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A king rules a small mountain kingdom which is in the form of a square of length 4 kilometres. The square is described by the co-ordinate system 0 <* < 4, 0

A king rules a small mountain kingdom which is in the form of a square of length 4 kilometres. The square is described by the co-ordinate system 0 <* < 4, 0

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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A king rules a small mountain kingdom which is in the form of a square of length 4 kilometres. The square is described by the co-ordinate system 0<z<4,0<y八4. The king has four adult children, each of which has a luxu palace located at the points (1, 1), (3, 1), (1, 3), (3, 3). Each child owns all the land that is nearer their palace than any other palace. The king has a fifth (youngest) child who is now just growing up. He installs her in a new palace situated at point (2, 2). The rule about ownership of la is then reapplied. a. Sketch a Voronoi diagram to represent this information. b. Sketch a new Voronoi diagram to represent this new situation. c. State what the shape of the land, owned by the youngest child, is. d. Find the area of thsyoungest child's land. e. Find how much land an older child has lost. f. State, with a reason, if all five children now own an equal amount of land.
Transcribed Image Text:A king rules a small mountain kingdom which is in the form of a square of length 4 kilometres. The square is described by the co-ordinate system 0<z<4,0<y八4. The king has four adult children, each of which has a luxu palace located at the points (1, 1), (3, 1), (1, 3), (3, 3). Each child owns all the land that is nearer their palace than any other palace. The king has a fifth (youngest) child who is now just growing up. He installs her in a new palace situated at point (2, 2). The rule about ownership of la is then reapplied. a. Sketch a Voronoi diagram to represent this information. b. Sketch a new Voronoi diagram to represent this new situation. c. State what the shape of the land, owned by the youngest child, is. d. Find the area of thsyoungest child's land. e. Find how much land an older child has lost. f. State, with a reason, if all five children now own an equal amount of land.
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