The table shows some of the flight distances (rounded to the nearest 10 km) between various Australian cities. --- 1 WORK AREA LINES (style=lined) --- a. b. `4190\ text{km}` a. b. `text{Hobart to Darwin (with 1 stop):}`
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`text{Distance}`
`=H→S + S→D`
`=1040+3150`
`=4190\ text{km}`
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The table below shows the distances, in kilometres, between a number of towns.
- Using the vertices given, draw a weighted network diagram to represent the information shown in the table. (2 marks)
- A tourist wishes to visit each town.
- Draw the minimum spanning tree which will allow for this AND determine its length. (3 marks)
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- `1015\ text{km}`
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a.
b. `text{Using Prim’s algorithm (starting at}\ Y):`
`text{1st edge:}\ YC`
`text{2nd edge:}\ CB`
`text{3rd edge:}\ SB`
`text{4th edge:}\ YM`
`text{Length of minimum spanning tree}`
`=275 + 150+60+530`
`=1015\ text{km}`
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A regional airline operates flights in Queensland. Flight times between connected towns are shown in the table.
Draw a network diagram to show how the towns are connected, with weights on the edges showing the flight times. (2 marks)
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`text(Edge weights are in minutes duration.)`
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In central Queensland, there are four petrol stations `A`, `B`, `C` and `D`. The table shows the length, in kilometres, of roads connecting these petrol stations.
- Construct a network diagram to represent the information in the table. (2 marks)
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- A petrol tanker needs to refill each station. It starts at Station `A` and visits each station.
Calculate the shortest distance that can be travelled by the petrol tanker. In your answer, include the order the petrol stations are refilled. (2 marks)
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- `380\ text(km)`
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| a. | |
b. `text(Shortest Path from)\ A\ (text(visiting all stations))`
`A – B – D – C`
| `text(Distance)` | `= 170 + 90 + 120` |
| `= 380\ text(km)` |
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The table below represents a directed network.
Complete the network diagram below to accurately reflect the network described in the above table. (2 marks)
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Networks, STD2 N2 2009 FUR2 1
The city of Robville is divided into five suburbs labelled as `A` to `E` on the map below.
A lake which is situated in the city is shaded on the map.
A table is constructed to represent the number of land borders between suburbs.
If there is no land border between two suburbs, the table records a '0'. If there is a single land border between two suburbs, the table records a '1', and if there are two separate land borders between the same two suburbs, the table records a '2'.
`{:({:qquadqquadAquadBquadCquadDquadE:}),({:(A),(B),(C),(D),(E):}[(0,1,1,1,0),(1,0,1,2,0),(1,1,0,0,0),(1,2,0,0,0),(0,0,0,0,0)]):}`
- Explain why all values in the final row and final column of the table are zero. (1 mark)
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In the network diagram below, vertices represent suburbs and edges represent land borders between suburbs.
The diagram has been started but is not finished.
- The network diagram is missing one edge and one vertex.
On the diagram
- draw the missing edge (1 mark)
- draw and label the missing vertex. (1 mark)
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- `E\ text(has no land borders with other suburbs.)`
- i. & ii.
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a. `E\ text(has no land borders with other suburbs.)`
| b.i. & ii. |  |