3.9: Social Media Jobs. Why Understanding Basic Marketing Principles Will Put You Ahead of the Rest
It’s a prevalent myth that social media management is all about mastering different social media websites. The better you are with using the latest technology and creating and posting content across social accounts, the more successful you will be along the journey.
However, social media management is more about marketing than using social accounts. Therefore, you ought to grasp basic marketing principles. If you understand basic marketing concepts, you can stand out and do well as compared to other candidates.
The evolution of technology has offered a variety of platforms to marketers, but marketing principles stay almost the same. If you know marketing, you can apply these principles to promote a brand online and generate results.
The Intern Always Gets Blamed
At the beginning of your professional journey, you may need to work as an intern to get experience, increase knowledge, and learn useful skills alongside experienced professionals.
The internship is a rewarding yet challenging job. You get the opportunity to gain plenty of useful information, but the tasks can be never-ending. Moreover, if anything goes wrong, there is a good chance you will be blamed for the mistake as the junior-most staff member in the organization.
It’s a part of the learning journey. You need to be headstrong and accept feedback without getting angry. This knowledge will help you when you start working as a regular social media management employee and can use this learning to your advantage.
How Boring is Your Resume?
When you apply for a job, the resume is your first introduction to potential employers. They decide whether or not it’s a good idea to interview you for the job based on this professional document. If it’s too boring, lacks information, and doesn’t highlight the information they are looking for, you can already say goodbye to that internship opportunity you have been dreaming of.
Recruiters evaluate your skills, personality, strengths, and qualifications with the help of your resume. So, you can’t ignore the importance of this document. If you have got rejected by recruiters or afraid that recruiters may not consider your application, then it’s a good idea to update and redesign your resume.
It’s best to invest in an attractive resume design that highlights your skills, qualifications, experience, and personal strengths. At the beginning of the career, you may benefit from a chronological order resume or design a custom theme that fits the specifications of organizations where you want to apply for a social media marketing vacancy.
Since recruiters get a huge number of candidate resumes, you can get more visibility and an edge over other candidates with the help of an attractive document format. Before finalizing it, make sure you proofread the document for potential errors and spice it up with attractive designs to increase your chance of getting hired.
Is Linkedin Still a Thing?
Launched in 2003 as a social network for professionals, LinkedIn has been going strong since its inception. It is one of the best websites to set up your professional profile and interact with professional experts from different fields.
LinkedIn facilitates you to share thoughts and knowledge with other users on the platform who might be interested in the insights you share. You can also have one-on-one chats with people via its secure private message service.
Since LinkedIn is getting old, it is rumored that this platform is losing its charm. However, it’s an evergreen platform that is extremely useful in this era of technology.
Many recruiters prefer to invite and hire candidates via LinkedIn. It’s because they can evaluate the person to some extent before the interview with the help of their profile and the content they share. In fact, many recruiters conduct short interviews through LinkedIn to save time and make the recruitment process much simpler.
So, it’s recommended for business professionals, especially marketers to create LinkedIn profiles. If you stay active and regularly post relevant and informative content, you can build relationships and get job offers with ease.
Going Solo
Working as a social media marketer with an expert team of professionals can offer you learning opportunities. You can get useful tips those team members learned through years of experience. They can also guide you about enhancing your skills and the right path for progressing in the industry.
However, taking up a full-time job isn’t for everyone. You may have dreams of making your name as an established social media marketer and this dream can come true only by working solo and launching your entrepreneurial career.
You may want to become a freelancer and gradually set up your social media marketing agency once you build a network of business connections and clients.
Before starting your agency, you ought to develop a business plan that covers necessary information about the business such as potential customers, vendors, business strategy, financial resources to execute plans, and your team that can work hard for the future of the organization. You may want to invest in a professional website to build authenticity and credibility.
Building Your Portfolio
Whether you plan to take up a job as a social media marketer or aim to launch your social media agency, you need a portfolio. A portfolio is a set of previous work that demonstrates your skills.
When you send your resume to a potential employer, they would ask for your portfolio to determine how good you are at what you do. Similarly, this portfolio will prove helpful when you reach clients and offer your social media management services for their business or professional needs.
As a beginner at social media marketing, you may struggle to get your first job or assignment. You can create social media profiles for your freelancing journey. By managing these accounts the right way, you can show clients and recruiters that you are good at the job.
Furthermore, you can also present detailed insights into the performance of social media campaigns you may carry out to promote your personal brand.


13.15: Design and Sales
- Use an example of store design that would likely impact sales
IKEA: A Case Study in Leveraging Store Layout to Impact Sales
We mentioned in the last section that the forced path layout is not the most logical or pleasant shopping experience for the customer, who more often likes to wander around at his leisure, looking at the things he wants to see, when he wants to see them. Imagine, for instance, if your grocery store was set up in a forced path layout. You’d have to go through the baby food section even if you didn’t have kids. You’d go past alcohol even if you weren’t a drinker, and through the junk food section even if you were on a diet. No one wants to waste their time on a forced path layout, right?
IKEA begs to differ. In fact, IKEA breaks all the rules, and yet they win in the end.
We learned that customers like to shop on the same floor they entered the store on. Not at IKEA. Almost always, a shopper enters the store and is shepherded right up an escalator to the second floor, like in the diagram above.
We learned that customers also like to start out going to the right. Not at IKEA. Left is okay at IKEA. Clockwise is also very okay at IKEA. In the diagram above, people head to their left and start their way around the display showrooms. And, before you question it . . . you almost never see people going in the opposite direction of the suggested path. That’s not okay at IKEA.
Finally, we learned that people like wide aisles, which IKEA features in their paths . . . but not in their room displays. And yet, in an IKEA display, people will gather three and four deep to marvel at how the Swedish can live so economically in such a small amount of space.
IKEA breaks all the rules, and yet it provides a shopping experience beyond all others. Shoppers clamor for it. So why does this forced path floor plan work for them?
Alan Penn, director of the Virtual Reality Centre for the Built Environment, claims, “IKEA’s store layout is a psychological weapon used to confuse and disorientate (sic) shoppers into spending more.”
Learn More
You can watch Alan Penn’s full lecture here:
You can view the transcript for “Who enjoys shopping in IKEA? (18 Jan 2011)” here (opens in new window) .
At first blush, you may not think such a thing is even possible, but it’s absolutely true. Think about the simplest form of that: You find something you like as you’re wandering through the maze of rooms, and you’re afraid to put it down for fear you may not find it again.
This also holds true for the flat-packed furniture the customer will pick up later in the warehouse. As they roam the IKEA offerings in the showroom, they can’t pick up the item right where they see it. They have to grab a slip of paper and write down the location of that item in the warehouse, which is the second part of the IKEA experience. Which table does the customer want? Well, maybe this one, maybe that. He writes them both down, and then finds they’re so inexpensive when he gets to the warehouse that he buys both. At this point, he’s seen how adaptable the piece is. It was shown to him being used in four different rooms.
The “people following each other” in the forced flow format allows for every area of the store to be shopped—every part of the store experiences uniform foot traffic. As we well know, merchandise not seen is merchandise not bought. Almost nothing is unseen at an IKEA.
Finally, to get to the part of the warehouse where you buy the flat-packed furniture, you have to go through a “marketplace” of deeply discounted items, everyday items like napkin holders and light bulbs, casserole dishes and martini glasses. The price is a compelling enough reason to add them to your basket, but again, the forced flow is making a play: shoppers grab them because they don’t want to buck the flow of foot traffic, they don’t want to have to go back and find it.
IKEA’s unconventional choice of layout impacts their sales very positively, so much so that they have over 250 stores in 26 countries, and their profits are in the billions.
Contributors and Attributions
- Design and Sales. Authored by : Freedom Learning Group. Provided by : Lumen Learning. License : CC BY: Attribution
- IKEA Building Warehouse. Authored by : mastrminda. Provided by : Pixabay. Located at : https://pixabay.com/photos/ikea-building-warehouse-furniture-1376853/ . License : CC0: No Rights Reserved
- Who enjoys shopping in IKEA? (18 Jan 2011). Authored by : UCL Lunch Hour Lectures. Located at : https://youtu.be/NkePRXxH9D4 . License : All Rights Reserved . License Terms : Standard YouTube License


10.7: Why It Matters- Retail Operations and Managing the Store
What you’ll learn to do: Define the operational policies and tasks to be implemented in a retail business
Effective employees are the backbone of any company. In a retail company, employees are the first people your customers meet. Without an excellent workforce filled with people who are happy with their work, your business might suffer.
How do you find the right people for your organization?
Finding the right people and matching them up with the correct job is a component of the tasks of your human resources department.
What are the specific tasks that they need to accomplish? How do they accomplish your hiring goals? In this section, we’ll discuss employee screening, interviewing and hiring. Once you have hired people then the real training begins in order to help them serve your customers.
Contributors and Attributions
- Why It Matters: Retail Operations and Managing the Store. Authored by : Freedom Learning Group. Provided by : Lumen Learning. License : CC BY: Attribution
- See Different . Authored by : Photo by BBH Singapore. Provided by : Unsplash. Located at : https://unsplash.com/photos/ym7vBCce9L8 . License : CC BY: Attribution


9.3: Intimate Partner Violence
Intimate partner violence (IPV) is a serious, preventable public health problem that affects millions of Americans. The term “intimate partner violence” describes physical, sexual, or psychological harm by a current or former partner or spouse. This type of violence can occur among heterosexual or same-sex couples and does not require sexual intimacy.
The goal is to stop IPV before it begins. There is a lot to learn about how to prevent IPV. We do know that strategies that promote healthy behaviors in relationships are important. Programs that teach young people skills for dating can prevent violence. These programs can stop violence in dating relationships before it occurs.IPV can vary in frequency and severity. It occurs on a continuum, ranging from one episode that might or might not have lasting impact to chronic and severe episodes over a period of years.
The Four Main Types of Intimate Partner Violence
- Physical violence is the intentional use of physical force with the potential for causing death, disability, injury, or harm. Physical violence includes, but is not limited to, scratching; pushing; shoving; throwing; grabbing; biting; choking; shaking; aggressive hair pulling; slapping; punching; hitting; burning; use of a weapon; and use of restraints or one’s body, size, or strength against another person. Physical violence also includes coercing other people to commit any of the above acts.
-
Sexual violence
is divided into five categories.  Additionally all of these acts occur without the victim’s freely given consent, including cases in which the victim is unable to consent due to being too intoxicated (e.g., incapacitation, lack of consciousness, or lack of awareness) through their voluntary or involuntary use of alcohol or drugs.
- Rape or penetration of victim – This includes completed or attempted, forced or alcohol/drug-facilitated unwanted vaginal, oral, or anal insertion. Forced penetration occurs through the perpetrator’s use of physical force against the victim or threats to physically harm the victim.
- Victim was made to penetrate someone else – This includes completed or attempted, forced or alcohol/drug-facilitated incidents when the victim was made to sexually penetrate a perpetrator or someone else without the victim’s consent.
- Non-physically pressured unwanted penetration – This includes incidents in which the victim was pressured verbally or through intimidation or misuse of authority to consent or acquiesce to being penetrated.
- Unwanted sexual contact – This includes intentional touching of the victim or making the victim touch the perpetrator, either directly or through the clothing, on the genitalia, anus, groin, breast, inner thigh, or buttocks without the victim’s consent
- Non-contact unwanted sexual experiences – This includes unwanted sexual events that are not of a physical nature that occur without the victim’s consent.
- Stalking is a pattern of repeated, unwanted, attention and contact that causes fear or concern for one’s own safety or the safety of someone else (e.g., family member or friend). Some examples include repeated, unwanted phone calls, emails, or texts; leaving cards, letters, flowers, or other items when the victim does not want them; watching or following from a distance; spying; approaching or showing up in places when the victim does not want to see them; sneaking into the victim’s home or car; damaging the victim’s personal property; harming or threatening the victim’s pet; and making threats to physically harm the victim.
- Psychological Aggression i s the use of verbal and non-verbal communication with the intent to harm another person mentally or emotionally, and/or to exert control over another person. Psychological aggression can include expressive aggression (e.g., name-calling, humiliating); coercive control (e.g., limiting access to transportation, money, friends, and family; excessive monitoring of whereabouts); threats of physical or sexual violence; control of reproductive or sexual health (e.g., refusal to use birth control; coerced pregnancy termination); exploitation of victim’s vulnerability (e.g., immigration status, disability); exploitation of perpetrator’s vulnerability; and presenting false information to the victim with the intent of making them doubt their own memory or perception (e.g., mind games).
Risk Factors for Intimate Partner Violence
Persons with certain risk factors are more likely to become perpetrators or victims of intimate partner violence (IPV). Those risk factors contribute to IPV but might not be direct causes. Not everyone who is identified as “at risk” becomes involved in violence.
A combination of individual, relational, community, and societal factors contribute to the risk of becoming an IPV perpetrator or victim. Understanding these multilevel factors can help identify various opportunities for prevention.
Individual Risk Factors
- Low self-esteem
- Low income
- Low academic achievement
- Young age
- Aggressive or delinquent behavior as a youth
- Heavy alcohol and drug use
- Depression
- Anger and hostility
- Antisocial personality traits
- Borderline personality traits
- Prior history of being physically abusive
- Having few friends and being isolated from other people
- Unemployment
- Emotional dependence and insecurity
- Belief in strict gender roles (e.g., male dominance and aggression in relationships)
- Desire for power and control in relationships
- Perpetrating psychological aggression
- Seeing or being a victim of physical or psychological abuse (consistently one of the strongest predictors of perpetration)
- History of experiencing poor parenting as a child
- History of experiencing physical discipline as a child
Relationship Factors
- Marital conflict-fights, tension, and other struggles
- Marital instability-divorces or separations
- Dominance and control of the relationship by one partner over the other
- Economic stress
- Unhealthy family relationships and interactions
Community Factors
- Poverty and associated factors (e.g., overcrowding)
- Low social capital-lack of institutions, relationships, and norms that shape a community’s social interactions
- Weak community sanctions against IPV (e.g., unwillingness of neighbors to intervene in situations where they witness violence)
Societal Factors
- Traditional gender norms (e.g., women should stay at home, not enter workforce, and be submissive; men support the family and make the decisions)
Protecting Yourself from Relationship Violence
It can be hard to know if your relationship is headed down the wrong path. While it’s not always possible to prevent relationship violence, there are steps you can take to protect yourself.
If you think your partner might be controlling or abusive, it’s important to:
- Trust your feelings. If something doesn’t seem right, take it seriously.
- Learn the warning signs of someone who might become controlling or violent.
- Get help. Talk to experts in relationship violence.
If your partner is controlling or abusive, it’s better to get help now than to wait. Controlling or violent relationships usually get worse over time.
Remember: if your partner hurts you, it’s not your fault.
What is relationship violence?
Relationship violence is when one person in a relationship is abusive or controlling toward the other person – especially when they disagree about something.
Relationship violence is sometimes called dating violence, domestic violence, or intimate partner violence. In some relationships, both partners act in abusive or controlling ways.
When many people think about relationship violence, they think about physical violence, like hitting or pushing. But people can also use other methods, like threats or insults, to control their partners.
Relationship violence can include:
- Physical violence, like pushing, hitting, or throwing things
- Sexual violence, like forcing or trying to force someone to do something sexual
- Threats of physical or sexual violence, which may include threatening to hurt another person or a pet
- Emotional abuse, like embarrassing a partner or keeping that person away from family and friends
If you feel controlled by or afraid of your partner – even if you haven’t been hurt physically – trust yourself. There are people who can help you figure out what to do next.
How do I know if my relationship might become violent?
Relationship violence can start slowly and be hard to recognize at first. For example, when people first start dating, it’s common to want to spend a lot of time together. But spending less time with other people can also be a sign that your partner is trying to control your time.
Try asking yourself these questions:
- Does my partner respect me?
- Does my partner blame me for everything that goes wrong?
- Does my partner make most of the decisions in our relationship?
- Am I ever afraid to tell my partner something?
- Do I ever feel forced to do things that I don’t want to do?

- Does my partner promise to change and then keep doing the same things?
Get more information about the signs of abusive relationships .
What if I’m not sure if my relationship is violent?
It’s okay if you aren’t sure – you can still get help. Domestic violence agencies have counselors who are experts at helping people with questions about their relationships.
If you have questions about your relationship, call the National Domestic Violence Hotline at 1-800-799-SAFE (1-800-799-7233) or chat online with a trained advocate.
If you are in danger right now, call 911.
Take Action!
If you think your partner is controlling or abusive, take steps to protect yourself.
Trust your instincts.
 If you think your relationship is unhealthy or you are worried about your safety, trust your gut.
Plan for your safety.
- If you are in a relationship with someone who is violent or might become violent, make a plan to keep yourself safe. This is important whether you are planning to leave your partner or not.
Start with a phone call.
- If you need help or have questions about your relationship, call the National Domestic Violence Hotline at 1-800-799-SAFE (1-800-799-7233). You’ll be able to find a domestic violence agency near you or talk to a counselor over the phone. If you are in danger right now, call 911.
What kind of help can I get?
Domestic violence agencies provide:
- Emotional support
- Safety planning
- A safe place to stay in an emergency
- Legal help
- Help with housing
What about cost?
Domestic violence agencies offer free services, like hotlines, counseling, and help finding resources such as housing or lawyers.
Contributors and Attributions
Public Domain Content
- Intimate Parnter Violence Risk Factors. Authored by: National Center for Injury Prevention and Control, Division of Violence Prevention. Provided by: Centers for Disease Control and Prevention. Located at: http://www.cdc.gov/violenceprevention/intimatepartnerviolence/riskprotectivefactors.html . License: Public Domain: No Known Copyright
- Intimate Parnter Violence. Authored by: National Center for Injury Prevention and Control, Division of Violence Prevention. Provided by: Centers for Disease Control and Prevention. Located at: http://www.cdc.gov/violenceprevention/intimatepartnerviolence/index.html . License: Public Domain: No Known Copyright
- Take Steps to Protect Yourself from Relationship Violence . Authored by: healthfinder.gov. Provided by: U.S. Department of Health and Human Services. Located at: healthfinder.gov/HealthTopic...e#the-basics_4. License: Public Domain: No Known Copyright


7: The Properties of Real Numbers
A quilt is formed by sewing many different pieces of fabric together. The pieces can vary in color, size, and shape. The combinations of different kinds of pieces provide for an endless possibility of patterns. Much like the pieces of fabric, mathematicians distinguish among different types of numbers. The kinds of numbers in an expression provide for an endless possibility of outcomes. We have already described counting numbers, whole numbers, and integers. In this chapter, we will learn about other types of numbers and their properties.
-
- 7.1: Rational and Irrational Numbers
- A rational number is a number that can be written in the form p/q, where p and q are integers and q ≠ 0. Rational numbers consist of many decimals and all fractions and integers, both positive and negative. An irrational number is a number that cannot be written as the ratio of two integers. Its decimal form neither stops nor repeats. Some irrational numbers include pi and the square roots of numbers that are not perfect squares. Real numbers are numbers that are either rational or irrational.
-
- 7.2: Commutative and Associative Properties (Part 1)
- The commutative properties have to do with order. If you change the order of the numbers when adding or multiplying, the result is the same. When adding or multiplying three numbers, changing the grouping of the numbers does not change the result. This is known as the Associative Property of Addition and Multiplication, respectively. So, addition and multiplication are commutative and associative. But, subtraction and division are neither commutative nor associative.
-
- 7.3: Commutative and Associative Properties (Part 2)
- When we have to simplify algebraic expressions, we can often make the work easier by applying the Commutative or Associative Property first instead of automatically following the order of operations. No matter what you are doing, it is always a good idea to think ahead. When simplifying an expression, think about what your steps will be. For example, when adding and subtracting three or more terms involving decimals, look for terms that combine to give whole numbers.
-
- 7.4: Distributive Property
- The Distributive Property states that if a, b, c are real numbers, then a(b + c) = ab + ac. In algebra, we use the Distributive Property to remove parentheses as we simplify expressions. When you distribute a negative number, you need to be extra careful to get the signs correct. Sometimes we need to use the Distributive Property as part of the order of operations.
-
- 7.5: Properties of Identity, Inverses, and Zero
- Adding zero to any number doesn’t change the value. For this reason, we call 0 the additive identity. The opposite of a number is its additive inverse. The reciprocal of a number is its multiplicative inverse. A number and its reciprocal multiply to 1, which is the multiplicative identity. The product of any real number and 0 is 0. Zero divided by any real number except zero is zero. But division by zero is undefined.
-
- 7.6: Systems of Measurement (Part 1)
- In this section we will see how to convert among different types of units, such as feet to miles or kilograms to pounds. The basic idea in all of the unit conversions will be to use a form of 1, the multiplicative identity, to change the units but not the value of a quantity.
-
- 7.7: Systems of Measurement (Part 2)
- Performing arithmetic operations on measurements with mixed units of measures in the metric system requires the same care we used in the U.S. system. Many measurements in the United States are made in metric units. We make conversions between the systems just as we do within the systems—by multiplying by unit conversion factors. The U.S. and metric systems use different scales to measure temperature. The U.S. system uses degrees Fahrenheit. The metric system uses degrees Celsius.
Figure 7.1 - Quiltmakers know that by rearranging the same basic blocks the resulting quilts can look very different. What happens when we rearrange the numbers in an expression? Does the resulting value change? We will answer these questions in this chapter as we will learn about the properties of numbers. (credit: Hans, Public Domain)
Contributors and Attributions
-
Lynn Marecek (Santa Ana College) and MaryAnne Anthony-Smith (Formerly of Santa Ana College). This content is licensed under Creative Commons Attribution License v4.0 "Download for free at<EMAIL_ADDRESS>."


1.3: Hands-on Activity
Overview
This three-part assignment uses the online FEMA Emergency Management Institute courses and exam certifications that cover the following three topics:
- IS-860.C: The National Infrastructure Protection Plan, An Introduction
- IS-913.A: Critical Infrastructure Security and Resilience: Achieving Results through Partnership and Collaboration
- IS-921.A: Implementing Critical Infrastructure Security and Resilience
The focus is on five key subject sectors that the National Infrastructure Protection Plan identifies as “Lifeline” sectors: Energy, Water and Wastewater Systems, Communications, Transportation Systems, and Emergency Services. This module gives students a better understanding of what those assets are, what components are considered “critical,” and how to identify them for entry into the IP Gateway that serves as the single interface through which Department of Homeland Security (DHS) partners can access its integrated infrastructure protection tools and information.
Hands-on Activity Objectives
- Understand the roles and responsibilities of entities such as the DHS, sector-specific agencies, and state, local, tribal, and territorial governments.
- Describe the processes that support critical infrastructure security and resilience.
- Define critical infrastructure, protection, and resilience in the context of the National Infrastructure Protection Plan (NIPP).
- Identify strategies and methods for achieving results through critical infrastructure partnerships.
- Identify various methods for assessing and validating information.
- Describe critical infrastructure in communities and the impact Lifeline sector assets have on a community’s resiliency.
-
Discuss common standards bodies, such as the North American Electricity Reliability Council (NAERC) and National Institute of Standards and Technologies (NIST).
Independent Study Exams require a FEMA Student Identification (SID) Number. Students who do not have a SID can register for one at https://cdp.dhs.gov/femasid .
Questions regarding the FEMA Independent Study Program or other Emergency Management Institute (EMI) related requests, such as requests for certificates, transcripts, or online test scores/results, should be referred to the FEMA Independent Study program office at<PHONE_NUMBER> or emailed to<EMAIL_ADDRESS>. Please do not contact the FEMA SID Help Desk, as they are unable to provide assistance with such requests.
IS-860.C: The National Infrastructure Protection Plan, An Introduction
https://training.fema.gov/is/courseoverview.aspx?code=IS-860.c
Course Overview
Ensuring the security and resilience of the critical infrastructure of the United States is essential to the nation’s security, public health and safety, economic vitality, and way of life.
The purpose of this course is to present an overview of the National Infrastructure Protection Plan (NIPP). The NIPP provides the unifying structure for the integration of existing and future critical infrastructure security and resilience efforts into a single national program.
Learning Objectives
- Explain the importance of ensuring the security and resilience of critical infrastructure of the United States.
- Describe how the NIPP provides the unifying structure for the integration of critical infrastructure protection efforts into a single national program.
- Define critical infrastructure, protection, and resilience in the context of the NIPP.
Primary Audience
The course is intended for DHS and other federal staff responsible for implementing the NIPP, and tribal, state, local, and private sector emergency management professionals. The course is also designed to teach potential security partners about the benefits of participating in the NIPP.
Prerequisites
None
Course Length
2 hours
IS-913.A: Critical Infrastructure Security and Resilience: Achieving Results through Partnership and Collaboration
http://training.fema.gov/is/courseoverview.aspx?code=IS-913.a
Course Overview
The purpose of this course is to introduce the skills and tools to effectively achieve results for critical infrastructure security and resilience through partnership and collaboration.
The course provides an overview of the elements of and processes to develop and sustain successful critical infrastructure partnerships.
Learning Objectives
- Explain the value of partnerships to infrastructure security and resilience.
- Identify strategies to build successful critical infrastructure partnerships.
- Describe methods to work effectively in a critical infrastructure partnership.
- Identify processes and techniques used to sustain critical infrastructure partnerships.
- Identify strategies and methods for achieving results through critical infrastructure partnerships.
Primary Audience
The course is designed for critical infrastructure owners and operators from both the government and private sector and those with critical infrastructure duties and responsibilities at the state, local, tribal, and territorial levels.
Prerequisites
None. The following is recommended prior to starting the course:
- IS-921.A, Implementing Critical Infrastructure Security and Resilience
Course Length
2 hours
IS-921.A: Implementing Critical Infrastructure Security and Resilience
http://training.fema.gov/is/courseoverview.aspx?code=IS-921.a
Course Overview
This course introduces those with critical infrastructure duties and responsibilities at the state, local, tribal, and territorial levels to the information they need and the resources available to them in the execution of the mission to secure and improve resilience in the nation’s critical infrastructure.
Learning Objectives
- Summarize critical infrastructure responsibilities.
- Identify the range of critical infrastructure government and private-sector partners at the state, local, tribal, territorial, regional, and federal levels.
- Describe processes for effectively sharing information with critical infrastructure partners.
- Identify various methods for assessing and validating information.
Primary Audience
This course is designed for all individuals with critical infrastructure protection responsibilities.
Prerequisites
None. The following are recommended prior to starting the course:
- Review of the National Infrastructure Protection Plan (NIPP) and Critical Infrastructure Support Annex to the National Response Framework (NRF) documents.
OR
-
Completion of the following Independent Study courses:
- IS-860.B, National Infrastructure Protection Plan (NIPP); and
- IS-821.A, Critical Infrastructure Support Annex.
Course Length
3 hours
Assignment Deliverables
- Completion of all three FEMA Emergency Management Institute courses and exam certifications.
Grading Criteria Rubric
- Students should submit copies of all three exam completion certificates.
Grade points: 300


11: The Genetic Code and Translation
-
- 11.1: Introduction
- We begin this chapter with a look at how the genetic code was broken (deciphered). The very terms genetic code, broken and deciphered came from what was at the time, the recent history of the World War II. We will look at the elegant experiments that first deciphered the amino acid meaning of a few 3-base codons, and then all 64 codons. Of these, 61 encode amino acids and three are stop codons.
-
- 11.2: An Overview of the Genetic Code
- The genetic code is the information for linking amino acids into polypeptides in an order based on the base sequence of 3-base code words (codons) in a gene and its messenger RNA (mRNA). With a few exceptions (some prokaryotes, mitochondria, chloroplasts), the genetic code is universal – it’s the same in all organisms from viruses and bacteria to humans.
-
- 11.3: Gene and Protein Colinearity and Triplet Codons
- Serious efforts to understand how proteins are encoded began after Watson and Crick used the experimental evidence of Maurice Wilkins and Rosalind Franklin (among others) to determine the structure of DNA. Most hypotheses about the genetic code assumed that DNA (i.e., genes) and polypeptides were colinear.
-
- 11.4: Translation
- Like any polymerization in a cell, translation occurs in three steps: initiation brings a ribosome, mRNA and an initiator tRNA together to form an initiation complex. Elongation is the successive addition of amino acids to a growing polypeptide. Termination is signaled by sequences (one of the stop codons) in the mRNA and protein termination factors that interrupt elongation and release a finished polypeptide. The events of translation occur at specific A, P and E sites on the ribosome.
Thumbanil: Diagram of RNA translation. (CC BY 3.0 - unported; Kelvinsong ).


8.3: Constitutional Protections Afforded Juveniles
The United States Supreme Court has held that in juvenile commitment proceedings, juvenile courts must afford to juvenile’s basic constitutional protections, such as advance notice of the charges, the right to counsel, the right to confront and cross-examine adverse witnesses, and the right to remain silent. [ In re Gault , 387 U.S. 1, 87 S. Ct. 1428, 18 L. Ed. 2d 527 (1967).] The Supreme Court has extended the search and seizure protections of the Fourth Amendment to juveniles. [ New Jersey v. T.L.O. , 469 U.S. 325, 333, 105 S. Ct. 733, 738, 83 L. Ed. 2d 720 (1985).] It has also been held that the Fourth Amendment requires that a juvenile arrested without a warrant be provided a probable cause hearing. [ Moss v. Weaver , 525 F. 2d 1258, 1259-60 (5th Cir. 1976).] The exclusionary rule also applies to federal delinquency adjudications. [ United States v. Doe , 801 F. Supp. 1562, 1567-72 (E.D. Tex. 1992). ]
Juveniles are entitled to Fifth Amendment protection against self-incrimination in juvenile proceedings despite the non-criminal nature of those proceedings. [ In re Gault , 387 U.S. at 49-50, 87 S. Ct. at 1455-56 .] Substance, not form, controls in determining the applicability of the Fifth Amendment to proceedings not labeled criminal. Id. at 49-50, 87 S. Ct. at 1455-56. Since a juvenile defendant's liberty is at stake, the Fifth Amendment applies.
Juveniles are not, however, accorded the full panoply of rights that adult criminal defendants are accorded, such as the right to trial by jury. [ McKeiver v. Pennsylvania , 403 U.S. 528, 91 S. Ct. 1976, 29 L. Ed. 2d 647 (1971).] Most of the opinions reason that a jury trial is not required because the Act does not treat alleged juvenile delinquents as alleged criminals, and therefore, the Constitution does not mandate it.
Figure 8.2 Juvenile Justice Center in Kern County. JJC by Tabitha Raber is used under a CC BY 4.0 license.
The McKeiver court stated that, "(t)here is a possibility, at least, that the jury trial, if required..., will remake the juvenile proceeding into a fully adversary process and will put an effective end to what has been the idealistic prospect of an intimate, informal protective proceeding." [403 U.S. at 545, 91 S. Ct. at 1986.] As a result, juvenile courts still process juvenile delinquents in a manner more paternal and diagnostic than that afforded their adult criminal counterparts. [ Alexander S. by and through Bowers v. Boyd , 876 F. Supp. 773, 781 (D.S.C. 1995). ]
A juvenile is accorded all due process rights at a juvenile hearing which includes the right to contest the value of the evidence offered by the government. [ Kent v. United States , 383 U.S. 541, 563, 86 S. Ct. 1045, 1058, 16 L. Ed. 2d 84 (1966).] Although juvenile adjudications are adjudications of status rather than criminal liability, the government must still prove beyond a reasonable doubt that a juvenile is a delinquent. [In re Winship, 397 U.S. 358, 90 S. Ct. 1068, 25 L. Ed. 2d 368 (1970). ]
Proceedings for adjudication of a juvenile as a delinquent shall be in district court. [ 18 U.S.C.A. § 5032 (West Supp. 1995).] The court may convene at any time and place within the district, in chambers or otherwise, to take up the proceedings of juvenile delinquency. A juvenile may consent to having a magistrate judge preside over cases involving a Class B or C misdemeanor, or an infraction. [ 18 U.S.C.A. § 3401(g) (West Supp. 1995).] There is a certain advantage to the juvenile in exercising this option since a magistrate judge cannot impose a term of imprisonment in these situations. Id. Proceedings in misdemeanor cases can be ordered to be conducted before a district judge rather than a magistrate judge by the court's own motion or upon petition with good cause by the United States Attorney. [18 U.S.C.A. § 3401(f) (West 1985). ]


5.5: Intellectual Property
What you’ll learn to do: explain the purpose and characteristics of intellectual property law
In this section we’ll discuss the importance of intellectual property law and explain what is covered by it.
Learning Objectives
- Explain patents
- Explain trademarks
Intellectual Property
Patent pending: Solar Puff is a solar-powered inflatable light that was designed to provide an affordable and renewable light source to disaster-relief victims. The light uses the principles of origami and foldable design to “pop” open from a flat envelope into a cube.
To this point we have discussed laws governing people and things, but what about laws protecting knowledge or ideas?
The notion that knowledge is valuable goes back to ancient times. In the 1st century AD, Juvenal (55–130) observed, “All wish to know but none wish to pay the price.” However, the value of knowledge in an economic or business sense—knowledge recognized as a type of asset or property that one might wish to protect—is much more recent, dating back to the seventeenth century or so (the Statute of Monopolies [1624] and the British Statute of Anne [1710] are seen as firmly establishing the concept of “intellectual property”). Since then, a special body of law concerning the protection of knowledge and ideas has developed. Known as intellectual property law, these laws cover intangible assets such as patents, trademarks, and copyright.
What Is Intellectual Property?
The term intellectual property refers to creations of the mind—creative works or ideas embodied in a form that can be shared or enable others to recreate, emulate, or manufacture them. There are three main ways to protect intellectual property: patents, trademarks, and copyrights.
Patents protect inventions and improvements to existing inventions for a limited period of time in exchange for detailed public disclosure of those inventions.
Trademarks include any word, name, symbol, or device, or any combination, used, or intended to be used in commerce to identify and distinguish the goods of one manufacturer or seller from goods manufactured or sold by others, and to indicate the source of the goods. Service marks include any word, name, symbol, device, or any combination, used, or intended to be used, in commerce, to identify and distinguish the services of one provider from services provided by others, and to indicate the source of the services.
Copyright is a form of protection provided by the laws of the United States (title 17, U.S.Code) to the authors of “original works of authorship,” including literary, dramatic, musical, artistic, and certain other intellectual works. This protection is available to both published and unpublished works.
A Creative Commons (CC) license is one of several public copyright licenses that enable the free distribution of an otherwise copyrighted work. A CC license is used when an author wants to give people the right to share, use, and build upon a work that they have created. CC provides an author flexibility and protects the people who use or redistribute an author’s work from concerns of copyright infringement as long as they abide by the conditions that are specified in the license by which the author distributes the work.
According to Cornell University Law School, “intellectual property is any product of the human intellect that the law protects from unauthorized use by others.” Take a look at the following video to learn more about what intellectual property is and why it matters.


2.3: Types of Inventory
Identifying Types of Inventory
Organizations typically manage several types of inventory, including:
- Raw materials or purchased parts: These are the basic components or materials required for production or assembly processes.
- Work in process (WIP) or work in progress: These are semi-finished or partially completed items found in the middle of assembly lines and manufacturing facilities.
- Finished goods or merchandise: These are the final products ready for sale and distribution to customers, commonly found in retail stores and warehouses.
- Spare parts, tools, and supplies: These are additional inventory items required for maintenance, repair, and operational purposes within the organization.
Understanding and effectively managing these different types of inventory is crucial for organizations to ensure smooth operations, meet customer demand, and maintain optimal inventory levels. The inventory management models discussed in this chapter will provide insights and techniques to help organizations make informed decisions regarding order quantities and timing, ultimately leading to improved customer service and cost efficiency.
Source
" 8.2 Types of Inventory " from Fundamentals of Operations Management Copyright © 2024 by Azim Abbas and Seyed Goosheh is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.


2.1: Prelude to Thinking
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How do you feel about the ways you think? Take this quick survey to figure it out, ranking questions on a scale of 1–4, 1 meaning “least like me” and 4 meaning “most like me.” These questions will help you determine how the chapter concepts relate to you right now. As you are introduced to new concepts and practices, it can be informative to reflect on how your understanding changes over time. We’ll revisit these questions at the end of the chapter to see whether your feelings have changed.
You can also take the Chapter 7 Survey anonymously online.
STUDENT PROFILE
"I never considered myself a problem solver. I was more creative. I wrote music and fiction, and saw myself in a musical theater career. Two years of college and two majors later, I had moved into a related pathway: entertainment management. I was thrilled to find something that suited my passions and gave me a great shot at a number of jobs. But I hadn’t counted on the business and math courses I needed to take. Solving these types of problems wasn’t in my skill set. I didn’t have the background, and kept missing half the ideas. I started going to the academic success center and office hours, and managed to keep my grades in the passing range. But I wasn’t excelling and couldn’t stay ahead. It was a struggle.
"During a study session, a success counselor noticed that I was approaching a problem all wrong. She helped me for the next hour -- not working on the problem itself, but on how I was thinking about it and others like it. She asked me about the information I knew, how I put it together, and so on. She taught me a progression of steps to analyze the components, get the data I needed, ignore the unimportant information, and run the numbers. Then she had me watch a TED talk with some more information.
"I realized that it wasn’t my prior knowledge that was holding me back. It was the way I was thinking about the work. I started asking my professors more about how to approach the courses -- how to think about them. I didn’t start getting A’s right away, but I did get better results, and even felt more creative as I started to try new things."
In this chapter, you’ll be introduced to different ways of thinking about the way you think. By the time you complete this chapter, you should be able to do the following:
Whether we admit it or not or even consider it or not, we cannot stop thinking. We think during intense work situations, while we’re playing games, when we eat, as we watch a movie, even during meditation that purports to empty the mind of all thought. Skilled and practiced yogis may be able to get into a state that resembles non-thinking, but most of us keep thinking all the time. Perhaps as you read these lines, you doubt their accuracy suggesting that you don’t really think when you’re just relaxing with friends. But you do. You may think about the other people in the group and what you do or do not know about them. You may wonder what you’ll eat for your next meal. Your mind may flit to question whether you locked the door on the way out. Or you may debate internally whether you’ll finish on time the assignment due for one of your classes. Now, you may not act on any of those random thoughts during this relaxing time, but you are nonetheless thinking. As you begin this exploration of thinking, consider all the ways we turn to technology to assist with our thinking and how thinking impacts and defines various careers.
When you consider the word thinking, does your mind drift toward:
Reflect on your answer, and write one or two sentences on why you associate this idea with thinking.
In this chapter, we’ll look more closely at several distinct types of thinking including creative, analytical, and critical thinking, all of which come into play for problem-solving. We’ll also explore the multitude of resources available relative to understanding and enhancing your thinking skills, all of which constitutes metacognition, the practice of thinking about your thinking.


21.1: Operators in Quantum Mechanics
The central concept in this new framework of quantum mechanics is that every observable (i.e., any quantity that can be measured in a physical experiment) is associated with an operator. To distinguish between classical mechanics operators and quantum mechanical ones, we use a hat symbol \(\hat{}\) on top of the latter. Physical pure states in quantum mechanics are represented as unit-norm (probabilities are normalized to one) vectors in a special complex Hilbert space. Following the definition, an operator is a function that projects a vector in the Hilbert space onto the space of physical observables. Since observables are values that come up as the result of the experiment, quantum mechanical operators must yield real eigenvalues. 16 Operators that possess this property are called Hermitian . In the wave mechanics formulation of quantum mechanics that we have seen so far, the wave function varies with space and time—or equivalently momentum and time—and observables are differential operators. A completely analogous formulation is possible in terms of matrices. In the matrix formulation of quantum mechanics, the norm of the physical state should stay fixed, so the evolution operator should be unitary, and the operators can be represented as matrices.
The expectation value of an operator \(\hat{A}\) for a system with wave function \(\psi(\mathbf{r})\) living in a Hilbert space with unit vector \(\mathbf{r}\) (i.e., in three-dimensional Cartesian space \(\mathbf{r} = \left\{ x,y,z \right\}\)), is given by:
\[ \langle A \rangle = \int \psi^{*}({\bf r}) \hat{A} \psi({\bf r}) d{\bf r}, \label{22.1.1} \]
and if \(\hat{A}\) is a Hermitian operator, all physical observables are represented by such expectation values. It is easy to show that if \(\hat{A}\) is a linear operator with an eigenfunction \(g\), then any multiple of \(g\) is also an eigenfunction of \(\hat{A}\).
Basic Properties of Operators
Most of the properties of operators are obvious, but they are summarized below for completeness.  The identity operator \(\hat{1}\) does nothing (or multiplies by 1):
\[ {\hat 1} f = f \label{22.1.5} \]
The associative law holds for operators:
\[ \hat{A}(\hat{B}\hat{C}) = (\hat{A}\hat{B})\hat{C} \label{22.1.6} \]
The commutative law does not generally hold for operators. In general, \(\hat{A} \hat{B} \neq \hat{B} \hat{A}\). It is convenient to define the quantity:
\[ [\hat{A}, \hat{B}]\equiv \hat{A} \hat{B} - \hat{B} \hat{A} \label{22.1.7} \]
which is called the commutator of \(\hat{A}\) and \(\hat{B}\). Note that the order matters, so that \([ \hat{A}, \hat{B}] = - [ \hat{B}, \hat{A}]\). If \(\hat{A}\) and \(\hat{B}\) happen to commute, then \([\hat{A}, \hat{B}] = 0\).
Linear Operators
Almost all operators encountered in quantum mechanics are linear. A linear operator is any operator \(\hat{A}\) satisfying the following two conditions:
\[ \begin{equation} \begin{aligned} \hat{A} (f + g) &= \hat{A} f + \hat{A} g, \\ \hat{A} (c f) &= c \hat{A} f, \end{aligned} \end{equation}\label{22.1.8} \]
where \(c\) is a constant and \(f\) and \(g\) are functions. As an example, consider the operators \(\dfrac{d}{dx}\) and \(()^2\). We can see that \(\dfrac{d}{dx}\) is a linear operator because:
\[ \begin{equation} \begin{aligned} \dfrac{d}{dx}[f(x) + g(x)] &=\dfrac{d}{dx}f(x) + \dfrac{d}{dx}g(x), \\ \dfrac{d}{dx}[c f(x)] &= c (d/dx) f(x). \end{aligned} \end{equation}\label{22.1.9} \]
However, \(()^2\) is not a linear operator because:
\[ (f(x) + g(x))^2 \neq (f(x))^2 + (g(x))^2 \label{22.1.10} \]
Hermitian Operators
Hermitian operators are characterized by the self-adjoint property:
\[ \int \psi_a^{*} (\hat{A} \psi_a)d{\bf r} = \int \psi_a (\hat{A} \psi_a)^{*}d{\bf r}, \label{22.1.11} \]
where the integral is performed over all space. This property guarantees that all the eigenvalues of the operators are real. Defining \(a\) as the eigenvalue of operator \(\hat{A}\) using:
\[ \hat{A} \psi({\bf r}) = a \psi({\bf r}), \label{22.1.12} \]
we can prove that \(a\) is real by replacing Equation \ref{22.1.12} into Equation \ref{22.1.11}:
\[ \begin{equation} \begin{aligned} a \int \psi_a^{*} \psi_a d{\bf r}&= a^{*} \int \psi_a \psi_a^{*} d{\bf r}\\ (a - a^{*}) \int \vert\psi_a\vert^2 d{\bf r} &= 0, \end{aligned} \end{equation}\label{22.1.13} \]
and since \(\vert\psi_a\vert^2\) is never negative, either \(a = a^{*}\) or \(\psi_a = 0\). Since \(\psi_a = 0\) is not an acceptable wavefunction, \(a = a^{*}\), and \(a\) is real.
The following additional properties of Hermitian operators can also be proven with some work:
\[ \int \psi^{*}\hat{A} \psi d{\bf r} = \int (\hat{A} \psi)^{*} \psi d{\bf r}, \label{22.1.14} \]
and for any two states \(\psi_1\) and \(\psi_2\):
\[ \int \psi_1^{*} \hat{A} \psi_2 d{\bf r}= \int (\hat{A} \psi_1)^{*} \psi_2 d{\bf r}. \label{22.1.15} \]
Taking \(\psi_a\) and \(\psi_b\) as eigenfunctions of \(\hat{A}\) with eigenvalues \(a\) and \(b\) with \(a \neq b\), and using Equation \ref{22.1.15}, we obtain:
\[ \begin{equation} \begin{aligned} \int \psi_a^{*} \hat{A} \psi_b d{\bf r} &= \int (\hat{A} \psi_a)^{*} \psi_b d{\bf r}\\ b \int \psi_a^{*} \psi_b d{\bf r} &= a^{*} \int \psi_a^{*} \psi_b d{\bf r}\\ (b - a) \int \psi_a^{*} \psi_b d{\bf r} &= 0. \end{aligned} \end{equation}\label{22.1.16} \]
Thus, since \(a = a^{*}\), and since we assumed \(b \neq a\), we must have \(\int \psi_a^{*} \psi_b d{\bf r} = 0\), i.e. \(\psi_a\) and \(\psi_b\) are orthogonal. In other words, eigenfunctions of a Hermitian operator with different eigenvalues are orthogonal (or can be chosen to be so).
- But they might not be strictly real.


3.2: Introduction to Biological Foundations of Human Development
What you’ll learn to do: explain the role of genetics in prenatal development
Contributors and Attributions
CC licensed content, Shared previously
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In this section, we will look at some of the ways in which heredity helps to shape the way we are. Heredity involves more than genetic information from our parents. According to evolutionary psychology, our genetic inheritance comes from the most adaptive genes of our ancestors. We will look at what happens genetically during conception and take a brief look at some genetic abnormalities. Before going into these topics, however, it is important to emphasize the interplay between heredity and the environment.  As you consider some of your features (height, weight, personality, health, etc.), ask yourself whether these features are a result of heredity, or environmental factors, or both. Chances are, you can see the ways in which both heredity and environmental factors (such as lifestyle, diet, and so on) have contributed to these features.


18.5: Newton's Laws of Motion
Check Your Understanding
5.1. 14 N, 56° measured from the positive x-axis
5.2. a. His weight acts downward, and the force of air resistance with the parachute acts upward. b. neither; the forces are equal in magnitude
5.3. 0.1 m/s 2
5.4. 40 m/s 2
5.5. a. 159.0 \(\hat{i}\) + 770.0 \(\hat{j}\) N; b. 0.1590 \(\hat{i}\) + 0.7700 \(\hat{j}\) N
5.6. a = 2.78 m/s 2
5.7. a. 3.0 m/s 2 ; b. 18 N
5.8. a. 1.7 m/s 2 ; b. 1.3 m/s 2
5.9. 6.0 × 10 2 N
5.10.
Conceptual Questions
1. Forces are directional and have magnitude.
3. The cupcake velocity before the braking action was the same as that of the car. Therefore, the cupcakes were unrestricted bodies in motion, and when the car suddenly stopped, the cupcakes kept moving forward according to Newton’s first law.
5. No. If the force were zero at this point, then there would be nothing to change the object’s momentary zero velocity. Since we do not observe the object hanging motionless in the air, the force could not be zero.
7. The astronaut is truly weightless in the location described, because there is no large body (planet or star) nearby to exert a gravitational force. Her mass is 70 kg regardless of where she is located.
9. The force you exert (a contact force equal in magnitude to your weight) is small. Earth is extremely massive by comparison. Thus, the acceleration of Earth would be incredibly small. To see this, use Newton’s second law to calculate the acceleration you would cause if your weight is 600.0 N and the mass of Earth is 6.00 x 10 24 kg.
11. a. action: Earth pulls on the Moon, reaction: Moon pulls on Earth; b. action: foot applies force to ball, reaction: ball applies force to foot; c. action: rocket pushes on gas, reaction: gas pushes back on rocket; d. action: car tires push backward on road, reaction: road pushes forward on tires; e. action: jumper pushes down on ground, reaction: ground pushes up on jumper; f. action: gun pushes forward on bullet, reaction: bullet pushes backward on gun.
13. a. The rifle (the shell supported by the rifle) exerts a force to expel the bullet; the reaction to this force is the force that the bullet exerts on the rifle (shell) in opposite direction. b. In a recoilless rifle, the shell is not secured in the rifle; hence, as the bullet is pushed to move forward, the shell is pushed to eject from the opposite end of the barrel. c. It is not safe to stand behind a recoilless rifle.
15. a. Yes, the force can be acting to the left; the particle would experience deceleration and lose speed. b. Yes, the force can be acting downward because its weight acts downward even as it moves to the right.
17. Two forces of different types: weight acting downward and normal force acting upward
Problems
19. a. \(\vec{F}_{net}\) = 5.0 \(\hat{i}\) + 10.0 \(\hat{j}\) N
b. The magnitude is F net = 11 N, and the direction is \(\theta\) = 63°
21. a. \(\vec{F}_{net}\) = 660.0 \(\hat{i}\) + 150.0 \(\hat{j}\) N
b. F net = 676.6 N at \(\theta\) = 12.8° from David’s rope
23. a. \(\vec{F}_{net}\) = 95.0 \(\hat{i}\) + 283 \(\hat{j}\) N
b. 299 N at 71° north of east
c. \(\vec{F}_{DS}\) = − (95.0 \(\hat{i}\) + 283 \(\hat{j}\)) N
25. Running from rest, the sprinter attains a velocity of v = 12.96 m/s, at end of acceleration. We find the time for acceleration using x = 20.00 m = 0 + 0.5at 1 2 , or t 1 = 3.086 s. For maintained velocity, x 2 = vt 2 , or t 2 = \(\frac{x_{2}}{v}\) = \(\frac{80.00\; m}{12.96\; m/s}\) = 6.173 s. Total time = 9.259 s.
27. a. m = 56.0 kg
b. a meas = a astro + a ship , where a ship = \(\frac{m_{astro} a_{astro}}{m_{ship}}\)
c. If the force could be exerted on the astronaut by another source (other than the spaceship), then the spaceship would not experience a recoil.
29. F net = 4.12 x 10 5 N
31. a = 253 m/s 2
33.  a. \(\vec{F}_{net}\) = m\(\vec{a} \Rightarrow \vec{a}\) = 9.0 \(\hat{i}\) m/s 2
b. The acceleration has magnitude 9.0 m/s 2 , so x = 110 m.
39. 1.6 \(\hat{i}\) − 0.8 \(\hat{j}\) m/s 2
41. a. w Moon = mg Moon , m = 150 kg, w Earth = 1.5 x 10 3 N
b. Mass does not change, so the suited astronaut’s mass on both Earth and the Moon is 150 kg.
43. a. F h = 3.68 x 10 3 N and w = 7.35 x 10 2 N, \(\frac{F_{h}}{w}\) = 5.00 times greater than weight
b.  a. F net = 2.64 x 10 7 N
b. The force exerted on the ship is also 2.64 x 10 7 N because it is opposite the shell’s direction of motion.
53. Because the weight of the history book is the force exerted by Earth on the history book, we represent it as \(\vec{F}_{EH}\) = −14 \(\hat{j}\) N. Aside from this, the history book interacts only with the physics book. Because the acceleration of the history book is zero, the net force on it is zero by Newton’s second law: \(\vec{F}_{PH} + \vec{F}_{EH} = \vec{0}\), where \(\vec{F}_{PH}\) is the force exerted by the physics book on the history book. Thus, \(\vec{F}_{PH} = − \vec{F}_{EH} = −(−14\; \hat{j})\; N = 14\; \hat{j}\; N\). We find that the physics book exerts an upward force of magnitude 14 N on the history book. The physics book has three forces exerted on it: \(\vec{F}_{EP}\) due to Earth, \(\vec{F}_{HP}\) due to the history book, and \(\vec{F}_{DP}\) due to the desktop. Since the physics book weighs 18 N, \(\vec{F}_{EP} = −18\; \hat{j}\; N\). From Newton’s third law, \(\vec{F}_{HP} = − \vec{F}_{PH}\), so \(\vec{F}_{HP} = −14\; \hat{j}\; N\). Newton’s second law applied to the physics book gives \(\Sigma \vec{F} = \vec{0}\), or \(\vec{F}_{DP} + \vec{F}_{EP} + \vec{F}_{HP} = \vec{0}\), so \(\vec{F}_{DP}\) = −(−18 \(\hat{j}\)) − (−14 \(\hat{j}\)) = 32 \(\hat{j}\) N. The desk exerts an upward force of 32 N on the physics book. To arrive at this solution, we apply Newton’s second law twice and Newton’s third law once.
55. a. The free-body diagram of the pulley closest to the foot:
b. T = mg, F = 2T cos \(\theta\) = 2mg cos \(\theta\)
57. a. 1.95 m/s 2
b. 1960 N
59. a. T = 1.96 x 10 −4 N
b. T′ = 4.71 x 10 −4 N, \(\frac{T′}{T}\) = 2.40 times the tension in the vertical strand
61. \[\begin{split} F_{y\; net} = F_{\perp} - 2T \sin \theta & = 0 \\ F_{\perp} & = 2T \sin \theta \\ T & = \frac{F_{\perp}}{2 \sin \theta} \end{split}\]
63. a. see Example 5.13
b. 1.5 N
c. 15 N
65. a. 5.6 kg
b. 55 N
c. T 2 = 60 N
d.
67. a. 4.9 m/s 2 , 17 N
b. 9.8 N
69.
71.
Additional Problems
73. 5.90 kg
75.
77. a. F net = \(\frac{m(v^{2} - v_{0}^{2})}{2x}\)
b. 2590 N
79. \[\begin{split} \vec{F}_{net} & = 6.02\; \hat{i} + 14.0\; \hat{j}\; N \\ \vec{F}_{net} & = m \vec{a} \Rightarrow \vec{a} = 0.602\; \hat{i} + 1.40\; \hat{j}\; m/s^{2} \end{split}\]
81. \[\begin{split} \vec{F}_{net} & = \vec{F}_{A} + \vec{F}_{B} \\ \vec{F}_{net} & = A \hat{i} + (-1.1A\; \hat{i} - 1.41A\; \hat{j}) \\ \vec{F}_{net} & = A(-0.41\; \hat{i} - 1.41\; \hat{j}) \end{split}\]
\(\theta\) = 254° (We add 180°, because the angle is in quadrant IV.)
83. \(F = 2mk^{2}x^{2}\); First, take the derivative of the velocity function to obtain \(a = 2kxv = 2kx(kx^2) = 2k^{2}x^{3}\). Then apply Newton’s second law \(F = ma = 2mk^{2}x^{2}\).
85. a. For box A, N A = mg and N B = mg cos \(\theta\)
b.  a. 8.66 N
b. 0.433 m
89. 0.40 or 40%
91. 16 N
Challenge Problems
93. a.
b. No; \(\vec{F}_{R}\) is not shown, because it would replace \(\vec{F}_{1}\) and \(\vec{F}_{2}\). (If we want to show it, we could draw it and then place squiggly lines on \(\vec{F}_{1}\) and \(\vec{F}_{2}\) to show that they are no longer considered.
95. a. 14.1 m/s
b. 601 N
97. \(\frac{F}{m}\)t 2
99. 936 N
101. \(\vec{a}\) = −248 \(\hat{i}\) − 433 \(\hat{j}\) m/s 2
103. 0.548 m/s 2
105. a. T 1 = \(\frac{2mg}{\sin \theta}\), T 2 = \(\frac{mg}{\sin (\arctan(\frac{1}{2} \tan \theta))}\), T 3 = \(\frac{2mg}{\tan \theta}\)
b. \(\phi = \arctan(\frac{1}{2} \tan \theta)\)
c. 2.56°
d. x = d(2 cos \(\theta\) + 2 cos(arctan(\(\frac{1}{2}\) tan \(\theta\))) + 1)
107. a. \(\vec{a}\) = (5.00 m \(\hat{i}\) + 3.00 m \(\hat{j}\)) m/s 2
b. 1.38 kg
c. 21.2 m/s
d. \(\vec{v}\) = (18.1 \(\hat{i}\) + 10.9 \(\hat{j}\)) m/s 2
109. a. 0.900 \(\hat{i}\) + 0.600 \(\hat{j}\) N
b. 1.08 N
Contributors and Attributions
Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a
Creative Commons Attribution License (by 4.0)
.


9: Space
Space in Two-Dimensional Design
Discussion:
Open Space
Open space in a two-dimensional image creates a feeling of openness. Traditionally, this space is represented in broad vistas such as a landscapes. With new concepts of space, such as worlds beyond earth, and super-sized man-made digital environments, images of open space are only limited by our imaginations!
Enclosed Space
Enclosed visual spaces may create a sense of mystery, privacy, or intimacy.
Jan Van Eyck
Street art by Dan in Bristol, U.K.
Packed Space
Packed spaces may feel energized by the sheer numbers of objects and forms. Packed spaces provide opportunities for visual movement adding to the energized design.
Assignment:
Part 1:
Using cutouts from magazines or other print media, create an open space design. Consider color and value placement to help create a feeling of openness.
Part 2:
Using cutouts from magazines or other print media, create an enclosed space design. Consider color and value placement to help create a feeling of a contained, intimate space. What is enclosing the space should be a major consideration in the design.
Part 3:
Using cutouts from magazines or other print media, create a packed space design. Consider color and value placement as well as carefully selected shapes to help create a feeling of movement and energy.


5.4: Unit 5 Summary
This unit introduced the learner to the peripheral device that can be connected to the computer. It dealt on the conversions of analog to digital data. the different wave forms representing conversions of the analog to digital data were also introduced. Also the multimedia data and what needs to be done for it to be transmitted across networks. The peripherals include computer mouse, keyboard, image scanners, tape drives, microphones, loudspeakers, webcams, and digital cameras.
Unit Assessment
The following section will test the learners understanding of this unit
Instructions
Answer the following questions
- Explain digitization of an analog signal?
- What is sampling in digitization?
- Explain the term animation
- Grading Scheme
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The marks will be awarded as shown below
Question Sub-question marks awarded 1 Explanation award 2 mark. extars like examples and diagrams award 2 extra marks; maximum 2 giving total 6 6 2 Definition award 2 marks 2 3 Explanation only 2 marks. 2 Total 10
Feedback
1. Digitalization of an analog signal involves two operations:
1) Sampling, and
2) Quantization
Analog signals consist of continuous values for both axes. An analog signal exists throughout a continuous interval of time and/or takes on a continuous range of values. A sinusoidal signal (also called a pure tone in acoustics) has both of these properties.
2.Sampling is the process of recording an analog signal at regular discrete moments of time.
3.Computer animation lies somewhere between the motionless world of still images and the real-time world of video images.


10.1.2: Problem Solving Approaches and Interventions
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There are six problem solving approaches and interventions most commonly used among practitioners. Each approach examines a different aspect of a social problem. The nature of the problem and people involved determines the most appropriate intervention to apply.
A social systems approach examines the social structure surrounding the problem or issue. This approach requires macro, meso, and micro levels of analysis (see pages 12-13) to help understand the structure of the problem and the arrangement of individuals and social groups involved. Analysis requires comprehension of the entire issue and parts associated, as well as, which components and protocols of the structure are independent or dependent of each other. Application of this approach requires grasp of the complete problem including the hierarchy, order, patterns, and boundaries of individuals and social groups including their interactions, relationships, and processes as a body or structure surrounding the issue (Bruhn and Rebach 2007).
The interventions deployed using a social systems approach focus on establishing and maintaining stability for all parties even while change is occurring. Social system interventions require change agents or leaders such as sociological practitioners to help control and guide inputs (what is put in or taken into the problem) and outputs (what is produced, delivered, or supplied resulting from change) used in problem solving (Bruhn and Rebach 2007). This approach requires the involvement of everyone in the social structure to design or re-design the system and processes around the issue.
The human ecology approach examines the “web of life” or the ecosystem of a social problem or issue. This approach is often visually represented by a spider web to demonstrate how lives are interlinked and interdependent. A human ecology approach focuses on macro and meso levels of analysis to develop knowledge about the social bonds, personal needs, and environmental conditions that impede or support life challenges and opportunities for individuals. Practitioners evaluate and analyze where individuals and groups fit in the social structure or ecosystem and their roles. The purpose of this approach is to identify cognitive and emotional boundaries people experience living in social systems to help confront and remove the obstacles they face.
Interventions applied in a human ecological approach target changes in families, institutions, and small communities. The goal is to confront the stressors and strain created by social situations and settings. Interventions from a human ecology approach help people determine acceptable behaviors within different social environments (Bruhn and Rebach 2007). Practitioners work with social groups to remove collaborative challenges between groups in a social ecosystem and the individuals working and living within them. Change is concentrated on developing a new system and process to support and remove obstacles for individuals effected by a social problem.
- Describe the social systems approach and explain what type of social problems or issues this approach is the most valid method to use.
- Describe the human ecology approach and explain what type of social problem or issues this approach is the most valid method to use.
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Which approach is the most appropriate for assessing and addressing the social conditions listed below. Use supporting evidence to justify your analysis.
- A county mental health court
- Gender neutral bathrooms on a college campus
- Anti-bullying campaign in local K-12 schools
A life cycle approach examines the developmental stages and experiences of individuals facing issues or various life crises. Meso and micro levels of analysis are required with this method. Data gathered assists practitioners in understanding the adaption of individuals or groups to change, challenges, and demands at each developmental stage of life (Bruhn and Rebach 2007). Analysis incorporates evaluation of interpersonal connections between a person and the environment, life transitions, and patterns. This approach if applicable when working with individuals, groups, and organizations, which all have and go through a life cycle and stages of development.
Interventions using this approach target changes in social norms and expectations of individuals or groups facing difficulties. Practitioners help identify the context and issues creating anxiety among individuals or groups and facilitate coping strategies to attack their issues. This approach builds on positive personal and social resources and networks to mend, retrain, or enable development and growth.
The clinical approach evaluates disease, illness, and distress. Both meso and micro levels of analysis are required for this method. Practitioners assess biological, personal, and environmental connections by surveying the patient or client’s background, and current and recent conditions (Bruhn and Rebach 2007). A Patient Evaluation Grid (PEG) is the most commonly used tool for data collection. This approach requires in-depth interactions with the patient or client to identify themes associated with their condition and the structure of the social system related to their illness and support. When applying this approach in medical practice, the evaluation and analysis leads to a diagnosis.
- Describe the life cycle approach and explain what type of social problems or issues this approach is the most valid method to use.
- Describe the clinical approach and explain what type of social problem or issues this approach is the most valid method to use.
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Which approach is the most appropriate for assessing and addressing the social issues listed below. Use supporting evidence to justify your analysis.
- Policing strategies to reduce crime and improve community relationships
- Reductions in self-injury or cutting among teens
- A community college social work education degree program
Intervention in a clinical approach concentrates on removal of symptoms, condition, or changes in the individual to solve the problem. The overarching goal of this method is to prevent the problem from reoccurring and the solution from interfering with the individual’s functioning. Problem management must minimally disrupt the social system of the patient or client.
A social norms approach focuses on peer influences to provide individuals with accurate information and role models to induce change (Bruhn and Rebach 2007). This approach observes macro, meso, and micro levels of analysis. Intervention centers on providing correct perceptions about thinking and behavior to induce change in one’s thoughts and actions. This technique is a proactive prevention model aimed at addressing something from happening or arising.
There are three levels of intervention when applying a social norms approach (Bruhn and Rebach 2007). Practitioners use interventions independently or together for a comprehensive solution. At the universal level of intervention , all members of a population receive the intervention without identifying which individuals are at risk. A selective level of intervention directs assistance or services to an entire group of at risk individuals. When specific individuals are beyond risk and already show signs of the problem, they receive an indicated level of intervention . A comprehensive intervention requires an integration of all three levels.
Practitioners assist communities in problem solving by applying a community based approach . All three levels of analysis (macro, meso, and micro) are required for this method. The aim of this approach is to plan, develop, and implement community based interventions whereby local institutions and residents participate in problem solving and work towards preventing future issues. Practitioners work with communities on three outcomes, individual empowerment, connecting people, and improving social interactions and cooperation (Bruhn and Rebach 2007). Concentrating on these outcomes builds on community assets while tailoring solutions to local political, economic, and social conditions. By building bridges among individuals and groups in the community, practitioners facilitate connections between services, programs, and policies while attacking the problem from multiple vantage points.
A community based approach helps ensure problem analysis, evaluation, and interventions are culturally and geographically appropriate for local residents, groups, and organizations. To operate effectively, this intervention requires practitioners to help facilitate face-to-face interactions among community members and develop a communication pattern for solving community problems. To build an appropriate intervention, practitioners must develop knowledge and understanding about the purpose, structure, and process of each group, organization, and collaboration within the community (Bruhn and Rebach 2007). Upon implementation, a community based approach endows local residents and organizations to observe and monitor their own progress and solutions directly.
- Describe the social norms approach and explain what type of social problems or issues this approach is the most valid method to use.
- Describe the community based approach and explain what type of social problem or issues this approach is the most valid method to use.
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Which approach is the most appropriate for assessing and addressing the social problems listed below. Use supporting evidence to justify your analysis.
- Human trafficking prevention program
- Reductions in electronic cigarette, vaping, and new tobacco product usage


9.11: Solve a Formula for a Specific Variable
- Use the distance, rate, and time formula
- Solve a formula for a specific variable
Before you get started, take this readiness quiz.
- Write 35 miles per gallon as a unit rate. If you missed this problem, review Example 5.11.8 .
- Solve 6x + 24 = 96. If you missed this problem, review Example 8.4.1 .
- Find the simple interest earned after 5 years on $1,000 at an interest rate of 4%. If you missed this problem, review Example 6.4.1 .
Use the Distance, Rate, and Time Formula
One formula you’ll use often in algebra and in everyday life is the formula for distance traveled by an object moving at a constant speed. The basic idea is probably already familiar to you. Do you know what distance you travel if you drove at a steady rate of 60 miles per hour for 2 hours? (This might happen if you use your car’s cruise control while driving on the Interstate.) If you said 120 miles, you already know how to use this formula!
The math to calculate the distance might look like this:
\[\begin{split} distance &= \left(\dfrac{60\; miles}{1\; hour}\right) (2\; hours) \\ distance &= 120\; miles \end{split}\]
In general, the formula relating distance, rate, and time is
\[distance = rate \cdot time\]
For an object moving in at a uniform (constant) rate, the distance traveled, the elapsed time, and the rate are related by the formula
\[d = rt\]
where d = distance, r = rate, and t = time.
Notice that the units we used above for the rate were miles per hour, which we can write as a ratio \(\dfrac{miles}{hour}\). Then when we multiplied by the time, in hours, the common units ‘hour’ divided out. The answer was in miles.
Jamal rides his bike at a uniform rate of 12 miles per hour for \(3 \dfrac{1}{2}\) hours. How much distance has he traveled?
Solution
| Step 1. Read the problem. You may want to create a mini-chart to summarize the information in the problem. | $$\begin{split} d &=\; ? \\ r &= 12\; mph \\ t &= 3 \dfrac{1}{2}\; hours \end{split}$$ |
| Step 2. Identify what you are looking for. | distance traveled |
| Step 3. Name . Choose a variable to represent it. | let d = distance |
| Step 4. Translate . Write the appropriate formula for the situation. Substitute in the given information. | $$\begin{split} d &= rt \\ d &= 12 \cdot 3 \dfrac{1}{2} \end{split}$$ |
| Step 5. Solve the equation. | d = 42 miles |
| Step 6. Check : Does 42 miles make sense? | |
| Step 7. Answer the question with a complete sentence. | Jamal rode 42 miles. |
Lindsay drove for \(5 \dfrac{1}{2}\) hours at 60 miles per hour. How much distance did she travel?
- Answer
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330 mi
Trinh walked for \(2 \dfrac{1}{3}\) hours at 3 miles per hour. How far did she walk?
- Answer
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7 mi
Rey is planning to drive from his house in San Diego to visit his grandmother in Sacramento, a distance of 520 miles. If he can drive at a steady rate of 65 miles per hour, how many hours will the trip take?
Solution
| Step 1. Read the problem. Summarize the information in the problem. | $$\begin{split} d &= 520\; miles \\ r &= 65\; mph \\ t &=\; ? \end{split}$$ |
| Step 2. Identify what you are looking for. | how many hours (time) |
| Step 3. Name . Choose a variable to represent it. | let t = time |
| Step 4. Translate . Write the appropriate formula for the situation. Substitute in the given information. | $$\begin{split} d &= rt \\ 520 &= 65t \end{split}$$ |
| Step 5. Solve the equation. | t = 8 |
| Step 6. Check : Substitute the numbers into the formula and make sure the result is a true statement. | $$\begin{split} d &= rt \\ 520 &\stackrel{?}{=} 65 \cdot 8 \\ 520 &= 520\; \checkmark \end{split}$$ |
| Step 7. Answer the question with a complete sentence. We know the units of time will be hours because we divided miles by miles per hour. | Rey's trip will take 8 hours. |
Lee wants to drive from Phoenix to his brother’s apartment in San Francisco, a distance of 770 miles. If he drives at a steady rate of 70 miles per hour, how many hours will the trip take?
- Answer
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11 hours
Yesenia is 168 miles from Chicago. If she needs to be in Chicago in 3 hours, at what rate does she need to drive?
- Answer
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56 mph
Solve a Formula for a Specific Variable
In this chapter, you became familiar with some formulas used in geometry. Formulas are also very useful in the sciences and social sciences—fields such as chemistry, physics, biology, psychology, sociology, and criminal justice. Healthcare workers use formulas, too, even for something as routine as dispensing medicine. The widely used spreadsheet program Microsoft Excel TM relies on formulas to do its calculations. Many teachers use spreadsheets to apply formulas to compute student grades. It is important to be familiar with formulas and be able to manipulate them easily.
In Example 9.57 and Example 9.58, we used the formula d = rt. This formula gives the value of d when you substitute in the values of r and t. But in Example 9.58, we had to find the value of t. We substituted in values of d and r and then used algebra to solve to t. If you had to do this often, you might wonder why there isn’t a formula that gives the value of t when you substitute in the values of d and r. We can get a formula like this by solving the formula d = rt for t.
To solve a formula for a specific variable means to get that variable by itself with a coefficient of 1 on one side of the equation and all the other variables and constants on the other side. We will call this solving an equation for a specific variable in general. This process is also called solving a literal equation. The result is another formula, made up only of variables. The formula contains letters, or literals.
Let’s try a few examples, starting with the distance, rate, and time formula we used above.
Solve the formula d = rt for t: (a) when d = 520 and r = 65 (b) in general.
Solution
We’ll write the solutions side-by-side so you can see that solving a formula in general uses the same steps as when we have numbers to substitute.
| (a) when d = 520 and r = 65 | (b) in general | |
| Write the formula. | d = rt | d = rt |
| Substitute any given values. | 520 = 65t | |
| Divide to isolate t. | $$\dfrac{520}{65} = \dfrac{65t}{65}$$ | $$\dfrac{d}{r} = \dfrac{rt}{r}$$ |
| Simplify. | $$\begin{split} 8 &= t \\ t &= 8 \end{split}$$ | $$\begin{split} \dfrac{d}{r} &= t \\ t &= \dfrac{d}{r} \end{split}$$ |
Notice that the solution for (a) is the same as that in Example 9.58. We say the formula t = \(\dfrac{d}{r}\) is solved for t. We can use this version of the formula anytime we are given the distance and rate and need to find the time.
Solve the formula d = rt for r: (a) when d = 180 and t = 4 (b) in general
- Answer a
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\(r = 45\)
- Answer b
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\(r = \frac{d}{t}\)
Solve the formula d = rt for r: (a) when d = 780 and t = 12 (b) in general
- Answer a
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\(r = 65\)
- Answer b
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\(r = \frac{d}{t}\)
We used the formula A = \(\dfrac{1}{2}\)bh in Use Properties of Rectangles, Triangles, and Trapezoids to find the area of a triangle when we were given the base and height. In the next example, we will solve this formula for the height.
The formula for area of a triangle is A = \(\dfrac{1}{2}\)bh. Solve this formula for h: (a) when A = 90 and b = 15 (b) in general
Solution
| (a) when A = 90 and b = 15 | (b) in general | |
| Write the formula. | A = \(\dfrac{1}{2}\)bh | A = \(\dfrac{1}{2}\)bh |
| Substitute any given values. | $$90 = \dfrac{1}{2} \cdot 15 \cdot h$$ | |
| Clear the fractions. | $$\textcolor{red}{2} \cdot 90 = \textcolor{red}{2} \cdot \dfrac{1}{2} \cdot 15 \cdot h$$ | $$\textcolor{red}{2} \cdot A = \textcolor{red}{2} \cdot \dfrac{1}{2} \cdot b \cdot h$$ |
| Simplify. | 180 = 15h | 2A = bh |
| Solve for h. | 12 = h | \(\dfrac{2A}{b}\) = h |
We can now find the height of a triangle, if we know the area and the base, by using the formula
\[h = \dfrac{2A}{b}\]
Use the formula A = \(\dfrac{1}{2}\)bh to solve for h: (a) when A = 170 and b = 17 (b) in general
- Answer a
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\(h = 20\)
- Answer b
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\(h = \frac{2A}{b}\)
Use the formula A = \(\dfrac{1}{2}\)bh to solve for b: (a) when A = 62 and h = 31 (b) in general
- Answer a
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\(b = 4\)
- Answer b
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\(b = \frac{2A}{h}\)
In Solve Simple Interest Applications , we used the formula I = Prt to calculate simple interest, where I is interest, P is principal, r is rate as a decimal, and t is time in years.
Solve the formula I = Prt to find the principal, P: (a) when I = $5,600, r = 4%, t = 7 years (b) in general
Solution
| (a) when I = $5,600, r = 4%, t = 7 years | (b) in general | |
| Write the forumla. | I = Prt | I = Prt |
| Substitute any given values. | 5600 = P(0.04)(7) | I = Prt |
| Multiply r • t. | 5600 = P(0.28) | I = P(rt) |
| Divide to isolate P. | $$\dfrac{5600}{\textcolor{red}{0.28}} = \dfrac{P(0.28)}{\textcolor{red}{0.28}}$$ | $$\dfrac{I}{\textcolor{red}{rt}} = \dfrac{P(rt)}{\textcolor{red}{rt}}$$ |
| Simplify. | 20,000 = P | \(\dfrac{I}{rt}\) = P |
| State the answer. | The principal is $20,000. | $$P = \dfrac{I}{rt}$$ |
Use the formula I = Prt. Find t: (a) when I = $2,160, r = 6%, P = $12,000; (b) in general
- Answer a
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\(t = 3\) years
- Answer b
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\(t = \frac{I}{Pr}\)
Use the formula I = Prt. Find r: (a) when I = $5,400, P = $9,000, t = 5 years; (b) in general
- Answer a
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\(r = 0.12 = 12\%\)
- Answer b
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\(t = \frac{I}{Pt}\)
Later in this course, and in future algebra classes, you’ll encounter equations that relate two variables, usually x and y. You might be given an equation that is solved for y and need to solve it for x, or vice versa. In the following example, we’re given an equation with both x and y on the same side and we’ll solve it for y. To do this, we will follow the same steps that we used to solve a formula for a specific variable.
Solve the formula 3x + 2y = 18 for y: (a) when x = 4 (b) in general
Solution
| (a) when x = 4 | (b) in general | |
| Write the equation. | 3x + 2y = 18 | 3x + 2y = 18 |
| Substitute any given values. | 3(4) + 2y = 18 | 3x + 2y = 18 |
| Simplify if possible. | 12 + 2y = 18 | 3x + 2y = 18 |
| Subtract to isolate the y-term. | $$12 \textcolor{red}{-12} + 2y = 18 \textcolor{red}{-12}$$ | $$3x \textcolor{red}{-3x}+ 2y = 18 \textcolor{red}{-3x}$$ |
| Simplify. | 2y = 6 | 2y = 18 - 3x |
| Divide. | $$\dfrac{2y}{\textcolor{red}{2}} = \dfrac{6}{\textcolor{red}{2}}$$ | $$\dfrac{2y}{\textcolor{red}{2}} = \dfrac{18 - 3x}{\textcolor{red}{2}}$$ |
| Simplify. | y = 3 | $$y = \dfrac{18 - 3x}{2}$$ |
Solve the formula 3x + 4y = 10 for y: (a) when x = 2 (b) in general
- Answer a
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\(y = 1\)
- Answer b
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\(y = \frac{10-3x}{4}\)
Solve the formula 5x + 2y = 18 for y: (a) when x = 4 (b) in general
- Answer a
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\(y = -1\)
- Answer b
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\(y = \frac{18-5x}{2}\)
In the previous examples, we used the numbers in part (a) as a guide to solving in general in part (b). Do you think you’re ready to solve a formula in general without using numbers as a guide?
Solve the formula P = a + b + c for a.
Solution
We will isolate a on one side of the equation.
| We will isolate a on one side of the equation. | |
| Write the equation. | P = a + b + c |
| Subtract b and c from both sides to isolate a. | $$P \textcolor{red}{-b -c} = a + b + c \textcolor{red}{-b -c}$$ |
| Simplify. | P − b − c = a |
So, a = P − b − c.
Solve the formula P = a + b + c for b.
- Answer
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b = P - a - c
Solve the formula P = a + b + c for c.
- Answer
- c = P - a - b
Solve the equation 3x + y = 10 for y.
Solution
We will isolate y on one side of the equation.
| We will isolate y on one side of the equation. | |
| Write the equation. | 3x + y = 10 |
| Subtract 3x from both sides to isolate y. | $$3x \textcolor{red}{-3x} + y= 10 \textcolor{red}{-3x}$$ |
| Simplify. | y = 10 - 3x |
Solve the formula 7x + y = 11 for y
- Answer
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y = 11 - 7x
Solve the formula 11x + y = 8 for y.
- Answer
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y = 8 - 11x
Solve the equation 6x + 5y = 13 for y.
Solution
We will isolate y on one side of the equation.
| We will isolate y on one side of the equation. | |
| Write the equation. | 6x + 5y = 13 |
| Subtract to isolate the term with y. | $$6x + 5y \textcolor{red}{-6x} = 13 \textcolor{red}{-6x}$$ |
| Simplify. | 5y = 13 - 6x |
| Divide 5 to make the coefficient 1. | $$\dfrac{5y}{\textcolor{red}{5}} = \dfrac{13 - 6x}{\textcolor{red}{5}}$$ |
| Simplify. | $$y = \dfrac{13 - 6x}{5}$$ |
Solve the formula 4x + 7y = 9 for y.
- Answer
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\(y = \frac{9-4x}{7}\)
Solve the formula 5x + 8y = 1 for y.
- Answer
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\(y = \frac{1-5x}{8}\)
Distance = Rate x Time
Distance, Rate, Time
Simple Interest
Solving a Formula for a Specific Variable
Solving a Formula for a Specific Variable
Practice Makes Perfect
Use the Distance, Rate, and Time Formula
In the following exercises, solve.
- Steve drove for \(8 \dfrac{1}{2}\) hours at 72 miles per hour. How much distance did he travel?
- Socorro drove for \(4 \dfrac{5}{6}\) hours at 60 miles per hour. How much distance did she travel?
- Yuki walked for \(1 \dfrac{3}{4}\) hours at 4 miles per hour. How far did she walk?
- Francie rode her bike for \(2 \dfrac{1}{2}\) hours at 12 miles per hour. How far did she ride?
- Connor wants to drive from Tucson to the Grand Canyon, a distance of 338 miles. If he drives at a steady rate of 52 miles per hour, how many hours will the trip take?
- Megan is taking the bus from New York City to Montreal. The distance is 384 miles and the bus travels at a steady rate of 64 miles per hour. How long will the bus ride be?
- Aurelia is driving from Miami to Orlando at a rate of 65 miles per hour. The distance is 235 miles. To the nearest tenth of an hour, how long will the trip take?
- Kareem wants to ride his bike from St. Louis, Missouri to Champaign, Illinois. The distance is 180 miles. If he rides at a steady rate of 16 miles per hour, how many hours will the trip take?
- Javier is driving to Bangor, Maine, which is 240 miles away from his current location. If he needs to be in Bangor in 4 hours, at what rate does he need to drive?
- Alejandra is driving to Cincinnati, Ohio, 450 miles away. If she wants to be there in 6 hours, at what rate does she need to drive?
- Aisha took the train from Spokane to Seattle. The distance is 280 miles, and the trip took 3.5 hours. What was the speed of the train?
- Philip got a ride with a friend from Denver to Las Vegas, a distance of 750 miles. If the trip took 10 hours, how fast was the friend driving?
Solve a Formula for a Specific Variable
In the following exercises, use the formula. d = rt.
- Solve for t: (a) when d = 350 and r = 70 (b) in general
- Solve for t: (a) when d = 240 and r = 60 (b) in general
- Solve for t: (a) when d = 510 and r = 60 (b) in general
- Solve for t: (a) when d = 175 and r = 50 (b) in general
- Solve for r: (a) when d = 204 and t = 3 (b) in general
- Solve for r: (a) when d = 420 and t = 6 (b) in general
- Solve for r: (a) when d = 160 and t = 2.5 (b) in general
- Solve for r: (a) when d = 180 and t = 4.5 (b) in general.
In the following exercises, use the formula A = \(\dfrac{1}{2}\)bh.
- Solve for b: (a) when A = 126 and h = 18 (b) in general
- Solve for h: (a) when A = 176 and b = 22 (b) in general
- Solve for h: (a) when A = 375 and b = 25 (b) in general
- Solve for b: (a) when A = 65 and h = 13 (b) in general
In the following exercises, use the formula I = Prt.
- Solve for the principal, P for: (a) I = $5,480, r = 4%, t = 7 years (b) in general
- Solve for the principal, P for: (a) I = $3,950, r = 6%, t = 5 years (b) in general
- Solve for the time, t for: (a) I = $2,376, P = $9,000, r = 4.4% (b) in general
- Solve for the time, t for: (a) I = $624, P = $6,000, r = 5.2% (b) in general
In the following exercises, solve.
- Solve the formula 2x + 3y = 12 for y: (a) when x = 3 (b) in general
- Solve the formula 5x + 2y = 10 for y: (a) when x = 4 (b) in general
- Solve the formula 3x + y = 7 for y: (a) when x = −2 (b) in general
- Solve the formula 4x + y = 5 for y: (a) when x = −3 (b) in general
- Solve a + b = 90 for b.
- Solve a + b = 90 for a.
- Solve 180 = a + b + c for a.
- Solve 180 = a + b + c for c.
- Solve the formula 8x + y = 15 for y.
- Solve the formula 9x + y = 13 for y.
- Solve the formula −4x + y = −6 for y.
- Solve the formula −5x + y = −1 for y.
- Solve the formula 4x + 3y = 7 for y.
- Solve the formula 3x + 2y = 11 for y.
- Solve the formula x − y = −4 for y.
- Solve the formula x − y = −3 for y.
- Solve the formula P = 2L + 2W for L.
- Solve the formula P = 2L + 2W for W.
- Solve the formula C = \(\pi\)d for d.
- Solve the formula C = \(\pi\)d for \(\pi\).
- Solve the formula V = LWH for L.
- Solve the formula V = LWH for H.
Everyday Math
- Converting temperature While on a tour in Greece, Tatyana saw that the temperature was 40° Celsius. Solve for F in the formula C = \(\dfrac{5}{9}\)(F − 32) to find the temperature in Fahrenheit.
- Converting temperature Yon was visiting the United States and he saw that the temperature in Seattle was 50° Fahrenheit. Solve for C in the formula F = \(\dfrac{9}{5}\)C + 32 to find the temperature in Celsius.
Writing Exercises
- Solve the equation 2x + 3y = 6 for y: (a) when x = −3 (b) in general (c) Which solution is easier for you? Explain why.
- Solve the equation 5x − 2y = 10 for x: (a) when y = 10 (b) in general (c) Which solution is easier for you? Explain why.
Self Check
(a) After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
(b) Overall, after looking at the checklist, do you think you are well-prepared for the next Chapter? Why or why not?
Contributors and Attributions
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Lynn Marecek (Santa Ana College) and MaryAnne Anthony-Smith (Formerly of Santa Ana College). This content is licensed under Creative Commons Attribution License v4.0 "Download for free at<EMAIL_ADDRESS>."


3.3: Hands-on Activity
Overview
Explore the interactive graphic Secure Architecture Design . This secure design is the result of an evolutionary process of technology advancement and increasing cyber vulnerability presented in the Recommended Practice document Improving Industrial Control Systems Cybersecurity with Defense-in-Depth Strategies.
Hands-on Activity Objectives
- List several types of networking hardware and explain the purpose of each.
- List and describe the functions of common communications protocols and network standards used within CI.
- Explain how existing network administration principles can be applied to secure CIKR.
- Identify new types of network applications and how they can be secured.
Assignment
Use the ICS-Cert learning portal to examine an enterprise diagram for an overview of a network. If you are not registered yet, please register.
Hover over the various areas of the Secure Architecture Design graphic, located at https://ics-cert.us-cert.gov/Secure-Architecture-Design . Click inside the box for additional information associated with the system elements.
After downloading and reading Recommended Practice: Improving Industrial Control Systems Cybersecurity with Defense-In-Depth Strategies (see Required Reading ), navigate through the embedded description in the Secure Architectural Design diagram.
Write a short paper describing the following recommended practices for improving industrial control systems cybersecurity with Defense-In-Depth Strategies for your team’s fictitious sector-based company:
- Security Challenges within Industrial Control Systems
- Isolating and Protecting Assets: Defense-in-Depth Strategies
- Recommendations and Countermeasures
Grading Criteria Rubric
- Content
- Evidence of teamwork
- References
- Use of American Psychological Association (APA) style in writing the assignment
Grade points: 100


8.3: Workflow Management
Infrastructure management involves long term cycles of asset management planning and implementation, often for periods of a year or even longer. But another aspect of infrastructure management is dealing with the day to day desired work tasks. For example, on a military base, a campus or a large building, there will be requests for repair and re-stocking tasks as well as scheduled activities such as inspection and maintenance. Workflow management is the process of identifying these tasks, assigning tasks to workers (or contractors), setting priorities among tasks, and documenting the resulting work. Analysis of workflow tasks is also a useful activity, as problems can be identified (e.g. which elevator is breaking down most often?) and worker productivity monitored.
Work tasks may have a variety of forms and involve distinct skills. For example, author Don Coffelt’s facility management group provides the following services to campus departments:
- Heating and air conditioning
- Carpentry
- Custodial services
- Roof and gutter repair
- Electrical repairs
- Window washing
- Elevator maintenance
- Gardening
- Pest Control
- Plumbing
- Meeting setup
- Trash and recycling
- Painting
- Locksmith
In addition to service requests from departments, there are a large number of tasks generated from the facilities management group itself, such as ice and snow clearance and preventive maintenance. Figure 8.3.1 illustrates a typical preventive maintenance task, in this case clearing debris from a stormwater sewer sump. Departmental payments may also be required for work flow tasks, such as changing locks in the events of lost or misplaced keys.
Setting priorities among tasks is an important component of workflow management strategy. If tasks are simply handled in a first come, first served basis, then critical tasks such as safety hazards may be neglected. At the same time, a general buildup of unfulfilled tasks may require special efforts to catch up, such as contracting out more tasks or hiring more staff.
As with many aspects of infrastructure management, software and communication aids are available for workflow management. Service requests can be made directly and digitally, rather than using paper or telephone requests. Task completion can be documented by workers using mobile devices. Databases can track the status of tasks. Geographic information and computer aided design software can help route planning or identifying problem areas.