This final project discusses the development of Van Aubel’s theorem on nonconvex quadrilaterals with semicircles. The process of proving this theorem uses the cosine rule, and the congruence and congruence approaches. In a nonconvex quadrilateral, each side is constructed as a semicircle, with the diameter of each semicircle being a side of the non-convex quadrilateral. If the midpoints …
This final project presents fractional derivatives of polynomial functions with Caputo concept and related with gamma function and beta function. The fractional derivative is denoted by D(α)f (x) with α is fractional number greater than 0 and x is a variable. The result of the final project present that fractional derivatives provide more subtle and detailed changes from the original function…
This final project discusses general inverse on interval matrices and its applicationto climate change data. The topic of interval number arithmetic has attracted the attention of a number of researchers, especially in the context of multiplication operations. Some definitions of multiplication operations by researchers do not produce identities when interval numbers are multiplied by their i…
This final project presents increasingly rapid development of interval numbers. Many researchers have discussed algebraic operations on the number of intervals by presenting different formulas mainly on the multiplication formula and the division of two interval numbers. The formula given by many such researchers has a weakness that multiplication of an interval number with its inverse does not…
The Ministry of Education and Culture emphasizes that the five elements of mathematical ability are very important for students, one of which is mathematical reasoning ability. Current conditions show that students' mathematical reasoning skills are still low, this is influenced by the lack of independent learning habits, limited learning resources, and the lack of variations in learning approa…
This final project discusses the validity of Hamiltonian and Hypohamiltonian properties of the Petersen graph and the generalized Petersen graph (GPn,6) by constructing steps to find the existence of the Hamilton cycle. A graph that has a Hamilton cycle is called a Hamiltonian graph. Furthermore, a graph that is not Hamiltonian and if one of the vertices is removed then it will form a Hamilto…
This research aims to enhance the learning process and boost the Mathematical Problem Solving Ability (KPMM) among Class XII MIPA students at SMA Negeri 1 Langgam through the implementation of the Problem-Based Learning (PBL) model. Conducted as classroom action research, the study proceeded in two cycles and employed various learning tools and data collection instruments. These tools included …
This final project discusses the Moore-Penrose inverse of interval matrices. The development of interval numbers has been studied by many researchers. For example, the multiplication operation of interval numbers, but the operation used by most researchers still has a weakness, namely the result of multiplying an interval number with its inverse does not produce an identity. Therefore, a modi�…
The topic of interval numbers is growing quite fast. There are many researchers who have discussed the arithmetic of interval numbers. However, the multipli- cation operation defined by some researchers does not produce an identity when an interval number is multiplied by its inverse, so in this study a modification is needed for the arithmetic of interval numbers, especially in the multiplica-…
Development of interval numbers have shown various beliefs regarding the arith- metic and the formulas. There are several multiplication and division operations that apply to interval numbers, but those operations have the same problems such as the result of multiplying an interval number and its inverse does not produce an identity and division is undefined if several conditions are not met. …
One of the problems in the field of optimization is the determination of vehicle routes. Determining the shortest route is very important because waste pickup must be done in a short and timely manner by maximizing the use of trans- portation equipment to reduce transportation costs. Therefore, it is important to design the route and pickup of waste. This research focuses on the design of the V…
This final project discusses the entry age normal and projected unit credit methods with Pareto distribution to determine normal pension contributions. The entry age normal method is a method that assumes that every employee is already a participant in the pension program when first hired or after meeting the requirements and the projected unit credit method is a method that divides the total p…
This final project discusses the alternative diagonalization process on the tri- angular fuzzy number matrix of size n n in parametric form. Many forms of arithmetic operations have been given by the author, especially triangular fuzzy numbers. For addition, subtraction and scalar multiplication operations there is not much difference while for multiplication, division and inverse there are m…
This final project discusses the pattern generation method to solve the cut- ting stock problem with a 2-dimensional size. The pattern generation method produces a feasible cutting pattern which is then converted to a linear program- ming model with an objective function to minimum the use of stock materials. The research was conducted at Handal Karya Buana company which is a glass cutting comp…
This final project presents fractional derivatives for composition of trigonome- tric functions using the Caputo concept and the limit concept. The fractional derivative order is 0 < α 1, α is a fractional number. This final project re- sulting a present comparison of the performance of the Caputo concept and the limit concept in handling composition of trigonometric functions. Fractional …
A worker is eager for a guaranteed life in old age. A worker is not always in maximum condition, so a worker must have a plan from the beginning so that they can guarantee their old age. worker must have a plan from the start in order to guarantee welfare in the future when entering retirement age, among other solutions is by participating in a pension fund insurance program. This thesis discus…
Each insurance participant pays a premium to the insurance company during the coverage period. In paying the sum insured to insurance participants, insurance companies need to prepare reserve costs. This reserve fee is used to pay for the needs of insurance companies and insurance participants. The purpose of this research is to determine the full preliminary term reserve of last survivor endow…
This final of project discusses the solution of sensitivity analysis of grey linear programming using simplex method. Sensitivity analysis is used to determine the limits of grey number changes in the objective function coefficients, changes in the value of the right-hand side of the constraint function, and changes in the nonbasic column coefficients of the constraint function so that the opti…
This final project discusses the interaction of two populations consisting of predator population and prey population in an ecosystem. The predator-prey model used is the Lotka-Volterra model with nonlinear prey harvesting and square root functional response. The nonlinear prey harvesting considers pre- dator harvesting rates that are not proportional to prey population size. The predator-prey …