I'm going wrong. Any advice?

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&quot;A 10-meter length of wire is available for making a circle and a square. How should the wire be distributed between the two shapes to maximize the sum of the enclosed areas?&quot;Here&#039;s what I have:  A  r  e      a    c    =  π      r    2    A  r  e      a    s    =  4      r    2  So, I&#039;m thinking that I need to find the maximized radius size to figure everything else out.  A  r  e      a    c    +  A  r  e      a    s    =  10  (  π      r    2    )  +  (  4      r    2    )  =  10            d              d        ⁡        r              [  (  π      r    2    )  +  (  4      r    2    )  −  10  ]  =  2  π  r  +  8  rBut here&#039;s my dilemma; if I take the derivative of that and solve for r, it comes out 0. So I&#039;m not sure where I&#039;m going wrong. Any advice?

alisonhleel3 · Accepted Answer

If   r is the radius of the circle and   x is the side of the square then you are given that   2  π  r  +  4  x  =  10, or   x  =            10      −      2      π      r        4  . You want to maximize   π      r    2    +      x    2    =  π      r    2    +  (            10      −      2      π      r        4        )    2  . We know that   0  ≤  r  ≤  10. So now you need to differentiate   π      r    2    +  (            10      −      2      π      r        4        )    2  , find all critical points, and then compare the values of this function at the end points (  r  =  0 and   r  =  10) and also at the critical points.

Leland Morrow · Accepted Answer

You want to maximize   π      x    2    +      y    2   subject to   2  π  x  +  4  y  =  10,   x  ≥  0,   y  ≥  0.

"A 10-meter length of wire is available for making a circle and a square. How should the wire be dis

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