Within a city, consider 3 districts A, B, and C, each with n houses. Each house iscontained in exactly 1 district (i.e. there is no overlap between districts). Construct a networkof roads as follows:• There is a road between every house in A and every house in B.• There is a road between every house in B and every house in C.• There is a road between every house in C and every house in A.• There are no other roads except those specified above.(a) Express the number of roads in the city, in terms of n. Justify your answer.(b) Prove that you can walk to any house from any other house through some sequence ofroads.(c) Express the length of the longest cycle of roads in the city in terms of n. Justify youranswer.

Let us consider the houses as the nodes and the roads as the edges of the graph. Then, the…

Answered: Within a city, consider 3 districts A,…

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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You want to thank your professors this year by giving them some cookies. You have 5 professors and 15 cookies, in how many ways can you distribute them given:a. The cookies are identical and each professor gets at least one.b. The cookies are identical and some professors may get none.c. The cookies are unique (each one is a different kind) and some professors might get none.
A large bakery has many different products for sale. Suppose that 200 come in between 6am and 10am. Of the 200 customers 140 order donuts, 100 order cinnamon rolls, and 80 order both. Make a Venn Diagram to model the situation.
A university has to conduct a training course for professors of seven different courses- GART, NSTP. GSELF, GENTREP, GWORLD, GEARTH, and GMATH from 22nd July to 29th July a. The course should start with NSTP b. 23 July, being Sunday, should be a holiday c. The GEARTH course should be on the previous day of the GMATH course. d. The training should end with GART. e. GSELF should be done immediately after the holiday. f. There should be a one day gap between GENTREP and GMATH. g. There should be two days gap between GENTREP and GWORLD Which course will be held on Tuesday?
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A group of 650 tourists includes 248 who have visited Germany, 115 who have visited Holland,and 319 who have visited neither Germany nor Holland. Use the Addition Principle to computehow many have visited both Germany and Holland.
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