EXAMPLE 1: APPLY POLYA’S STRATEGY (SOLVE ASIMILAR BUT SIMPLER PROBLEM)Consider the map shown in Figure 1. Allison wishes to walk along the streets from Point A to Point B. Howmany direct routes can Allison take?Figure 1: City MapAFirst AvenueNESGodivaSecond AvenueSubwayThird AvenueStarbucksB Fourth AvenueRiver WalkBoardWalkParkAvenueGateway BoulevardCrest Boulevard

Allison want to go from point A to point B. We need to find the possible number of direct routes…

EXAMPLE 1: APPLY (SOLVE A SIMILAR BUT SIMPLER PROBLEM) POLYA'S STRATEGY Consider the map shown in Figure 1. Allison wishes to walk along the stroets from Point A to Point B. How many direct routes can Allison take? First Avenue Figure 1: City Map Godiva Secɔnd Avenue Subway Third Avenue Starbucks B Fourth Avenue River Walk Board Walk Park Avenue Gateway Boulevard Crest Boulevard

EXAMPLE 1: APPLY (SOLVE A SIMILAR BUT SIMPLER PROBLEM) POLYA'S STRATEGY Consider the map shown in Figure 1. Allison wishes to walk along the stroets from Point A to Point B. How many direct routes can Allison take? First Avenue Figure 1: City Map Godiva Secɔnd Avenue Subway Third Avenue Starbucks B Fourth Avenue River Walk Board Walk Park Avenue Gateway Boulevard Crest Boulevard

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.1: Sets And Geometry

Problem 5E: Which type of path straight, curved, circular, or scattered is determined by: a a roller coaster? b...

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Monroe County is trying to determine where to place the county fire station. The locations of the county’s four major towns are as follows: (10, 20), (60, 20), (40, 30), and (80, 60) (see Figure 7.50). Town 1 averages 40 fires per year; town 2, 25 fires; town3, 20 fires; and town 4, 30 fires. The county wants to build the fire station in a location that minimizes the average distance that a fire engine must travel to respond to a fire. Because most roads run in either an east-west or a north-south direction, the fire engine must do the same. For example, if the fire station islocated at (30, 40) and a fire occurs at town 4, the fire engine has to travel *80 2 30* 1 * 60 2 40* 5 70 miles to the fire. a. Determine where the fire station should be located.b. Use SolverTable to see how the optimal location of the fire station changes as the number of fires at town 3 changes.
Monroe County is trying to determine where to place the county fire station. The locations of the county’s four major towns are as follows: (10, 20), (60, 20), (40, 30), and (80, 60) (see Figure 7.50). Town 1 averages 40 fires per year; town 2, 25 fires; town 3, 20 fires; and town 4, 30 fires. The county wants to build the fire station in a location that minimizes the average distance that a fire engine must travel to respond to a fire. Because most roads run in either an east-west or a north-south direction, the fire engine must do the same. For example, if the fire station is located at (30, 40) and a fire occurs at town 4, the fire engine has to travel |80 - 30| + |60 - 40| = 70 miles to the fire. a. Determine where the fire station should be located. Round your answers to three decimal places. X Y Location of fire station
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1. Amy, Jim, John, and Kelly are standing on the east bank of the river and wish to cross to the west side using a canoe. The canoe can hold at most two people at a time. Amy, being the most athletic, can row across the river in 1 minute. Jim, John, and Kelly would take 2, 5, and 10 minutes respectively. If two people are in the canoe, the slower person dictates the crossing time. The objective is for all four people to be on the other side of the river in the shortest time possible. a. Identify at least two feasible plans for crossing the river (remember, the canoe is the only mode of transportation and it cannot be shuttled empty). b. Define the criterion for evaluating the alternatives. c. What is the smallest time for moving all four people to the other side of the river?