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Yuki888 [10]
3 years ago
8

A king rules a small mountain kingdom which is in the form of a square of length 4 kilometers. The square is described by the co

ordinate system0≤≤4,0≤≤4. The king has four adult children, each of which has a luxury 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.
Sketch a Voronoi diagram to represent this information.
Mathematics
1 answer:
Andrei [34K]3 years ago
6 0

Answer:

i can not get the answer

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5/6 divided by 1/12 equals?
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0.06944444444

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Does 3 (x-1) = 2x + 9 have one solution, no solution, or infinite solutions?
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one solution

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A prism, bases of which are equilateral triangles, circumscribes a sphere of radius 6. What is the volume of the prism?
koban [17]

Answer:

  1296√3 cubic units

Step-by-step explanation:

The volume of the prism will be the product of its base area and its height. Since it circumscribes a sphere with diameter 12, that is the height of the prism.

The central cross section of the sphere is a circle of radius 6, and that will be the size of the incircle of the base. That is, the base will have an altitude of 3 times that incircle radius, and an edge length of 2√3 times that incircle radius. Hence the area of the triangular base is ...

  B = (1/2)(6×2√3)(6×3) = 108√3 . . . . . square units

The volume of the prism is then ...

  V = Bh = (108√3)(12) = 1296√3 . . . cubic units

_____

<em>Comment on the geometry</em>

The centroid of an equilateral triangle is also the incenter and the circumcenter. The distance of that center from any edge of the triangle is 1/3 the height of the triangle. So, for an inradius of 6, the triangle height is 3×6 = 18. The side length of an equilateral triangle is 2/√3 times the altitude, so is 12√3 units for this triangle.

6 0
3 years ago
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noname [10]

Answer:

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Step-by-step explanation:

5 0
2 years ago
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