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06 Oct 2023, 01:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
78% (01:21) correct
22%
(01:46)
wrong
based on 134
sessions
History
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Time
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Of all the points that satisfy the equation x^2+y^2=25, approximately what percentage of the points also satisfy the inequality xy ≥ 0?
A. 25%
B. 33%
C. 50%
D. 75%
E. 80%
A. 25%
B. 33%
C. 50%
D. 75%
E. 80%
06 Oct 2023, 11:31
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↧↧↧ Detailed Video Solution to the Problem ↧↧↧
We need to find of all the points that satisfy the equation \(x^2+y^2=25\), approximately what percentage of the points also satisfy the inequality xy ≥ 0?
\(x^2+y^2 = 25 = 5^2\) is the equation of a circle with center at (0,0) and radius as 5
(Watch this video to know about the Basics of Circles)
xy ≥ 0 in all cases except
1. x < 0 and y > 0
2. x > 0 and y < 0
=> All cases when x and y are in \(1^{st}\) or \(3^{rd}\) quadrant or x and y are on X or Y-Axis respectively.
=> We will have following cases as shown in the figure (Approximately)
xy GTE 0.png [ 7.37 KiB | Viewed 2302 times ]
=> 2 (in yellow) out of 4 quarter circles
=> \(\frac{2}{4} * 100%\) = 50%
So, Answer will be C
Hope it helps!
Watch the following video to learn the Basics of Inequalities
We need to find of all the points that satisfy the equation \(x^2+y^2=25\), approximately what percentage of the points also satisfy the inequality xy ≥ 0?
\(x^2+y^2 = 25 = 5^2\) is the equation of a circle with center at (0,0) and radius as 5
(Watch this video to know about the Basics of Circles)
xy ≥ 0 in all cases except
1. x < 0 and y > 0
2. x > 0 and y < 0
=> All cases when x and y are in \(1^{st}\) or \(3^{rd}\) quadrant or x and y are on X or Y-Axis respectively.
=> We will have following cases as shown in the figure (Approximately)
Attachment:
xy GTE 0.png [ 7.37 KiB | Viewed 2302 times ]
=> 2 (in yellow) out of 4 quarter circles
=> \(\frac{2}{4} * 100%\) = 50%
So, Answer will be C
Hope it helps!
Watch the following video to learn the Basics of Inequalities
19 Oct 2023, 01:30
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x^2 + y^2 = 25 forms the equation of the circle with center (0, 0) and radius 5.
Since the circle has the center at origin, it is divided by the x and y axes in 4 equal parts, in the respective 4 quadrants.
For xy >= 0,
Either : x >= 0 and y >= 0 ( 1st quadrant )
Or : x <= 0 and y <= 0 ( 3rd quadrant )
Total outcomes = t = points on the circle which spans all 4 quadrants
Favorable outcomes = f = points on the 2 parts of the circle which span the 1st and 3rd quadrant respectively.
Therefore, probability = t / f = 2/4 = 1/2
Answer: (C) 50%
Since the circle has the center at origin, it is divided by the x and y axes in 4 equal parts, in the respective 4 quadrants.
For xy >= 0,
Either : x >= 0 and y >= 0 ( 1st quadrant )
Or : x <= 0 and y <= 0 ( 3rd quadrant )
Total outcomes = t = points on the circle which spans all 4 quadrants
Favorable outcomes = f = points on the 2 parts of the circle which span the 1st and 3rd quadrant respectively.
Therefore, probability = t / f = 2/4 = 1/2
Answer: (C) 50%
