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What is the area enclosed of the region enclosed by y = |x – 1| + 2, x

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Bunuel
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What is the area enclosed of the region enclosed by y = |x – 1| + 2, x [#permalink] New post   05 May 2020, 04:03
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What is the area enclosed of the region enclosed by y = |x – 1| + 2, x = 1, x–axis and y–axis?

A. 2.5
B. 5
C. 7
D. 9
E. 10


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nick1816
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Re: What is the area enclosed of the region enclosed by y = |x – 1| + 2, x [#permalink] New post   03 Jun 2020, 02:07
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Area \(= (2*1)+\frac{1}{2} *1*1 = 2.5\)

Bunuel wrote:
What is the area enclosed of the region enclosed by y = |x – 1| + 2, x = 1, x–axis and y–axis?

A. 2.5
B. 5
C. 7
D. 9
E. 10


Are You Up For the Challenge: 700 Level Questions
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hiranmay
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Re: What is the area enclosed of the region enclosed by y = |x – 1| + 2, x [#permalink] New post   05 May 2020, 08:39
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What is the area enclosed of the region enclosed by y = |x – 1| + 2, x = 1, x–axis and y–axis?

A. 2.5 --> correct: y = |x – 1| + 2, so (1) x=1, y=2 & if you increase or decrease x, y will always increase linearly with slop of 1, and intersect y-axis (2) @x=0, y=3, so enclosure enclosed by x = 1, x–axis and y–axis looks like trapezium with height=1, and two unequal side length = 2&3, so the area= (1/2)*(2+3)*1=5/2=2.5
B. 5
C. 7
D. 9
E. 10
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shafinkhan
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Re: What is the area enclosed of the region enclosed by y = |x – 1| + 2, x [#permalink] New post   27 May 2020, 00:59
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hiranmay wrote:
What is the area enclosed of the region enclosed by y = |x – 1| + 2, x = 1, x–axis and y–axis?

A. 2.5 --> correct: y = |x – 1| + 2, so (1) x=1, y=2 & if you increase or decrease x, y will always increase linearly with slop of 1, and intersect y-axis (2) @x=0, y=3, so enclosure enclosed by x = 1, x–axis and y–axis looks like trapezium with height=1, and two unequal side length = 2&3, so the area= (1/2)*(2+3)*1=5/2=2.5
B. 5
C. 7
D. 9
E. 10



Hi,

How do we deal with the absolute sign in the equation above. We should be having 2 equations to remove the absolute sign on? One >0 and the other one <0?
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minirana
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Re: What is the area enclosed of the region enclosed by y = |x – 1| + 2, x [#permalink] New post   02 Jun 2020, 20:19
While i am trying to put values in the x and y , i am not getting a trapezium. Can someone explain the plotting bit.
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minirana
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Re: What is the area enclosed of the region enclosed by y = |x – 1| + 2, x [#permalink] New post   03 Jun 2020, 02:38
nick1816 wrote:
Attachment:
Untitled.png


Area \(= (2*1)+\frac{1}{2} *1*1 = 2.5\)

Bunuel wrote:
What is the area enclosed of the region enclosed by y = |x – 1| + 2, x = 1, x–axis and y–axis?

A. 2.5
B. 5
C. 7
D. 9
E. 10


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Thanks a lot! I understood my mistake, I did not understand the problem correctly.
x=1 was another line (represented as red in the graph).
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nicbo
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Re: What is the area enclosed of the region enclosed by y = |x 1| + 2, x [#permalink] New post   20 Apr 2023, 01:37
gmatophobia Bunuel I am stuck here. Could you please explain how to deal with such problems?

Thank you in advance.
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Re: What is the area enclosed of the region enclosed by y = |x 1| + 2, x [#permalink]
20 Apr 2023, 01:37
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