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1. The graph below represents five cities and the routes between them. An out-of-state road inspector is asked
to fly into Pottsville (P). From Pottsville, the inspector must inspect each road on the map, making only one
trip along each road, and then fly out of Tinkertown (T).
a.) Will the road inspector be able to complete the inspection as described? Mathematically explain why
or why not and, if such an inspection is possible, describe the route.
b.) The inspector would prefer to fly into and out of the same town, but still drive each road only once.
Would that be possible? Mathematically explain why or why not and, if such an inspection is possible,
describe the route.
c.) Below, the map has been expanded to show additional cities and routes. A trucker who lives in
Jonesboro (J) needs to make deliveries in each town and then return home without passing through
any of the towns more than once. What type of mathematical circuit is the trucker hoping to use? If
the trucker can complete the circuit, describe the route.
2. Compare and contrast Euclidean geometry and spherical geometry. Be sure to include these points:
a.) Describe the role of the Parallel Postulate in spherical geometry.
b.) How are triangles different in spherical geometry as opposed to Euclidean geometry?
c.) Geodesics
d.) Applications of spherical geometry
a.) 10001 base 2
= ______
b.) 1101101 base 2
base 10
= _____
base 10
c.) What type of gate does this input-output table correspond to?
Input
Output
A
B
?
0
0
1
1
1
0
0
1
1
0
1
1
d.) The expression that describes the network of logic gates:
Is [A AND (NOT B)] OR (NOT B).
e.) Complete the input-output table for the network:

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