I am struggling in these questions attached below about voronoi diagrams

sure how to tell which rules to use and where to go from there. And In the last photo, I am specifically struggling with questions 29, 45, and 53.

ersity maths). I would like some assistance as soon as possible (in the next few hours), so if you are unavailable, I would love it if another tutor could help. These are the questions that are similar to, but are not exactly the ones I am struggling with. Solving these would give me a better chance of solving my assignment. I don't know where to begin with these: Provide a non-solvable finite group G with solvable subgroups L, K, M such that G = LK = LM, M \neq K , and show that it fits the criteria. ///// Define G, a finite p -group, such that G isn't abelian. Let K \le G such that |G:K| = p , where K is abelian. Prove that there are either 1 or p + 1 such abelian subgroups, and if there are p + 1 , then the index of Z(G) in G is p^2 ///// Define N normal subgroup, G finite group, O the intersection of all maximal subgroups of G . Prove that G = ON and N \cap O is nilpotent. ///// Define p a prime number, G a finite group, K a Sylow p -subgroup of G . Assume M \le K and g^{-1}Mg \le K , where g \in G . Prove that g = km for some k \in N_G(K) (normaliser of K in G ) and some m \in C_G(M) (centraliser of K in G)

s the 6 pillars of a social media marketing plan that are needed to achieve the company's goals; set social media marketing goals, research audience, analyze competition, establish important metrics, asses results and optimize. I am going to go into detail about each pillar for this paragraph. My second point is "Once the marketing plan is set in place, business uses social media to facilitate consumers through the purchase process." I am going to talk about the stages of the purchasing process. My first two points flow together in my opinion. I am not sure what my third point will be. I want to talk about how the business uses social media to reach out to consumers and inform them about their product. The business also uses social media platforms to interact with social influencers who can promote their products on their social media. My idea of the third point does not really flow well with my first two points. Can you help me with a third point that does flow together with my first two? I am sorry if this is a bit confusing. Time is really against me on this one.

mit proofs. Attached is the file of questions I require help with.