Answered: a 4 5 b) e 3 8 3 4 4 6

Math

Advanced Math

a 4 5 b) e 3 8 3 4 4 6

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1st graph.) A coordinate plane has "People (in thousands)" on the horizontal axis and "Years since 2000" on the vertical axis. The origin is at (0, 20000). The curve enters the window at approximately 1.8 on the positive horizontal axis, goes up and right becoming less steep, changes direction at the approximate point (10, 46600), goes down and right becoming more steep, and exits the window at approximately 18.2 on the positive horizontal axis. 2nd graph.) A coordinate plane has "Years since 2000" on the horizontal axis and "People (in thousands)" on the vertical axis. The origin is at (0, 20000). The curve enters the window at approximately 2.7 on the positive horizontal axis, goes up and right becoming less steep, changes direction at the approximate point (12, 46600), goes down and right becoming more steep, and exits the window at approximately 21.3 on the positive horizontal axis. 3rd graph.) A coordinate plane has "Years since 2000" on the horizontal axis and "People (in…
9. Dashiell is taking a walk around the neighborhood and tracks his location using an app. Consider the graph of his walk where the y-axis represents his distance from home and the z-axis represents the time that has passed in minutes. His graph intersects the line y-1 exactly twice once at (23, 1) and again at (48,1). Interpret the meaning of these intersections in the context of this problem
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5. Let G₁ = (V₁, E₁1) be the following graph. We will show that it is not planar in three ways. E D F H G B (a) Find a subgraph that is isomorphic to a subdivision of either K5 or K3,3. Be sure to label the vertices! (b) Assume on the contrary that G is planar. Find V₁ and E₁, and use only these to explain that G is not planar. (c) Assume on the contrary that G is planar. Use Euler's Formula to find the number of faces and explain that G is not planar (hint: think about how we showed K is not planar)
(h) Suppose that G is an unconnected graph that consists of 4 connected components. The first component is K4, the second is K2,2, the third is C4 and the fourth is a single vertex. Your job is to show how to add edges to G so that the graph has an Euler tour. Justify that your solution is the minimum number of edges added.
1. Phrase the below story and claim in terms of graph theory, and prove the claim it makes:In an alternate universe the solution to ghting Coronavirus is to change how airports work in Canada. From now on, intercity ights can now only go in one direction. The plane between Calgary and Edmonton either only goes to Calgary (from Edmonton) or vice versa. Further, between any pair of cities, one of them can y to the other. In this setup, there will be some city that from any other city you can either y immediately to it, or y through one other airport to get there. In this world Canada has n airports.Hint: think about complete graphs, directed graphs and also the airport with the most incoming ights.
9. Let G2 be depicted in the following diagram: b h a d 9(d) Give an example of a walk of length five in G2 that is not a path.
B1. Advance maths
Find a Hamilton path for each graph below. Hamilton path for Ki: Hamilton path for Kg Hamilton path for Kg:
A 39 B á 38 62 5 F 42 G ß. В 40 20 14 a D C Fig 1 a=10*a B=10*b, where a = 1 and b = 2 Use the graph as in but now the dots (vertices) are locations inthecity of Stockholm, and the dashed lines are paths between the locations (edges). The numbers now show the length (in meters) of the paths. The goal here is to find the shortest path between location A and location D! Use the steps of Dijkstras algorithm to find the minimal distance spanning tree from A to all other locations in fig 1! Build up the minimal distance tree from vertex A by adding one edge and one vertex at a time (and report every new graph as it builds up), always picking the new edge and new vertex which attaches to the current tree and gives the minimum distance to vertex A (remember to avoid circuits!). When you have built up the total minimal distance spanning tree from vertex A, containing all vertices of the graph, answer what the minimal distance from vertex A to vertex D is and which path this corresponds to!
b). We all use antennas at our homes and a fact lies that antennas transmit some form of radiation. The radiation, however is not uniform in all directions. While conducting a research of the antenna radiation, a group of scientists modeled the intensity from a particular antenna by r= acos? 0. (). Convert the polar equation to rectangular coordinates. (ii). Use Mathematica to plot the model for a = 4 and a = 6. (ii). Find the area of the geographical region between the two curves in past (ii). c). In polar coordinates, a polar function exists by the name of strophoid, with equationr=sec 0-2 cos 0. Consider the equation of this strophoid that is bounded as <0<: (1). Plot the strophoid. (ii). Convert the strophoid equation to rectangular coordinates. (iii). Find the area enclosed by the loop.