Let the "tree shortcut algorithm" be the factor-2 approximation algorithm (using mst) for tsp instances satisfying triangle inequality. show by an example that if we don’t assume the triangle inequality, then the tour found by the tree shortcut algorithm can be longer than 1000 times the optimal tour

Find measure angle 1 and measure angle 3 in the kite the diagram is not drawn on the scale

Read the excerpt from gilgamesh: a new english version. gilgamesh backed away. he said,"how dreadful humbaba's face has become! it is changing into a thousand nightmarefaces, more horrible than i can bear. i feel haunted. i am too afraid to go on." §enkidu answered, "why, dear friend, do you speak like a coward? what you just saidis unworthy of you. it grieves my heartwe must not hesitate or retreat."

13 is the same as 1÷3. what is the exact quotient in decimal form of 1÷3?