Maths

The Importance of Mathematics in Modern LifeMathematics is a crucial part, especially in modern life; without it, life has no much meaning. From the olden days, mathematics existed and has undergone a series of changes in the methods and approaches used to calculate them. Before the arrival of modern-day electronic calculators, people would spend time doing calculations by hand, which was considered a profession. Mechanical calculators, as wel...

Logicism: Mathematics as a Subset of LogicAccording to the philosophy of mathematics, logicism is a based program on the theses that mathematics is a continuation of logic, most or all of mathematics is reducible to logic, and most or all of mathematics may be modeled in logic, all of which are true for some coherent meaning of the word "logic." One of the researchers, identified only as Dedekind, was able to develop a model that satisfied the a...

Challenges in Frequency AllocationThis paper provides an explanation and analysis of the industrial application of graph theory. The paper relies mainly on secondary sources of the information and course knowledge gathered in discrete mathematics class. For, in Motorola company seeks to solve recoloring challenge in cell phone and communication system operation. Motorola poses a problem that is minimized by employing discrete mathematics knowl...

Discount rate 10% Project Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Total Costs $50,000 $10,000 $10,000 $10,000 $10,000 $10,000 Discount factor 1 0.909 0.826 0.751 0.683 0.621 Discounted costs $50,000 $9,091 $8,264 $7,513 $6,830 ...

Definition of mathematicsIn many scenarios, people apply mathematics to everyday life activities either knowingly or unknowingly. For example, mathematics is involved in the running of computers, to fly the aircraft, and used to enhance communication in a secured system (Bianco, 2015). However, people underappreciate or underestimate the value and applications of mathematics. This paper discusses mathematics, numeracy and its use in daily phen...

Let A and B be not on the same side of CD. Let AB cuts CD at F. As ABCD is a Saccheri quadrilateral so BAD =90? and CDA=90?. Now one of the triangles DAF and BFC contains a right angle and an obtuse angle because one of the linear pair of angles of F must be an obtuse or a right angle. In this case, angles FAD=90? and FDA=90?. As a result of which, the sum of the three angles of a triangle will be more than 180?. Contradiction!!!! Hence A a...

3X+3Y/5=`12/5 Y=-4-5X Substituting the value of y in the 2nd equation onto the first equation 3x+3/5(-4-5x) =12/5 3x-3x=12/5-12/5 Hence the linear equation has no solution  2.-2r+4s-5t=-16     5r+5s+4t=-7     -5r-3s+t  Eliminating r by multiplying equation 1 by 5 and equation 2 by 2 you get 10r+20s-25=-80 10r+10s+8t=-14 30s-17t=-94 2s+5t=6 Eliminating s -60s-28t=-188 60...

Hall's condition and matching in bipartite graphsRemember to prepare your answers in LaTeX. Refer to hw-template.tex for help in preparing your HW file. Also, please create an individual page for each solution. Use the command \pagebreak to force page breaks. Let G be a bipartite graph with classes A and B and let d ≤ |A| be a fixed positive integer. Suppose that for every set S ⊂ A we have |N(S)| ≥ |S| − d. Prove that G...

Answer: Prove by strong induction that T(n) = 3n − 2 n for all n ∈ N .Solution. : Given : T0 = 0, T1 = 1Base case :T2 = 5T1 − 6T0 = 5 = 32 − 2 2T3 = 5T2 − 6T1 = 19 = 33 − 2 3Assumption :T(n) = 3n − 2n and T(n−1) = 3(n−1) − 2 (n−1) Proving :T(n+1) = 3(n+1) − 2 (n+1) T(n+1) = 5T(n) − 6T(n−1)= 5(3n − 2 n ) − 6(3(n−1) − 2 (n−1) = 5(3n &m...

Simple Random SamplingA simple random sampling involves selecting out units to form a desired sample size, in which each unit on this population will have an equal probability of being selected if possible. In our case we had a population of  94 units representing weight  of the male students, but our desired size was 36 units, therefore the following were the steps used in sampling out 36 units from a population of 94 units that wer...

BackgroundSince the age of industrialization and even well before that, there have been curiosity to realize what characterizes the pay that a given employee gets. In a salary survey conducted by Zabel (2015) to determine what kind of factors influence salaries, several factors such as level of education, overtime working and skills are proposed. For instance, in the study outcome, a job whose position is hardest to fill attracted higher pay c...

Relationship between internal and external nodes in a TreeWhen nI = 1, then nE = 2nI + 1 = 2+1=3.  When  nI = 2, then nE = 2nI +1 = 4+1 = 5. Let’s propose that the equation nE is correct for k’< k, that is, for any nI = k’< k, nE = 2nI +1. Now let’s consider k= nI. Then, 2(k − 1) + 1 + (3 − 1) is equals to nE.  The number of nodes which are external   is equal to the nodes w...

Definition and Branches of GeometryGeometry can be defined as a branch of mathematics concerned with measurements, relationship between points, lines and planes as well as properties of certain dimensions of a given nature. This term originated from two Greek words. That is geo standing for earth and metria which meant measure (Tabak, 2014). Geometry covers a wide range of concepts which are usually encountered in our daily life. The study of ...

Domestic Cars             Z-scores List Price in K Sale Price in K Days to Sell             List Price in  Sale Price in  Days to Sell 9 8.3 40   Descriptive Statistics for Domestic Cars   -1.26 -1.17 0.40 34 30.2 5     List Price in K Sale Price in K Days to Sell   0.10 0.03 -1.56 23.9 ...

Local Maximum and Minimum Points is the derivative of  with respect to power rule, subtraction and additional rule we obtain         For  is the derivative of  with respect to , addition and the subtraction rule we obtain    Since  then  for The stationery points are at point Hence the stationery points will be at the roots of Using the quadratic ...

Question 1 Differentiating  (a).  f(x)=6x^2ln(4x) f’(x)=d/dx(6x^2ln(4x)) First we remove the constant f’(x)=6 d/dx(x^2ln(4x)) Second the product rule (f*g)’=f’*g+f*g’ f=x^2 , g=ln(4x) f’=d/dx(x^2)=2x ,  g’=d/dx(ln(4x))=1/x Third substitute the values into the product rule f’(x)=6 (2xln(4x)+(1/x)*x^2) Final Result f’(x)=6(2xln(4x)+x)  (b).  f(x)= f&rsq...

Problem Statement1.a)                                                                                          b) c)                           ...

Question1: Given that, A =  , B =  A + B =  +  =  (Ans) 2A – 3B = 2- 3 =  (Ans) AB = =  (Ans) AB + BA =    =  =  (Ans) A = , B =  2A + x = B x = B – 2A. x = -  2      =      = (Ans) c. Given, A = det(A) = = 18 -2 = 16 (Ans). A = Matrix of minors of A is :-    ...

1. The mathematical approach to computation1.The mathematical approach to computation in the 30s and the 40s generated a number of equivalent definitions: of these, the notion of effective computability by mechanical means given by the model of a machine defined by Turing was the one to have the longest impact and to result the most intuitive one. We shall see in the next part of this volume how in parallel to the mathematical foundation, an e...

Statistics on the Number of Students Who Play Cricket, Hockey, and Volleyball For ease with the calculations let’s use letters to represent the games. That is  Cricket             H for Hockey         V for Volley Drawing the Venn diagram to represent the scenario The number of students who play: Cricket 50 Hockey 50 Volley 40 Cricket an...

a)The general cubic polynomial y=ax3+bx2+cx+ d There are four unknowns Using (5,150) = 150= 125a +25 b +5c +d………………………………. (1) Using (7,200) = 200 =343a +49b +7c +d………………………………... (2) Using (9,250) =250=729a +81b+9c +d………………&hellip...

Problem definitionThe Travelling Salesman Problem (TSP) is all around characterized and know enhancement problem that is applied to locate the shortest route visiting every individual from an accumulation of destinations and restoring the beginning stage4. 2It is once in a while considered as the most serious problem in the computational science however yet no better/viable arrangement technique is known for the general cases. In most cases, t...

Evolution and Function of Spider WebsDiscuss About The Mathematical Exploration Symmetries Spider? The ability of spiders to spin their webs with great precision, strength, and weaving of the threats at the equidistant interval is an intriguing occurrence that frequently goes unnoticed. To common observers, spiders construct the webs for the sake of catching their preys. However, mathematicians have dug deeper to investigate the shape a...

Differences between numeracy and mathematicsDiscuss about the Report for Numeracy and Mathematics of Communicating Ideas. Mathematics is concerned with communicating ideas, searching for patterns, and solving problems. It involves the ability to apply logical and abstract reasoning to answer certain kinds of problems. On other words, mathematics is a language that assists in relaying complex concepts and ideas in a concise and precise man...