Final answer:
The statement that a graph can have many spanning trees is true. Spanning trees are subgraphs that include all vertices and no cycles, allowing for multiple spanning tree configurations in complex graphs.
Step-by-step explanation:
The statement: A graph can have many spanning trees is true. Every connected graph has at least one spanning tree, and complex graphs can have many different spanning trees. A spanning tree of a graph is a subgraph that includes all the vertices of the original graph and is itself a tree. Because trees do not contain cycles by definition, this implies different connections and thus, multiple possibilities for spanning trees.
Regarding the GRASP CHECK questions from physics:
- The statement that voltage is the same at every point in a given wire in a circuit diagram is false. Voltage changes occur when there is resistance or an electrical component in the circuit.
- Waves can superimpose if their frequencies are different, and this statement is true. When waves overlap, they can interfere constructively or destructively, irrespective of their individual frequencies.
- The position vs time graph of an object that is speeding up is not a straight line; hence, the statement is false. Such a graph would typically be curved, showing acceleration.
- The high-voltage wires are indeed held aloft by insulating connectors, but they are typically not wrapped in insulating material due to the practical challenges involved; so, this statement is false.
- The electric-field lines from a positive point charge indeed spread out radially and point outward. This statement is true.
- It is true that there are two types of interference for waves: constructive and destructive.
- Wave-particle duality does not exist for objects on the macroscopic scale; therefore, this statement is false.
- Wood is an insulator, but lightning can create a path through a tree, making the statement true that lightning can travel through a tree to reach Earth.
- For the amplitudes of waves to add up, it is not necessary for them to propagate in the same line; hence, this statement is false.
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