Title: To find the maximum volume of a box using the method of differentiation. Problem statement: Mr. Lee, owner of a private cake company, sells a square 5 inch cake in a box made from 50 x 50 cm sheets of material. He would like to put a bigger square 8 inch cake in a box made from the same 50 x 50 com sheets of material. He decided to use the method of differentiation to help him with his task. Method:
1. Three squares measuring 50 x 50 cm were cut from bristol board sheets using rulers, set squares, pencils and scissors. It is from this square that the smaller squares of sides (x) will be cut from the edge. 2. The differential of the volume of the box was found, and the value of (x) that would give the maximum volume was found by substituting the (x) values into the second differential. 3. Then smaller squares of size (x), which was found to be 8.33 x 8.33 cm, were cut from the edges of the 50 x 50 cm square. The cut shape was then folded and taped to provide the box with the maximum volume. 4. A square of sides 2 cm was cut from the edge of the 50 x 50 cm sheet. The flat shape was also folded and taped to produce a box. 5. A square of sides 20 cm was also cut from the edge of the 50 x 50 cm sheet. The flat shape was also folded to produce a box. 6. Appropriate calculations were made to prove that the square 2 cm and the square 20 cm did not produce a box with the maximum volume.
The concept used to solve the problem
To calculate the volume of the cube, length x breadth x height was utilized. This gave a cubic equation. This equation was then differentiated which gave a quadratic formula. dydx was then equated = 0. The quadratic was then solved using the quadratic formula ( x=b±b24ac2a) to obtain two values of (x). These values were then substituted into the second differential (d2ydx2). If the value substituted produced a negative value, then that will be the length of...
...Title of Project
An investigation into a quadratic expression used to represent a parabolic edge in designing a flower garden utilizing calculus to determine the maximum area of the lawn
Purpose of the Project
Mr. Jack is an avid gardener and he is considering a new design for his garden. He has a rectangular lawn measuring 5 metres by 3 metres and wants to dig up part of it to include a flower bed. He desires to have a parabolic edge for the flower bed as shown below in Figure 1.
FIGURE 1
Objectives of Project
To find an expression that would best represent the parabolic edge.
To use Integration to find an expression for the area of the lawn.
To Differentiate the expression for the area to determine the maximum area of the lawn.
To investigate possible lawn design options with the area found in objective
Mathematical Formulation
y
p
h q x FIGURE 2
1) Finding an expression to represent the parabolic edge of the flower bed which is also the parabolic edge of...
...Ruel Wallace
Add Maths S.B.A
Mr. Teesdale
58
Table of Contents
Cover page……………………………………………………………………………………………1
Table of contents…………………………………………………………………………………..2
Title……………………………………………………………………………………………………...3
Problem Statement………………………………………………………………………………..4
Mathematical Formulation…………………………………………………………………….5
Problem Solution…………………………………………………………………………………..7
Application of Solution…………………………………………………………………………14
Conclusion…………………………………………………………………………………………...15
Title
A mathematical investigation of an experimental package design by Trini Chocolate Designs Ltd. with the goal of minimizing volume of content of packaging and manufacturing cost using Calculus, Trigonometry and Pythagoras Theorem.
Problem Statement
To determine how effective a container is, in adequately storing chocolate and how innovative the use of the package will be. Trigonometry Pythagoras Theorem and Calculus is used to determine:
1) The max cross sectional area of the pentagonal prism
2) The minimum value of the contents
3) Amount material needed for packaging
4) The minimum number of containers in order to make a profit
Mathematical Formulation
In part, (a) we insert a perpendicular bisector at A...
...Innovating new packaging by determining the best suitable level of efficiency with the use of calculus for Trini Chocolate Delights.
JABARI BOWMAN
ADD MATH
SBA
CLASS: 56
SCHOOL: ST. MARY’S COLLEGE
TEACHER: MR. YIPYOUNG
Problem Statement
The project’s purpose is to work out the best level of production to suit the new packaging for ‘Trini Chocolate Delights ltd.’
The company’s objective is to maximize produce of their new product but minimize manufacturing cost. To fulfill this task the use of calculus is needed along with other mathematical methods to help design a best suitable and cheap packaging that will be used to carry a grand amount of smaller products while cost remain in a stead/safe amount.
Mathematical Formulation
Below is a list of formulas applied to each question
A. Tan =

B. Substitution
Area of triangle + Area of rectangle= Area of pentagon
C. Differentiation
D. The quadratic equation
The quadratic formula
OR
Factorization of the quadratic formula
E.
Problem solution
A
Problem diagram
E B
ycm
D 8xcm C
i) F is the midpoint of line EB and it’s also the perpendicular of triangle EAB. The line AF cuts triangle EAF in half resulting in two isosceles triangles.
Since AFB= AFE and DC=EB, then FB and EF are both equal to 4xcm.
,...
...Abstract
This research engineers an examination on the types of documents and equipment used in the accounts office. It is completed in three parts:
Criteria One – Preparation
Criteria Two – Gathering Data
Criteria Three – Presentation
Introduction
This School based Assessment was done by a fifth form student of the Nehemiah Comprehensive School. It is based on a research which was done on the types of document and equipment used in Digicel (a cellular phone company).
Title of Project
Documents and equipments used in the accounts office of Digicel.
Aims of Project
* To research the various methods used in securing the documents and equipment used in the accounts department of Digicel.
* Find out what documents and equipments are used in the accounting department.
Functions of the Accounts Office
The accounts office in Digicel has many functions. Some of these functions are:
* To calculate the profit and loss of the business.
* Advise the manager on how to maximize profits and cut back on expenses.
Questionnaire
1. Are there any Branches of this company around the country? If so how many?
________________________________________________________________________________________________________________________________________________________________________________
2. What type of leadership would you say is portrayed in the accounts office?...
...
VANSA DOOKERAN Additional Mathematics SBA
School Based Assessment
Vansa Dookeran 5X
TABLE OF CONTENTS
Page #
Project Title 3
Purpose of Project 3
Method of Data Collection 4
Presentation of Data 6
Analysis of Data 18
Discussion of Findings and Conclusion 31
Bibliography 33
Appendix 34
Title: To investigate the time taken to achieve knockdown of crawling insects using two different types of insecticide.
Purpose of Project :
Mr Del Rey has an infestation of the leaf cutter ant, locally known as the ‘bachac’ in his garden. He needs to get rid of them as soon as possible and wants to use an insecticide that will get the job done quickly and efficiently. This experiment seeks to help Mr Del Rey choose the more effective insecticide by comparing the time taken to kill or achieve knockdown of bachacs using two different types of insectide; a commercial spray insecticide and a powder insecticide. The insect will be declared dead (i.e. knockdown would have been achieved) when it has flipped on its side or back, laying motionless. The effectiveness of each insecticide will be determined by the average time taken to kill the bachacs; the shorter the time taken, the more effective the insecticide.
Controlled Variables:
* The shape and size of containers used : 100 8oz cylindrical Styrofoam...
...DESCRIPTION OF THE BUSINESS
The name of the proposed business is Palmer’s Chocolate Delights. This business will be a sole trader business which will be owned and controlled by Mr. Renardo Palmer. The entrepreneur venture into this type of business because it is easy to manage and control and also because all the profits will generated to him as he is the sole proprietor. Chocolate based products are in high demand and as such Mr. Palmer thought that it would be more profitable to produce goods of that nature.
The business specializes in a wide variety of chocolate based products such as doughnuts, cakes, milk, candy etc… The main objective will to be a profit but also to focus on providing employment and pleasing customers in the best way possible.
ROLE OF THE ENTREPRENEUR
An entrepreneur is an individual who organizes and operates a business or businesses taking on financial risk to do so.
As an entrepreneur I will have the responsibility of ensuring this business venture gets off the ground with the limited resources I have available. In addition I will have to spend a number of hours working out details, finalizing the business plan meeting with loan officers, interviewing applicants and ironing out problems that may surface at times. In planning for this business I will have to decide on policies and procedures so that I can look ahead and determine the short and long term goals of the business.
In organizing for the success...
...ADVERTORIAL
JPS to Invest over $800 Million
in Munro Wind Project
Only two months after the recommissioning of the Constant Spring Hydroelectric
Plant, JPS is again laying the foundation for another renewable energy project.
This time the source is wind
energy – with the prospective
wind generation facilities
being earmarked in the
Munro/Hermitage
community of St. Elizabeth.
The project will see the
erection of four wind
“The project will see
the erection of four
wind turbines,
utilizing the most
modern engineering
design...”
turbines, utilizing the most
modern engineering design
approved for electrical grid
application. The project will
cost JPS over J$800 Million,
and is scheduled for
completion by the 4th quarter
of 2010. It will result in the
addition of 3 megawatts of
electricity to the national grid.
In preparation for the new
development, on Thursday,
February 4, JPS hosted a
public meeting at Munro
College in St. Elizabeth to
discuss the Environmental
Impact Assessment report, in
keeping
with
the
requirements of the National
Environment and Planning
Agency (NEPA).
The discussion covered the
social and economic impact
Mayor of Black River, His Worship Jeremy Palmer (left), listens keenly as JPS Vice President of Generation Expansion,
Valentine Fagan (centre), explains how the Munro Wind Project, will operate. Also sharing in the moment is Principal of
Munro College, Branford Gayle.
of the wind project on...
... INTRODUCTION
In what ways did the culture and lifestyle of the Tainos people differ from or resemble that of the Kalinagos?
The Tainos and Kalinagos were two different indigenous groups which inhabited the islands of the Caribbean. The Tainos were generally characterised as a peaceful people. They resided on the islands of the Greater Antilles such as Cuba, Jamaica, Puerto Rico, Hispaniola, and the Bahamas. The Kalinagos, who were far more hostile than the Tainos ,lived in the islands of the Lesser Antilles such as St.Kitts and Nevis ,Grenada, St. Vincent, St. Lucia and Dominica. Although the Tainos and the Kalinagos were indigenous peoples, they had differences and similarities in their culture. Three aspects which were most prominent and will be further studied between both groups were their social organisation, religious beliefs and political organisation.
AREA OF RESEARCH
Caribbean History of Indigenous People during the PreColumbian Period
Aim: To highlight the differences and similarities between the culture and lifestyle of of the Tainos and Kalinagos and conduct a comparative analysis thereof.
RATIONALE
During his four years at secondary school the researcher was enthralled by the early history of the Caribbean, more precisely, the...