06.05 Applications of Systems of Equations
Part 1
1. Tony and Belinda have a combined age of 56. Belinda is 8 more than twice Tony’s age. How old is each? Tony’s age = t years, Belinda’s age = 56 - t years
56 - t = 2t + 8
56 - 8 = 2t + t ==> 3t = 48 ==> t = 16 years
THUS Tony = 16 years, and Belinda = 40 years
2. Salisbury High School decided to take their students on a field trip to a theme park. A total of 150 people went on the trip. Adults pay $45.00 for a ticket and students pay $28.50 for a ticket. How many students and how many adults went to the park if they paid a total of $4770? Adults = a, and Students = 150 - a

45a + 28.5(150 - a) = 4770
45a + 4275 - 28.5a = 4770 ==> 16.5a = 4770 - 4275 = 495
a = 495 / 16.5 = 30,
Adult = 30, Students = 120
3. Your piggy bank has a total of 46 coins in it; some are dimes and some are quarters. If you have a total of $7.00, how many quarters and how many dimes do you have? Dimes = d, and Quarter = 46 - d

d/10 + (46 - d) /4 = 7
Multiply both sides by 20, which gives
2d + 5(46 - d) = 140 ==> 2d + 230 - 5d = 140
-3d = 140 - 230 = -90 ==> d = 30
Dimes = 30, and Quarters = 16
Part 2
c = current of river
b = rate of boat
d = s(t) will represent (distance = speed X time)
Upstream: 60 = 6(b-c)
Downstream: 60 = 3(b+c)
There are now two separate equations: 60 = 6b - 6c and 60 = 3b + 3c Solve both equations for b:
b = 10 + c
b = 10 – c
Now make both equations equal each other and solve for c:
10 + c = 20 – c
2c = 10
c = 5
The speed of the current was 5 mph
Now, plug the numbers into one of either the original equations to find the speed of the boat in still water. I chose the first equation: b = 10 + c or b = 10 + 5 b = 15 The speed of the boat in still water must remain a consistent 15 mph or more in order for Wayne and his daughter to make it home in time or dinner.

...Hall
Differential Equations
March 2013
Differential Equations in Mechanical Engineering
Often times college students question the courses they are required to take and the relevance they have to their intended career. As engineers and scientists we are taught, and even “wired” in a way, to question things through-out our lives. We question the way things work, such as the way the shocks in our car work to give us a smooth ride back and forth to school, or what really happens to an object as it falls through the air, even how that people can predict an approximate future population. These questions, and many more, can be answered and explained through different variations of differential equations. By explaining and answering even just one of these questions through different differential equations I will also be answering two other important questions. Why is differential equations required for many students and how does it apply in the career of a mechanical engineer?
First some background. What is a differential equation?
A differential equation is a mathematical statement that contains one or more derivatives. It states a relationship involving the rates of change of continuously changing quantities modeled by functions. They are used whenever a rate of change is known but the process
giving rise to it is not. The solution of a differential equation...

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x y 8 x y 2
by graphing
by substitution
by elimination
by Cramer’s rule
2.
2 x 5 y 9 0 x 3y 1 0
by graphing
by substitution
by elimination
by Cramer’s rule
3.
4 x 5 y 7 0 2 x 3 y 11 0
by graphing
by substitution
by elimination
by Cramer’s rule
CASE 1: intersecting lines independent & consistent m1m2
CASE 2: parallel lines inconsistent m1 = m2 ; b1 b2
CASE 3: coinciding lines consistent & dependent m1 = m2 ; b1 = b2
Classify the following system, whether (a) intersecting, (b) parallel, or (c) coinciding lines 1.
3 x 4 y 1 0 3 x 4 y 2 0 3 x 4 y 1 0 6 x 8 y 2 0
Solve the following systems in three variables: 1. 3 x 4 y z 1 2. x y 2
x 4 y 3z 3 3 x 2 y 2 z 0
________
3 y z 1 x 2 z 7
2.
________
3.
2 x 5 y 1 0 5 x 2 y 2 0
2 x y 1 4 x 2 y 3 x 2 y 1 0 2 x y 1
________
4.
________
5.
________
1 x Solve 1 x
2 3 y 3 2 y
Problem solving Form a system of equations from the problems given below. A) (MIXTURE PROBLEM 1) How many pounds of a 35% salt solution and a 14% salt solution should be combined so that a 50 pounds of a...

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MSc. Esra DİRGAR 1, Assoc. Prof. Dr. Ziynet ÖNDOĞAN 2
1
2
Ege University Bergama Vocation School, Bergama – Izmir / Turkey
Ege University Engineering Faculty Textile Engineering Department, Bornova - Izmir / Turkey
INTRODUCTION
Consumers now demand more variety in product lines and retailers expect faster delivery, better quality and
lower costs. As global markets change, manufacturing strategies are also changing. Flexible manufacturing
that strives to be responsive to customer demand. For the apparel manufacturing plant, flexible
manufacturing means the capability to quickly and efficiently produce a variety of styles in small production
runs with no defects. This may require philosophy changes, new performance criteria, effective use of new
technology and beter development and use of resources than with traditional production systems. The
underlying philosophy is that the manufacturing firm will operate with the flexibility needed to meet the
needs of its customers and the inherent ability to adapt to immediate changes in the apparel market.
Firms that are able to operate in a flexible manufacturing environment have a strategic advantage in the
marketplace. Although flexible manufacturing involves the entire firm, much of the focus for improving
flexibility has been on the production function.
METHODOLOGY
An apparel production system...

...INFORMATION SYSTEMS AND SOFTWARE APPLICATIONS
Information Systems and Software Applications
Christine Jones
University of Phoenix
Information Systems and Software Applications
In today’s world the use of information systems and software applications are critical to the workplace. “Information systems (IS) collects, processes, stores, analyzes, and disseminates information for a specific purpose” (Rainer & Turban, 2008). “Information systems refers to technology designed to handle the data that institutions receive, process, generate, save, backup, disseminate, and use to make decisions” (Smith, 2007). IS do not have to be used with computers, but with today’s technology, most IS are associated with them. Computer-based information systems (CBIS) are made up of a few components including hardware, software and people, just to name a few. Software applications are “a set of computer instructions that provide more specific functionality to a user” (Rainer & Turban, 2008). An example of a software application is Microsoft Word, the popular word processing application that is standard on most computers. Software applications exist to make work easier for computer users. The same can be said for information systems, both IS and software...

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Moreover, a CRM system fails may be attributable to limited scalability. MYCUSTOMER (2012) reviews that if more users are added, the system would slow to an extent being unusable. When the capacity cannot expend serve more users, errors will occur causing inaccurate and inconsistent record. This leads to low utilization of CRM system.
Low adoption from employees is also a major cause of failure when introducing CRM system. The reason why a CRM system is unpopular is just because it is too complicated to use. According to a view of Paterson (2007, as cited in Sims, 2007), firms usually...

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University of Phoenix
BSA 411, Systems Analysis Methodologies
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Business ApplicationSystem
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University of Phoenix
BIS/320
January 14, 2013
Dr. Kathryn J. Moland, PMP
TWC: Operating Systems and Software Applications
Time Warner Cable (TWC) is one of the nation’s largest cable companies and being such has a large network of hardware and software at its disposal. According to "Time Warner Cable" (2013), its mission statement is to connect people and businesses with information, entertainment, and to give customers controls that are simple and easy to use. TWC utilizes Microsoft Windows XP and Microsoft Office giving the employees access from a TWC location or by a virtual private network (VPN) setup by the employee. Employees also have access to web based email that can be accessed via the internet anywhere in the World. In today’s business environment, technology is continually changing and improving. Operating systems and applications are used within companies worldwide to gather, disseminate, and control the flow of information. The application software can range from general covering a broad spectrum of information to addressing very specific information, enabling an organization to meet objectives.
Reaching Company Objectives
Both the operating system and software applications improve the organizations ability to operate in an efficient and effective manner. There are...

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Shirlene Furbush
Axia College, University of Phoenix
The advent of technology in the workplace has revolutionized the way the world does business. This is true with computers, which sets the stage for the technology globally. Global businesses can now be run by a single person, and a single computer can do the work of thousands. Large organizations have taken advantage of cutting-edge technology and developed powerful tools to help them harvest, analyze, and disseminate information, in order to make them more competitive. Human Resources, Marketing, and Accounting are just a few organizational departments running “smart” applications to run the business more smoothly.
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