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In the xy-plane, Region R is bounded by the line segments with equations, 2x + |4y| = 20 and x=0, whereas Region P is bounded by the line segments with equations |4x| + 2y = 20 and y = 0. If the function A(B) is defined as the area of Region B, what is the value of |A(P) – 2A(R)|?
- a)0
- b)25
- c)50
- d)75
- e)100
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
In the xy-plane, Region R is bounded by the line segments with equatio...
Given
- Region R is bounded by
- 2x + |4y| = 20 and
- x=0, whereas
- Region P is bounded by
- |4x| + 2y = 20 and
- y = 0
- A(B) = area of Region B
To Find: |A(P) – 2A(R)|?
- We need to find the area of regions P and R to answer the question
Approach
- Region R
- For finding the area of region R, we need to draw the following line segments:
- x = 0
- 2x +4|y| = 20. As we are given |y|, the value of |y| will depend on the value of y
- If y ≥0, then |y| = y.
- So, we have equation of the line segment as 2x + 4y = 20, i.e. x + 2y = 10 and
- If y < 0, then |y| = -y.
- So, we have equation of the line segment as 2x – 4y = 20, i.e. x – 2y = 10
- If y ≥0, then |y| = y.
- Once we draw these line segments, we will find the area of the region bounded by the line segments using standard formulas.
- For finding the area of region R, we need to draw the following line segments:
- Region P
- For finding the area of region R, we need to draw the following line segments:
- y = 0
- |4x| + 2y = 20. As we are given |x|, the value of |x| will depend on the value of x.
- If x ≥0, then |x| = x.
- So, we have the equation as 4x + 2y = 20, i.e. 2x + y = 10 and
- If x < 0, then |x| = -x.
- So, we have the equation of the line segment as 4x – 2y = -20, i.e. 2x – y = -10
- If x ≥0, then |x| = x.
- For finding the area of region R, we need to draw the following line segments:
- Once we draw these line segments, we will find the area of the region bounded by the line segments using standard formulas
Working out
1. Finding A(R)
a. Assuming y-axis to be the base, we have EF = 5 – (-5) = 10
b. Height = x-coordinate of point D = 10
c. Area of region R = ½ * 10 * 10 = 50
d. A(R) = 50……. (1)
a. Assuming y-axis to be the base, we have EF = 5 – (-5) = 10
b. Height = x-coordinate of point D = 10
c. Area of region R = ½ * 10 * 10 = 50
d. A(R) = 50……. (1)
2. Finding A(P)
a. Assuming x-axis to be the base, we have BD = 5 – (-5) = 10
b. Height = y-coordinate of point A = 10
a. Assuming x-axis to be the base, we have BD = 5 – (-5) = 10
b. Height = y-coordinate of point A = 10
c. Area of region P = ½ * 10 * 10 = 50
d. A(P) = 50…….(2)
d. A(P) = 50…….(2)
3. Using (1) and (2), we have
a. |A(P) – 2A(R)| = | 50 – 2*50| = |-50| = 50
Answer: C
a. |A(P) – 2A(R)| = | 50 – 2*50| = |-50| = 50
Answer: C
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In the xy-plane, Region R is bounded by the line segments with equations, 2x + |4y| = 20 and x=0, whereas Region P is bounded by the line segments with equations |4x| + 2y = 20 and y = 0. If the function A(B) is defined as the area of Region B, what is the value of |A(P) – 2A(R)|?a)0b)25c)50d)75e)100Correct answer is option 'C'. Can you explain this answer?
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In the xy-plane, Region R is bounded by the line segments with equations, 2x + |4y| = 20 and x=0, whereas Region P is bounded by the line segments with equations |4x| + 2y = 20 and y = 0. If the function A(B) is defined as the area of Region B, what is the value of |A(P) – 2A(R)|?a)0b)25c)50d)75e)100Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about In the xy-plane, Region R is bounded by the line segments with equations, 2x + |4y| = 20 and x=0, whereas Region P is bounded by the line segments with equations |4x| + 2y = 20 and y = 0. If the function A(B) is defined as the area of Region B, what is the value of |A(P) – 2A(R)|?a)0b)25c)50d)75e)100Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the xy-plane, Region R is bounded by the line segments with equations, 2x + |4y| = 20 and x=0, whereas Region P is bounded by the line segments with equations |4x| + 2y = 20 and y = 0. If the function A(B) is defined as the area of Region B, what is the value of |A(P) – 2A(R)|?a)0b)25c)50d)75e)100Correct answer is option 'C'. Can you explain this answer?.
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