Vector Theorems Math Problem Example | Topics and Well Written Essays - 500 words

Vector Theorems - Math Problem Example Since we have a medial triangle DEF as shown above, for convenience we draw the same triangle separately as shown below. Here D (a, 0, 0), E (0, b, 0), and F (0, 0, c) be the vertices of medial triangle while N is the centroid of the triangle. By distance formula, N has the coordinates as (a/3, b/3, c/3). Let D†² be the mid-point of EF, therefore its coordinates will be (0, b/2, c/2). Now we find the distance between N and D†². Similarly 2 E†²N = EN, and 2 F†²N = FN. Thus, it means that the centroid is located two thirds of the way from the original vertex to the midpoint of the opposite side of the triangle. Now, since we have a triangle ABC and E is the middle point of BC, and P is the centroid of ABC. Therefore, by using above theorem we have OP = OA + 2/3 AE. Now we will find the centroid of ABC. Now we will find the centroid of DEF. Let Q = centroid of DEF = OQ = OD + 2/3 DM/ From above equation no.2 and equation no.3 it is evident that P=Q. Thus it has been proved that the centroid of the triangle ABC is equal to the centroid of medial triangle DEF

Dollar Tree Case Study Example | Topics and Well Written Essays - 1750 words

Dollar Tree - Case Study Example As such, multiple branches are needed of any one retailer in order to truly realize profit on the scale that would sustain the viability of any company for any length of time. Dollar Tree has been able to become such a company, gradually acquiring other discount chains over the years, to now have a presence throughout the entire continental United States and Canada. This paper serves to explain some of the reasons behind their success, as well as providing a description of some future challenges on the horizon. Case Challenge 1 The first challenge facing Dollar Tree rests in the reality that the company’s initial growth was accomplished almost exclusively through acquisition. The question then becomes whether or not this will be an attractive option in the near future. The reality is that expansion through acquisition will likely be quite difficult in today’s economic climate. The company is already struggling to keep its pricing model in tact (all items at $1), and the cost of acquiring other companies will make this increasingly difficult. With the company now poised to pass the 5,000 location mark in the near future, the reality is that it does not need to continue to grow in the manner. Already being considered the industry leader, there are few chains that are in direct competition with it to begin with. If they desire to acquire even more discount dollar chains, it will likely only be in areas of the country where they do not already have an established presence. Case Challenge 2 Dollar Tree also faces the challenge moving forward of being able to continue to offer