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March 29, 2017

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so its this picture of a rectangle inscribed in a circle. the circle has a radius of 2. the vertexes of the circle are present in every quadrant, but you cant tell exactly whgat point they represent. point Q (x,y) is the vertex of the rectangle in Quadrant I and is on the circle. the equation of the circle is : x^2 + y^2 = 4
a.) express the area of the rectangle as a function of x.
b.) give the domain of the area
c.) epxress the perimeter as a function of x.
d.) give the domain of Q
PLEASE HELP IM SO LOST. and friday afternoon is my scheduled math homework day. (dont ask im psycho) please this is bother ing me like crazyy

  • math (pre clac) - ,

    a)
    x^2 + y ^2 = 4
    area = 4 |x y| (so it works in each quadrant)
    y = sqrt(4-x^2)
    area = 4 x sqrt(4-x^2)

    b)
    the area can be 0 (at x = 0 and x = 2)and it has a maximum at x = y = sqrt 2
    to show that take derivative and set to zero
    0 = -4 x^2/sqrt(4-x^2) +4 sqrt(4-x^2)
    0 = -4x^2 + 16 - 4 x^2
    8 x^2 = 16
    x = sqrt 2
    so domain of area is 0 to x = sqrt 2 where the area is 8

    c)
    L = 2 x + 2 y
    = 2 x + 2 sqrt(4-x^2)
    = 2 ( x + sqrt (4-x^2))

    d)
    Q goes from x = 0 to x = 2 in Quadrant 1

  • math (pre clac) - ,

    What do you mean?

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