leopard7982
15.07.2021 •
Mathematics
Consider the function z(x,y) describing the paraboloid \[z = (2x - y)^2 - 2y^2 - 3y.\]Archimedes and Brahmagupta are playing a game. Archimedes first chooses $x.$ Afterwards, Brahmagupta chooses $y.$ Archimedes wishes to minimize $z$ while Brahmagupta wishes to maximize $z.$ Assuming that Brahmagupta will play optimally, what value of $x$ should Archimedes choose?
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Ответ:
-3/8
Step-by-step explanation:
Expanding z we get
z = 4x^2 - 4xy + y^2 - 2y^2 - 3y
= -y^2 - (4x + 3) y + 4x^2.
After Archimedes chooses x, Brahmagupta will choose
y=-(4x+3/2) in order to maximize z
Then
z=-((-4x+3)/2)^2 -(4x+3)(-4x+3)/2)^2)+4x^2
z=8x^2+6x+9/4
To minimize this expression, Archimedes should choose x=-3/8
Ответ:
=your mom
Step-by-step explanation:
dont so it to other peole if you dont want it happening to you