15.2: Exercises
LAB 15 EXERCISES \(\PageIndex{1}\)
Identify the 3 major components of a hematocrit:
LAB 15 EXERCISES \(\PageIndex{2}\)
Blood Cell Identification
Identify the formed elements by their picture below:
Label the image below
Fill in the Following Table
| Blood Type | Can Safely Receive | Can Safely Donate T0 |
|---|---|---|
| O+ | ||
| A- | ||
| B+ | ||
| AB- | ||
| AB+ |
LAB 15 EXERCISES \(\PageIndex{3}\)
1. Obtain a slide of blood from the slide box at your table.
2. Follow the checklist above to set up your slide for viewing.
3. View the slide on the objective which provides the best view (400X). Find the representative object.
4. In the circle below the name, draw a representative sample of the blood cell, taking care to correctly and clearly draw their true shape in the slide. Draw your structures proportionately to their size in your microscope’s field of view.
Repeat this for each of the blood cell types seen below
|
Erythrocytes Total Magnification: _________________ Type of eptiheleum:__________________ Source of tissue: ____________________ Function : _________________________ __________________________________ |
|
Thrombocytes Total Magnification: _________________ Type of eptiheleum:__________________ Source of tissue: ____________________ Function : _________________________ __________________________________ |
|
Leukocytes Total Magnification: _________________ Type of eptiheleum:__________________ Source of tissue: ____________________ Function : _________________________ __________________________________ |


3.6: Introduction to People Analytics
What you’ll learn to do: Explain the concept of people analytics
People analytics is a practice that has been an “emerging trend” for over a decade. Indeed, research and advisory firm Garter still categorizes analytics as an emerging technology, estimating time to mainstream adoption (as of October 2018) at 2–5 years. [1] However, practice thought leaders are declaring that “the people data revolution, predicted for years, has finally arrived.” In this section, we’ll get beyond the hype, defining people analytics and discussing adoption trends and implications for HR.
-
George, Sharon. "
6 Trends in the Gartner Hype Cycle for Human Capital Management, 2018
." Gartner. October 30, 2018. Accessed August 06, 2019. ↵


9.5: Death and Dying
Learning Objectives
- Discuss hospice care
- Describe the five stages of grief
- Define living will and DNR
Every story has an ending. Death marks the end of your life story (See Figure \(\PageIndex{1}\)). Our culture and individual backgrounds influence how we view death. In some cultures, death is accepted as a natural part of life and is embraced. In contrast, until about 50 years ago in the United States, a doctor might not inform someone that they were dying, and the majority of deaths occurred in hospitals. In 1967 that reality began to change with Cicely Saunders, who created the first modern hospice in England. The aim of hospice is to help provide a death with dignity and pain management in a humane and comfortable environment, which is usually outside of a hospital setting. In 1974, Florence Wald founded the first hospice in the United States. Today, hospice provides care for 1.65 million Americans and their families.
Research has indicated that hospice care is beneficial for the patient (Brumley, Enquidanos, & Cherin, 2003; Brumley et al., 2007; Godkin, Krant, & Doster, 1984) and for the patient’s family (Rhodes, Mitchell, Miller, Connor, & Teno, 2008; Godkin et al., 1984). Hospice patients report high levels of satisfaction with hospice care because they are able to remain at home and are not completely dependent on strangers for care (Brumley et al., 2007). In addition, hospice patients tend to live longer than non-hospice patients (Connor, Pyenson, Fitch, Spence, & Iwasaki, 2007; Temel et al., 2010). Family members receive emotional support and are regularly informed of their loved one’s treatment and condition. The family member’s burden of care is also reduced (McMillan et al., 2006). Both the patient and the patient’s family members report increased family support, increased social support, and improved coping while receiving hospice services (Godkin et al., 1984).
How do you think you might react if you were diagnosed with a terminal illness like cancer? Elizabeth Kübler-Ross (1969), who worked with the founders of hospice care, described the process of an individual accepting his own death. She proposed five stages of grief: denial, anger, bargaining, depression, and acceptance. Most individuals experience these stages, but the stages may occur in different orders, depending on the individual. In addition, not all people experience all of the stages. It is also important to note that some psychologists believe that the more a dying person fights death, the more likely he is to remain stuck in the denial phase. This could make it difficult for the dying person to face death with dignity. However, other psychologists believe that not facing death until the very end is an adaptive coping mechanism for some people.
Whether due to illness or old age, not everyone facing death or the loss of a loved one experiences the negative emotions outlined in the Kübler-Ross model (Nolen-Hoeksema & Larson, 1999). For example, research suggests that people with religious or spiritual beliefs are better able to cope with death because of their hope in an afterlife and because of social support from religious or spiritual associations (Hood, Spilka, Hunsberger, & Corsuch, 1996; McIntosh, Silver, & Wortman, 1993; Paloutzian, 1996; Samarel, 1991; Wortman & Park, 2008).
A prominent example of a person creating meaning through death is Randy Pausch, who was a well-loved and respected professor at Carnegie Mellon University. Diagnosed with terminal pancreatic cancer in his mid-\(40s\) and given only \(3-6\) months to live, Pausch focused on living in a fulfilling way in the time he had left. Instead of becoming angry and depressed, he presented his now famous last lecture called “Really Achieving Your Childhood Dreams.” In his moving, yet humorous talk, he shares his insights on seeing the good in others, overcoming obstacles, and experiencing zero gravity, among many other things. Despite his terminal diagnosis, Pausch lived the final year of his life with joy and hope, showing us that our plans for the future still matter, even if we know that we are dying.
Summary
Death marks the endpoint of our lifespan. There are many ways that we might react when facing death. Kübler-Ross developed a five-stage model of grief as a way to explain this process. Many people facing death choose hospice care, which allows their last days to be spent at home in a comfortable, supportive environment.
Glossary
- hospice
- service that provides a death with dignity; pain management in a humane and comfortable environment; usually outside of a hospital setting
Contributors and Attributions
-
Rose M. Spielman with many significant contributors. The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the creative commons license and may not be reproduced without the prior and express written consent of Rice University. For questions regarding this license, please contact<EMAIL_ADDRESS>.Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>.


11.6: Dividing Fractions- Invert and Multiply
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The missing factor method is a particularly nice way to understand fraction division. It builds on what we know about multiplication and division, reinforcing that these operations have the same relationship whether the numbers are whole number, fractions, or anything else. It makes sense. But we’ve seen that it doesn’t always work out nicely. For example,
\[\frac{3}{4} \div \frac{1}{3} = \_\_ \nonumber \]
can be rewritten as
\[\frac{1}{3} \cdot \_\_ = \frac{3}{4} \ldotp \nonumber \]
You want to ask:
- For the numerator: \(1 \cdot \_\_ = 3\). We can fill in the blank with a 3.
- For the denominator: \(3 \cdot \_\_ = 4\). We can fill in the blank with \(\frac{4}{3}\). (Why does that work?)
So we have: \[\frac{1}{3} \cdot \frac{3}{\frac{4}{3}} = \frac{3}{4} \ldotp \nonumber \]
You learned about fractions like \[\frac{3}{\frac{4}{3}} \nonumber \]
back in the “What is a Fraction?” chapter. This means that each \(\frac{4}{3}\) of a kid gets 3 pies. So how much does an individual kid (one whole kid) get? You could draw a picture to help you figure it out. But we can also use the key fraction rule to help us out.
\[\frac{3}{\frac{4}{3}} = \frac{3 \cdot 3}{3 \cdot \frac{4}{3}} = \frac{9}{4} \ldotp \nonumber \]
This process is going to be key to understanding why the “invert and multiply” rule for fraction division actually makes sense.
Simplify an Ugly Fraction
Example \(\PageIndex{1}\):
\(7 \frac{2}{3}\) pies are shared equally by \(5 \frac{1}{4}\) children. How much pie does each child get?
Technically, we could just write down the answer as $$\frac{7 \frac{2}{3}}{5 \frac{1}{4}}$$and be done! The answer is equivalent to this fraction, so why not?
Is there a way to make this look friendlier? Well, if we change those mixed numbers to “improper” fractions, it helps a little:
\[\frac{7 \frac{2}{3}}{5 \frac{1}{4}} = \frac{\frac{23}{3}}{\frac{21}{4}} \nonumber \]
That’s a bit better, but it’s still not clear how much pie each kid gets. Let’s use the key fraction rule to make the fraction even friendlier. Let’s multiply the numerator and denominator each by 3. (Why three?) Remember, this means we’re multiplying the fraction by \(\frac{3}{3}\), which is just a special form of 1, so we don’t change its value.
\[\frac{3 \cdot \frac{23}{3}}{3 \cdot \frac{21}{4}} = \frac{23}{\frac{63}{4}} \ldotp \nonumber \]
Now multiply numerator and denominator each by 4. (Why four?)
\[\frac{4 \cdot 23}{4 \cdot \frac{63}{4}} = \frac{92}{63} \ldotp \nonumber \]
We now see that the answer is \(\frac{92}{63}\). That means that sharing \(7 \frac{2}{3}\) pies among \(5 \frac{1}{4}\) children is the same as sharing 92 pies among 63 children. (In both situations, the individual child get exactly the same amount of pie.)
Example \(\PageIndex{2}\):
Let’s forget the context now and just focus on the calculations so that we can see what is going on more clearly. Try this one:
\[\frac{\frac{3}{5}}{\frac{2}{3}} \ldotp \nonumber \]
Multiplying the numerator and denominator each by 5 (why did we choose 5?) gives
\[\frac{\frac{3}{5}}{\frac{2}{3}} = \frac{5 \cdot \frac{3}{5}}{5 \cdot \frac{2}{3}} = \frac{3}{\frac{10}{3}} \ldotp \nonumber \]
Now multiply the numerator and denominator each by 3 (why did we choose 3?):
\[\frac{3 \cdot 3}{3 \cdot \frac{10}{3}} = \frac{9}{10} \ldotp \nonumber \]
On Your Own
- Each of the following is a perfectly nice fraction, but it could be written in a simpler form. So do that! Write each of them in a simpler form following the examples above. $$\frac{\frac{2}{3}}{\frac{1}{3}}, \qquad \frac{2 \frac{1}{5}}{2 \frac{1}{4}}, \qquad \frac{\frac{5}{7}}{\frac{3}{5}}, \qquad \frac{\frac{3}{7}}{\frac{4}{5}} \ldotp$$
Think / Pair / Share
- Jessica calculated the second exercise above this way: $$\frac{2 \frac{1}{5}}{2 \frac{1}{4}} = \frac{\frac{1}{5}}{\frac{1}{4}} = \frac{\frac{1}{5} \cdot 4}{\frac{1}{4} \cdot 4} = \frac{\frac{4}{5}}{1} = \frac{4}{5} \ldotp$$Is her solution correct, or is she misunderstanding something? Carefully explain what is going on with her solution, and what you would do as Jessica’s teacher.
- Isaac calculated the last exercise above this way: $$\frac{\frac{3}{7}}{\frac{4}{5}} = \frac{\frac{3}{7} \cdot 7}{\frac{4}{5} \cdot 5} = \frac{3}{4} \ldotp$$Is his solution correct, or is he misunderstanding something? Carefully explain what is going on with his solution, and what you would do as Isaac’s teacher.
Perhaps without realizing it, you have just found another method to divide fractions.
Example: 3/5 ÷ 4/7
Consider \(\frac{3}{5} \div \frac{4}{7}\). We know that a fraction is the answer to a division problem, meaning
\[\frac{3}{5} \div \frac{4}{7} = \frac{\frac{3}{5}}{\frac{4}{7}} \ldotp \nonumber \]
And now we know how to simplify ugly fractions like this one! Multiply the numerator and denominator each by 5:
\[\frac{(\frac{3}{5}) \cdot 5}{(\frac{4}{7}) \cdot 5} = \frac{3}{\frac{20}{7}} \ldotp \nonumber \]
Now multiply them each by 7:
\[\frac{(3) \cdot 7}{(\frac{20}{7}) \cdot 7} = \frac{21}{20} \ldotp \nonumber \]
Done! So
\[\frac{3}{5} \div \frac{4}{7} = \frac{21}{20} \ldotp \nonumber \]
Example: 5/9 ÷ 8/11
Let’s do another! Consider \(\frac{5}{9} \div \frac{8}{11}\):
\[\frac{5}{9} \div \frac{8}{11} = \frac{\frac{5}{9}}{\frac{8}{11}} \ldotp \nonumber \]
Let’s multiply numerator and denominator each by 9 and by 11 at the same time. (Why not?)
\[\frac{\frac{5}{9}}{\frac{8}{11}} = \frac{(\frac{5}{9}) \cdot 9 \cdot 11}{(\frac{8}{11}) \cdot 9 \cdot 11} = \frac{5 \cdot 11}{8 \cdot 9} \ldotp \nonumber \]
(Do you see what happened here?)
So we have
\[\frac{\frac{5}{9}}{\frac{8}{11}} = \frac{5 \cdot 11}{8 \cdot 9} = \frac{55}{72} \ldotp \nonumber \]
On Your Own
Compute each of the following, using the simplification technique in the examples above.
\[\frac{1}{2} \div \frac{1}{3}, \qquad \frac{4}{5} \div \frac{3}{7}, \qquad \frac{2}{3} \div \frac{1}{5}, \qquad \frac{45}{59} \div \frac{902}{902}, \qquad \frac{10}{13} \div \frac{2}{13} \ldotp \nonumber \]
Invert and multiply
Consider the problem \(\frac{5}{12} \div \frac{7}{11}\). Janine wrote:
\[\frac{\frac{5}{12}}{\frac{7}{11}} = \frac{\frac{5}{12} \cdot 12 \cdot 11}{\frac{7}{11} \cdot 12 \cdot 11} = \frac{5 \cdot 11}{7 \cdot 12} = \frac{5}{12} \cdot \frac{11}{7} \ldotp \nonumber \]
She stopped before completing her final step and exclaimed: “Dividing one fraction by another is the same as multiplying the first fraction with the second fraction upside down!”
Think / Pair / Share
First check each step of Janine’s work here and make sure that she is correct in what she did up to this point. Then answer these questions:
- Do you understand what Janine is saying? Explain it very clearly.
- Work out \(\frac{\frac{3}{7}}{\frac{4}{13}}\) using the simplification method. Is the answer the same as \(\frac{3}{7} \cdot \frac{13}{4}\)?
- Work out \(\frac{\frac{2}{5}}{\frac{3}{10}}\) using the simplification method. Is the answer the same as \(\frac{2}{5} \cdot \frac{10}{3}\)?
- Work out \(\frac{\frac{a}{b}}{\frac{c}{d}}\) using the simplification method. Is the answer the same as \(\frac{a}{b} \cdot \frac{d}{c}\)?
- Is Janine right? Is dividing two fractions always the same as multiplying the two fractions with the second one turned upside down? What do you think? (Do not just think about examples. This is a question if something is always true .)
Summary
We now have several methods for solving problems that require dividing fractions:
Dividing fractions:
- Draw a picture using the rectangle method, and use that to solve the division problem.
- Find a common denominator and divide the numerators.
- Rewrite the division as a missing factor multiplication problem, and solve that problem.

- Invert the second fraction (the dividend) and then multiply.
Think / Pair / Share
Discuss your opinions about our four methods for solving fraction division problems with a partner:
- Which method for division of fractions is the easiest to understand why it works ?
- Which method for division of fractions is the easiest to use in computations ?
- What are the benefits and drawbacks of each method? (Think both as a future teacher and as someone solving math problems here.)


13.10: Bibliography
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- Jennifer Hasty, David G. Lewis, & Marjorie M. Snipes
- OpenStax
Bado-Fralick, Nikki. 2002. “Mapping the Wiccan Ritual Landscape: Circles of Transformation.” Folklore Forum 33 (1/2): 45–65. http://hdl.handle.net/2022/2424 .
BBC News. 2021. “Who Are the Uyghurs and Why Is China Being Accused of Genocide?” June 21, 2021. https://www.bbc.com/news/world-asia-china-22278037 .
Beauchamp, Zack. 2018. “Juche, the State Ideology That Makes North Korea Revere Kim Jong Un, Explained.” Vox. June 18, 2018. https://www.vox.com/world/2018/6/18/...ideology-juche .
Bell, Diane. 1993. Daughters of the Dreaming . Minneapolis: University of Minnesota Press.
Bellah, Robert N. 1967. “Civil Religion in America.” Daedalus 96 (1): 1–21.
Boas, Franz. 1916. Tsimshian Mythology . Washington, D.C.: GPO. https://archive.org/details/tsimshianmytholo00boas/ .
Carey, Harold, Jr. 2010. “Kinaalda: Celebrating Maturity of Girls among the Navajo.” Navajo People. December 16, 2010. http://navajopeople.org/blog/kinaald...ng-the-navajo/ .
Clark, Christopher. 1995. “Thinking about American Utopian Communities: The Origins of a Discourse.” Irish Journal of American Studies 4:1–22.
Dubois, Thomas A. 2009. An Introduction to Shamanism . Cambridge: Cambridge University Press.
Dundes, Alan. 1962. “Earth-Diver: Creation of the Mythopoeic Male.” American Anthropologist 64 (5): 1032–1051.
Durkheim, Émile. 1915. The Elementary Forms of the Religious Life . Translated by Joseph Ward Swain. London: George Allen & Unwin.
Eliade, Mircea. 1959. The Sacred and the Profane: The Nature of Religion . Translated by Willard R. Trask. New York: Harcourt, Brace.
Frazer, James George. (1922) 1925. The Golden Bough: A Study in Magic and Religion . Abridged ed. New York: MacMillan. https://archive.org/stream/cu31924021569128/ .
Geertz, Clifford. 1973. The Interpretation of Cultures: Selected Essays . New York: Basic Books.
Gennep, Arnold van. 1960. The Rites of Passage: A Classic Study of Cultural Celebrations . Translated by Monika B. Vizedom and Gabrielle L. Caffee. Chicago: University of Chicago Press.
Gottlieb, Alma. 2008. “How Are Anthropological Studies of Witchcraft Relevant Today?” Interview by Diana Yates. News Bureau. October 27, 2008. https://news.illinois.edu/view/6367/198785 .
Harner, Michael. 1980. The Way of the Shaman: A Guide to Power and Healing . San Francisco: Harper & Row.
Harvey, Graham, ed. 2003. Shamanism: A Reader . New York: Routledge.
Ingold, Tim. 2018. Anthropology: Why It Matters . Medford, MA: Polity Press.
Ingold, Tim. 2019. “169: Tim Ingold.” Cultures of Energy: The Energy Humanities Podcast . Hosted by Dominic Boyer and Cymene Howe. March 21, 2019. Podcast, 1:05:42. http://culturesofenergy.com/169-tim-ingold/ .
Istomin, Kirill Vladimirovich, and Mark James Dwyer. 2010. “Dynamic Mutual Adaptation: Human-Animal Interaction in Reindeer Herding Pastoralism.” Human Ecology 38 (5): 613–623.
Kanter, Rosabeth Moss. 1968. “Commitment and Social Organization: A Study of Commitment Mechanisms in Utopian Communities.” American Sociological Review 33 (4): 499–517.
King, Barbara J. 2007. Evolving God: A Provocative View of the Origins of Religion . New York: Doubleday.
Kroeber, Karl. 1996. “Unaesthetic Imaginings: Native American Myth as Speech Genre.” Boundary 2 23 (2): 171–197. https://doi.org/10.2307/303811 .
Laugrand, Frédéric B., and Jarich G. Oosten. 2013. “‘We’re Back with Our Ancestors’: Inuit Bowhead Whaling in the Canadian Eastern Arctic.” Anthropos 108 (2): 431–443.
Lévi-Strauss, Claude. 1964–1971. Mythologiques . 4 vols. Paris: Plon.
Lipka, Michael. 2015. “A Closer Look at America’s Rapidly Growing Religious ‘Nones.’” Pew Research Center. May 13, 2015. https://www.pewresearch.org/fact-tan...ligious-nones/ .
Lipka, Michael, and Claire Gecewicz. 2017. “More Americans Now Say They’re Spiritual but Not Religious.” Pew Research Center. September 6, 2017. https://www.pewresearch.org/fact-tan...not-religious/ .
Marshall, John. (1969) 2009. N/um Tchai: The Ceremonial Dance of the !Kung Bushmen . Disc 1. !Kung Short Films . DVD. Watertown, MA: Documentary Educational Resources.
Meza, Vivian. 2019. “Kinaaldá: A Navajo Girl Comes of Age in Traditional Ceremony.” Navajo-Hopi Observer . June 4, 2019. https://www.nhonews.com/news/2019/ju...ional-ceremon/ .
Moro, Pamela A., ed. 2012. Magic, Witchcraft, and Religion: A Reader in the Anthropology of Religion . 9th ed. Dubuque, IA: McGraw-Hill.
Ong, Walter. 2012. Orality and Literacy . 3rd ed. With additional chapters by John Hartley. New York: Routledge.
Pallasmaa, Juhani. 2012. The Eyes of the Skin: Architecture and the Senses . 3rd ed. Hoboken, NJ: John Wiley & Sons.
Pew Research Center. 2015. “Religious Landscape Study.” May 11, 2015. https://www.pewforum.org/religious-landscape-study/ .
Pew Research Center. 2018. “Why America’s ‘Nones’ Don’t Identify with a Religion.” August 8, 2018. https://www.pewresearch.org/fact-tan...th-a-religion/ .
Shermer, Michael. 2018. “The Number of Americans with No Religious Affiliation Is Rising.” Scientific American . April 1, 2018. https://www.scientificamerican.com/a...ion-is-rising/ .
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Stephan, Karen H., and G. Edward Stephan. 1973. “Religion and the Survival of Utopian Communities.” Journal for the Scientific Study of Religion 12 (1): 89–100.
Turner, Victor W. 1967. The Forest of Symbols: Aspects of Ndembu Ritual . Ithaca, NY: Cornell University Press.
Turner, Victor W. 1968. The Drums of Affliction: A Study of Religious Processes among the Ndembu of Zambia . Oxford: Clarendon Press.
Turner, Victor W. 1969. The Ritual Process: Structure and Anti-structure . Ithaca, NY: Cornell University Press.
Tylor, Edward Burnett. 1871. Primitive Culture . 2 vols. New York: G. P. Putnam’s Sons.
Vansina, Jan. 1985. Oral Tradition as History . Madison: University of Wisconsin Press.
Weber, Max. 1947. The Theory of Social and Economic Organization . Translated by A. M. Henderson and Talcott Parsons. Glencoe, IL: Free Press.
Zapata Olivella, Manuel. 1983. Changó, el gran putas . Bogotá: Editorial Oveja Negra.
Zapata Olivella, Manuel. 2010. Por los senderos de sus ancestros: Textos escogidos, 1940–2000 , compiled and presented by Alfonso Múnera. Bogotá: Ministerio de Cultura.
Zapata Olivella, Manuel. Selected Correspondence. Jean and Alexander Heard Library, Vanderbilt University. https://mzo.library.vanderbilt.edu/c...ence/index.php .


1.6: Respiratory System Anatomy
- Identify respiratory system gross anatomical structures.
- Identify respiratory system microscopic structures.
Gross and Microscopic Anatomy
Use local resources to view structures of the respiratory system.
Respiratory System Structures List
Respiratory System- Complete- Anterior view
- Trachea
- Upper right lobe of lungs
- Middle right lobe of lungs
- Lower right lobe of lungs
- Upper left lobe of lungs
- Lower left lobe of lungs
Respiratory System- Circulatory vessels and heart
- Right subclavian vein
- Right internal jugular vein
- Right brachiocephalic vein
- Superior vena cava
- Right atrium
- Right ventricle
- Pulmonary trunk
- Pulmonary veins
- Left atrium
- Left ventricle
- Aorta
Respiratory System- Tracheobronchial tree and lungs
- Right primary bronchus
- Left primary bronchus
- Diaphragm
Respiratory System- Larynx- Anterior view
- Hyoid
- Thyroid membrane
- Thyroid cartilage
- Cricoid cartilage
Respiratory System- Larynx- Posterior view
- Arytenoid cartilage
Respiratory System- Larynx- Left lateral view
- Esophagus
Supplemental Structures
- Horizontal fissure
- Oblique fissure
Attributions for chapter 6: Respiratory System Structures List by Marissa Sumida / CC BY 4.0


1.1: Types of Disabilities and Barriers
In order to understand why web accessibility is necessary, it is helpful to have a basic understanding of the range of disabilities and their related barriers with respect to the consumption of web content.
Not all people with disabilities encounter barriers on the Web, and those with different types of disabilities encounter different types of barriers . For instance, if a person is in a wheelchair they may encounter no barriers at all in web content. A person who is blind will experience different barriers than a person with limited vision. Different types of disabilities and some of their commonly associated barriers are described here.
Watch the following video to see how students with disabilities experience the Internet.
Video: Experiences of Students with Disabilities (1:59)
© Jared Smith. Released under the terms of a Standard YouTube License. All rights reserved.
In this video, David Berman talks about types of disabilities and their associated barriers.
Video: Web Accessibility Matters: Difficulties and Technologies: Avoiding Tradeoffs (9:52)
© davidbermancom. Released under the terms of a Standard YouTube License. All rights reserved.
People Who Are Blind
People who are blind tend to face many barriers in web content, given the visual nature of the Web. They will often use a screen reader to access their computer or device and may use a refreshable Braille display to convert text to Braille.
Common barriers for this group include:
- Visual content that has no text alternative
- Functional elements that cannot be controlled with a keyboard
- Overly complex or excessive amounts of content
- Inability to navigate within a page of content
- Content that is not structured
- Inconsistent navigation
- Time limits (insufficient time to complete tasks)
- Unexpected actions (e.g., redirect when an element receives focus)
- Multimedia without audio description
For a quick look at how a person who is blind might use a screen reader like JAWS to navigate the Web, watch the following video.
Video: Accessing the web using screen reading software (3:07)
© rscnescotland. Released under the terms of a Standard YouTube License. All rights reserved.
People with Low Vision
People with low vision are often able to see web content if it is magnified. They may use a screen magnification program to increase the size and contrast of the content to make it more visible. They are less likely to use a screen reader than a person who is blind, though in some cases they will. People with low vision may rely on the magnification or text customization features in their web browser, or they may install other magnification or text reading software.
Common barriers for this group include:
- Content sized with absolute measures, so it is not resizable
- Inconsistent navigation
- Images of text that degrade or pixelate when magnified
- Low contrast (inability to distinguish text from background)
- Time limits (insufficient time to complete tasks)
- Unexpected actions (e.g., redirect when an element receives focus)
See the following video for a description of some of the common barriers for people with low vision.
Video: Creating an accessible web (AD) (4:39)
© Centre for Inclusive Design. Released under the terms of a Standard YouTube License. All rights reserved.
People Who Are Deaf or Hard of Hearing
For most people who are deaf the greatest barrier on the Web is audio content that is presented without text-based alternatives. They encounter relatively few barriers on the Web otherwise. Those who are deaf and blind will face many more barriers, including those described for people who are blind. For those who communicate with American Sign Language (ASL) or other sign languages, such as langue des signes québécoise (LSQ), the written language of a website may produce barriers similar to those faced when reading in a second language.
Common barriers for this group include:
- Audio without a transcript
- Multimedia without captions or a transcript
- Lack of ASL interpretation (for ASL/Deaf community)
People with Mobility-Related Disabilities
Mobility-related disabilities are quite varied. As mentioned earlier, one could be limited to a wheelchair for getting around and face no significant barriers in web content. Those who have limited use of their hands or who have fine motor impairments that limit their ability to target web content elements with a mouse pointer may not use a mouse at all. Instead, they might rely on a keyboard or perhaps their voice to control movement through web content along with switches to control mouse clicks.
Common barriers for this group include:
- Clickable areas that are too small
- Functional elements that cannot be controlled with a keyboard
- Time limits (insufficient time to complete tasks)
People with Some Types of Learning or Cognitive Disabilities
Learning and cognitive-related disabilities can be as varied as mobility-related disabilities, perhaps more so. These disabilities can range from a mild reading-related disability to very severe cognitive impairments that may result in a limited use of language and difficulty processing complex information. For most of the disabilities in this range, there are some common barriers and others that only affect those with more severe cognitive disabilities.
Common barriers for this group include:
- Use of overly complex/advanced language
- Inconsistent navigation
- Overly complex or excessive amounts of content
- Time limits (insufficient time to complete tasks)
- Unstructured content (no visible headings, sections, topics, etc.)
- Unexpected actions (e.g., redirect when an element receives focus)
More specific disability-related issues include:
- Reading: Text justification (inconsistent spacing between words)
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While we generally think of barriers in terms of access for people with disabilities, there are some barriers that impact all types of users, though these are often thought of in terms of usability. Usability and accessibility go hand-in-hand. Adding accessibility features improves usability for others. Many people, including those who do not consider themselves to have a specific disability (such as those over the age of 50), may find themselves experiencing typical age-related loss of sight, hearing, or cognitive ability. Those with varying levels of colour blindness may also fall into this group.
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1.1: Introduction (2015)
“The Peyote Cult”
The Peyote Cult, or Native American Church, involved the use of peyote which is a small, spineless cactus that contains mescaline and can be used for the hallucinogenic effects it provides. The use of peyote as a medicine and a way to reach divine clarity took place before Columbus came to America, but the religion became fully realized and started spreading in 1885. Peyote practices around and after this time had cultural characteristics from both Mexican and Native American practices.
The Native American Church uses several instruments in their rituals. The peyote gourd rattle is used when singing peyote songs during rituals. There is also a water drummer that uses a modified iron kettle as a drum while the singer sings and uses his rattle. The water drummer uses a hard wooden stick made from thick wood that produces a strong sound when used on the drum. The last ritual tool they use is the peyote staff, which is passed around the group and is held upwards during ceremonies as it is a representation of a holy god.
There are various different ceremonies and ways of conducting them, but there are/were two main styles used. The first one is known as a “half-moon” fireplace. This ceremony involves the use of tobacco and very little connection to the Bible. The second ceremonial meeting, the “cross fire” fireplace, is the opposite because tobacco is not used and the Bible is used almost exclusively. This is one example of how indigenous religion blended together with the Christian doctrine and belief system.
Source:
“Native American Church.” Wikipedia . Wikimedia Foundation, n.d. Web. 23 Sept. 2015.
“Of The Girl Who Married Mount Katahdin”
The story you are about to read, Of The Girl Who Married Mount Katahdin, is one of many early Penobscot Indian stories. These stories, however, were not originally written down. This story, as well as countless others within the Penobscot tribe, were oral stories. These were traditionally kept alive by the act of passing the story down from elder members of the tribe to younger members. The Penobscots were natives of Maine, therefore crafting stories about their landscape. Mount Katahdin, which means “The Greatest Mountain” in Penobscot culture, is the highest point in Maine, and was originally named by the Penobscot natives. It wasn’t until white ethnographers began recording these cross cultural encounters that these stories became solidified in literature.
Charles Leland, the self-claimed “author” of the story as well as one of the first ethnographers to collaborate with the Penobscot natives, was a man of many interests. Originally born in Philadelphia, Pennsylvania on August 15th, 1824, Charles Godfrey Leland was educated at Princeton University, where he became interested in both European and American folklore. After spending time in France and Germany, Leland came to America, where he made contact with the Algonquian tribes. These tribes were situated all throughout northeastern New England, as well as large parts of Canada. He studied as well as lived with the Penobscot natives, recording their culture.
The term Ethnography is defined in the Merriam-Webster Dictionary as “the study and systematic recording of human cultures.” The ethnographic researcher views the society from the subjects view. The use of ethnography is to study, understand, and ultimately preserve a culture. The use of ethnography within the Penobscot culture was to help the “American” people that lived in New England at the time to better understand the life and culture of the natives. Since it is a holistic study, meaning all encompassing, ethnographers were encouraged to include everything they possibly could about their experience with the culture. Of the Girl who married Mount Katahdin is an example of Realistic Ethnography, which is described as a simple, objective account of their experience, story. In Leland’s case, he simply wrote down the story that he heard from Mrs. Marie Sakis, an older Penobscot story-teller.
Of the Girl who married Mount Katahdin is the story of a young woman who was outside gathering berries. This girl is romantically enticed, and ultimately seduced by the spirit of Mount Katahdin. Together, they conceive a child, and she returns to her village three years later with the young boy, whose eyebrows are made of stone. The child, who has the ability to kill animals with the pointing of a finger, is used by the tribe to collect an abundance of food. Eventually, the natives of the tribe began to ostracize and make fun of the young boy, to which his mother replies by retreating back to the mountain with the child. The natives lose the powers of the child, and ultimately, their source of food. Finally, Leland states at the end of his passage that it was the American’s own fault for similarly abusing the trust and dignity of the native people, destroying “confidence and respect for them among the Indians.”
Discussion Questions:
1) What might be the significance of the child’s eyebrows being stone? Why not any other part of his body?
2.) How might this story tell the “fall of man” through a native standpoint? What are some surefire signs that it is or isn’t?
Sources Cited:
Wikipedia Contributors. “Charles Godfrey Leland.” Wikipedia . Wikimedia Foundation, n.d. Web. 28 Sept. 2015.
“Native Languages of the Americas: Penobscot (Eastern Abnaki, Penawahpskewi, Penobscott).” Native Americans: Penobscot Indian Tribe (Penobscot Nation, Penobscott, Penobscots) . N.p., n.d. Web. 28 Sept. 2015.
“Ethnography Definition.” Merriam-Webster . Merriam-Webster, n.d. Web. 28 Sept. 2015.
“The Origin and Disease of Medicine”
On The Cherokee Tribe
The Cherokee tribe originates in the southeastern region of the United States, more specifically present-day Tennessee, Georgia, North Carolina, and South Carolina. The Cherokee refer to themselves as Ani-Yuwiya, which translates to “principal people”. In the 19th century, the Cherokees were viewed as one of, if not the most socially and culturally advanced native tribe in the United States. They were referred to as one of the “five civilized tribes”. Once gold was discovered on Cherokee land, prospectors and settlers alike scrambled to the area in an attempt to acquire the bounty of earthly riches. Despite their impressive reputation, the Cherokee were forcibly removed by then president Andrew Jackson under the Indian Removal Act of 1830. This mass exodus, also known as the Trail of Tears, disrupted the lives of the Cherokee people and ended in the death of 4,000 Cherokee whether by hunger, disease, or exhaustion.
On The Origin of Disease and Medicine
The following story, entitled The Origin of Disease and Medicine, weaves a tale of how disease came to be and the way in which the cures for these diseases were discovered. This text, told orally before it was translated by James Mooney, portrays the natural conflict between animals and plants. The animals are irked by humanity’s careless attitude towards them and wish to eradicate them, while the plants are sympathetic towards humanity and seek to save them from certain death. The Cherokee tribe has a strong connection not only to the natural world itself, but more specifically to botany. As a culture entrenched in herbal healing and plant identification, it is only appropriate that their literature would too be steeped in naturalistic themes and information.
“How Glooskap Went to England and France”
This next Native American text was written down by Charles Lelands in 1884 in a collection of stories called The Algonquin Legends of New England , but because it is likely that the story was originally told orally before it was transcribed into written words, its unclear when exactly it was created. This story focuses on the Algonquin mythical figure of Glooskap (also spelled Glooscap), as many Algonquin legends do. According to Wikipedia, the Algonquian people “are one of the most populous and widespread North American native language groups, with tribes originally numbering in the hundreds of thousands” ( Wikipedia ).
In “How Glooskap went to England and France,” the mythical being, Glooskap , builds a stone canoe and sails to England with his mother. When he lands in London, he tells the Europeans about America. From there, he continues on to France to have his mother baptized as a Catholic before returning to America. The legend states that Glooskap and his mother’s return sparked the influx of Europeans to America. This is an example of a “first contact” or “discovery” story because it tells of an initial interaction between Natives and Europeans. Legends like these are important because they help to give us a sense of how the initial interactions between Native Americans and Europeans were experienced.


10.1: Introduction to Alkenes
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Objective
After completing this section, you should be able to give an example of a naturally occurring compound that contains at least one double bond.
Key Terms
Make certain that you can define, and use in context, the key term below.
- olefin
Study Notes
Alkenes are a class of hydrocarbons (i.e., containing only carbon and hydrogen). They are unsaturated compounds with at least one carbon-to-carbon double bond. The double bond makes Alkenes more reactive than alkanes. Olefin is another term used to describe alkenes.
The graphic shows three alkenes. The more complex alkene is commonly known as 1-menthene, but its full proper IUPAC name is 1-methyl-2-(1-methylethyl)-cyclohexene.
Alkenes
Alkenes are a class of hydrocarbons (i.e., containing only carbon and hydrogen). They are unsaturated compounds with at least one carbon-to-carbon double bond. The double bond makes alkenes more reactive than alkanes. Olefin is another term used to describe alkenes. The alkene group can also be called a vinyl group and the carbons sharing the double bond can be called vinyl carbons.
Structure of Ethene - the Simplest Alkene
Ethene is often written as CH 2 =CH 2 which stands for:
The double bond is shared by the two carbon atoms and does not involve the hydrogen atoms, although the condensed formula does not make this point obvious. Note that the molecular formula for ethene is C 2 H 4 , whereas that for ethane is C 2 H 6 .
Ethene is not a very complicated molecule.  These carbon atoms already have four electrons, but they each want to get four more so that they have a full eight (octet) in the valence shell. Having eight valence electrons around carbon gives the atom the same electron configuration as neon, a noble gas. Carbon wants to have the same configuration as neon because when it has eight valence electrons carbon is at its most stable, lowest energy state.
This forms a total of three bonds to each carbon atom, giving them an \(sp^2\) hybridization. Since the carbon atom is forming three sigma bonds instead of the four that it can, it only needs to hybridize three of its outer orbitals, instead of four. It does this by using the \(2s\) electron and two of the \(2p\) electrons, leaving the other unchanged. This new orbital is called an \(sp^2\) hybrid because it is made from one s orbital and two p orbitals.
When atoms use \(sp^2\) hybrids they have a trigonal planar structure. These structures are very similar to a 'peace' sign, there is a central atom with three atoms around it, all on one plane. Trigonal planar molecules have an ideal bond angle of 120° on each side.
The H-C-H bond angle is 117°, which is very close to the ideal 120° of a carbon with \(sp^2\) hybridization. The other two angles (H-C=C) are both 121.5°.
Rigidity in Ethene
There is rigidity in the ethene molecule due to the double-bonded carbons. A double bond consists of one sigma bond formed by overlap of sp 2 hybrid orbitals and one pi bond formed by overlap of parallel 2 p orbitals. In ethene there is no free rotation about the carbon-carbon sigma bond because these two carbons also share a \(\pi\) bond. A \(\pi\) bond is only formed when there is adequate overlap between both top and bottom p-orbitals. Rotation of the p-orbitals causes them to be 90° from each other breaking the \(\pi\) bond because there would be no overlap. There is a much larger energy barrier to rotation than there is about a carbon-carbon sigma bond.
(a) The σ-bonded framework is formed by the overlap of two sets of singly occupied carbon sp 2 hybrid orbitals and four singly occupied hydrogen 1 s orbitals to form electron-pair bonds. This uses 10 of the 12 valence electrons to form a total of five σ bonds (four C–H bonds and one C–C bond).
(b) One singly occupied unhybridized 2 p z orbital remains on each carbon atom to form a carbon–carbon π bond. (Note: by convention, in planar molecules the axis perpendicular to the molecular plane is the z -axis.)
Exercise
1. Although there is only one alkene with the formula C 2 H 4 (ethene) and only one with the formula C 3 H 6 (propene), there are several alkenes with the formula C 4 H 8 . Draw all of the possible bond line structures for alkenes with the formula C 4 H 8 including all possible structural and stereoisomers.
- Answer
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1.1: Introduction
In single-variable calculus, the functions that one encounters are functions of a variable (usually \(x\) or \(t\)) that varies over some subset of the real number line (which we denote by \(\mathbb{R}\)). For such a function, say, \(y = f(x)\), the \(\textbf{graph}\) of the function \(f\) consists of the points \((x, y) = (x, f(x))\). These points lie in the \(\textbf{Euclidean plane}\), which, in the \(\textbf{Cartesian}\) or \(\textbf{rectangular}\) coordinate system, consists of all ordered pairs of real numbers \((a, b)\). We use the word ``Euclidean'' to denote a system in which all the usual rules of Euclidean geometry hold. We denote the Euclidean plane by \(\mathbb{R}^{2}\); the "2'' represents the number of \(\textit{dimensions}\) of the plane. The Euclidean plane has two perpendicular \(\textbf{coordinate axes}\): the \(x\)-axis and the \(y\)-axis.
In vector (or multivariable) calculus, we will deal with functions of two or three variables (usually \(x, y\) or \(x, y, z\), respectively). The graph of a function of two variables, say, \(z = f(x,y)\), lies in Euclidean space , which in the Cartesian coordinate system consists of all ordered triples of real numbers \((a, b, c)\). Since Euclidean space is 3-dimensional, we denote it by \(\mathbb{R}^{3}\). The graph of \(f\) consists of the points \((x, y, z) = (x, y, f(x, y))\). The 3-dimensional coordinate system of Euclidean space can be represented on a flat surface, such as this page or a blackboard, only by giving the illusion of three dimensions, in the manner shown in Figure \(\PageIndex{1}\) . Euclidean space has three mutually perpendicular coordinate axes (\(x, y\) and \(z\)), and three mutually perpendicular coordinate planes\index{plane!coordinate}: the \(xy\)-plane, \(yz\)-plane and \(xz\)-plane (Figure \(\PageIndex{2}\) ).
The coordinate system shown in Figure \(\PageIndex{1}\) is known as a \(\textbf{right-handed coordinate system}\), because it is possible, using the right hand, to point the index finger in the positive direction of the \(x\)-axis, the middle finger in the positive direction of the \(y\)-axis, and the thumb in the positive direction of the \(z\)-axis, as in Figure \(\PageIndex{3}\)
Fig \(\PageIndex{3}\) : Right-handed coordinate system.
An equivalent way of defining a right-handed system is if you can point your thumb upwards in the positive \(z\)-axis direction while using the remaining four fingers to rotate the \(x\)-axis towards the \(y\)-axis. Doing the same thing with the left hand is what defines a \(\textbf{left-handed coordinate system}\). Notice that switching the \(x\)- and \(y\)-axes in a right-handed system results in a left-handed system, and that rotating either type of system does not change its ``handedness''. Throughout the book we will use a right-handed system.
For functions of three variables, the graphs exist in 4-dimensional space (i.e. \(\mathbb{R}^{4}\)), which we can not see in our 3-dimensional space, let alone simulate in 2-dimensional space. So we can only think of 4-dimensional space abstractly. For an entertaining discussion of this subject, see the book by ABBOT.
So far, we have discussed the \(\textit{position}\) of an object in 2-dimensional or 3-dimensional space. But what about something such as the velocity of the object, or its acceleration? Or the gravitational force acting on the object? These phenomena all seem to involve motion and \(\textit{direction}\) in some way. This is where the idea of a \(\textit{vector}\) comes in.
You have already dealt with velocity and acceleration in single-variable calculus. For example, for motion along a straight line, if \(y = f(t)\) gives the displacement of an object after time \(t\), then \(dy/dt = f\,'(t)\) is the velocity of the object at time \(t\). The derivative \(f\,'(t)\) is just a number, which is positive if the object is moving in an agreed-upon "positive'' direction, and negative if it moves in the opposite of that direction. So you can think of that number, which was called the velocity of the object, as having two components: a \(\textit{magnitude}\), indicated by a nonnegative number, preceded by a direction , indicated by a plus or minus symbol (representing motion in the positive direction or the negative direction, respectively), i.e. \(f\,'(t) = \pm a\) for some number \(a \ge 0\). Then \(a\) is the magnitude of the velocity (normally called the \(\textit{speed}\) of the object), and the \(\pm\) represents the direction of the velocity (though the \(+\) is usually omitted for the positive direction).
For motion along a straight line, i.e. in a 1-dimensional space, the velocities are also contained in that 1-dimensional space, since they are just numbers. For general motion along a curve in 2- or 3-dimensional space, however, velocity will need to be represented by a multidimensional object which should have both a magnitude and a direction. A geometric object which has those features is an arrow, which in elementary geometry is called a ``directed line segment''. This is the motivation for how we will define a vector.
Definition \(\PageIndex{1}\)
A (nonzero) \(\textbf{vector}\) is a directed line segment drawn from a point \(P\) (called its \(\textbf{initial point}\)) to a point \(Q\) (called its \(\textbf{terminal point}\)), with \(P\) and \(Q\) being distinct points. The vector is denoted by \(\overrightarrow{PQ}\). Its \(\textbf{magnitude}\) is the length of the line segment, denoted by \(\norm{\overrightarrow{PQ}}\), and its \(\textbf{direction}\) is the same as that of the directed line segment. The \(\textbf{zero vector}\) is just a point, and it is denoted by \(\textbf{0}\).
To indicate the direction of a vector, we draw an arrow from its initial point to its terminal point. We will often denote a vector by a single bold-faced letter (e.g. \(\textbf{v}\)) and use the terms ``magnitude" and ``length'' interchangeably. Note that our definition could apply to systems with any number of dimensions (Figure 1.1.4 (a)-(c)).
A few things need to be noted about the zero vector. Our motivation for what a vector is included the notions of magnitude and direction. What is the magnitude of the zero vector? We define it to be zero, i.e. \(\norm{\textbf{0}} = 0\). This agrees with the definition of the zero vector as just a point, which has zero length. What about the direction of the zero vector? A single point really has no well-defined direction. Notice that we were careful to only define the direction of a \(\textit{nonzero}\) vector, which is well-defined since the initial and terminal points are distinct. Not everyone agrees on the direction of the zero vector. Some contend that the zero vector has \(\textit{arbitrary}\) direction (i.e. can take any direction), some say that it has \(\textit{indeterminate}\) direction (i.e. the direction cannot be determined), while others say that it has \(\textit{no}\) direction. Our definition of the zero vector, however, does not require it to have a direction, and we will leave it at that.
Now that we know what a vector is, we need a way of determining when two vectors are equal. This leads us to the following definition.
Definition \(\PageIndex{2}\)
Two nonzero vectors are \(\textbf{equal}\) if they have the same magnitude and the same direction. Any vector with zero magnitude is equal to the zero vector.
By this definition, vectors with the same magnitude and direction but with different initial points would be equal. For example, in Figure 1.1.5 the vectors \(\textbf{u}\), \(\textbf{v}\) and \(\textbf{w}\) all have the same magnitude \(\sqrt{5}\) (by the Pythagorean Theorem). And we see that \(\textbf{u}\) and \(\textbf{w}\) are parallel, since they lie on lines having the same slope \(\frac{1}{2}\), and they point in the same direction. So \(\textbf{u} = \textbf{w}\), even though they have different initial points. We also see that \(\textbf{v}\) is parallel to \(\textbf{u}\) but points in the opposite direction. So \(\textbf{u} \ne \textbf{v}\).
So we can see that there are an infinite number of vectors for a given magnitude and direction, those vectors all being equal and differing only by their initial and terminal points. Is there a single vector which we can choose to represent all those equal vectors? The answer is yes, and is suggested by the vector \(\textbf{w}\) in Figure \(\PageIndex{5}\).
Unless otherwise indicated, when speaking of "the vector" with a given magnitude and direction, we will mean the one whose initial point is at the origin of the coordinate system.
Thinking of vectors as starting from the origin provides a way of dealing with vectors in a standard way, since every coordinate system has an origin. But there will be times when it is convenient to consider a different initial point for a vector (for example, when adding vectors, which we will do in the next section). Another advantage of using the origin as the initial point is that it provides an easy correspondence between a vector and its terminal point.
Example \(\PageIndex{1}\)
Let \(\textbf{v}\) be the vector in \(\mathbb{R}^{3}\) whose initial point is at the origin and whose terminal point is \((3,4,5)\). Though the \(\textit{point}\) \((3,4,5)\) and the vector \(\textbf{v}\) are different objects, it is convenient to write \(\textbf{v} = (3,4,5)\). When doing this, it is understood that the initial point of \(\textbf{v}\) is at the origin \((0,0,0)\) and the terminal point is \((3,4,5)\).
Unless otherwise stated, when we refer to vectors as \(\textbf{v} = (a,b)\) in \(\mathbb{R}^{2}\) or \(\textbf{v} = (a,b,c)\) in \(\mathbb{R}^{3}\), we mean vectors in Cartesian coordinates starting at the origin. Also, we will write the zero vector \(\textbf{0}\) in \(\mathbb{R}^{2}\) and \(\mathbb{R}^{3}\) as \((0,0)\) and \((0,0,0)\), respectively.
The point-vector correspondence provides an easy way to check if two vectors are equal, without having to determine their magnitude and direction. Similar to seeing if two points are the same, you are now seeing if the terminal points of vectors starting at the origin are the same. For each vector, find the (unique!) vector it equals whose initial point is the origin. Then compare the coordinates of the terminal points of these ``new'' vectors: if those coordinates are the same, then the original vectors are equal. To get the ``new'' vectors starting at the origin, you \(\textit{translate}\) each vector to start at the origin by subtracting the coordinates of the original initial point from the original terminal point. The resulting point will be the terminal point of the ``new'' vector whose initial point is the origin. Do this for each original vector then compare.
Example \(\PageIndex{2}\)
Consider the vectors \(\overrightarrow{PQ}\) and \(\overrightarrow{RS}\) in \(\mathbb{R}^{3}\), where \(P = (2,1,5), Q = (3,5,7), R = (1,-3,-2)\) and \(S = (2,1,0)\). Does \(\overrightarrow{PQ} = \overrightarrow{RS}\)?
The vector \(\overrightarrow{PQ}\) is equal to the vector \(\textbf{v}\) with initial point \((0,0,0)\) and terminal point \(Q - P = (3,5,7) - (2,1,5) = (3 - 2,5 - 1,7 - 5) = (1,4,2)\).
Similarly, \(\overrightarrow{RS}\) is equal to the vector \(\textbf{w}\) with initial point \((0,0,0)\) and terminal point \(S - R = (2,1,0) - (1,-3,-2) = (2 - 1, 1 - (-3),0 - (-2)) = (1,4,2)\).
So \(\overrightarrow{PQ} = \textbf{v} = (1,4,2)\) and \(\overrightarrow{RS} = \textbf{w} = (1,4,2)\).
\(\therefore \overrightarrow{PQ} = \overrightarrow{RS}\)
Recall the distance formula for points in the Euclidean plane:
For points \(P = (x_{1}, y_{1})\), \(Q = (x_{2}, y_{2})\) in \(\mathbb{R}^{2}\), the distance \(d\) between \(P\) and \(Q\) is:
\[d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}\]
By this formula, we have the following result:
Note
For a vector \(\overrightarrow{PQ}\) in \(\mathbb{R}^{2}\) with initial point \(P = (x_{1}, y_{1})\) and terminal point \(Q = (x_{2}, y_{2})\), the magnitude of \(\overrightarrow{PQ}\) is:
\[\norm{\overrightarrow{PQ}} = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}\]
Finding the magnitude of a vector \(\textbf{v} = (a,b)\) in \(\mathbb{R}^{2}\) is a special case of the above formula with \(P = (0,0)\) and \(Q = (a,b)\):
For a vector \(\textbf{v} = (a,b)\) in \(\mathbb{R}^{2}\), the magnitude of \(\textbf{v}\) is:
\[\norm{\textbf{v}} = \sqrt{a^{2} + b^{2}}\]
To calculate the magnitude of vectors in \(\mathbb{R}^{3}\), we need a distance formula for points in Euclidean space (we will postpone the proof until the next section):
Theorem \(\PageIndex{1}\)
The distance \(d\) between points \(P = (x_{1}, y_{1}, z_{1})\) and \(Q = (x_{2}, y_{2}, z_{2})\) in \(\mathbb{R}^{3}\) is:
\[d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} + (z_{2} - z_{1})^{2}}\]
The proof will use the following result:
Theorem \(\PageIndex{2}\)
For a vector \(\textbf{v} = (a,b,c)\) in \(\mathbb{R}^{3}\), the magnitude of \(\textbf{v}\) is:
\[\norm{\textbf{v}} = \sqrt{a^{2} + b^{2} + c^{2}}\]
Proof:
There are four cases to consider:
\(\textit{Case 1:}\) \(a = b = c = 0\). Then \(\textbf{v} = \textbf{0}\), so \(\norm{\textbf{v}} = 0 = \sqrt{0^{2} + 0^{2} + 0^{2}} = \sqrt{a^{2} + b^{2} + c^{2}}\).
\(\textit{Case 2:}\) \(\textit{exactly two of }\)\(a, b, c\) are \(0\). Without loss of generality, we assume that \(a = b = 0\) and \(c \ne 0\) (the other two possibilities are handled in a similar manner). Then \(\textbf{v} = (0,0,c)\), which is a vector of length \(|c|\) along the \(z\)-axis. So \(\norm{\textbf{v}} = | c | = \sqrt{c^{2}} = \sqrt{0^{2} + 0^{2} + c^{2}} = \sqrt{a^{2} + b^{2} + c^{2}}\).
\(\textit{Case 3:}\) \(\textit{exactly one of }\)\(a, b, c\) is \(0\). Without loss of generality, we assume that \(a = 0\), \(b \ne 0\) and \(c \ne 0\) (the other two possibilities are handled in a similar manner). Then \(\textbf{v} = (0,b,c)\), which is a vector in the \(yz\)-plane, so by the Pythagorean Theorem we have \(\norm{\textbf{v}} = \sqrt{b^{2} + c^{2}} = \sqrt{0^{2} + b^{2} + c^{2}} = \sqrt{a^{2} + b^{2} + c^{2}}\).
\(\textit{Case 4:}\) \(\textit{none of }\)\(a, b, c\) are \(0\). Without loss of generality, we can assume that \(a, b, c\) are all positive (the other seven possibilities are handled in a similar manner). Consider the points \(P = (0,0,0)\), \(Q = (a,b,c)\), \(R =(a,b,0),\) and \(S = (a,0,0)\), as shown in Figure 1.1.8. Applying the Pythagorean Theorem to the right triangle \(\triangle PSR\) gives \(\left\vert PR \right\vert^{2} = a^{2} + b^{2}\). A second application of the Pythagorean Theorem, this time to the right triangle \(\triangle PQR\), gives \(\norm{\textbf{v}} = \left\lvert PQ \right\rvert = \sqrt{\left\vert PR \right\vert^{2} + \left\vert QR \right\vert^{2}} = \sqrt{a^{2} + b^{2} + c^{2}}\). This proves the theorem.
\(\tag{\(\textbf{QED}\)}\)
Example 1.3
Calculate the following:
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The magnitude of the vector \(\overrightarrow{PQ}\) in \(\mathbb{R}^{2}\) with \(P = (-1,2)\) and \(Q = (5,5)\).
\( \textit{Solution:}\) By formula (1.2), \(\norm{\overrightarrow{PQ}} = \sqrt{(5 - (-1))^{2} + (5 - 2)^{2}} = \sqrt{36 + 9} = \sqrt{45} = 3 \sqrt{5}\). -
The magnitude of the vector \(\textbf{v} = (8,3)\) in \(\mathbb{R}^{2}\).
\(\textit{Solution:}\) By formula (1.3), \(\norm{\textbf{v}} = \sqrt{8^{2} + 3^{2}} = \sqrt{73}\). -
The distance between the points \(P = (2, -1, 4)\) and \(Q = (4, 2, -3)\) in \(\mathbb{R}^{2}\).
\(\textit{Solution:}\) By formula (1.4), the distance \(d = \sqrt{(4 - 2)^{2} + (2 - (-1))^{2} + (-3 - 4)^{2}} = \sqrt{4 + 9 + 49} = \sqrt{62}\). -
The magnitude of the vector \(\textbf{v} = (5,8,-2)\) in \(\mathbb{R}^{3}\).
\(\textit{Solution:}\) By formula (1.5), \(\norm{\textbf{v}} = \sqrt{5^{2} + 8^{2} + (-2)^{2}} = \sqrt{25 + 64 + 4} = \sqrt{93}\).


11: Ethics and Legal Issues in Education
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Learning Objectives
What the teacher is, is more important than what he teaches -Karl Meninge
Teachers are important role models for their students both in and out of the classroom. Whether teachers are in school or involved in community functions, there are high standards of behavior expected of them. What is meant by the term professionalism? The term professionalism relates to a certain level of degree, skill or expertise in one’s specialized area. Indeed, teachers must obtain schooling, required clinical experience and certain tests in order to enter the field of teaching. In addition to this level of knowledge, teachers must demonstrate integrity, impartiality and ethical behavior in the classroom and in their conduct with parents and coworkers. Teachers must model strong character traits, such as reliability, honesty, respect, lawfulness, patience, fairness, responsibility and collaboration.
In Loco Parentis translates to “in place of parent”. Historically schools are basically responsible for students while in the hands of teachers. Therefore, teachers have a great deal of responsibility for the welfare of their students.


3.5: The Bible as Musical, Oratorio, and Opera
In this chapter you will
- begin learning about one of Johann Sebastian Bach’s famous contemporaries, George Frideric Handel
- consider their very different careers as composers
- learn what an oratorio is and why some of Handel’s were controversial in their day
- situate Handel’s oratorios within the context of more recent works that may be more familiar to you
Introduction: Musical Entertainment Based on the Bible
George Frideric Handel lived at the same time as J. S. Bach. They were both born in the same year, 1685 . Yet their trajectories, despite both pursuing careers in music, took them in significantly different directions, even though both interacted with the Bible extensively in their compositions. Bach was a church musician from a musical family. Handel was an entrepreneur who composed for performance in theaters and other secular venues.
Handel composed many different kinds of works, but he is especially famous for his oratorios, and those works also connect most directly with our interest in this book in the intersection of the Bible and music. An oratorio is essentially an opera without the acting. Different individuals nonetheless depict different roles. Ben Finane writes, “The roots of oratorio…stretch back to the settings of sacred texts in the Middle Ages as well as Medieval mystery plays, whose purpose was to provide education in key points of the Bible to a population that was largely illiterate or lacked access to the Good Book. Biblical texts were set to music and men were taught to sing them—chiefly to learn their verses.” [1] Oratorios were not always on sacred themes, of course, and those who are interested might wish to investigate what, if anything, apart from the words themselves, distinguishes religious oratorios from others. [2] Handel wrote quite a number both sacred and secular , and it is the biblical ones that will be our focus here, once we provide a bit more historical context.
Historically, in many churches, the visual arts had played an important role in conveying stories from the Bible to those who could not read them. Many Eastern Orthodox churches are literally covered with artwork in their interior, with icons focused on biblical stories and people as well as those from later in church history. Catholic churches will typically include statues, and many also include significant amounts of visual artistry of other types. Catholic churches and some Protestant ones may have stained glass windows. Some Protestant churches will have none of those things. The history behind these differences is not something we can explore here. It does, however, indicate how Protestantism may have created a space and a desire or need for musical artistry to replace the visual that certain theological stances rejected .
Cultures that valued biblical stories also created a space for performances aimed primarily at entertainment. If you watch the story of Jesus on television or in the cinema, however much it may perhaps connect with a personal faith that you have, the very nature of the venue and medium makes the experience and meaning different from what would be expected in a church or other religious setting. When religion and entertainment coincide, the result is not always welcomed by either the religious or consumers. You have probably encountered some examples in the news at some point of people objecting to a movie, song, or something else because of religion. They may complain that it promotes religion or that it denigrates it. These kinds of negative reactions to religion and entertainment joining forces have a long history.
Rock Operas and Musicals
You probably will not be surprised that controversy surrounded Jesus Christ Superstar . The rock opera by Andrew Lloyd Webber (discussed briefly in the preceding chapter) is known to many from the 1970s and found a new following more recently with the television version starring John Legend as Jesus . Its take on the story of Jesus is offered through the lens of Judas Iscariot (the disciple said to have betrayed Jesus) and so is controversial because of its story even apart from anything one might say about things like musical choices. Other modern depictions for the purpose of entertainment, such as the animated movie The Prince of Egyp t, are less controversial in that sense. But they still raise questions about the use of the Bible for entertainment, the appropriateness of making money by telling stories from the Bible, and so on. Here is a clip from the movie The Prince of Egypt for those who may not have seen it. [3]
Controversies about sacred stories serving as mere entertainment are nothing new. Centuries ago, Handel faced objections from those who considered it inappropriate to have the words of Scripture performed on a secular stage. When studying music from the past, it can be helpful to think about the closest modern equivalents in order to better appreciate the role that music played in its own time and how music from our own era performs similar or different roles.
More on Handel’s Oratorios
Handel created quite a number of oratorios that retell biblical stories. These include the stories of Jephthah , Deborah , Samson, Solomon , and Athalia , as well as those of Susanna and Judas Maccabeus, which are based on texts from the Apocrypha or deuterocanonical books (i.e., those not found in most Protestant Bibles). The choice of attire and other aspects when these are performed today can create new layers of meaning, as for instance in this performance of Jephtha , which is based on a story in Judges 11 . [4]
In the present day, it is not uncommon for an oratorio to be performed in a manner more like an opera and conversely for an opera to be performed as a concert without the theatrical element. If you read the libretto of Jephthah , which Handel set to music, you will see the great lengths to which it goes to make some kind of theological sense of this disturbing story of child sacrifice. You may wish to compare it with the concert aria “Jephthah’s Daughter” by American composer Amy Beach , which sets a French poem by C. L. Mollevant. That work focuses more on the tragedy of the situation as viewed from the daughter’s perspective. [5] The story of Jephthah is also given musical treatment by Giacomo Meyerbeer ( Jephtas Gelübde ), Giacomo Carissimi ( Jephte ), and Aharon Harlap ( Bat Yiftach ). [6] There is also a completely instrumental exploration of the story by Ernst Toch, which we discuss briefly in chapter 21 on biblical music without words.
Handel’s musical retellings of stories such as those of Judas Maccabeus and Susanna , considered alongside the ones that are about stories found in Protestant Bibles, raise the question of whether audiences may respond to the same work differently depending on whether they view it as “biblical” or not. Either way, most oratorios use libretti that are not exclusively composed of biblical text and thus at the very least expand on and supplement the Bible. [7] This is all the more true when the story is told not just set to music but with songs placed on the lips of characters. Anyone who has seen a musical knows that it is not simply the same thing as telling a story. A movie that is not a musical will still be full of music. The fact that characters sing makes a difference. What happens to a biblical story when it is given that sort of treatment? One might perhaps place most oratorios under the heading of “biblical Apocrypha” just like the many ancient texts we have that expand on biblical narratives.
The libretto for Handel’s Israel in Egypt , on the other hand, is drawn almost entirely from the biblical text, unlike many of the others. You may find it interesting to compare it with the more dramatized explorations of biblical stories by Handel on the one hand and the modern exploration of the same story in The Prince of Egypt on the other. What if anything is different other than the style, reflecting differences between the musical languages of the eighteenth century and today? Have a listen. [8]
It is hard for modern listeners to imagine that a work such as this could have been controversial and met with opposition from religious people in England . For many, bringing sacred Scripture into the secular venue of the concert hall was strictly taboo.
Handel reused and incorporated some existing music into this new work. Of course, Bach did the same thing, most famously with “O Sacred Head.” That was church music being used in other church music, however. The reuse of music, both one’s own and that of others, is nothing new, nor has it ceased. Alfred Newman incorporated music by Handel and also Verdi at key moments in his score for The Greatest Story Ever Told , from which we shared a video clip in chapter 26 about Passions. In all sorts of ways, music sometimes makes connections between different musical works as well as with life and experiences outside the story being told.
The next chapter will discuss Handel’s most famous work, the Messiah . For now, listen to it. It is a long work, not always performed in its entirety, and offers an interesting combination of texts from all over the Bible. The very famous sections that just about every reader will recognize may take on a different meaning when heard in the context of the whole, just as these texts may take on new meanings when arranged in this manner. [9]
For Further Reading
Aaron, Clarissa E. “A Story of Feminine Sacrifice: The Music, Text, and Biographical Connections in Amy Beach’s Concert Aria Jephthah’s Daughter.” Seattle Pacific University Honors Projects 72 (2018). https://digitalcommons.spu.edu/honorsprojects/72/ .
Block, Adrienne Fried. Amy Beach, Passionate Victorian: The Life and Work of an American Composer, 1867–1944 . New York: Oxford University Press, 1998.
Leneman, Helen. The Voice of Judith in 300 Years of Oratorio and Opera . London: Bloomsbury, 2021.
Rooke, Deborah W. Handel’s Israelite Oratorio Libretti: Sacred Drama and Biblical Exegesis . New York: Oxford University Press, 2012.
Shapiro, Alexander H. “‘Drama of an Infinitely Superior Nature’: Handel’s Early English Oratorios and the Religious Sublime.” Music & Letters 74, no. 2 (1993): 215–45.
Webb, Ralph T. “Handel’s Oratorios as Drama.” College Music Symposium 23, no. 2 (1983): 122–44.
- Ben Finane, Handel’s Messiah and His English Oratorios: A Closer Look (New York: Continuum, 2009), 26. ↵
- The first secular oratorio we know of is Claudio Monteverdi’s Il combattimento di Tancredi e Clorinda from 1624. ↵
- Licensed by Universal to the Movieclips YouTube channel. ↵
- Ivor Bolton conducts the Freiburger Barockorchester. Soloists are Topi Lehtipuu, Carolyn Sampson, Ann Hallenberg, and Andrew Foster-Williams. ↵
- There are many other musical treatments of the story of Jephthah’s daughter, including those by Michel de Monteclair, Luis Cepeda, Ruperto Chapí, Elma Ehrich Levinger, Lucien Haudebert, and Lazare Saminsky. ↵
- Harlap, like many of the composers mentioned in this book and here in this chapter, has explored many more biblical stories than we can mention here. The composer’s website has much more that is worth exploring. ↵
- There are many oratorios and other works based on stories in the Apocrypha, such as Vivaldi’s Juditha Triumphans . ↵
- The SCM Chamber Choir and SCM Early Music Ensemble, conducted by Neil McEwan, perform G. F. Handel’s Israel in Egypt on October 14, 2016, at Verbrugghen Hall. Shared on YouTube by the University of Sydney. ↵
- Live performance at the Sydney Opera House by the Sydney Philharmonia Choirs and Christmas Choir and Sydney Philharmonia Orchestra, conducted by Brett Weymark. Shared on YouTube by ABC Classic. ↵


9.9: Some Issues to Consider
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What I’ve described to you in this chapter is the orthodox framework for null hypothesis significance testing (NHST). Understanding how NHST works is an absolute necessity, since it has been the dominant approach to inferential statistics ever since it came to prominence in the early 20th century. It’s what the vast majority of working scientists rely on for their data analysis, so even if you hate it you need to know it. However, the approach is not without problems. There are a number of quirks in the framework, historical oddities in how it came to be, theoretical disputes over whether or not the framework is right, and a lot of practical traps for the unwary. I’m not going to go into a lot of detail on this topic, but I think it’s worth briefly discussing a few of these issues.
Neyman versus Fisher
The first thing you should be aware of is that orthodox NHST is actually a mash-up of two rather different approaches to hypothesis testing, one proposed by Sir Ronald Fisher and the other proposed by Jerzy Neyman (for a historical summary see Lehmann 2011). The history is messy because Fisher and Neyman were real people whose opinions changed over time, and at no point did either of them offer “the definitive statement” of how we should interpret their work many decades later. That said, here’s a quick summary of what I take these two approaches to be.
First, let’s talk about Fisher’s approach. As far as I can tell, Fisher assumed that you only had the one hypothesis (the null), and what you want to do is find out if the null hypothesis is inconsistent with the data. From his perspective, what you should do is check to see if the data are “sufficiently unlikely” according to the null. In fact, if you remember back to our earlier discussion, that’s how Fisher defines the p-value. According to Fisher, if the null hypothesis provided a very poor account of the data, you could safely reject it. But, since you don’t have any other hypotheses to compare it to, there’s no way of “accepting the alternative” because you don’t necessarily have an explicitly stated alternative. That’s more or less all that there was to it.
In contrast, Neyman thought that the point of hypothesis testing was as a guide to action, and his approach was somewhat more formal than Fisher’s. His view was that there are multiple things that you could do (accept the null or accept the alternative) and the point of the test was to tell you which one the data support. From this perspective, it is critical to specify your alternative hypothesis properly. If you don’t know what the alternative hypothesis is, then you don’t know how powerful the test is, or even which action makes sense. His framework genuinely requires a competition between different hypotheses. For Neyman, the p value didn’t directly measure the probability of the data (or data more extreme) under the null, it was more of an abstract description about which “possible tests” were telling you to accept the null, and which “possible tests” were telling you to accept the alternative.
As you can see, what we have today is an odd mishmash of the two. We talk about having both a null hypothesis and an alternative (Neyman), but usually 168 define the p value in terms of exreme data (Fisher), but we still have α values (Neyman). Some of the statistical tests have explicitly specified alternatives (Neyman) but others are quite vague about it (Fisher). And, according to some people at least, we’re not allowed to talk about accepting the alternative (Fisher). It’s a mess: but I hope this at least explains why it’s a mess.
Bayesians versus frequentists
Earlier on in this chapter I was quite emphatic about the fact that you cannot interpret the p value as the probability that the null hypothesis is true. NHST is fundamentally a frequentist tool (see Chapter 9) and as such it does not allow you to assign probabilities to hypotheses: the null hypothesis is either true or it is not. The Bayesian approach to statistics interprets probability as a degree of belief, so it’s totally okay to say that there is a 10% chance that the null hypothesis is true: that’s just a reflection of the degree of confidence that you have in this hypothesis. You aren’t allowed to do this within the frequentist approach. Remember, if you’re a frequentist, a probability can only be defined in terms of what happens after a large number of independent replications (i.e., a long run frequency). If this is your interpretation of probability, talking about the “probability” that the null hypothesis is true is complete gibberish: a null hypothesis is either true or it is false. There’s no way you can talk about a long run frequency for this statement. To talk about “the probability of the null hypothesis” is as meaningless as “the colour of freedom”. It doesn’t have one!
Most importantly, this isn’t a purely ideological matter. If you decide that you are a Bayesian and that you’re okay with making probability statements about hypotheses, you have to follow the Bayesian rules for calculating those probabilities. I’ll talk more about this in Chapter 17, but for now what I want to point out to you is the p value is a terrible approximation to the probability that H 0 is true. If what you want to know is the probability of the null, then the p value is not what you’re looking for!
Traps
As you can see, the theory behind hypothesis testing is a mess, and even now there are arguments in statistics about how it “should” work. However, disagreements among statisticians are not our real concern here. Our real concern is practical data analysis. And while the “orthodox” approach to null hypothesis significance testing has many drawbacks, even an unrepentant Bayesian like myself would agree that they can be useful if used responsibly. Most of the time they give sensible answers, and you can use them to learn interesting things. Setting aside the various ideologies and historical confusions that we’ve discussed, the fact remains that the biggest danger in all of statistics is thoughtlessness . I don’t mean stupidity, here: I literally mean thoughtlessness. The rush to interpret a result without spending time thinking through what each test actually says about the data, and checking whether that’s consistent with how you’ve interpreted it. That’s where the biggest trap lies.
To give an example of this, consider the following example (see Gelman and Stern 2006). Suppose I’m running my ESP study, and I’ve decided to analyse the data separately for the male participants and the female participants. Of the male participants, 33 out of 50 guessed the colour of the card correctly. This is a significant effect (p=.03). Of the female participants, 29 out of 50 guessed correctly. This is not a significant effect (p=.32). Upon observing this, it is extremely tempting for people to start wondering why there is a difference between males and females in terms of their psychic abilities. However, this is wrong. If you think about it, we haven’t actually run a test that explicitly compares males to females. All we have done is compare males to chance (binomial test was significant) and compared females to chance (binomial test was non significant). If we want to argue that there is a real difference between the males and the females, we should probably run a test of the null hypothesis that there is no difference! We can do that using a different hypothesis test, 169 but when we do that it turns out that we have no evidence that males and females are significantly different (p=.54). Now do you think that there’s anything fundamentally different between the two groups? Of course not. What’s happened here is that the data from both groups (male and female) are pretty borderline: by pure chance, one of them happened to end up on the magic side of the p=.05 line, and the other one didn’t. That doesn’t actually imply that males and females are different. This mistake is so common that you should always be wary of it: the difference between significant and not-significant is not evidence of a real difference – if you want to say that there’s a difference between two groups, then you have to test for that difference!
The example above is just that: an example. I’ve singled it out because it’s such a common one, but the bigger picture is that data analysis can be tricky to get right. Think about what it is you want to test, why you want to test it, and whether or not the answers that your test gives could possibly make any sense in the real world.


10.3: Functional groups
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Harper College Chemistry Department
Adapted from LibreTexts: Organic Chemistry With a Biological Emphasis by Tim Soderberg (University of Minnesota, Morris) 1.2: Functional Groups and Organic nomenclature
Functional groups in organic compounds
Functional groups are structural units within organic compounds that are defined by specific bonding arrangements between specific atoms. The structure of capsaicin (Figure 1) incorporates several functional groups, labeled in the figure below and explained throughout this section.
Figure 1. Structure of capsaicin with labeled functional groups.
As we progress in our study of organic chemistry, it will become extremely important to be able to quickly recognize the most common functional groups, because they are the key structural elements that define how organic molecules react . For now, we will only worry about drawing and recognizing each functional group, as depicted by Lewis and line structures.
The ‘default’ in organic chemistry (essentially, the lack of any functional groups) is given the term alkane , characterized by single bonds between carbon and carbon, or between carbon and hydrogen. Methane, CH 4 , is the natural gas you may burn in your furnace. Octane, C 8 H 18 , is a component of gasoline.
Alkanes
Alkenes (sometimes called olefins ) have carbon-carbon double bonds, and alkynes have carbon-carbon triple bonds. Ethene, the simplest alkene example, is a gas that serves as a cellular signal in fruits to stimulate ripening. If you want bananas to ripen quickly, put them in a paper bag along with an apple – the apple emits ethene gas, setting off the ripening process in the bananas. Ethyne, commonly called acetylene, is used as a fuel in welding blow torches.
Alkenes and alkynes
The bonding nature in alkenes is trigonal planar and in alkynes is linear. Furthermore, many alkenes can take two geometric forms: cis or trans . The cis and trans forms of a given alkene are different molecules with different physical properties because there is a very high energy barrier to rotation about a double bond. In the example below, the difference between cis and trans alkenes is readily apparent.
Alkanes, alkenes, and alkynes are all classified as hydrocarbons , because they are composed solely of carbon and hydrogen atoms. Alkanes are said to be saturated hydrocarbons , because the carbons are bonded to the maximum possible number of hydrogens – in other words, they are saturated with hydrogen atoms. The double and triple-bonded carbons in alkenes and alkynes have fewer hydrogen atoms bonded to them – they are thus referred to as unsaturated hydrocarbons . Hydrogen can be added to double and triple bonds, in a type of reaction called ‘hydrogenation,’ which will be discussed in a later chapter.
The aromatic group is exemplified by benzene (which used to be a commonly used solvent in the organic lab, but was shown to be carcinogenic later), and naphthalene, a compound with a distinctive ‘mothball’ smell. Aromatic groups are planar (flat) ring structures and are widespread in nature.
Aromatics
When the carbon of an alkane is bonded to one or more halogens, the group is referred to as a alkyl halide or haloalkane . Chloroform is a useful solvent in the laboratory and was one of the earlier anesthetics used in surgery. Chlorodifluoromethane was used as a refrigerant and a propellant in aerosol sprays until the late twentieth century; but its use was discontinued after it was found to have harmful effects on the ozone layer. Bromoethane is a simple alkyl halide often used in organic synthesis. Alkyl halides groups are quite rare in biomolecules.
HaloalkanesI n the alcohol functional group, a single-bonded carbon is bonded to an OH group (the OH group, by itself, is referred to as a hydroxyl ) not to be confused with the hydroxide polyatomic ion, OH – . Except for methanol, all alcohols can be classified as primary, secondary, or tertiary. In a primary alcohol , the carbon bonded to the hydroxyl group is also bonded to only one other carbon. In a secondary alcohol and tertiary alcohol, the carbon is bonded to two or three other carbons, respectively. When the hydroxyl group is directly attached to an aromatic ring, the resulting group is called a phenol . The sulfur analog of an alcohol is called a thiol (from the Greek thio , for sulfur).
Alcohols, phenols, and thiols Note that the definition of a phenol states that the hydroxyl oxygen must be directly attached to one of the carbons of the aromatic ring. The compound below, therefore, is not a phenol – it is a primary alcohol.
The distinction is important, as there is a significant difference in the reactivity of alcohols and phenols.
In an ether functional group, a central oxygen is bonded to two carbons. Below is the structure of diethyl ether, a common laboratory solvent and also one of the first compounds to be used as an anesthetic during operations. The sulfur analog of an ether is called a thioether or sulfide .
Ethers and sulfides
Amines are characterized by nitrogen atoms with single bonds to hydrogen and carbon. Just as there are primary, secondary and tertiary alcohols, there are primary, secondary and tertiary amines. Ammonia is a special case with no carbon atoms, only hydrogen.
One of the most important properties of amines is that they are basic and are readily protonated to form ammonium cations. In the case where a nitrogen has four bonds to carbon (which is somewhat unusual in biomolecules), it is called a quaternary ammonium ion.
Amines
Note: Do not be confused by how the terms, ‘primary’, ‘secondary’, and ‘tertiary’ are applied to alcohols and amines – the definitions are different. In alcohols, what matters is how many other carbons the alcohol carbon is bonded to, while in amines, what matters is how many carbons the nitrogen is bonded to.
Phosphate and its derivative functional groups are ubiquitous in biomolecules. A phosphate linked to a single organic group is called a phosphate ester ; when it has links to two organic groups it is called a phosphate diester . A linkage between two phosphates creates a phosphate anhydride .
Organic phosphates
There are a number of functional groups that contain a carbon-oxygen double bond, which is commonly referred to as a carbonyl . Ketones and aldehydes are two closely related carbonyl-based functional groups that react in very similar ways. In a ketone , the carbon atom of a carbonyl is bonded to two other carbons. In an aldehyde , the carbonyl carbon is bonded on one side to a hydrogen, and on the other side to a carbon. The exception to this definition is formaldehyde, in which the carbonyl carbon has bonds to two hydrogens.
A group with a carbon-nitrogen double bond is called an imine , or sometimes a Schiff base.
Aldehydes, ketones, and imines
When a carbonyl carbon is bonded on one side to a carbon (or hydrogen) and on the other side to an oxygen, nitrogen, or sulfur, the functional group is considered to be one of the ‘ carboxylic acid derivatives ’, a designation that describes a set of related functional groups. The eponymous member of this family is the carboxylic acid functional group, in which the carbonyl is bonded to a hydroxyl group. The conjugate base of a carboxylic acid is a carboxylate . Other derivatives are carboxylic esters (usually just called ‘esters’ ) and amides, to name a few. These carboxylic acid derivatives are very common in biological molecules and metabolic pathways.
Carboxylic acid derivativesA single compound often contains several functional groups, particularly in biological organic chemistry. The six-carbon sugar molecules glucose and fructose, for example, contain aldehyde and ketone groups, respectively, and both contain five alcohol groups (a compound with several alcohol groups is often referred to as a ‘ polyol’ ).
The hormone testosterone, the amino acid phenylalanine, and the glycolysis metabolite dihydroxyacetone phosphate all contain multiple functional groups, as labeled below.
While not in any way a complete list, this section has covered most of the important functional groups that we will encounter in biological organic chemistry.
The table here summarizes the structures discussed in this chapter:
Examples
- Identify the functional groups (other than alkanes) in the following organic compounds. State whether alcohols and amines are primary, secondary, or tertiary.
2. Draw one example each of compounds fitting the descriptions below, using line structures. Be sure to designate the location of all non-zero formal charges. All atoms should have complete octets (phosphorus may exceed the octet rule). There are many possible correct answers for these, so be sure to check your structures with your instructor or tutor.
a) a compound with molecular formula C 6 H 11 NO that includes alkene, secondary amine, and primary alcohol functional groups
b) an ion with molecular formula C 3 H 5 O 6 P 2- that includes aldehyde, secondary alcohol, and phosphate functional groups.
c) A compound with molecular formula C 6 H 9 NO that has an amide functional group and does not have an alkene group.


2.5: Equilibrium Analysis for Concurrent Force Systems
If a body is in static equilibrium, then by definition that body is not accelerating. If we know that the body is not accelerating then we know that the sum of the forces acting on that body must be equal to zero . This is the basis for equilibrium analysis for a particle.
In order to solve for any unknowns in our sum of forces equation, we actually need to turn the one vector equation into a set of scalar equations. For two dimensional problems, we will split our one vector equation down into two scalar equations. We do this by summing up all the \(x\) components of the force vectors and setting them equal to zero in our first equation, and summing up all the \(y\) components of the force vectors and setting them equal to zero in our second equation.
\[ \sum \vec{F} \, = \, 0 \]
\[ \sum F_x \, = \, 0 \, ; \,\,\, \sum F_y \, = \, 0 \]
Once we have written out the equilibrium equations, we can solve the equations for any unknown forces.
Finding the Equilibrium Equations:
The first step in finding the equilibrium equations is to draw a free body diagram of the body being analyzed. This diagram should show all the known and unknown force vectors acting on the body. In the free body diagram, provide values for any of the know magnitudes or directions for the force vectors and provide variable names for any unknowns (either magnitudes or directions).
Next you will need to chose the \(x\), \(y\), and \(z\) axes. These axes do need to be perpendicular to one another, but they do not necessarily have to be horizontal or vertical. If you choose coordinate axes that line up with some of your force vectors you will simplify later analysis.
Once you have chosen axes, you need to break down all of the force vectors into components along the \(x\), \(y\) and \(z\) directions (see the vectors page in Appendix 1 if you need more guidance on this). Your first equation will be the sum of the magnitudes of the components in the \(x\) direction being equal to zero, the second equation will be the sum of the magnitudes of the components in the \(y\) direction being equal to zero, and the third (if you have a 3D problem) will be the sum of the magnitudes in the \(z\) direction being equal to zero. Collectively these are known as the equilibrium equations .
Once you have your equilibrium equations, you can solve them for unknowns using algebra. The number of unknowns that you will be able to solve for will be the number of equilibrium equations that you have. In instances where you have more unknowns than equations, the problem is known as a statically indeterminate problem and you will need additional information to solve for the given unknowns.
The diagram below shows a 3-lb box (Box A) sitting on top of a 5-lb box (box B). Determine the magnitude and direction of all the forces acting on box B.
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A 600-lb barrel rests in a trough as shown below. The barrel is supported by two normal forces (\(F_2\) and \(F_3\)). Determine the magnitude of both of these normal forces.
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A 6-kg traffic light is supported by two cables as shown below. Find the tension in each of the cables supporting the traffic light.
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A 400-kg wrecking ball rests against a surface as shown below. Assuming the wrecking ball is currently in equilibrium, determine the tension force in the cable supporting the wrecking ball and the normal force that exists between the wrecking ball and the surface.
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Barrels A and B are supported in a foot truck as seen below. Assuming the barrels are in equilibrium, determine all forces acting on barrel B.
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Three soda cans, each weighing 0.75 lbs and having a diameter of 4 inches, are stacked in a formation as shown below. Assuming no friction forces, determine the normal forces acting on can B.
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