Numerical Methods for Engineers
Numerical Methods for Engineers
7th Edition
ISBN: 9780073397924
Author: Steven C. Chapra Dr., Raymond P. Canale
Publisher: McGraw-Hill Education
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Chapter 21, Problem 25P

A transportation engineering study requires that you determine the number of cars that pass through an intersection travelingduring morning rush hour. You stand at the side of the road andcount the number of cars that pass every 4 minutes at several timesas tabulated below. Use the best numerical method to determine

(a) The total number of cars that pass between 7:30 and 9:15, and

(b) The rate of cars going through the intersection per minute.(Hint: Becareful with units.)

Time (hr) 7:30 7:45 8:00 8:15 8:45 9:15
Rate (cars per 4 min) 18 24 14 24 21 9
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A graph G of order 12 has vertex set V(G) = {c1, c2, …, c12} for the twelve configurations inFigure 1.4. A “move” on this checkerboard corresponds to moving a single coin to anunoccupied square, where(1) the gold coin can only be moved horizontally or diagonally,(2) the silver coin can only be moved vertically or diagonally.Two vertices ci and cj (i ≠ j) are adjacent if it is possible to move ci to cj by a single move. (a) What vertices are adjacent to c1 in G?(c) Draw the subgraph of G induced by {c2, c6, c9, c11}.
i) Consider the set S = {−6, −3, 0, 3, 6}. Draw a graph G whose set of verti- ces be S and such that for i, j ∈ S, ij ∈ E(G) if ij are related to a rule that t'u you choose to apply to i and j. (ii) A graph G of order 12 has as a set of vertices c1, c2, . . . , c12 for the do- ce configurations of figure 1. A movement on said board corresponds to moving a coin to an unoccupied square using the following two rules: 1. the gold coin can move only horizontally or diagonally, 2. the silver coin can move only vertically or diagonally. Two vertices ci, cj, i̸ = j are adjacent if it is possible to move ci to cj in a single movement. a) What vertices are adjacent to c1 in G? b) Draw the subgraph induced by {c2, c6, c9, c11}

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