anonymous
  • anonymous
Optimization question: Find the dimensions of a rectangle of largest area that can be inscribed in the circle x^2 + y^2=9
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
what is the area?
amistre64
  • amistre64
its a square.... just to let you know ;)
anonymous
  • anonymous
can you please help me out and tell me how to get the solution?

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amistre64
  • amistre64
the solution to this is to just use 1/4 of the circle the part that lies in the first qudrant
amistre64
  • amistre64
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...
anonymous
  • anonymous
yes i got y= square root of 9-x^2
amistre64
  • amistre64
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
amistre64
  • amistre64
y = ... is fine to; doesnt matter lol
anonymous
  • anonymous
lol okay then just substitute inside the equation A=xy
amistre64
  • amistre64
yes; then derive :)
anonymous
  • anonymous
okay thank you so much
amistre64
  • amistre64
just to let you know; the optimum is at 45 degrees; or rather when y = 9sin(45) :)
anonymous
  • anonymous
okay thank you

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