The volume of a right circular cone.

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Chapter 63, Problem 8A

To determine

The volume of a right circular cone.

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9. (a) Use pseudocode to describe an algo- rithm for determining the value of a game tree when both players follow a minmax strategy. (b) Suppose that T₁ and T2 are spanning trees of a simple graph G. Moreover, suppose that ₁ is an edge in T₁ that is not in T2. Show that there is an edge 2 in T2 that is not in T₁ such that T₁ remains a spanning tree if ₁ is removed from it and 2 is added to it, and T2 remains a spanning tree if 2 is removed from it and e₁ is added to it. (c) Show that a degree-constrained spanning tree of a simple graph in which each vertex has degree not exceeding 2 2 consists of a single Hamiltonian path in the graph.