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  • Nov 12, 2007, 11:11 AM
    helpless06
    Area and Systems
    FInd the area of the figure given on the coordinate plane (XOY) as a system of inequalities:
    x(x + y - sqrt2) < 0
    x^2 + y^2 < 2
  • Nov 12, 2007, 11:13 AM
    CaptainRich
    https://www.askmehelpdesk.com/other-...board-b-u.html
  • Nov 12, 2007, 05:58 PM
    nycfunction
    Quote:

    Originally Posted by helpless06
    FInd the area of the figure given on the coordinate plane (XOY) as a system of inequalities:
    x(x + y - sqrt2) < 0
    x^2 + y^2 < 2


    Where's the figure? Your question states "figure given" but you forgot to upload the picture of the figure.
  • Nov 13, 2007, 06:42 PM
    terryg752
    Quote:

    Originally Posted by helpless06
    FInd the area of the figure given on the coordinate plane (XOY) as a system of inequalities:
    x(x + y - sqrt2) < 0
    x^2 + y^2 < 2

    x^2 + y^2 < 2

    The above figure consists of all points within the circle x^2 + y^2 = 2 i.e. circle whose centre is the Origin and whose radius is sqrt 2

    Regarding second condition: x(x + y - sqrt2) < 0

    This is possible when

    1. x is negative but x + y - sqrt2 is positive.

    Note: x + y - sqrt2 = 0 is a straight line as follows:

    Suppose the circle cuts positive side of X axis at A and positive side of Y axis at B
    then the line is AB

    So x + y - sqrt2 is positive only for points lying above AB

    None of the points in the circle meet the above TWO conditions

    2. x is positive but x + y - sqrt2 is negative.

    All points within the circle, on right of Y-axis, but below the straight line AB
    meet the above 2 conditions.

    The figure consists of:

    Triangle OAB + a quarter of the circle

    AREA = 1/2(OA times OB) + 1/4 pi r^2

    OA = OB = sqrt 2

    r = sqrt 2

    AREA = 1/2 2 + 1/4 pi 2

    = 1 + 1/2 pi

    = Approx 1 + 1/2 3.14

    = 2.57

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