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29 Dec 2007, 07:40
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R is the region consisting of all points x,y such that 3<x^2+y^2<6. which of the following best approximates the area of R in square units?
A.6
B.7
C.8
D.9
E.10
A.6
B.7
C.8
D.9
E.10
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29 Dec 2007, 07:45
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enclosed region will be region between two circles of radius sqrt(6) and sqrt(3)
so the area of R =pi.(6-3) =9.42 hence 9 is the closest area.
I would go with D
so the area of R =pi.(6-3) =9.42 hence 9 is the closest area.
I would go with D
29 Dec 2007, 07:57
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The equation of a circle is :
(x - h)^2 + (y - k)^2 = r^2
where h and k are the x- and y-coordinates of the center of the circle and r is the radius.
( For more, go to https://www.analyzemath.com/CircleEq/CircleEq.html )
So in this problem, 3<x^2+y^2<6, the region is inclosed inside two circles, both which are centered at (0,0) and have a radius of sqrt(3) and sqrt(6), respectively.
The area is then pi (sqrt(6))^2 - pi (sqrt(3))^2 = 3 pi ~ 9.4
I would go with D
(x - h)^2 + (y - k)^2 = r^2
where h and k are the x- and y-coordinates of the center of the circle and r is the radius.
( For more, go to https://www.analyzemath.com/CircleEq/CircleEq.html )
So in this problem, 3<x^2+y^2<6, the region is inclosed inside two circles, both which are centered at (0,0) and have a radius of sqrt(3) and sqrt(6), respectively.
The area is then pi (sqrt(6))^2 - pi (sqrt(3))^2 = 3 pi ~ 9.4
I would go with D
