6.11: Proficiency Exam
The product is \(27a^3+9a^2+9a\) and a factor is \(3a\). Find the other factor.
- Answer
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\(9a^2+3a+3\)
The product is \(15x^{n+5}y^{3n−2}\). Find the other factor.
- Answer
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\(5x^ny^{2n−3}\)
For the following problems, factor, if possible, the polynomials.
\(−14x^2y^4b−28x^2y^3b−42x^2y^2\)
- Answer
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\(−14x^2y^2(y^2b+2yb+3)\)
\((y+2)a+(y+2)c\)
- Answer
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\((a+c)(y+2)\)
\( 6x^2y^2z+5x^2y^3−12xyz−10xy^2\)
- Answer
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\(xy(xy−2)(6z+5y)\)
\(4a^2−16c^2\)
- Answer
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\(4(a+2c)(a−2c)\)
\(m^4−n^4\)
- Answer
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\((m^2+n^2)(m+n)(m−n)\)
\(b^2+8b+16\)
- Answer
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\((b+4)^2\)
\(9y^2−30y+25\)
- Answer
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\((3y−5)^2\)
\(x^2+5x−15\)
- Answer
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not factorable
\(x^2−x−30\)
- Answer
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\((x−6)(x+5)\)
\(4x^6−36x^4+80x^2\)
- Answer
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\(4x^2(x^2−5)(x+2)(x−2)\)
\(9x^2+25x−6\)
- Answer
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\((9x−2)(x+3)\)


2.1: Basic Notions
The set of complex numbers is obtained algebraically by adjoining the number \(i\) to the set \(\mathbb{R}\) of real numbers, where \(i\) is defined by the property that \(i^2=−1\). We will take a geometric approach and define a complex number to be an ordered pair \((x,y)\) of real numbers. We let \(\mathbb{C}\) denote the set of all complex numbers,
\[\mathbb{C} =\{(x,y) | x,y∈ \mathbb{R}\}.\]
Given the complex number \(z=(x,y)\), \(x\) is called the real part of \(z\), denoted Re\((z)\); and \(y\) is called the imaginary part of \(z\), denoted Im\((z)\). The set of real numbers is a subset of \(\mathbb{C}\) under the identification \(x↔(x,0)\), for any real number \(x\).
Addition in \(\mathbb{C}\) is componentwise,
\[(x,y)+(s,t)=(x+s,y+t),\]
and if \(k\) is a real number, we define scalar multiplication by
\[k⋅(x,y)=(kx,ky).\]
Within this framework, \(i=(0,1)\), meaning that any complex number \((x,y)\) can be expressed as \(x+yi\) as suggested here:
\[ \begin{array} (x,y) &= (x,0)+(0,y) \\ &= x(1,0)+y(0,1) \\ &= x + yi \end{array} \]
The expression \(x+yi\) is called the Cartesian form of the complex number. This form can be helpful when doing arithmetic of complex numbers, but it can also be a bit gangly. We often let a single letter such as \(z\) or \(w\) represent a complex number. So, \(z=x+yi\) means that the complex number we're calling \(z\) corresponds to the point \((x,y)\) in the plane.
It is sometimes helpful to view a complex number as a vector, and complex addition corresponds to vector addition in the plane. The same holds for scalar multiplication. For instance, in Figure \(\PageIndex{1}\) we have represented \(z=2+i\), \(w=−1+1.5i\), as well as \(z+w=1+2.5i\), as vectors from the origin to these points in \(\mathbb{C}\). The complex number \(z−w\) can be represented by the vector from \(w\) to \(z\) in the plane.
We define complex multiplication using the fact that \(i^2=−1\).
\[ \begin{array} (x+yi)⋅(s+ti) &= xs+ysi+xti+yti^2 \\ &= (xs−yt)+(ys+xt)i \end{array} \]
The modulus of \(z=x+yi\), denoted \(|z|\), is given by
\[|z|= \sqrt{x^2+y^2}.\]
Note that \(|z|\) gives the Euclidean distance of \(z\) to the point \((0,0)\).
The conjugate of \(z=x+yi\), denoted \(\overline{z}\), is
\[\overline{z} =x−yi\]
In the exercises, the reader is asked to prove various useful properties of the modulus and conjugate.
Suppose \(z=3−4i\) and \(w=2+7i\).
Then \(z+w=5+3i\), and
\[ \begin{equation} \begin{array} \cdot z \cdot w &= (3−4i)(2+7i) \\ &= 6+28−8i+21i \\ &= 34+13i \end{array} \end{equation} \]
A few other computations:
\[ \begin{array} 4z &= 12−16i \\ |z| &= \sqrt{3^2 + (-4)^2} = 5 \\ \overline{zw} &= 34-13i \end{array} \]
Exercises
In each case, determine \(z+w\), \(sz\), \(|z|\), and \(z⋅w\).
- \(z=5+2i\), \(s=−4\), \(w=−1+2i\)
- \(z=3i\), \(s= \dfrac{1}{2}\), \(w=−3+2i\)
- \(z=1+i\), \(s=0.6\), \(w=1−i\)
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a. \(z+w=4+4i\), \(sz=−20−8i\), \(|z|=\sqrt{29}\), and \(zw=−9+8i\).
Show that \(z⋅ \overline{z} =|z|^2\), where \(\overline{z}\) is the conjugate of \(z\).
- Hint
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Let \(z=a+bi\), and show that the two sides of the equation agree.
Suppose \(z=x+yi\) and \(w=s+ti\) are two complex numbers. Prove the following properties of the conjugate and the modulus.
- \(|w⋅z|=|w|⋅|z|\).
- \(\overline{zw}= \overline{z} \cdot \overline{w}\)
- \(\overline{z+w}= \overline{z} + \overline{w}\)
- \(z+\overline{z}= 2 \text{ Re} (z).\) (Hence, \(z+ \overline{z}\) is a real number.)
- \(z- \overline{z}= 2 \text{ Im} (z)i.\)
- \(|z|=|\overline{z}|.\)
A Pythagorean triple consists of three integers \((a,b,c)\) such that \(a^2+b^2=c^2\). We can use complex numbers to generate Pythagorean triples. Suppose \(z=x+yi\) where \(x\) and \(y\) are positive integers. Let
\(a= \text{ Re}(z^2) \;\;\;\;\; b= \text{ Im}(z^2) \;\;\;\;\; c=z \overline{z}.\)
- Prove that \(a^2+b^2=c^2\).
- Find the complex number \(z=x+yi\) that generates the famous triple \((3,4,5)\).
- Find the complex number that generates the triple \((5,12,13)\).
- Find five other Pythagorean triples, generated using complex numbers of the form \(z=x+yi\), where \(x\) and \(y\) are positive integers with no common divisors.


10.8: Alkalides and Electrides
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Another interesting consequence of lattice energies involves the formation of certain salts containing Na - and e - anions. These compounds are known as alkalides and electrides , respectively. [9] Most of these compounds have been discovered by Prof. James Dye at Michigan State University.
The alkali metals have one electron in their valence shell. For example, the electronic configurations of Na and K are [Ar]3s 1 and [Kr]4s 1 , respectively. Although we are accustomed to seeing these very electropositive elements give up their electrons when they make compounds with electronegative elements, they can also gain an electron to achieve a [noble gas]ns 2 configuration. This is possible with strong electron donors such as alkali metals, especially when the cation that is formed is stabilized by coordination to a crown ether. Typically, these compounds are synthesized by combining the alkali metal and the appropriate crown ether in liquid ammonia, and then evaporating the ammonia.
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Cavities and channels in an electride |
Electride salts are formed under similar conditions, except in this case the anion is simply an electron that exists in an anion "cavity" in the crystal. The crystal structures are clearly salt-like, with the cations (alkali cations stabilized by crown or cryptand ligands) alternating in the structure with electrons.
Alkalide Salt
\[\ce{2Na ->[NH_{3}] Na^{+}(NH3)+ e^{-}(NH3) ->[18C6] [Na(18C6)]^{+} Na^{-}}\]
Electride Salt
\[\ce{2Cs ->[NH_{3}][18C6] [Cs(18C6)]^{+} e^{-}}\]
Complexing Na + (K + , Rb + , Cs + ) with crown ether ligands stabilizes the M + form of the metal ("salt" form). Because the metal cation with its ligand shell is rather large, the lattice energy of these salts is rather low.
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18-Crown-6, a crown ether that strongly complexes Na + cations |
Solutions of electride salts are powerful reducing agents, as demonstrated by their use in the Birch reduction, in which aromatic compounds are hydrogenated to produce dienes. Electrides are also useful for reducing metal ions to metals. Evaporation of blue electride solutions in anhydrous ammonia affords a mirror of Na. Such solutions slowly lose their color as the electrons reduce ammonia to the amide anion:
\(\ce{[Na(NH3)6]^{+}e^{-} + NH3 -> NaNH2 + H2}\)
It is interesting to consider, in the context of lattice energies and Born-Haber cycles, what might happen without these ligands present. That is, we can ask the question of whether sodium metal would prefer to exist in the metallic form as Na(s), or to form the sodide salt Na + Na - , or the electride salt Na + e - . Of course, we already know the answer to this question. Elemental sodium is clearly a metal (it is shiny, conducts electricity, and has a bcc crystal structure) and has never been observed in either of the "salt" forms. But how far away are these forms energetically?
We can calculate the energetics by assuming that the Na- ion is about the same size as Br - , and that the e - anion is about the same size as Cl - . Then the lattice energies in the cycles become the same as those of NaBr and NaCl:
The rather surprising result from these calculations is that sodium would be marginally stable as a sodide salt and very stable (by 161 kJ) as an electride. All the terms in these simple cycles are known precisely. But we must be doing something wrong here, because Na(s) is clearly metallic.
The key, subtle point here is that Born-Haber cycles consider only the potential energy (rather than the total energy) of the substances in the cycle. Normally we can ignore the kinetic energy part of the total energy, but in this case we cannot because of the quantum mechanical effect of resonance .


5: Trees
A tree is a non-empty set with an element that is designated as the root of the tree while the remaining elements are partitioned into non-empty sets each of which is a subtree of the root.
Tree nodes have many useful properties. The depth of a node is the length of the path (or the number of edges) from the root to that node. The height of a node is the longest path from that node to its leaves. The height of a tree is the height of the root. A leaf node has no children—its only path is up to its parent.
See the axiomatic development of trees and its consequences for more information.
Types of trees:
Binary: Each node has zero, one, or two children. This assertion makes many tree operations simple and efficient.
Binary Search: A binary tree where any left child node has a value less than its parent node and any right child node has a value greater than or equal to that of its parent node.


2.4: Campus Involvement as a Commuter Student
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Commuter students are defined as students who do not live in institutionally owned housing (Jacoby, 2000). Nationally, commuter students make up over 85% of college students in the United States (Horn & Nevill, 2006). Despite being in the majority on college campuses, commuter students can find difficulty in making a successful transition to college life. Commuter students often have difficulty accessing campus services, because co-curricular events and activities normally take place outside the classroom and at odd hours of the day (Dickson & Thayer, 1993). Furthermore, these students typically have significantly more time demands and commitments than other students. Commuter students often enroll in fewer classes, devote significant time to off-campus employment, and sometimes have commitments to family, home, or community that reduce their involvement in campus life (Henry, 2004). Being a commuter student can be a challenging experience.
Thought Question
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What are some of the challenges that commuter students face?
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How can you, as a commuter student, be proactive in ensuring your success at UT Arlington?
It is important for you to develop a sense of belonging on campus while maintaining your continued affiliation with high school friends, family, off-campus employment, and community groups (Upcraft, Gardner, & Associates, 1989). Commuter students can have difficulty in forming peer groups because they are afforded fewer opportunities to interact than residential students and often do so only in classroom settings, which is only one part of the overall collegiate experience. There are myriad opportunities on college and university campuses to interact with peers, as well as faculty and staff, in and outside of the class- room. Social and intellectual interaction can be just as beneficial as coursework and academic involvement (Pascarella, 1989). These interactions can occur by avoiding the “parking lot, to class, back to the parking lot” mentality that many commuter students experience. It is important for you as a commuter student to find ways to integrate into campus life. Consider staying after class to speak with a professor in an informal setting or eat lunch on campus with friends from class.
Thought Question
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What do commuter students need to be successful?
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Where can you go to meet these needs on campus?
All students should find a way to develop a sense of belonging on campus by becoming engaged in university life. You must find avenues to connect with peers and reach out to university administrators to ensure that institutional planning and programming considers your needs. Commuter students may opt out of voicing their needs because they may assume that “this must be the way college is” and often are not given the opportunity to speak out (Clark, 2006). College is what you make of the experience. Take advantage of the opportunities that college life has to offer. Plan class and work schedules in such a way that getting involved on campus is a possibility.  Join a student club or organization to meet friends outside of the classroom. Work out on campus or join a campus intramural team. Take advantage of mentoring programs when possible to get advice from an advanced student who has been through similar experiences. Even attend a program or event on campus just to spend some added time at the university. Most importantly, find your “best fit” by becoming involved and engaged on campus. Make this your home away from home.
Thought Question
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What are some other ways that you can ensure that your voice is heard on campus? What are other ways to avoid being a silent majority on campus?
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Which of the University of Texas Arlington’s almost 300 clubs or organisations could you join?
Table 3-2. Challenges and Solutions for Commuter Students
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Challenges for Commuter Students
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Solutions
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“It is difficult to make new friends and feel socially connected to campus.”
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• Join a student organization or a fraternity or sorority in Greek Life.
• Invite classmates to join you after class for studying or a coffee break.
• Swap phone numbers and e-mail addresses with classmates and propose a study group.
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“I do not have enough time to participate in on-campus activities.”
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• Arrive on campus an hour or two before your classes start to get an early start to the day.
• Consider getting an on-campus job, which will often have understanding bosses and co-workers and a flexible evening schedule.

• Join a student organization to interact with faculty and staff advisors.
• Faculty and staff hang out on campus just like you. Some even play intramurals. Make an effort to be on campus, and you will likely increase your interaction with faculty and staff.
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“I drive a long distance to come to class every day, and parking is always a problem.”
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• Arrive early to campus to ensure that you get a good parking spot.
• Check the UTA Web site to make sure there are no cancellations or delays.
• Carpool with friends or classmates to cut down on gas money.
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“I never know what’s going on.”
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• Pick up a copy of The Shorthorn, the student newspaper, every day as you come to campus to see what other students are talking about.
• Establish a relationship with a mentor, a faculty or a staff member, or a student who can help you become connected to campus.
• Sign up for newsletters or listservs through University Communications and Student Governance and Organizations to keep up-to-date.
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You may have noticed that the term “leadership” seems to be just about every- where you look lately. If you haven’t, take a closer look around. Our bookstore shelves include popular books on the subject (e.g., Northouse,
2007). A simple Google search of the term yields an astounding 784,000,000 results! And the interest in leadership extends far beyond popular culture. Increasingly, colleges and universities identify the development of leaders as central to their missions. Over the past ten years many institutions of higher education have begun in- vesting resources into the creation of leadership centers which sponsor a variety of leadership activities and programs, and more recently, universities have begun to establish academic programs dedicated to leadership studies (Bennis & Goldsmith, 1997; Dugan, 2006). So, what is driving this intensive interest in leadership?
One driving factor may be that leadership skills are a highly valued commodity in the workplace. Did you know that employers consistently identify leadership skills as among the top qualities they are seeking in new employees? Every year corporations invest millions of dollars in leadership training and development for their workers (Nelson & Quick, 2009). Another and perhaps even more significant factor may be what some have called a “global crisis of leadership” that is resulting in the deterioration of our corporations, political systems, and communities (Burns, 1978; Gardner, 1990; Bennis & Goldsmith, 1997). Scholars have suggested that this pervasive failure of leadership not only impedes our ability to address many of the urgent problems which threaten our society, but also contributes to an increasing skepticism of leaders in general (Komives, Lucas, & McMahon, 1998). It follows then, that if we hope to improve our world, we must give careful consideration to the ways in which we conceptualize and practice leadership.
Thought Question
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Do you believe that we are experiencing a crisis of leadership in this country? If so, what evidence supports that belief? If not, what is your perception of our current leaders?
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What do you think it takes to develop strong and ethical leaders?
Leadership Development among College Students
Leadership development occurs in various arenas throughout the collegiate environment, but a good deal of what is known about college student leadership development has emerged from the work of scholars and practitioners in various fields related to Student Affairs, College Student Personnel, and Educational Leadership. Dugan (2006) states that the “research has demonstrated that college students can and do increase their leadership skills while in college” (p. 335). And this growth is attributable, in part, to their involvement outside of the classroom, in various types of student organizations and activities. Astin (1993) found a significant correlation between student involvement and leadership development. Studies also show that involvement in leadership activities enhances students’ sense of themselves as citizens of a broad societal community (Dugan, 2006). More specifically, the work of Komives, Owen, Longerbeam, Mainella, and Osteen (2005) suggests that it is through organizational involvement that college students 1) learn about themselves in relation to others; 2) practice various leadership skills; 3) examine and reflect on their leadership experiences; and 4) deepen their understanding of leadership and their own leadership identity. This is consistent with Kolb’s Cycle of Experiential Learning (see Figure 3-3) which emphasizes the importance of experience in the learning process.
Figure 3-3. Kolb’s Cycle of Experiential Learning
Source: Learning Theories Knowledge (2010)
Though Question
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When you think back over your life, which experience/activities have aided you most in the development of your leadership skills? What made them particularly beneficial for you?
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Are you currently involved or planning to be involved at UT Arlington? What kinds of activities do you want to get involved in while in college? What attracts you to these?
Leadership at UT Arlington
There are many interesting and fun opportunities for you to be involved and to develop your leadership skills during your years at UT Arlington. One of them is through the programs offered by the Leadership Center which is located in the Division of Student Affairs. The Center collaborates with staff in the various departments of Student Affairs, as well as faculty and staff from departments across campus to provide a broad range of leadership opportunities for you. These include:
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Academic Courses
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A minor in Leadership Studies which will be instituted in Fall 2010 in partnership with the Department of Educational Leadership and Policy Studies
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Leadership Retreats
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Lectures and Organizational Field Trips
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A Campus-wide Leadership Recognition Ceremony
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Leadership Development programs (Mavericks Acting, Collaborating, and Transforming, also known as MavsACT, and the Leadership Academy)
You can engage in the practice of leadership as a small group leader or a presenter of a breakout session at a retreat. You might also choose to be a MavsACT Leader or graduate with leadership honors through the Leadership Academy. There are so many options for you to choose from.
The Center’s approach to leadership development is explicitly guided by two leadership development models (Relational Leadership and Social Change) which reflect what Rost (1993) has termed the post-industrial paradigm of leadership. According to this approach, leadership is a process which involves the development of collaborative relationships, the use of non-coercive influence, the achievement of shared purpose and vision, and a focus on making transformational changes in the service of organizations, communities, and society. This view of leadership represents a significant departure from what Rost calls the pre-industrial paradigm of leadership which focused heavily on the traits, attitudes, and behaviors of “the leader” and viewed the people in management positions as the primary “doers” of leadership in an organization. The post- industrial paradigm suggests that leadership is, instead, a dynamic process that is influenced by all of the participants involved in it. From this perspective, leadership can and should emerge from anyone and everyone in the organization regardless of title and position. The “leader” is no longer viewed as the authority but rather as a facilitator of the change process or the achievement of shared goals. Many scholars view this paradigm shift as critical to our ability to manage complex organizations and address the multifaceted issues confronting us in this new millennium. What do you think?
While the Center’s work is explicitly guided by a particular view of leadership, there are many other leadership development opportunities within the Division of Student Affairs that operate from slightly different perspectives. Each of these programs possesses unique characteristics and foci. But all of the leadership programs in Student Affairs are knitted together by an emphasis on some or all of five Core Leadership Competencies, which are identified in the table below. You will also see some examples of the programs the Division offers that will help you develop these particular skills.
Table 3-1. Leadership Competencies and Where to Develop Them
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Student Affairs Core Leadership Competencies
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Description of Competency
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Sample Programs in Student Affairs That Will Help You Develop These Skills
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Interpersonal Skills
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Interdependence, Collaboration, Meaningful Relationships, Respect for Others, Respect for Diversity
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Fraternity and Sorority Life, EXCEL, Orientation Leaders, Intramural & Sports Clubs, Resident & Office Assistants (RA & OA), Multicultural Affairs
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Intrapersonal Skills
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Realistic Self-Appraisal, Self-Understanding and Respect, Holistic Identity Development, Congruence Between Values and Behavior
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Resident Assistants, Shorthorn Writers, Leadership Academy, Student Governance
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Civic Engagement and Social Responsibility
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Participation in Relevant Governance Systems; Engaging in Critical Reflection and Principled Dissent; Appropriately Challenges Unjust, Unfair, or Uncivil Behavior towards Individuals and Groups; Participation in Service; Engagement in Responsible Stewardship of Human, Economic, and Environmental Resources
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(Freshman Leaders on Campus) FLOC, Student Governance, UTA Volunteers, MavsACT, Fraternity and Sorority Life
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Practical Leadership and Management Skills
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Critical Thinking, Decision-Making, Ability and Motivation to Pursue Goals, Delegating, Facilitation Skills, Public Speaking, Fiscal Management, Conflict Resolution Skills
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Shorthorn Editors, Leadership Academy, MAC Building Supervisors, Student Governance, FLOC, EXCEL
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As you can see, the opportunities for you to realize your leadership potential are plentiful. Leadership is indeed happening all around you here at UT Arlington. We invite you to find your place and participate.
Thought Question
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How do you define leadership? Are your views more aligned with the industrial or post-industrial views as defined by Rost?
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What kinds of leadership experiences will help you get to the next level of your leadership development?


<IP_ADDRESS>: Those Monsters
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- Robin DeRosa, Abby Goode et al.
- Plymouth State University/
It was a muggy Sunday morning when I heard the front door of my house slam open so hard it fell off the hinge, jumping me awake out of bed. All of a sudden I heard screams and glass shattering. My first instinct was to run to my mother, Mary Rowlandson, and cling on to her as any other six year old child would do. I found my mother out in the kitchen kicking and punching these scary, dark and tall men who had my brother in their arms. Before I could even comprehend what was happening, my brother was out the door in the hands of the scary dark men. I had no clue what was going on, leaving me even more terrified than before. I wondered if that would be the last time I ever saw my big brother.
Before I could even finish my thoughts, I saw more men come in and man handle my mom, like she was a puppet or something. I looked around my house only to realize, everyone had been taken, but me and my mom. All I could think to do was hold onto her leg for dear life and hope they take me with her. In the process of my mother fighting for her life and mine, we both were beat and injured by the monsters. I had open wounds, that I am sure would go untreated by the looks of the monsters and how they already treated us.
We were forced to follow them into the countryside, traveling through the wilderness on feet until it became too much. I started to feel weak, sick and very sweaty. I looked up into my mothers beautiful blue eyes and could distinct the worry in them. I could tell she wasn’t sure if we would survive. I myself, wasn’t so sure either.
The longer the travel, the more I started to become ill and unable to do much of anything. I could tell these monsters called “Indians” had no sympathy for me or my mother. It eventually got to the point where my knees and legs would refuse to work, so my mother, sick as well, had to carry me as we followed these men. I had no clue where we were going or why; all I knew was, I was scared I was going to die. Every time my mom looked down at me, I could see the worrisome on her pale, sunken face. We barely ate for days and it was starting to hit us both. Her skin used to be so beautiful with a bright glow, but when I looked at her, she didn’t look like my mother. Her eyes were sunken into dark purple circles and her face looked more pale than the moon. She then could no longer walk either, it became too much for her as it did for me long before her.  I didn’t understand.
Next thing I know, My weak and almost lifeless body in being thrown onto the back of horse that has no saddles or anything for support. I felt a body next to me and looked over to see my mom, very sick and weak. Did the Indians put us on this horse? Was it too much for my mother to carry me and herself?  As I closed my eyes to doze off into a sleep, I felt my tiny body hit the ground as I heard my mother’s body fall next to mine. Leaving us both covered in dirt and even more scratches. All I could think was, “when am I going to die? Will the pain and suffering ever end?” I didn’t want to leave this earth, nor my mother, but I wasn’t sure I could hold on much longer. Even breathing was becoming very hard for me.
I heard the Indians mention something to my mother about a wigman, master and King Philip and how she was to report to them. She didn’t want to leave my lifeless body, but the men insisted she go. I was worried for her sake, so I let myself go, in order to save my mother. I finally slipped into a peaceful sleep, where I no longer felt any pain or fear.


2.2.0: Gramática
In the Módulo introductorio , we saw that we use nouns ( los sustantivos ) to talk about people, animals, places, things, and ideas, and we learned that los sustantivos have gender ( género--femenino o masculino ). Of course, this does not mean that Spanish speakers believe that all things have gender. In Spanish, gender is a grammatical feature. Sometimes, the ending in a noun can tell you if it has feminine or masculine gender. For example, most nouns ending in -a are feminine, and most nouns ending in -o are masculine. When a noun is accompanied by an indefinite article ( un o una ) or by a definite article ( el o la ), the article will match the gender of the noun. Have a look at these examples.
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Masculine Nouns |
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Definite Articles |
el niño el escritorio |
the boy the desk |
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Indefinite Articles |
un niño un escritorio |
a (one) boy a (one) desk |
Most nouns ending in -o are masculine.
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Feminine Nouns |
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Definite Articles |
la niña la puerta |
the girl the door |
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Indefinite Articles |
una niña una puerta |
a (one) girl a (one) door |
Most nouns ending in -a are feminine.
Unfortunately, with some endings, it is difficult to determine gender (e.g., those that end in a consonant, such as lápiz , which is masculine, or in other vowels, such as clase , which is feminine).
We recommend that when you learn a new word, you also learn the definite article that accompanies it. That way, you will remember the gender of the noun, and it will also be easy to figure out what the indefinite articles is when you need it.
Let's take a closer look at the two types of articles in Spanish:
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Definite Articles |
Indefinite Articles |
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· el - el profesor (Masculine & Singular) · los - los profesores (Masculine & Plural) · la - la profesora (Feminine & Singular) · las - las profesoras (Feminine & Plural) |
· un – un libro (Masculine & Singular) · unos – unos libros (Masculine & Plural) · una – una pluma (Feminine & Singular) · unas – unas plumas (Feminine & Plural) |
When a noun is accompanied by an indefinite article ( un o una ) or by a definite article ( el o la ), the article will match the noun in number and gender.
- el cuaderno / un cuaderno
- la mochila / una mochila


1.2: An Approach to Food Safety
Food safety does not happen by accident. To prepare safe food, you must follow certain steps and procedures throughout the entire food preparation process. You have to think, and you have to pay attention to how you prepare food to make sure it is safe. You do this by developing a food safety plan. A good food safety plan will make sure that anything that might make someone sick is under control.
A basic food safety plan uses the HACCP method. HACCP stands for hazard analysis critical control points. HACCP was originally developed by NASA to make sure the food on their space flights was safe to eat. HACCP is not a complicated process; it just means that you have to first identify the various steps you must take when you prepare your menu items, then look for possible sources of contamination, and then find ways to control these sources.
The HACCP approach
HACCP is an approach to food safety that is systematic and preventive. It is recommended by the Codex Alimentarius Commission, the United Nations international standards organization for food safety. HACCP is used by most countries around the world and has been in use since the 1960s.
HACCP goes beyond inspecting finished food products. It helps to find, correct, and prevent hazards throughout the production process. These include physical, chemical, and biological hazards.
There are seven universally accepted HACCP principles. Every country that uses HACCP follows these principles.
Principle 1: Hazard analysis
A plan is laid out to identify all possible food safety hazards that could cause a product to be unsafe for consumption, and the measures that can be taken to control those hazards. For example, at the cooking step of the production process, one of the identified hazards is the survival of pathogens due to inadequate cooking time or temperature.
Principle 2: Identifying critical control points
Critical control points are the points in the production process where an action can be taken to prevent, eliminate, or reduce a food safety hazard to an acceptable level. For example, the cooking step is considered a critical control point because control measures are necessary to deal with the hazard of pathogens surviving the cooking process.
Principle 3: Establishing critical limits for each critical control point
A critical limit is the limit at which a hazard is acceptable without compromising food safety. For example, critical limits at the cooking stage include specific time and temperature for cooking the product.
Principle 4: Establishing monitoring procedures for critical control points
Highly detailed monitoring activities are essential to make sure the process continues to operate safely and within the critical limits at each critical control point. For example, monitoring procedures at a cooking critical control point could include taking the internal temperature of the product with a specialized thermometer.
Principle 5: Establishing corrective actions
Actions must be taken to bring the production process back on track if monitoring indicates that deviation from critical limits has occurred. In food production, correcting problems before end-stage production is far more effective than waiting until a product is finished to test it. For example: If the required internal temperature has not been reached, a corrective action would require that the product be cooked further. If the cooking temperature cannot be reached, another corrective action would call for the product to be held and destroyed.
Principle 6: Establishing verification procedures
Verification means applying methods, procedures, tests, sampling and other evaluations (in addition to monitoring) to determine whether a control measure at a critical control point is or has been operating as intended. Verification activities also ensure that the monitoring and the corrective actions are done according to a company’s written HACCP program. For example, testing and calibrating thermometers is a verification procedure that is important to ensure accurate readings. The easiest way to test a thermometer’s accuracy is by submerging the probe into a pot of boiling water. If it does not read 100˚C (212˚F) then the thermometer must be adjusted to read the correct temperature.
Principle 7: Record keeping
The company must keep records to demonstrate the effective application of the critical control points and assist with official verification. In the United States this is done by the Food & Drug Administration (FDA). Records must be established to document the monitoring and verification results as well as all information and actions taken in response to any deviations found through monitoring and verification. For example, the employee responsible for monitoring a cooking critical control point completes a cooking log sheet. This sheet includes the date, the start and finish time, the temperature, and the employee’s signature. If a deviation has occurred in the production process, the responsible employee records the details in a deviation log book.
For more information on current food safety regulations in United States, see Food Safety Modernization Act .
Here is the link to the HACCP in the FDA web site.


1.6: Properties of Addition
- understand the commutative and associative properties of addition
- understand why 0 is the additive identity
We now consider three simple but very important properties of addition.
The Commutative Property of Addition
If two whole numbers are added in any order, the sum will not change.
Add the whole numbers
8 + 5 = 13
5 + 8 = 13
The numbers 8 and 5 can be added in any order. Regardless of the order they are added, the sum is 13.
Practice Set A
Use the commutative property of addition to find the sum of 12 and 41 in two different ways.
- Answer
-
12 + 41 = 53 and 41 + 12 = 53
Practice Set A
Add the whole numbers
- Answer
-
837 + 1,958 = 2,795 and 1,958 + 837 = 2,795
Associative Property of Addition
If three whole numbers are to be added, the sum will be the same if the first two are added first, then that sum is added to the third, or, the second two are added first, and that sum is added to the first.
Using Parentheses
It is a common mathematical practice to use parentheses to show which pair of numbers we wish to combine first.
Add the whole numbers.
Practice Set B
Use the associative property of addition to add the following whole numbers two different ways.
- Answer
-
(17 + 32) + 25 = 49 + 25 = 74 and 17 + (32 + 25) = 17 + 57 = 74
Practice Set B
- Answer
-
(1,629 + 806) + 429 = 2,435 + 429 = 2,864
1,629 + (806 + 429) = 1,629 + 1,235 = 2,864
The Additive Identity
0 Is the Additive Identity
The whole number 0 is called the additive identity , since when it is added to any whole number, the sum is identical to that whole number.
Add the whole numbers.
29 + 0 = 29
0 + 29 = 29
Zero added to 29 does not change the identity of 29.
Practice Set C
Add the following whole numbers.
- Answer
-
8
Practice Set C
- Answer
-
5
Suppose we let the letter x represent a choice for some whole number. For the first two problems, find the sums. For the third problem, find the sum provided we now know that x represents the whole number 17.
Practice Set C
- Answer
-
x
Practice Set C
- Answer
-
x
Practice Set C
- Answer
-
17
Exercises
For the following problems, add the numbers in two ways.
Exercise \(\PageIndex{1}\)
- Answer
-
37
Exercise \(\PageIndex{2}\)
Exercise \(\PageIndex{3}\)
- Answer
-
45
Exercise \(\PageIndex{4}\)
Exercise \(\PageIndex{5}\)
- Answer
-
568
Exercise \(\PageIndex{6}\)
Exercise \(\PageIndex{7}\)
- Answer
-
122,323
Exercise \(\PageIndex{8}\)
Exercise \(\PageIndex{9}\)
- Answer
-
45
Exercise \(\PageIndex{10}\)
Exercise \(\PageIndex{11}\)
- Answer
-
100
Exercise \(\PageIndex{12}\)
Exercise \(\PageIndex{13}\)
- Answer
-
556
Exercise \(\PageIndex{14}\)
Exercise \(\PageIndex{15}\)
- Answer
-
43,461
For the following problems, show that the pairs of quantities yield the same sum.
Exercise \(\PageIndex{16}\)
(11 + 27) + 9 and 11 + (27 + 9)
Exercise \(\PageIndex{17}\)
(80 + 52) + 6 and 80 + (52 + 6)
- Answer
-
132 + 6 = 80 + 58 = 138
Exercise \(\PageIndex{18}\)
(114 + 226) + 108 and 114 + (226 + 108)
Exercise \(\PageIndex{19}\)
(731 + 256) + 171 and 731 + (256 + 171)
- Answer
-
987 + 171 = 731 + 427 = 1,158
Exercise \(\PageIndex{20}\)
The fact that (a first number + a second number) + third number = a first number + (a second number + a third number) is an example of the property of addition.
Exercise \(\PageIndex{21}\)
The fact that 0 + any number = that particular number is an example of the property of addition.
- Answer
-
Identity
Exercise \(\PageIndex{22}\)
The fact that a first number + a second number = a second number + a first number is an example of the property of addition.
Exercise \(\PageIndex{23}\)
Use the numbers 15 and 8 to illustrate the commutative property of addition.
- Answer
-
15 + 8 = 8 + 15 = 23
Exercise \(\PageIndex{22}\)
Use the numbers 6, 5, and 11 to illustrate the associative property of addition.
Exercise \(\PageIndex{23}\)
The number zero is called the additive identity. Why is the term identity so appropriate?
- Answer
-
…because its partner in addition remains identically the same after that addition
Exercises for Review
Exercise \(\PageIndex{24}\)
How many hundreds in 46,581?
Exercise \(\PageIndex{25}\)
Write 2,218 as you would read it.
- Answer
-
Two thousand, two hundred eighteen.
Exercise \(\PageIndex{26}\)
Round 506,207 to the nearest thousand.
Exercise \(\PageIndex{27}\)
Find the sum of \(\begin{array} {r} {482} \\ {\underline{+\ \ 68}} \end{array}\)
- Answer
-
550
Exercise \(\PageIndex{28}\)
Find the difference: \(\begin{array} {r} {3,318} \\ {\underline{-\ \ 429}} \end{array}\)


12: Kinetics
Chemical kinetics is the study of rates of chemical processes and includes investigations of how different experimental conditions can influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition states, as well as the construction of mathematical models that can describe the characteristics of a chemical reaction.
-
- 12.0: Prelude to Kinetics
- The study of chemical kinetics concerns the rate at which a reaction yields products and the molecular-scale means by which a reaction occurs. In this chapter, we will examine the factors that influence the rates of chemical reactions, the mechanisms by which reactions proceed, and the quantitative techniques used to determine and describe the rate at which reactions occur.
-
- 12.1: Chemical Reaction Rates
- The rate of a reaction can be expressed either in terms of the decrease in the amount of a reactant or the increase in the amount of a product per unit time. Relations between different rate expressions for a given reaction are derived directly from the stoichiometric coefficients of the equation representing the reaction.
-
- 12.2: Factors Affecting Reaction Rates
- The rate of a chemical reaction is affected by several parameters. Reactions involving two phases proceed more rapidly when there is greater surface area contact. If temperature or reactant concentration is increased, the rate of a given reaction generally increases as well. A catalyst can increase the rate of a reaction by providing an alternative pathway that causes the activation energy of the reaction to decrease.
-
- 12.3: Rate Laws
- Rate laws provide a mathematical description of how changes in the amount of a substance affect the rate of a chemical reaction. Rate laws are determined experimentally and cannot be predicted by reaction stoichiometry. The order of reaction describes how much a change in the amount of each substance affects the overall rate, and the overall order of a reaction is the sum of the orders for each substance present in the reaction.
-
- 12.4: Integrated Rate Laws
- Differential rate laws can be determined by the method of initial rates or other methods. We measure values for the initial rates of a reaction at different concentrations of the reactants. From these measurements, we determine the order of the reaction in each reactant. Integrated rate laws are determined by integration of the corresponding differential rate laws. Rate constants for those rate laws are determined from measurements of concentration at various times during a reaction.
-
- 12.5: Collision Theory
- Chemical reactions require collisions between reactant species. These reactant collisions must be of proper orientation and sufficient energy in order to result in product formation. Collision theory provides a simple but effective explanation for the effect of many experimental parameters on reaction rates. The Arrhenius equation describes the relation between a reaction’s rate constant and its activation energy, temperature, and dependence on collision orientation.
-
- 12.6: Reaction Mechanisms
- The sequence of individual steps, or elementary reactions, by which reactants are converted into products during the course of a reaction is called the reaction mechanism. The overall rate of a reaction is determined by the rate of the slowest step, called the rate-determining step. Unimolecular elementary reactions have first-order rate laws, while bimolecular elementary reactions have second-order rate laws.
-
- 12.E: Kinetics (Exercises)
- These are homework exercises to accompany the Textmap created for "Chemistry" by OpenStax. Complementary General Chemistry question banks can be found for other Textmaps and can be accessed here. In addition to these publicly available questions, access to private problems bank for use in exams and homework is available to faculty only on an individual basis; please contact Delmar Larsen for an account with access permission.
Contributors
-
Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>).


1.13: Functions of Several Variables
For simplicity, we consider a function \(f = f(x, y)\) of two variables, though the results are easily generalized. The partial derivative of \(f\) with respect to \(x\) is defined as \[\frac{\partial f}{\partial x}=\underset{h\to 0}{\lim}\frac{f(x+h,y)-f(x,y)}{h},\nonumber\] and similarly for the partial derivative of \(f\) with respect to \(y\). To take the partial derivative of \(f\) with respect to \(x\), say, take the derivative of \(f\) with respect to \(x\) holding \(y\) fixed. As an example, consider \[f(x,y)=2x^3y^2+y^3.\nonumber\]
We have \[\frac{\partial f}{\partial x}=6x^2y^2,\quad\frac{\partial f}{\partial y}=4x^3y+3y^2.\nonumber\]
Second derivatives are defined as the derivatives of the first derivatives, so we have \[\frac{\partial ^2f}{\partial x^2}=12xy^2,\quad \frac{\partial ^2f}{\partial y^2}=4x^3+6y;\nonumber\] and the mixed second partial derivatives are \[\frac{\partial ^2f}{\partial x\partial y}=12x^2y,\quad\frac{\partial ^2f}{\partial y\partial x}=12x^2y.\nonumber\]
In general, mixed partial derivatives are independent of the order in which the derivatives are taken.
Partial derivatives are necessary for applying the chain rule. Consider \[df=f(x+dx, y+dy)-f(x,y).\nonumber\]
We can write \(df\) as \[\begin{aligned} df&= [ f(x + dx, y + dy) − f(x, y + dy)] + [ f(x, y + dy) − f(x, y)] \\ &=\frac{\partial f}{\partial x}dx+\frac{\partial f}{\partial y}dy.\end{aligned}\]
If one has \(f = f(x(t), y(t)),\) say, then \[\frac{df}{dt}=\frac{\partial f}{\partial x}\frac{dx}{dt}+\frac{\partial f}{\partial y}\frac{dy}{dt}.\nonumber\]
And if one has \(f = f(x(r, θ), y(r, θ)),\) say, then \[\frac{\partial f}{\partial r}=\frac{\partial f}{\partial x}\frac{\partial x}{\partial r}+\frac{\partial f}{\partial y}\frac{\partial y}{\partial r},\quad\frac{\partial f}{\partial\theta}=\frac{\partial f}{\partial x}\frac{\partial x}{\partial\theta}+\frac{\partial f}{\partial y}\frac{\partial y}{\partial\theta}.\nonumber\]
A Taylor series of a function of several variables can also be developed. Here, all partial derivatives of \(f(x, y)\) at \((a, b)\) match all the partial derivatives of the power series. With the notation \[f_x=\frac{\partial f}{\partial x},\quad f_y=\frac{\partial f}{\partial y},\quad f_{xx}=\frac{\partial ^2f}{\partial x^2},\quad f_{xy}=\frac{\partial ^2f}{\partial x\partial y},\quad f_{yy}=\frac{\partial ^2f}{\partial y^2},\quad\text{etc.,}\nonumber\] we have \[\begin{aligned} f(x,y)&=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b) \\ &+\frac{1}{2!}\left( f_{xx}(a,b)(x-a)^2+2f_{xy}(a,b)(x-a)(y-b)+f_{yy}(a,b)(y-b)^2\right)+\cdots\end{aligned}\]


10: Epidemiology
Epidemiology is the study of the patterns, causes, and effects of health and disease conditions in defined populations. It is the cornerstone of public health, and informs policy decisions and evidence-based medicine by identifying risk factors for disease and targets for preventive medicine. Epidemiologists help with study design, collection and statistical analysis of data, and interpretation and dissemination of results. Epidemiology has helped develop methodology used in clinical research, public health studies and, to a lesser extent, basic research in the biological sciences.
-
- 10.1: Principles of Epidemiology
- Epidemiology is the study of the patterns, causes, and effects of health and disease conditions in defined populations. It is the cornerstone of public health, and informs policy decisions and evidence-based medicine by identifying risk factors for disease and targets for preventive medicine. Epidemiologists help with study design, collection and statistical analysis of data, and interpretation and dissemination of results.
-
- 10.4: Nosocomial Infections
- A nosocomial infection is an infection that is acquired in a hospital or other health care facility. To emphasize both hospital and nonhospital settings, it is sometimes instead called a health care–associated infection. Such an infection can be acquired in hospital, nursing home, rehabilitation facility, outpatient clinic, or other clinical settings. Infection is spread to the susceptible patient in the clinical setting by various means.
-
- 10.5: Epidemiology and Public Health
- Epidemiology is the study and analysis of the distribution (who, when, and where) and determinants of health and disease conditions in defined populations.
-
- 10.5A: Descriptive Epidemiology
- 10.5B: Analytical Epidemiology
- 10.5C: Experimental Epidemiology
- 10.5D: Public Health Measures for Disease Control
- 10.5E: Global Health
- 10.5F: Emerging and Reemerging Infectious Diseases
- 10.5G: Biological Weapons
- 10.5H: Technology and New Infectious Agents
- 10.5I: Current Epidemics
Thumbnail: Mary Mallon, better known as Typhoid Mary, was the first person in the United States identified as an asymptomatic carrier of the pathogen associated with typhoid fever. She was presumed to have infected 22 people, three of whom died, over the course of her career as a cook. (Public Domain).


11.2: Basic Neurological Concepts
When completing a neurological assessment, it is important to understand the functions performed by different parts of the nervous system while analyzing findings. For example, damage to specific areas of the brain, such as that caused by a head injury or cerebrovascular accidents (i.e., strokes), can cause specific deficits in speech, facial movements, or use of the extremities. Damage to the spinal cord, such as that caused by a motor vehicle accident or diving accident, will cause specific motor and sensory deficits according to the level where the spinal cord was damaged.
The nervous system is divided into two parts, the central nervous system and the peripheral nervous system. See Figure \(\PageIndex{1}\) [1] for an image of the entire nervous system. The central nervous system (CNS) includes the brain and the spinal cord. The brain can be described as the interpretation center, and the spinal cord can be described as the transmission pathway. The peripheral nervous system (PNS) consists of the neurological system outside of the brain and spinal cord, including the cranial nerves that branch out from the brain and the spinal nerves that branch out from the spinal cord. The peripheral nervous system can be described as the communication network between the brain and the body parts. Both parts of the nervous system must work correctly for healthy body functioning.
Central Nervous System
There major regions of the brain are the cerebrum and cerebral cortex, the diencephalon, the brain stem, and the cerebellum. See Figure \(\PageIndex{2}\) [2] for an illustration of the cerebellum and the lobes of the cerebrum.
Cerebrum and Cerebral Cortex
The largest portion of our brain is the cerebrum. The cerebrum is covered by a wrinkled outer layer of gray matter called the cerebral cortex. See Figure \(\PageIndex{3}\) [3] for an image of the cerebral cortex. The cerebral cortex is responsible for the higher functions of the nervous system such as memory, emotion, and consciousness. The corpus callosum is the major pathway of communication between the right and left hemispheres of the cerebral cortex. The cerebral cortex is further divided into four lobes named the frontal, parietal, occipital, and temporal lobes. [4] Each lobe has specific functions.
Frontal Lobe
The frontal lobe is associated with movement because it contains neurons that instruct cells in the spinal cord to move skeletal muscles. The anterior portion of the frontal lobe is called the prefrontal lobe, and it provides cognitive functions such as planning and problem-solving that are the basis of our personality, short-term memory, and consciousness. Broca’s area is also located in the frontal lobe and is responsible for the production of language and controlling movements responsible for speech. [5]
Parietal Lobe
The parietal lobe processes general sensations from the body. All of the tactile senses are processed in this area, including touch, pressure, tickle, pain, itch, and vibration, as well as general senses of the body, such as proprioception (the sense of body position) and kinesthesia (the sense of movement). [6]
Temporal Lobe
The temporal lobe processes auditory information and is involved with language comprehension and production. Wernicke’s area and Broca’s area are located in the temporal lobe. Wernicke’s area is involved in the comprehension of written and spoken language, and Broca’s area is involved in the production of language. Because regions of the temporal lobe are part of the limbic system, memory is also an important function associated with the temporal lobe. [7] The limbic system is involved with our behavioral and emotional responses needed for survival, such as feeding, reproduction, and the fight – or – flight responses.
Occipital Lobe
The occipital lobe primarily processes visual information. [8]
Diencephalon
Information from the rest of the central and peripheral nervous system is sent to the cerebrum through the diencephalon, with the exception of the olfactory nerve that connects directly to the cerebrum. [9] See Figure \(\PageIndex{4}\) [10] for an illustration of the diencephalon deep within the cerebrum. The diencephalon contains the hypothalamus and the thalamus.
The hypothalamus helps regulate homeostasis such as body temperature, thirst, hunger, and sleep. The hypothalamus is also the executive region in charge of the autonomic nervous system and the endocrine system through its regulation of the anterior pituitary gland. Other parts of the hypothalamus are involved in memory and emotion as part of the limbic system. [11]
The thalamus relays sensory information and motor information in collaboration with the cerebellum. The thalamus does not just pass the information on, but it also processes and prioritizes that information. For example, the portion of the thalamus that receives visual information will influence what visual stimuli are considered important enough to receive further attention from the brain. [12]
Brain Stem
The brain stem is composed of the pons and the medulla. The pons and the medulla regulate several crucial autonomic functions in the body, including involuntary functions in the cardiovascular and respiratory systems, vasodilation, and reflexes like vomiting, coughing, sneezing, and swallowing. Cranial nerves also connect to the brain through the brain stem and provide sensory input and motor output. [13]
Cerebellum
The cerebellum is located in the posterior part of the brain behind the brain stem and is responsible for fine motor movements and coordination. For example, when the motor neurons in the frontal lobe of the cerebral cortex send a command down the spinal cord to initiate walking, a copy of that instruction is also sent to the cerebellum. Sensory feedback from the muscles and joints, proprioceptive information about the movements of walking, and sensations of balance are sent back to the cerebellum. If the person becomes unbalanced while walking because the ground is uneven, the cerebellum sends out a corrective command to compensate for the difference between the original cerebral cortex command and the sensory feedback. [14]
Spinal Cord
The spinal cord is a continuation of the brain stem that transmits sensory and motor impulses. The length of the spinal cord is divided into regions that correspond to the level at which spinal nerves pass through the vertebrae. Immediately adjacent to the brain stem is the cervical region, followed by the thoracic, the lumbar, and finally the sacral region. [15] The spinal nerves in each of these regions innervate specific parts of the body. See more information under the “Spinal Nerves” section.
Review the anatomy of the brain using following supplementary video.
Video Review for Anatomy of the Brain [16]
Peripheral Nervous System
The peripheral nervous system (PNS) consists of cranial nerves and spinal nerves that exist outside of the brain, spinal cord, and autonomic nervous system. The main function of the PNS is to connect the limbs and organs to the central nervous system (CNS). Sensory information from the body enters the CNS through cranial and spinal nerves. Cranial nerves are connected directly to the brain, whereas spinal nerves are connected to the brain via the spinal cord.
Peripheral nerves are classified as sensory nerves, motor nerves, or a combination of both. Sensory nerves carry impulses from the body to the brain for processing. Motor nerves transmit motor signals from the brain to the muscles to cause movement.
Cranial Nerves
Cranial nerves are directly connected from the periphery to the brain. They are primarily responsible for the sensory and motor functions of the head and neck. There are twelve cranial nerves that are designated by Roman numerals I through XII. See Figure \(\PageIndex{5}\) [17] for an image of cranial nerves. Three cranial nerves are strictly sensory nerves; five are strictly motor nerves; and the remaining four are mixed nerves. [18] A traditional mnemonic for memorizing the names of the cranial nerves is “ O n O ld O lympus T owering T ops A F inn A nd G erman V iewed S ome H ops,” in which the initial letter of each word corresponds to the initial letter in the name of each nerve.
- The o lfactory nerve is responsible for the sense of smell.
- The o ptic nerve is responsible for the sense of vision.
- The o culomotor nerve regulates eye movements by controlling four of the extraocular muscles, lifting the upper eyelid when the eyes point up and for constricting the pupils.
- The t rochlear nerve and the a bducens nerve are both responsible for eye movement, but do so by controlling different extraocular muscles.
- The t rigeminal nerve regulates skin sensations of the face and controls the muscles used for chewing.
- The f acial nerve is responsible for the muscles involved in facial expressions, as well as part of the sense of taste and the production of saliva.
- The a ccessory nerve controls movements of the neck.
- The v estibulocochlear nerve manages hearing and balance.
- The g lossopharyngeal nerve regulates the controlling muscles in the oral cavity and upper throat, as well as part of the sense of taste and the production of saliva.
- The v agus nerve is responsible for contributing to homeostatic control of the organs of the thoracic and upper abdominal cavities.
- The s pinal accessory nerve controls the muscles of the neck, along with cervical spinal nerves.
- The h ypoglossal nerve manages the muscles of the lower throat and tongue. [19] Methods for assessing each of these nerves are described in the “Assessing Cranial Nerves” section.
Video Review of Cranial Nerves [20]
Spinal Nerves
There are 31 spinal nerves that are named based on the level of the spinal cord where they emerge. See Figure \(\PageIndex{6}\) [21] for an illustration of spinal nerves. There are eight pairs of cervical nerves designated C1 to C8, twelve thoracic nerves designated T1 to T12, five pairs of lumbar nerves designated L1 to L5, five pairs of sacral nerves designated S1 to S5, and one pair of coccygeal nerves. All spinal nerves are combined sensory and motor nerves. Spinal nerves extend outward from the vertebral column to innervate the periphery while also transmitting sensory information back to the CNS. [22]
Functions of Spinal Nerves
Each spinal nerve innervates a specific region of the body:
- C1 provides motor innervation to muscles at the base of the skull. [23]
- C2 and C3 provide both sensory and motor control to the back of the head and behind the ears. [24]
- The phrenic nerve arises from nerve roots C3, C4, and C5. This is a vital nerve because it innervates the diaphragm to enable breathing. If a patient’s spinal cord is transected above C3 from an injury, then spontaneous breathing is not possible. [25]
- C5 through C8 and T1 combine to form the brachial plexus, a tangled array of nerves that serve the upper limbs and upper back. [26]
- The lumbar plexus arises from L1-L5 and innervates the pelvic region and the anterior leg. [27]
- The sacral plexus comes from the lower lumbar nerves L4 and L5 and the sacral nerves S1 to S4. The most significant systemic nerve to come from this plexus is the sciatic nerve. The sciatic nerve is associated with the painful medical condition sciatica, which is back and leg pain as a result of compression or irritation of the sciatic nerve. [28]
When a patient experiences a spinal cord injury, the degree of paralysis can be predicted by the location of the spinal cord injury. It is also important to remember when a patient has a spinal cord injury and their motor nerves are damaged, their sensory nerves may still be intact. If this occurs, the patient can still feel sensation even if they can’t move the extremity. Therefore, don’t assume that a paralyzed patient cannot feel pain in the affected extremity because this is not always the case.
Functions of the Nervous System
The nervous system receives information about the environment around us (sensation) and generates responses to that information (motor responses). The process of integration combines sensory perceptions and higher cognitive functions such as memories, learning, and emotion while producing a response.
Sensation
Sensation is defined as receiving information about the environment. The major senses are taste, smell, touch, sight, and hearing. Additional sensory stimuli are also provided from inside the body, such as the stretch of an organ wall or the concentration of certain ions in the blood. [29]
Response
The nervous system produces a response based on the stimuli perceived by sensory nerves. For example, withdrawing a hand from a hot stove is an example of a response to a painfully hot stimulus. Responses can be classified by those that are voluntary (such as contraction of a skeletal muscle) and those that are involuntary (such as contraction of smooth muscle in the intestine). Voluntary responses are governed by the somatic nervous system, and involuntary responses are governed by the autonomic nervous system. [30]
Integration
Integration occurs when stimuli received by sensory nerves are communicated to the nervous system and the information is processed, leading to the generation of a conscious response. Consider this example of sensory integration. A batter in a baseball game does not automatically swing when they see the baseball thrown to them by the pitcher. First, the trajectory of the ball and its speed will need to be considered before creating the motor response of a swing. Then, integration will occur as the batter generates a conscious decision of whether to swing or not. Perhaps the count is three balls and one strike, and the batter decides to let this pitch go by in the hope of getting a walk to first base. Perhaps the batter is afraid to strike out and doesn’t swing, or maybe the batter learned the pitcher’s nonverbal cues the previous time at bat and is confident to take a swing at an anticipated fast ball. All of these considerations are included as part of the batter’s integration response and the higher level functioning that occurs in the cerebral cortex. [31]
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1.4: How Business and Economics Work
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3. What are the primary features of the world’s economic systems, and how are the three sectors of the U.S. economy linked?
A business’s success depends in part on the economic systems of the countries where it is located and where its sells its products. A nation’s economic system is the combination of policies, laws, and choices made by its government to establish the systems that determine what goods and services are produced and how they are allocated. Economics is the study of how a society uses scarce resources to produce and distribute goods and services. The resources of a person, a firm, or a nation are limited. Hence, economics is the study of choices—what people, firms, or nations choose from among the available resources. Every economy is concerned with what types and amounts of goods and services should be produced, how they should be produced, and for whom. These decisions are made by the marketplace, the government, or both. In the United States, the government and the free-market system together guide the economy.
You probably know more about economics than you realize. Every day, many news stories deal with economic matters: a union wins wage increases at General Motors, the Federal Reserve Board lowers interest rates, Wall Street has a record day, the president proposes a cut in income taxes, consumer spending rises as the economy grows, or retail prices are on the rise, to mention just a few examples.
Global Economic Systems
Businesses and other organizations operate according to the economic systems of their home countries. Today the world’s major economic systems fall into two broad categories: free market, or capitalism; and planned economies, which include communism and socialism. However, in reality many countries use a mixed market system that incorporates elements from more than one economic system.
The major differentiator among economic systems is whether the government or individuals decide:
- How to allocate limited resources—the factors of production—to individuals and organizations to best satisfy unlimited societal needs
- What goods and services to produce and in what quantities
- How and by whom these goods and services are produced
- How to distribute goods and services to consumers
Managers must understand and adapt to the economic system or systems in which they operate. Companies that do business internationally may discover that they must make changes in production and selling methods to accommodate the economic system of other countries. Table 1.1 summarizes key factors of the world’s economic systems.
| Capitalism | Communism | Socialism | Mixed Economy | |
|---|---|---|---|---|
| Ownership of Business | Businesses are privately owned with minimal government ownership or interference. | Government owns all or most enterprises. | Basic industries such as railroads and utilities are owned by government. Very high taxation as government redistributes income from successful private businesses and entrepreneurs. | Private ownership of land and businesses but government control of some enterprises. The private sector is typically large |
| Control of Markets | Complete freedom of trade. No or little government control. | Complete government control of markets. | Some markets are controlled, and some are free. Significant central-government planning. State enterprises are managed by bureaucrats. These enterprises are rarely profitable. | Some markets, such as nuclear energy and the post office, are controlled or highly regulated. |
| Worker Incentives | Strong incentive to work and innovate because profits are retained by owners. | No incentive to work hard or produce quality products. | Private-sector incentives are the same as capitalism, and public-sector incentives are the same as in a planned economy. | Private-sector incentives are the same as capitalism. Limited incentives in the public sector. |
| Management of Enterprises | Each enterprise is managed by owners or professional managers with little government interference. | Centralized management by the government bureaucracy. Little or no flexibility in decision-making at the factory level. | Significant government planning and regulation. Bureaucrats run government enterprises. | Private-sector management similar to capitalism. Public sector similar to socialism. |
| Forecast for 2020 | Continued steady growth. | No growth and perhaps disappearance. | Stable with probable slight growth. | Continued growth. |
| Examples | United States | Cuba, North Korea | Finland, India, Israel | Great Britain, France, Sweden, Canada |
Capitalism
In recent years, more countries have shifted toward free-market economic systems and away from planned economies. Sometimes, as was the case of the former East Germany, the transition to capitalism was painful but fairly quick. In other countries, such as Russia, the movement has been characterized by false starts and backsliding. Capitalism , also known as the private enterprise system , is based on competition in the marketplace and private ownership of the factors of production (resources). In a competitive economic system, a large number of people and businesses buy and sell products freely in the marketplace. In pure capitalism, all the factors of production are owned privately, and the government does not try to set prices or coordinate economic activity.
A capitalist system guarantees certain economic rights: the right to own property, the right to make a profit, the right to make free choices, and the right to compete. The right to own property is central to capitalism. The main incentive in this system is profit, which encourages entrepreneurship. Profit is also necessary for producing goods and services, building manufacturing plants, paying dividends and taxes, and creating jobs. The freedom to choose whether to become an entrepreneur or to work for someone else means that people have the right to decide what they want to do on the basis of their own drive, interest, and training. The government does not create job quotas for each industry or give people tests to determine what they will do.
Competition is good for both businesses and consumers in a capitalist system. It leads to better and more diverse products, keeps prices stable, and increases the efficiency of producers. Companies try to produce their goods and services at the lowest possible cost and sell them at the highest possible price. But when profits are high, more businesses enter the market to seek a share of those profits. The resulting competition among companies tends to lower prices. Companies must then find new ways of operating more efficiently if they are to keep making a profit—and stay in business.
Exhibit 1.5 McDonald’s China Since joining the World Trade Organization in 2001, China has continued to embrace tenets of capitalism and grow its economy. China is the world’s largest producer of mobile phones, PCs, and tablets, and the country’s over one billion people constitute a gargantuan market. The explosion of McDonald’s and KFC franchises epitomizes the success of American-style capitalism in China, and Beijing’s bid to host the 2022 Winter Olympics is a symbol of economic openness. This McCafe is an example of changing Western products to suit Chinese tastes. This is an example of changing Western products to suit Chinese tastes. Do you think China’s capitalistic trend can continue to thrive under the ruling Chinese Communist Party that opposes workers’ rights, free speech, and democracy? (Credit: Marku Kudjerski/ flickr/ Attribution 2.0 Generic (CC BY 2.0)
Communism
The complete opposite of capitalism is communism . In a communist economic system, the government owns virtually all resources and controls all markets. Economic decision-making is centralized: the government, rather than the competitive forces in the marketplace, decides what will be produced, where it will be produced, how much will be produced, where the raw materials and supplies will come from, who will get the output, and what the prices will be. This form of centralized economic system offers little if any choice to a country’s citizens. Early in the 20th century, countries that chose communism, such as the former Soviet Union and China, believed that it would raise their standard of living. In practice, however, the tight controls over most aspects of people’s lives, such as what careers they can choose, where they can work, and what they can buy, led to lower productivity. Workers had no reasons to work harder or produce quality goods, because there were no rewards for excellence. Errors in planning and resource allocation led to shortages of even basic items.
These factors were among the reasons for the 1991 collapse of the Soviet Union into multiple independent nations. Recent reforms in Russia, China, and most of the eastern European nations have moved these economies toward more capitalistic, market-oriented systems. North Korea and Cuba are the best remaining examples of communist economic systems. Time will tell whether Cuba takes small steps toward a market economy now that the United States reestablished diplomatic relations with the island country a few years ago. 16
Socialism
Socialism is an economic system in which the basic industries are owned by the government or by the private sector under strong government control. A socialist state controls critical, large-scale industries such as transportation, communications, and utilities. Smaller businesses and those considered less critical, such as retail, may be privately owned. To varying degrees, the state also determines the goals of businesses, the prices and selection of goods, and the rights of workers. Socialist countries typically provide their citizens with a higher level of services, such as health care and unemployment benefits, than do most capitalist countries. As a result, taxes and unemployment may also be higher in socialist countries. For example, in 2017, the top individual tax rate in France was 45 percent, compared to 39.6 percent in the United States. With both countries electing new presidents in 2017, tax cuts may be a campaign promise that both President Macron and President Trump take on as part of their overall economic agendas in the coming years. 17
Many countries, including the United Kingdom, Denmark, India, and Israel, have socialist systems, but the systems vary from country to country. In Denmark, for example, most businesses are privately owned and operated, but two-thirds of the population is sustained by the state through government welfare programs.
Mixed Economic Systems
Pure capitalism and communism are extremes; real-world economies fall somewhere between the two. The U.S. economy leans toward pure capitalism, but it uses government policies to promote economic stability and growth. Also, through policies and laws, the government transfers money to the poor, the unemployed, and the elderly or disabled. American capitalism has produced some very powerful organizations in the form of large corporations, such as General Motors and Microsoft. To protect smaller firms and entrepreneurs, the government has passed legislation that requires that the giants compete fairly against weaker competitors.
Canada, Sweden, and the UK, among others, are also called mixed economies ; that is, they use more than one economic system. Sometimes, the government is basically socialist and owns basic industries. In Canada, for example, the government owns the communications, transportation, and utilities industries, as well as some of the natural-resource industries. It also provides health care to its citizens. But most other activity is carried on by private enterprise, as in a capitalist system. In 2016, UK citizens voted for Britain to leave the European Union, a move that will take two or more years to finalize. It is too early to tell what impact the Brexit decision will have on the UK economy and other economies around the world. 18
The few factors of production owned by the government in a mixed economy include some public lands, the postal service, and some water resources. But the government is extensively involved in the economic system through taxing, spending, and welfare activities. The economy is also mixed in the sense that the country tries to achieve many social goals—income redistribution and retirement pensions, for example—that may not be attempted in purely capitalist systems.
Macroeconomics and Microeconomics
The state of the economy affects both people and businesses. How you spend your money (or save it) is a personal economic decision. Whether you continue in school and whether you work part-time are also economic decisions. Every business also operates within the economy. Based on their economic expectations, businesses decide what products to produce, how to price them, how many people to employ, how much to pay these employees, how much to expand the business, and so on.
Economics has two main subareas. Macroeconomics is the study of the economy as a whole. It looks at aggregate data for large groups of people, companies, or products considered as a whole. In contrast, microeconomics focuses on individual parts of the economy, such as households or firms.
Both macroeconomics and microeconomics offer a valuable outlook on the economy. For example, Ford might use both to decide whether to introduce a new line of vehicles. The company would consider such macroeconomic factors as the national level of personal income, the unemployment rate, interest rates, fuel costs, and the national level of sales of new vehicles. From a microeconomic viewpoint, Ford would judge consumer demand for new vehicles versus the existing supply, competing models, labor and material costs and availability, and current prices and sales incentives.
Economics as a Circular Flow
Another way to see how the sectors of the economy interact is to examine the circular flow of inputs and outputs among households, businesses, and governments as shown in Exhibit 1.6 . Let’s review the exchanges by following the red circle around the inside of the diagram. Households provide inputs (natural resources, labor, capital, entrepreneurship, knowledge) to businesses, which convert these inputs into outputs (goods and services) for consumers. In return, households receive income from rent, wages, interest, and ownership profits (blue circle). Businesses receive revenue from consumer purchases of goods and services.
The other important exchange in Exhibit 1.6 takes place between governments (federal, state, and local) and both households and businesses. Governments supply many types of publicly provided goods and services (highways, schools, police, courts, health services, unemployment insurance, social security) that benefit consumers and businesses. Government purchases from businesses also contribute to business revenues. When a construction firm repairs a local stretch of state highway, for example, government pays for the work. As the diagram shows, government receives taxes from households and businesses to complete the flow.
Changes in one flow affect the others. If government raises taxes, households have less to spend on goods and services. Lower consumer spending causes businesses to reduce production, and economic activity declines; unemployment may rise. In contrast, cutting taxes can stimulate economic activity. Keep the circular flow in mind as we continue our study of economics. The way economic sectors interact will become more evident as we explore macroeconomics and microeconomics.
Exhibit 1.6 Economics as a Circular Flow (Attribution: Copyright Rice University, OpenStax, under CC-BY 4.0 license)
CONCEPT CHECK
- What is economics, and how can you benefit from understanding basic economic concepts?
- Compare and contrast the world’s major economic systems. Why is capitalism growing, communism declining, and socialism still popular?
- What is the difference between macroeconomics and microeconomics?