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anonymous

  • 5 years ago

Optimization question: Find the dimensions of a rectangle of largest area that can be inscribed in the circle x^2 + y^2=9

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  1. anonymous
    • 5 years ago
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    what is the area?

  2. amistre64
    • 5 years ago
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    its a square.... just to let you know ;)

  3. anonymous
    • 5 years ago
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    can you please help me out and tell me how to get the solution?

  4. amistre64
    • 5 years ago
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    the solution to this is to just use 1/4 of the circle the part that lies in the first qudrant

  5. amistre64
    • 5 years ago
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    we know the are of the 'rectangle' = xy right? and our 'line' is full of x and y options; so lets use the equation to define x or y in terms of the other...

  6. anonymous
    • 5 years ago
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    yes i got y= square root of 9-x^2

  7. amistre64
    • 5 years ago
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    x^2 + y^2 = 9 x^2 = 9 - y^2 x = sqrt(9-y^2) ; use this value of 'x' in the rectangle area equation

  8. amistre64
    • 5 years ago
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    y = ... is fine to; doesnt matter lol

  9. anonymous
    • 5 years ago
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    lol okay then just substitute inside the equation A=xy

  10. amistre64
    • 5 years ago
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    yes; then derive :)

  11. anonymous
    • 5 years ago
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    okay thank you so much

  12. amistre64
    • 5 years ago
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    just to let you know; the optimum is at 45 degrees; or rather when y = 9sin(45) :)

  13. anonymous
    • 5 years ago
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    okay thank you

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