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10 9 8 7 6 5 4 3 ON 2 1 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 2 Find the area inside the circle x² + y² Round your answer to four decimal places. 100 above the line y = 2.

10 9 8 7 6 5 4 3 ON 2 1 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 2 Find the area inside the circle x² + y² Round your answer to four decimal places. 100 above the line y = 2.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
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5.3.3

**Problem Statement:** Find the area inside the circle \( x^2 + y^2 = 100 \) above the line \( y = 2 \). Round your answer to four decimal places. **Graph Explanation:** The graph displays a semicircle with the equation \( x^2 + y^2 = 100 \). This circle has a center at the origin (0,0) and a radius of 10. The plot shows only the upper half of the circle, from \( x = -10 \) to \( x = 10 \), with the topmost point at \( y = 10 \). A horizontal line is drawn in blue at \( y = 2 \), which intersects the circle, dividing it into two regions. The problem requires finding the area of the region above this line within the circle. **Instructions:** 1. Calculate the total area of the semicircle. 2. Determine the area of the segment below the line \( y = 2 \). 3. Subtract the area of the segment from the total semicircle area to find the desired area above the line. Provide your final answer rounded to four decimal places in the designated box.
Transcribed Image Text:**Problem Statement:** Find the area inside the circle \( x^2 + y^2 = 100 \) above the line \( y = 2 \). Round your answer to four decimal places. **Graph Explanation:** The graph displays a semicircle with the equation \( x^2 + y^2 = 100 \). This circle has a center at the origin (0,0) and a radius of 10. The plot shows only the upper half of the circle, from \( x = -10 \) to \( x = 10 \), with the topmost point at \( y = 10 \). A horizontal line is drawn in blue at \( y = 2 \), which intersects the circle, dividing it into two regions. The problem requires finding the area of the region above this line within the circle. **Instructions:** 1. Calculate the total area of the semicircle. 2. Determine the area of the segment below the line \( y = 2 \). 3. Subtract the area of the segment from the total semicircle area to find the desired area above the line. Provide your final answer rounded to four decimal places in the designated box.
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