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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
27% (02:00) correct
73%
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wrong
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What is the area of the region enclosed by the graph of the equation \(x^2 + y^2 = |x| + |y|\)?
(A) \(\pi+\sqrt{2}\)
(B) \(\pi+2\)
(C) \(\pi+2\sqrt{2}\)
(D) \(2\pi+\sqrt{2}\)
(E) \(2\pi+2\sqrt{2}\)
(A) \(\pi+\sqrt{2}\)
(B) \(\pi+2\)
(C) \(\pi+2\sqrt{2}\)
(D) \(2\pi+\sqrt{2}\)
(E) \(2\pi+2\sqrt{2}\)
10 Mar 2023, 00:44
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nick1816 ThatDudeKnows area of semi circle + triangle aoc + triangle boc . didnt understand after that .. pls explain
10 Mar 2023, 09:17
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bethebest96
bethebest96
I wouldn't worry about this question, as I don't see it as the sort of question GMAC would ask...at least not with the answer choices provided...mayyyyyyybe if the answer choices were really spread out from each other and only one were in the ballpark, but even then, probably not.
That said, I'm sure your curiosity is getting the better of you and you're going to want to spend (waste?
) valuable study time satisfying that curiosity, so here goes.Point A is at (0,1) and point B is at (1,0). Triangle AOB therefore as an area 0.5*1*1 = 0.5.
The diameter of the semicircle is \(\sqrt{2}\), so the area of the semicircle is 0.25pi.
The graph provided by nick1816 only shows one quadrant...a mirror of that graph also applies to the other three quadrants, so the total area is 4*(0.5+0.25pi) = pi+2. Answer choice B.
