10.3: Applications and Solving Right Triangles
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Throughout its early development, trigonometry was often used as a means of indirect measurement, e.g. determining large distances or lengths by using measurements of angles and small, known distances. Today, trigonometry is widely used in physics, astronomy, engineering, navigation, surveying, and various fields of mathematics and other disciplines. In this section we will see some of the ways in which trigonometry can be applied. Your calculator should be in degree mode for these examples.
Example 1.11
A person stands \(150\) ft away from a flagpole and measures an angle of elevation of \(32^\circ\) from his horizontal line of sight to the top of the flagpole. Assume that the person's eyes are a vertical distance of 6 ft from the ground. What is the height of the flagpole?
Solution:
The picture on the right describes the situation. We see that the height of the flagpole is \(h + 6\) ft, where
\[\frac{h}{150} ~=~ \tan\;32^\circ \quad\Rightarrow\quad h ~=~ 150\;\tan\;32^\circ
~=~ 150\;(0.6249) ~=~ 94 ~. \nonumber \]
How did we know that \(\tan\;32^\circ = 0.6249\,\)? By using a calculator. And since none of the numbers we were given had decimal places, we rounded off the answer for \(h\) to the nearest integer. Thus, the height of the flagpole is \(\,h + 6 = 94 + 6 = \boxed{100 ~\text{ft}}\).
Example 1.12
A person standing \(400\) ft from the base of a mountain measures the angle of elevation from the ground to the top of the mountain to be \(25^\circ \). The person then walks \(500\) ft straight back and measures the angle of elevation to now be \(20^\circ \). How tall is the mountain?
Solution:
We will assume that the ground is flat and not inclined relative to the base of the mountain. Let \(h\) be the height of the mountain, and let \(x\) be the distance from the base of the mountain to the point directly beneath the top of the mountain, as in the picture on the right. Then we see that
\[ \begin{align*} \frac{h}{x + 400} ~=~ \tan\;25^\circ \quad &\Rightarrow \quad h ~=~ (x + 400)\;\tan\;25^\circ
~,~\text{and}\\[4pt] \frac{h}{x + 400 + 500} ~=~ \tan\;20^\circ \quad &\Rightarrow \quad h ~=~
(x + 900)\;\tan\;20^\circ, \end{align*} \nonumber \]
so
\((x + 400)\;\tan\;25^\circ ~=~ (x + 900)\;\tan\;20^\circ \), since they both equal \(h \). Use that equation to solve for \(x\):
\[ x\;\tan\;25^\circ ~-~ x\;\tan\;20^\circ ~=~ 900\;\tan\;20^\circ ~-~ 400\;\tan\;25^\circ
\quad\Rightarrow\quad
x ~=~ \frac{900\;\tan\;20^\circ ~-~ 400\;\tan\;25^\circ}{\tan\;25^\circ ~-~ \tan\;20^\circ}
~=~ 1378~ \text{ft} \nonumber \]
Finally, substitute \(x\) into the first formula for \(h\) to get the height of the mountain:
\[h ~=~ (1378 + 400)\;\tan\;25^\circ ~=~ 1778\;(0.4663) ~=~ \boxed{829~ \text{ft}} \nonumber \]
Example 1.13
A blimp \(4280\) ft above the ground measures an angle of depression of \(24^\circ\) from its horizontal line of sight to the base of a house on the ground. Assuming the ground is flat, how far away along the ground is the house from the blimp?
Solution:
Let \(x\) be the distance along the ground from the blimp to the house, as in the picture to the right. Since the ground and the blimp's horizontal line of sight are parallel, we know from elementary geometry that the angle of elevation \(\theta\) from the base of the house to the blimp is equal to the angle of depression from the blimp to the base of the house, i.e. \(\theta = 24^\circ \). Hence,
\[\frac{4280}{x} ~=~ \tan\;24^\circ \quad\Rightarrow\quad x ~=~ \frac{4280}{\tan\;24^\circ}
~=~ \boxed{9613 ~\text{ft}}~. \nonumber \]
Example 1.14
An observer at the top of a mountain \(3\) miles above sea level measures an angle of depression of \(2.23^\circ\) to the ocean horizon. Use this to estimate the radius of the earth.
Solution:
We will assume that the earth is a sphere. Let \(r\) be the radius of the earth. Let the point \(A\) represent the top of the mountain, and let \(H\) be the ocean horizon in the line of sight from \(A \), as in Figure 1.3.1. Let \(O\) be the center of the earth, and let \(B\) be a point on the horizontal line of sight from \(A\) (i.e. on the line perpendicular to \(\overline{OA}\)). Let \(\theta\) be the angle \(\angle\,AOH \).
Since \(A\) is \(3\) miles above sea level, we have \(OA = r + 3 \). Also, \(OH = r \). Now sincev\(\overline{AB} \perp \overline{OA} \), we have \(\angle\,OAB = 90^\circ \), so we see that \(\angle\,OAH = 90^\circ - 2.23^\circ = 87.77^\circ \). We see that the line through \(A\) and \(H\) is a tangent line to the surface of the earth (considering the surface as the circle of radius \(r\) through \(H\) as in the picture). So by Exercise 14 in Section 1.1, \(\overline{AH} \perp \overline{OH}\) and hence \(\angle\,OHA = 90^\circ \). Since the angles in the triangle \(\triangle\,OAH\) add up to \(180^\circ \), we have \(\theta = 180^\circ - 90^\circ - 87.77^\circ = 2.23^\circ \). Thus,
\[\cos\;\theta ~=~ \frac{OH}{OA} ~=~ \frac{r}{r+3} \quad\Rightarrow\quad \frac{r}{r+3} ~=~
\cos\;2.23^\circ ~, \nonumber \]
so solving for \(r\) we get
\[\begin{align*}
r ~=~ (r ~+~ 3)\;\cos\;2.23^\circ \quad &\Rightarrow \quad
r ~-~ r\;\cos\;2.23^\circ ~=~ 3\;\cos\;2.23^\circ \\[4pt]
&\Rightarrow \quad r ~=~ \frac{3\;\cos\;2.23^\circ}{1 ~-~ \cos\;2.23^\circ}\\
&\Rightarrow \quad \boxed{r ~=~ 3958.3 ~\text{miles}} ~.
\end{align*} \nonumber \]
Note: This answer is very close to the earth's actual (mean) radius of \(3956.6\) miles.
Example 1.15
As another application of trigonometry to astronomy, we will find the distance from the earth to the sun. Let \(O\) be the center of the earth, let \(A\) be a point on the equator, and let \(B\) represent an object (e.g. a star) in space, as in the picture on the right. If the earth is positioned in such a way that the angle \(\angle\,OAB = 90^\circ \), then we say that the angle \(\alpha = \angle\,OBA\) is the equatorial parallax of the object. The equatorial parallax of the sun has been observed to be approximately \(\alpha =0.00244^\circ \). Use this to estimate the distance from the center of the earth to the sun.
Solution:
Let \(B\) be the position of the sun. We want to find the length of \(\overline{OB} \). We will use the actual radius of the earth, mentioned at the end of Example 1.14, to get \(OA = 3956.6\) miles. Since \(\angle\,OAB = 90^\circ \), we have
\[\frac{OA}{OB} ~=~ \sin\;\alpha \quad\Rightarrow\quad OB ~=~ \frac{OA}{\sin\;\alpha} ~=~
\frac{3956.6}{\sin\;0.00244^\circ} ~=~ 92908394 ~, \nonumber \]
so the distance from the center of the earth to the sun is approximately \(\fbox{\(93\) million miles}~.\)
Note: The earth's orbit around the sun is an ellipse, so the actual distance to the sun varies.
In the above example we used a very small angle (\(0.00244^\circ\)). A degree can be divided into smaller units: a minute is one-sixtieth of a degree, and a second is one-sixtieth of a minute. The symbol for a minute is \('\) and the symbol for a second is \('' \). For example, \(4.5^\circ = 4^\circ\;30' \). And \(4.505^\circ = 4^\circ\;30'\;18''\):
\[4^\circ\;30'\;18'' ~=~ 4 ~+~ \frac{30}{60} ~+~ \frac{18}{3600} ~\text{degrees} ~=~ 4.505^\circ \nonumber \]
In Example 1.15 we used \(\alpha = 0.00244^\circ \approx 8.8'' \), which we mention only because some angle measurement devices do use minutes and seconds.
Example 1.16
An observer on earth measures an angle of \(32'\;4''\) from one visible edge of the sun to the other (opposite) edge, as in the picture on the right. Use this to estimate the radius of the sun.
Solution:
Let the point \(E\) be the earth and let \(S\) be the center of the sun. The observer's lines of sight to the visible edges of the sun are tangent lines to the sun's surface at the points \(A\) and \(B \). Thus, \(\angle\,EAS = \angle\,EBS = 90^\circ \). The radius of the sun equals \(AS \). Clearly \(AS = BS \). So since \(EB = EA\) (why?), the triangles \(\triangle\,EAS\) and \(\triangle\,EBS\) are similar. Thus, \(\angle\,AES = \angle\,BES = \frac{1}{2}\; \angle\,AEB = \frac{1}{2}\;(32'\;4'') = 16'\;2'' = (16/60) + (2/3600) = 0.26722^\circ \).
Now, \(ES\) is the distance from the surface of the earth (where the observer stands) to the center of the sun. In Example 1.15 we found the distance from the center of the earth to the sun to be \(92,908,394\) miles. Since we treated the sun in that example as a point, then we are justified in treating that distance as the distance between the centers of the earth and sun. So \(ES = 92908394 - ~\text{radius of earth} = 92908394 - 3956.6 = 92904437.4\) miles. Hence,
\[\sin\;(\angle\,AES) ~=~ \frac{AS}{ES} \quad\Rightarrow\quad AS ~=~ ES \;\sin\;0.26722^\circ
~=~ (92904437.4)\;\sin\;0.26722^\circ ~=~ \boxed{433,293 ~\text{miles}} ~. \nonumber \]
Note: This answer is close to the sun's actual (mean) radius of \(432,200\) miles.
You may have noticed that the solutions to the examples we have shown required at least one right triangle. In applied problems it is not always obvious which right triangle to use, which is why these sorts of problems can be difficult. Often no right triangle will be immediately evident, so you will have to create one. There is no general strategy for this, but remember that a right triangle requires a right angle, so look for places where you can form perpendicular line segments. When the problem contains a circle, you can create right angles by using the perpendicularity of the tangent line to the circle at a point with the line that joins that point to the center of the circle. We did exactly that in Examples 1.14, 1.15, and 1.16.
Example 1.17
The machine tool diagram on the right shows a symmetric V-block , in which one circular roller sits on top of a smaller circular roller. Each roller touches both slanted sides of the V-block. Find the diameter \(d\) of the large roller, given the information in the diagram.
Solution:
The diameter \(d\) of the large roller is twice the radius \(OB \), so we need to find \(OB \). To do this, we will show that \(\triangle\,OBC\) is a right triangle, then find the angle \(\angle\,BOC \), and then find \(BC \). The length \(OB\) will then be simple to determine.
Since the slanted sides are tangent to each roller, \(\angle\,ODA = \angle\,PEC =90^\circ \). By symmetry, since the vertical line through the centers of the rollers makes a \(37^\circ\) angle with each slanted side, we have \(\angle\,OAD = 37^\circ \). Hence, since \(\triangle\,ODA\) is a right triangle, \(\angle\,DOA\) is the complement of \(\angle\,OAD \). So \(\angle\,DOA = 53^\circ \).
Since the horizontal line segment \(\overline{BC}\) is tangent to each roller, \(\angle\,OBC =\angle\,PBC = 90^\circ \). Thus, \(\triangle\,OBC\) is a right triangle. And since \(\angle\,ODA = 90^\circ \), we know that \(\triangle\,ODC\) is a right triangle. Now, \(OB = OD\) (since they each equal the radius of the large roller), so by the Pythagorean Theorem we have \(BC = DC\):
\[BC^2 ~=~ OC^2 ~-~ OB^2 ~=~ OC^2 ~-~ OD^2 ~=~ DC^2 \quad\Rightarrow\quad BC ~=~ DC \nonumber \]
Thus, \(\triangle\,OBC\) and \(\triangle\,ODC\) are congruent triangles (which we denote by \(\triangle\,OBC \cong \triangle\,ODC\)), since their corresponding sides are equal. Thus, their corresponding angles are equal. So in particular, \(\angle\,BOC = \angle\,DOC \). We know that \(\angle\,DOB = \angle\,DOA = 53^\circ \). Thus,
\[53^\circ ~=~ \angle\,DOB ~=~ \angle\,BOC ~+~ \angle\,DOC = \angle\,BOC ~+~ \angle\,BOC ~=~
2\;\angle\,BOC \quad\Rightarrow\quad \angle\,BOC ~=~ 26.5^\circ ~. \nonumber \]
Likewise, since \(BP = EP\) and \(\angle\,PBC = \angle\,PEC = 90^\circ \), \(\triangle\,BPC\) and \(\triangle\,EPC\) are congruent right triangles. Thus, \(BC = EC \). But we know that \(BC = DC \), and we see from the diagram that \(EC + DC = 1.38 \). Thus, \(BC + BC = 1.38\) and so \(BC = 0.69 \). We now have all we need to find \(OB\):
\[\frac{BC}{OB} ~=~ \tan\;\angle\,BOC \quad\Rightarrow\quad OB ~=~ \frac{BC}{\tan\;\angle\,BOC} ~=~
\frac{0.69}{\tan\;26.5^\circ} ~=~ 1.384 \nonumber \]
Hence, the diameter of the large roller is \(\,d = 2 \times OB = 2\,(1.384) = \boxed{2.768}\)~.
Example 1.18
A slider-crank mechanism is shown in Figure 1.3.2 below. As the piston moves downward the connecting rod rotates the crank in the clockwise direction, as indicated.
The point \(A\) is the center of the connecting rod's wrist pin and only moves vertically. The point \(B\) is the center of the crank pin and moves around a circle of radius \(r\) centered at the point \(O \), which is directly below \(A\) and does not move. As the crank rotates it makes an angle \(\theta\) with the line \(\overline{OA} \). The instantaneous center of rotation of the connecting rod at a given time is the point \(C\) where the horizontal line through \(A\) intersects the extended line through \(O\) and \(B \). From Figure 1.3.2 we see that \(\angle\,OAC = 90^\circ \), and we let \(a = AC \), \(b = AB \), and \(c = BC \). In the exercises you will show that for \(0^\circ < \theta < 90^\circ \),
\[c ~=~ \frac{\sqrt{b^2 ~-~ r^2 \;(\sin\,\theta)^2}}{\cos\;\theta} ~\qquad\text{and}\qquad~
a ~=~ r\;\sin\;\theta ~+~ \sqrt{b^2 ~-~ r^2 \;(\sin\,\theta)^2}~\tan\;\theta ~. \nonumber \]
For some problems it may help to remember that when a right triangle has a hypotenuse of length \(r\) and an acute angle \(\theta \), as in the picture below, the adjacent side will have length \(r\,\cos\;\theta\) and the opposite side will have length \(r\,\sin\;\theta \). You can think of those lengths as the horizontal and vertical ``components'' of the hypotenuse.
Notice in the above right triangle that we were given two pieces of information: one of the acute angles and the length of the hypotenuse. From this we determined the lengths of the other two sides, and the other acute angle is just the complement of the known acute angle. In general, a triangle has six parts: three sides and three angles. Solving a triangle means finding the unknown parts based on the known parts. In the case of a right triangle, one part is always known: one of the angles is \(90^\circ \).
Example 1.19
Solve the right triangle in Figure 1.3.3 using the given information:
(a)
\(c = 10,\, A = 22^◦\)
Solution
: The unknown parts are \(a \), \(b \), and \(B \).   By the Pythagorean Theorem,
\[c ~=~ \sqrt{a^2 ~+~ b^2} ~=~ \sqrt{3^2 ~+~ 4^2} ~=~ \sqrt{25} ~=~ 5 ~. \nonumber \]
Now, \(\tan\;A = \frac{a}{b} = \frac{3}{4} = 0.75 \). So how do we find \(A\)? There should be a key labeled \(\fbox{\(\tan^{-1}\)}\) on your calculator, which works like this: give it a number \(x\) and it will tell you the angle \(\theta\) such that \(\tan\;\theta = x \). In our case, we want the angle \(A\) such that \(\tan\;A = 0.75\):
\[ \text{Enter: } 0.75 \quad \text{Press:}\fbox{\(\tan^{-1}\)} \quad \text{Answer: } 36.86989765 \nonumber \]
This tells us that \(A = 36.87^\circ \), approximately. Thus \(B = 90^\circ - A = 90^\circ - 36.87^\circ = 53.13^\circ \).
Note: The \(\fbox{ \(\sin^{-1}\)}\) and \(\fbox{ \(\cos^{-1}\)}\) keys work similarly for sine and cosine, respectively. These keys use the inverse trigonometric functions , which we will discuss in Chapter 5.


15.3: Putting Culture into Media Studies
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- Jennifer Hasty, David G. Lewis, & Marjorie M. Snipes
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Learning Objectives
By the end of this section, you will be able to:
- Describe how an anthropologist might use participant observation to study media.
- Explain the relationship between modernity and media.
- Give an example illustrating the complex relationship between media and culture.
- Define the concept of cosmopolitanism.
In this section, the author of this chapter, Jennifer Hasty, describes her own experience using participant observation.
In the early 1990s, I went to the West African county of Ghana to study media and politics. I was specifically interested in the role of newspapers in the great wave of democratization across many African countries in that decade (Hasty 2005). Because I had some undergraduate training in journalism, I decided to volunteer as an intern at several newspapers and learn how news is produced in Ghana. I wound up working as a journalist for five different news organizations in the Ghanaian capital city of Accra over a period of several years. Through these experiences, I learned a great deal about how culture and history shape local news production, texts, and reception.
When people outside of anthropology ask me about my fieldwork, I tell them (maybe too much) about working as a journalist in Ghana. They often respond with a perplexed look, saying, “Wait, I thought you said you were an anthropologist.” When most people think about anthropological fieldwork, they think of quaint villages and rural locations, seemingly disconnected from the rest of the world. When they think of the topics anthropologists typically pursue, they think of religious rituals, political pageantry, complex kinship systems, and folk arts. That is, they think of the realm of “tradition.”
In fact, the contexts in which anthropologists work are not cut off from the rest of the world at all—and they never have been. People all over the world, in both rural and urban communities, are hooked up to global flows of information, images, ideas, commodities, and people. Newspapers, photography, radio, television, and the Internet are woven into daily life nearly everywhere one might go in the world.
Recall the discussions of modernity in previous chapters. Historically speaking, modernity is the whole way of life associated with industrial and postindustrial societies—that is to say, the institutions and features of modernity emerged alongside industrialization and mass production. However, the features of modernity have spread across the globe to societies that are not primarily industrial or postindustrial. Features of modernity such as mass media, wage labor, and the nation-state shape the everyday lives of people in primarily agrarian, pastoral societies and gatherer-hunter societies. Anthropologists have abandoned the idea that some people live traditional lifestyles while others live modern ones. Rather, all people are modern in distinctive ways, shaped by local historical and cultural forces.
Since the early 1990s, anthropologists have been increasingly interested in the various forms of modernity that have emerged in non-European and non-American contexts. As a key tool of modernity, mass media have become the object of growing fascination in anthropology over the last three decades. My own first fieldwork was part of an early wave of media studies in anthropology, culminating in the establishment of an entire subdiscipline, media anthropology (Spitulnik 1993; Askew and Wilk 2002; Ginsburg, Abu-Lughod, and Larkin 2002).
By examining the use of media in contemporary sociocultural life, media anthropologists have learned that nearly all forms of culture are shaped by various genres of media. People take photographs and videos to commemorate cultural events and share their memories with others. They report on cultural topics in print media, radio, and television and discuss those issues on talk shows and social media. In fact, it’s fair to say that mass media have become primary tools for defining, reinforcing, and reproducing local cultures. Rather than being opposed to tradition, mass media are key instruments for preserving and transmitting traditional cultures as well as modernity.
A few months ago, a Ghanaian journalist friend of mine, George Sydney Abugri, emailed me to ask if I could help him self-publish several books on Kindle Direct Publishing (KDP). Now retired, Abugri wanted to share his essays, poetry, and memoirs with Ghanaians, journalists, and scholars all over the world. In order to publish on KDP, you need a bank account from the United States or another “approved” country, and Ghana was not on that list. After a bit of textual wrangling, I was able to set up an account for him and get his books online so that he could find his global audience.
Anthropologists have a term for the kind of worldly orientation evident in Abugri’s desire to speak to a global audience about global issues: cosmopolitanism . Cosmopolitanism refers to a type of worldly knowledge and sophistication. Contemporary anthropologists, working in rural, village, and urban contexts, find that people in all settings have remarkable awareness of current world issues such as climate change, the Arab Spring, and the Me Too movement. One of Abugri’s poems describes an incident on the German airline Lufthansa in which a White flight attendant claimed she could not understand Abugri’s request for a glass of water. Cosmopolitan writers such as Abugri link their personal experiences to global issues such as race, environmentalism, and gender equality. Global issues and modern media forms are tightly integrated in the lives of both rural and urban peoples in cultures all over the world.


5.16: Introduction to Complete Sentences
What you’ll learn to do: critique passages, revising for run-on sentences and fragments
Effective sentence structure is vital to readability. Readers become confused when sentences are incomplete, choppy, or convoluted. Writers need to pay attention to how sentence construction affects both their message and their audience. This section will help you better understand how to recognize and avoid two common sentence construction errors: fragments and run-on sentences. When you construct clearer sentences, you are able to better connect with your intended audience.
Contributors and Attributions
CC licensed content, Original
- Outcome: Fragments and Run-ons. Provided by : University of Mississippi. License : CC BY: Attribution
CC licensed content, Shared previously
- Image of water drop. Authored by : Erik Socha. Provided by : Pixabay. Located at : pixabay.com/photos/water-drop-liquid-splash-wet-1761027/. License : Other . License Terms : pixabay.com/service/terms/#license


<IP_ADDRESS>: Genomic Similiarities between Distant Species
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- Boundless
- Boundless
Learning Objectives
- Discuss the evolutionary implications of observed genome similarities between distant species
Genomic Similarities Between Distant Species
Genetic distance refers to the genetic divergence between species or between populations within a species. Smaller genetic distances indicate that the populations have more similar genes, which indicates they are closely related; they have a recent common ancestor, or recent interbreeding has taken place. Genetic distance is useful in reconstructing the history of populations. For example, evidence from genetic distance suggests that humans arrived in America about 30,000 years ago. By examining the difference between allele frequencies between the populations, genetic distance can estimate how long ago the two populations were together.
Phylogenetic Relationships
Phylogeny describes the relationships of an organism, such as the relationship with its ancestors and the species it is most closely related. Phylogenetic relationships provide information on shared ancestry but not necessarily on how organisms are similar or different. The use of advanced genomic analysis has allowed us to establish phylogenetic trees, which map the relationship between species at a genetic and molecular level. The ability to use these technologies has established previously unknown relationships and has contributed to a more complex evolutionary history. These technologies have established genomic similarities between distant species by establishing genetic distances. In addition, the mechanisms by which genomic similarities between distant species occur can include horizontal gene transfer.
Horizontal Gene Transfer
Horizontal gene transfer (HGT), also known as lateral gene transfer, is the transfer of genes between unrelated species. Genes have been shown to be passed between species which are only distantly related using standard phylogeny, thus adding a layer of complexity to the understanding of phylogenetic relationships. The various ways that HGT occurs in prokaryotes is important to understanding phylogenies. Although at present, HGT is not viewed as important to eukaryotic evolution, HGT does occur in this domain as well. Finally, as an example of the ultimate gene transfer, theories of genome fusion between symbiotic or endosymbiotic organisms have been proposed to explain an event of great importance—the evolution of the first eukaryotic cell, without which humans could not have come into existence.
The mechanism of HGT has been shown to be quite common in the prokaryotic domains of Bacteria and Archaea, significantly changing the way their evolution is viewed. The majority of evolutionary models, such as in the endosymbiont theory, propose that eukaryotes descended from multiple prokaryotes, which makes HGT all the more important to understanding the phylogenetic relationships of all extant and extinct species. These gene transfers between species are the major mechanism whereby bacteria acquire resistance to antibiotics. Classically, this type of transfer has been thought to occur by three different mechanisms: transformation, transduction and conjugation.
Although it is easy to see how prokaryotes exchange genetic material by HGT, it was initially thought that this process was absent in eukaryotes, followed by the idea that the gene transfers between multicellular eukaryotes should be more difficult. In spite of this fact, HGT between distantly related organisms has been demonstrated in several eukaryotic species.
In animals, a particularly interesting example of HGT occurs within the aphid species. Aphids are insects that vary in color based on carotenoid content. Carotenoids are pigments made by a variety of plants, fungi, and microbes, and they serve a variety of functions in animals, who obtain these chemicals from their food. Humans require carotenoids to synthesize vitamin A, and we obtain them by eating orange fruits and vegetables: carrots, apricots, mangoes, and sweet potatoes. On the other hand, aphids have acquired the ability to make the carotenoids on their own. According to DNA analysis, this ability is due to the transfer of fungal genes into the insect by HGT, presumably as the insect consumed fungi for food.
Key Points
- Genomic similarities between distant species can be explained by the theory that all organisms share a common ancestor.
- Genomic similarities between distant species can be analysed using genomic analysis tools to create phylogenetic trees that explain these relationships.
- Genetic distance is used to explain the genetic divergence between species or between populations within a species and can indicate how closely related they are and whether they have a recent common ancestor or recent interbreeding has taken place.
- Horizontal gene transfer (HGT) occurs when two unrelated species exchange genes, usually two prokaryotes, although HGT occurs in some eurokaryotes as well.
Key Terms
- conjugation : the temporary fusion of organisms, especially as part of sexual reproduction
- phylogeny : the evolutionary history of an organism
- horizontal gene transfer : the transfer of genetic material from one organism to another one that is not its offspring; especially common among bacteria
- transformation : the alteration of a bacterial cell caused by the transfer of DNA from another, especially if pathogenic
- transduction : horizontal gene transfer mechanism in prokaryotes where genes are transferred using a virus


2.3: Negation and Disjunction
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In this section we will introduce the second and third truth-functional connectives: negation and disjunction. We will start with negation, since it is the easier of the two to grasp. Negation is the truth-functional operator that switches the truth value of a proposition from false to true or from true to false. For example, if the statement “dogs are mammals” is true (which it is), then we can make that statement false by adding a negation. In English, the negation is most naturally added just before the noun phrase that follows the linking verb like this:
Dogs are not mammals.
But another way of adding the negation is with the phrase, “it is not the case that” like this:
It is not the case that dogs are mammals.
Either of these English sentences expresses the same proposition, which is simply the negation of the atomic proposition, “dogs are mammals.” Of course, that proposition is false since it is true that dogs are mammals. Just as we can make a true statement false by negating it, we can also make a false statement true by adding a negation. For example, the statement, “Cincinnati is the capital of Ohio” is false. But we can make that statement true by adding a negation:
Cincinnati is not the capital of Ohio
There are many different ways of expressing negations in English. Here are a few ways of expressing the previous proposition in different ways in English:
Cincinnati isn’t the capital of Ohio
It’s not true that Cincinnati is the capital of Ohio
It is not the case that Cincinnati is the capital of Ohio
Each of these English sentences express the same true proposition, which is simply the negation of the atomic proposition, “Cincinnati is the capital of Ohio.” Since that statement is false, its negation is true.
There is one respect in which negation differs from the other three truth- functional connectives that we will introduce in this chapter. Unlike the other three, negation does not connect two different propositions. Nonetheless, we call it a truth-functional connective because although it doesn’t actually connect two different propositions, it does change the truth value of propositions in a truth-functional way. That is, if we know the truth value of the proposition we are negating, then we know the truth value of the resulting negated proposition. We can represent this information in the truth table for negation. In the following table, the symbol we will use to represent negation is called the “tilde” (~). (You can find the tilde on the upper left-hand side of your keyboard.)
| p | ~p |
|---|---|
| T | F |
| F | T |
This truth table represents the meaning of the truth-functional connective, negation, which is represented by the tilde in our symbolic language. The header row of the table represents some proposition p (which could be any proposition) and the negation of that proposition, ~p. What the table says is simply that if a proposition is true, then the negation of that proposition is false (as in the first row of the table); and if a proposition is false, then the negation of that proposition is true (as in the second row of the table).
As we have seen, it is easy to form sentences in our symbolic language using the tilde. All we have to do is add a tilde to left-hand side of an existing sentence. For example, we could represent the statement “Cincinnati is the capital of Ohio” using the capital letter C, which is called a constant. In propositional logic, a constant is a capital letter that represents an atomic proposition. In that case, we could represent the statement “Cincinnati is not the capital of Ohio” like this:
~C
Likewise, we could represent the statement “Toledo is the capital of Ohio” using the constant T. In that case, we could represent the statement “Toledo is not the capital of Ohio” like this:
~T
We could also create a sentence that is a conjunction of these two negations, like this:
~C ⋅ ~T
Can you figure out what this complex proposition says? (Think about it; you should be able to figure it out given your understanding of the truth-functional connectives, negation and conjunction.) The propositions says (literally): “Cincinnati is not the capital of Ohio and Toledo is not the capital of Ohio.” In later sections we will learn how to form complex propositions using various combinations of each of the four truth-functional connectives. Before we can do that, however, we need to introduce our next truth-functional connective, disjunction.
The English word that most commonly functions as disjunction is the word “or.” It is also common that the “or” is preceded by an “either” earlier in the sentence, like this:
Either Charlie or Violet tracked mud through the house.
What this sentence asserts is that one or the other (and possibly both) of these individuals tracked mud through the house. Thus, it is composed out of the following two atomic propositions:
Charlie tracked mud through the house
Violet tracked mud through the house
If the fact is that Charlie tracked mud through the house, the statement is true. If the fact is that Violet tracked mud through the house, the statement is also true. This statement is only false if in fact neither Charlie nor Violet tracked mud through the house. This statement would also be true even if it was both Charlie and Violet who tracked mud through the house. Another example of a disjunction that has this same pattern can be seen in the “click it or ticket” campaign of the National Highway Traffic Safety Administration. Think about what the slogan means. What the campaign slogan is saying is:
Either buckle your seatbelt or get a ticket
This is a kind of warning: buckle your seatbelt or you’ll get a ticket. Think about the conditions under which this statement would be true. There are only four different scenarios:
| Your seatbelt is buckled | You do not get a ticket | True |
| Your seatbelt is not buckled | You get a ticket | True |
| Your seatbelt is buckled | You get a ticket | False |
| Your seatbelt is not buckled | You do not get a ticket | False |
The first and second scenarios (rows 1 and 2) are pretty straightforwardly true, according to the “click it or ticket” statement. But suppose that your seatbelt is buckled, is it still possible to get a ticket (as in the third scenario—row 3)? Of course it is! That is, the statement allows that it could both be true that your seatbelt is buckled and true that you get a ticket. How so? (Think about it for a second and you’ll probably realize the answer.) Suppose that your seatbelt is buckled but your are speeding, or your tail light is out, or you are driving under the influence of alcohol. In any of those cases, you would get a ticket even if you were wearing your seatbelt. So the disjunction, click it or ticket, clearly allows the statement to be true even when both of the disjuncts (the statements that form the disjunction) are true. The only way the disjunction would be shown to be false is if (when pulled over) you were not wearing your seatbelt and yet did not get a ticket. Thus, the only way for the disjunction to be false is when both of the disjuncts are false.
These examples reveal a pattern: a disjunction is a truth-functional statement that is true in every instance except where both of the disjuncts are false. In our symbolic language, the symbol we will use to represent a disjunction is called a “wedge” (v). (You can simply use a lowercase “v” to write the wedge.) Here is the truth table for disjunction:
| p | q | p v q |
|---|---|---|
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |
As before, the header of this truth table represents two propositions (first two columns) and their disjunction (last column). The following four rows represent the conditions under which the disjunction is true. As we have seen, the disjunction is true when at least one of its disjuncts is true, including when they are both true (the first three rows). A disjunction is false only if both disjuncts are false (last row).
As we have defined it, the wedge (v) is what is called an “inclusive or.” An inclusive or is a disjunction that is true even when both disjuncts are true.
However, sometimes a disjunction clearly implies that the statement is true only if either one or the other of the disjuncts is true, but not both. For example, suppose that you know that Bob placed either first or second in the race because you remember seeing a picture of him in the paper where he was standing on a podium (and you know that only the top two runners in the race get to stand on the podium). Although you can’t remember which place he was, you know that:
Bob placed either first or second in the race.
This is a disjunction that is built out of two different atomic propositions:
Bob placed first in the race
Bob placed second in the race
Although it sounds awkward to write it this way in English, we could simply connect each atomic statement with an “or”:
Bob placed first in the race or Bob placed second in the race.
That sentence makes explicit the fact that this statement is a disjunction of two separate statements. However, it is also clear that in this case the disjunction would not be true if all the disjuncts were true, because it is not possible for all the disjuncts to be true, since Bob cannot have placed both first and second. Thus, it is clear in a case such as this, that the “or” is meant as what is called an “exclusive or.” An exclusive or is a disjunction that is true only if one or the other, but not both, of its disjuncts is true. When you believe the best interpretation of a disjunction is as an exclusive or, there are ways to represent that using a combination of the disjunction, conjunction and negation. The reason we interpret the wedge as an inclusive or rather than an exclusive or is that while we can build an exclusive or out of a combination of an inclusive or and other truth-functional connectives (as I’ve just pointed out), there is no way to build an inclusive or out of the exclusive or and other truth-functional connectives. We will see how to represent an exclusive or in section 2.5.
Exercise
Translate the following English sentences into our formal language using conjunction (the dot), negation (the tilde), or disjunction (the wedge). Use the suggested constants to stand for the atomic propositions.
1. Either Bob will mop or Tom will mop. (B = Bob will mop; T = Tom will mop)
2. It is not sunny today. (S = it is sunny today)
3. It is not the case that Bob is a burglar. (B = Bob is a burglar)
4. Harry is arriving either tonight or tomorrow night. (A = Harry is arriving tonight; B = Harry is arriving tomorrow night)
5. Gareth does not like his name. (G = Gareth likes his name)
6. Either it will not rain on Monday or it will not rain on Tuesday. (M = It will rain on Monday; T = It will rain on Tuesday)
7. Tom does not like cheesecake. (T = Tom likes cheesecake)
8. Bob would like to have both a large cat and a small dog as a pet. (C = Bob would like to have a large cat as a pet; D = Bob would like to have a small dog as a pet)
9. Bob Saget is not actually very funny. (B = Bob Saget is very funny)
10.Albert Einstein did not believe in God. (A = Albert Einstein believed in God)


10.2: History of Care for Individuals With Mental Health Disorders and Developmental Disorders
In the past, individuals living with mental health disorders or developmental disorders were viewed as unable to be a part of general society and were often placed in large institutions with little to no access to the outside environment or the community. This unfortunate stigma was due to a vast misunderstanding of these diagnoses. We now know this misconception is detrimental to individuals, and legislative and societal changes have been made to better meet the needs of these individuals. As a health care professional, it is important to understand how you can continue to improve the quality of life in individuals with these diagnoses through your communication, awareness, and approach.
Historically, facilities for institutionalized individuals looked like the Willowbrook State School pictured in Figure 10.1. [1] Residents were typically cared for in large spaces and group settings and eating at long tables with little space for comfort. Often, residents slept in large rooms with several beds in close proximity to each other with no accommodations for privacy or noise reduction. This care environment often caused overstimulation, resulting in sleep disturbances and client behaviors that were difficult to manage. In contrast to current health care practices, individual preferences were not prioritized.
These institutions lacked funding, professional caregivers, and basic knowledge of what residents needed to successfully function to the best of their ability. Because of these conditions, individuals with developmental or behavioral health disorders were often looked down upon, shunned, stigmatized, vilified, criminalized, and, in some cases, imprisoned or tortured. This type of inhumane treatment has been documented as far back as the Middle Ages in Europe and up until the mid-1900s in the United States. [2]
In the United States, this type of care environment continued until 1963 when President John F. Kennedy signed the Community Mental Health Act (as seen in Figure 10.2 [3] ). President Kennedy described this act as “a bold new approach” and provided federal grants to states to construct community mental health centers (CMHC). This act aimed to improve the diagnosis, treatment, and delivery of mental health services to individuals and prevent acute episodes that could impact their safety. In 1965 federal funding was allocated by the Medicaid Act to statewide institutions to improve conditions, staff education, and treatment of residents. [4]
The Community Mental Health Act resulted in a mass “deinstitutionalization” across the country, and by 1980 the population of psychiatric hospitals had decreased by nearly 75%. Deinstitutionalization meant that individuals with behavioral and developmental disorders were cared for in group home settings that allowed for community involvement rather than being isolated in a facility with little or no interaction with general society. By 2009 less than 2% of individuals with mental health disorders lived in a large institution, thus greatly increasing their quality of life, attention to their individualized needs and preferences, and their ability to be active in the community. [5]
Additional consideration has also been given to school-aged children and adolescents with developmental disorders and disabilities to be educated in a mainstream environment. In 1975 the Education of Handicapped Children Act was passed to support special education and related service programming for children and youth with disabilities in public schools. This act mandated that everyone with an intellectual disability was granted equal access to a free education. It was renamed the Individuals with Disabilities Education Act (IDEA) in 1990. In 2010 President Barack Obama signed “Rosa’s Law,” which eliminated the term “mental retardation” and replaced it with “intellectual disability.” Deleting this term from legislation helped to change the negative stigma associated with disabilities.
Read the following PDF about Rosa’s Law .
The remaining sections of this chapter will describe common developmental disorders, mental health disorders, and dementias you may encounter as a caregiver. [6]
- “ Willowbrook_State_School_(NYPL_b15279351-105038)_-_cropped.jpg ” by unknown author is in the Public Domain ↵
- This work is a derivative of Introduction to Social Work at Ferris State University by Department of Social Work and is licensed under CC BY 4.0 ↵
- “ John_F._Kennedy_Signs_the_Community_Mental_Health_Act_-_ST-C376-2-63.jpg ” by Cecil W. Stoughton (1920–2008) is in the Public Domain ↵
- This work is a derivative of Introduction to Social Work at Ferris State University by Department of Social Work and is licensed under CC BY 4.0 ↵
- This work is a derivative of Introduction to Social Work at Ferris State University by Department of Social Work and is licensed under CC BY 4.0 ↵
- What is the Individuals With Disabilities Education Act? by University of Washington is licensed under CC BY-NC-SA 3.0 ↵


6.1: Presentation and Design Essentials
By the end of this section, you will be able to:
- Understand why and when presentations are used in business
- Understand the importance of knowing your audience and defining your presentation goals
- Describe two essential qualities of good digital presentation design
- Create an appropriate plan for a presentation
Whether we are in front of an audience or in an online meeting, today’s workers should know how to create digital presentation s to help communicate their ideas to diverse and different types of audiences. Our starting point is learning how to create a digital presentation, or slideshow. Each slide can contain text, pictures, videos, bullet item lists, WordArt—just about anything.
WorldCorp uses presentations for sales, training, internal communication programs, and external communication within its ever-growing community. This is accomplished by using the power of words and imagery to engage audiences. Always keep in mind that the person who delivers a presentation is front and center to their audience. Microsoft PowerPoint and Google Slides are tools to help facilitate the presentation for the presenter—not a distraction that takes away from the presentation. This chapter will help you understand both elements (the person and the program) as you construct your first presentation at WorldCorp called My Life in a Snapshot .
Why and When Presentations Are Used in Business
WorldCorp is a large, expansive corporation with a vast community of stakeholders. Business presentations in numerous operational settings share information with internal stakeholders such as employees, managers, and executives. They also are used to communicate with external stakeholders, such as customers, vendors, shareholders, and the local community. The marketing team and public relations (PR) professionals are typically the ones responsible for communicating messages to external stakeholders. But whatever your title within an organization, you may be expected to know how to build and give presentations.
For example, an employee in the human resources (HR) department may be expected to design and present on topics, such as business ethics or sexual harassment training, that are mandatory for all employees. These presentations could be used multiple times to help educate the entire team by using multiple presenters. Or a presentation may show something fun, such as the end-of-the-year awards celebration. A presentation can have any number of purposes, uses, and audiences. Your first presentation as a member of the marketing team will help you make a strong first impression with your coworkers.
Presentations typically fall into one of several categories: to educate or train, to sell an idea, or simply to convey information to others. The size of your audience doesn’t matter—even a one-on-one meeting may still necessitate the creation of a presentation. The location doesn’t matter, either. Technology has provided ever-growing opportunities for communicating effectively and efficiently. Often, a Zoom call, sharing a laptop screen, or screen casting to a TV may be the perfect option to conduct a presentation.
Keep in mind that a business presentation could be the audience’s first introduction to the topic. Audience members will expect the presentation to give them some information they can use to start their decision-making process.
As a new hire at WorldCorp, you need to craft a presentation to introduce yourself to the leadership in the marketing department as part of your training program. The My Life in a Snapshot , presentation poses a typical workplace presentation challenge: You have a limited amount of time to effectively express a complex topic. My Life in a Snapshot may feel like it takes longer than five minutes to fully explain. How can decades of information be condensed into such a narrow window of time? To achieve this, considering your audience’s requests and their needs becomes front and center.
Understanding Your Audience and Purpose
When you are conducting a presentation, your purpose should not be what you want to do; instead, it is what you want your audience to do as a result of listening to what you expressed. Your audience will consist of twenty-five WorldCorp employees. Ask yourself: What am I trying to convey? What is the best way to convey it to my audience? How will my presentation affect them? These are the questions you need to ask when developing a sense of purpose in a presentation.
You should also know how long your presentation should be. The recommended length will vary depending on the purpose and content of the presentation. In many cases, the length of your presentation is predefined. In that case, it will be up to you to maximize your use of limited time to cover everything you need to address. Planning, crafting, and practicing your presentation are all critical in ensuring the audience gets the most out of the available time.
Essentials of Good Digital Presentation Design
By following the best practices and helpful tips outlined here, you will be better able to craft effective digital presentation s. Two important concepts to keep in mind are consistency and coherence. Consistency refers to the presentation having a uniform look and feel. You can achieve this by having a unified color scheme or a defined layout for each slide in the presentation. Coherence—how all the elements work together to communicate the intended purpose of the presentation—includes the slides and the presenters themselves. The purpose or key message of the presentation should be the focal point when creating a presentation. Keeping the purpose at the forefront will help with both consistency and coherence. Consistency and coherence work hand in hand when creating an effective presentation. These two concepts will be explained in more detail in the following sections.
Consistency as an Essential Design Quality
WorldCorp has developed a corporate-wide PowerPoint design template that makes it easy for team members to maintain consistent brand messaging. Most companies will have established template s and style guides for creating presentations. Consistency is the quality of always behaving or performing in a similar way, or of something always appearing or occurring in a similar way. Font styles, background color themes, and company logos are built into the brand to maintain consistent messaging. WorldCorp’s corporate color is blue, as we saw in the previous chapters on creating document files. To be consistent with WorldCorp’s brand image, we want the presentation template to follow that same color scheme. All the slides in the template will have a similar layout that includes the slide title and some visual elements with the blue WorldCorp branding. A consistently designed presentation would not use a different color scheme and layout for each slide. This would appear chaotic and unprofessional. Likewise, you would expect a consistently designed presentation to use similar font types and size on each slide. Figure 6.2 shows an example.
Coherence as an Essential Design Quality
In addition to slides needing to be consistent in design, the presentation must also be coherent. Each slide should have a logical reason for being a part of the entire slideshow and should connect to the overall purpose of the presentation. Good digital presentation design will enhance both the presenter and whom they represent. As you advance in creating digital presentations at WorldCorp, design will become part of your own messaging and branding of ideas. In designing a digital presentation, coherency refers to the smooth and logical flow of the slideshow while connecting to the overall message you want to convey. A coherent presentation includes elements and text that are connected to each other logically. For example, if a WorldCorp employee is presenting a quarterly sales recap for their team, a coherent presentation will be centered on sales data, include visuals and text related to sales goals, and maintain an overall professional and businesslike appearance.
The presenter should also be dressed in business attire, to match the goals of the presentation. See Figure 6.3 for a sample agenda slide for a coherent sales presentation.
Create a Plan Before Getting Started
To create an effective presentation, you will need to become a storyteller. Start by thinking about how you want the presentation to unfold. As with dividing an essay into paragraphs, you will need to find an easy way to separate out the distinct topics in your presentation while also building a cohesive storyline that connects them. When you choose the ideas that you want to emphasize and the order in which you want to present them, you are building a plan. This plan will help much like developing an outline for a paper.
Before you begin designing the storyboard for My Life in a Snapshot , you will want to sketch out (either digitally or by hand) a general plan for the content of each topic. A plan can allow you to organize the content of your presentation in a visual and logical manner. It breaks down the presentation into individual slides and shows the flow and progression of information. This can help ensure that the presentation is clear and easy to follow and that all the important points are covered.
Link to Learning
One of the tools that can aid the process of developing stories with imagery is a storyboard. A storyboard divides the elements of a story into impactful moments, each with its own setting, characters, and storyline. Writers, directors, cartoonists—all sorts of creators use—storyboards.
Crafting a workplace presentation shares many of these storytelling best practices. Watch this video to view an example of storyboard creation and storytelling to see how storyboarding can aid in presentation design.
For this project, your outline will cover five topics. Each topic should be unique, with each section of your presentation clearly distinguished from the next. Let’s revisit the example of the quarterly sales goals presentation that we discussed in this chapter's section on Coherence as an Essential Design Quality. The presenter wants the presentation to be informative about WorldCorp’s sales performance last quarter, as well as help set the stage for next quarter’s goals. One way to approach this is to remind the audience of the sales goals first. Then, present the sales results from this quarter. Next, talk about how the results connect to the overall company goals for the quarter or year. And then, finally, discuss how this quarter’s performance can be used to set goals for the next quarter.
This linear method can be easily sketched out using the bulleted list tool in Microsoft Word or Google Docs that you learned about in previous chapters. You can then use this outline to create the slides for the presentation. Figure 6.4 shows an example of a presentation plan using a bulleted list.
You could create a similar outline for your My Life in a Snapshot presentation to help you plan out the slides and flow of the presentation.
Once you have your presentation planned out, you will need to revisit its length and whether your plan can be achieved within the amount of time that you have. Rather than rewriting the entire presentation, you can look at your presentation in terms of topics, and see which topics can be lengthened or shortened. For example, if you think your presentation will take twenty minutes but you have only ten minutes, start by considering whether you’ve devoted too much time to the introduction. You could also consider which details, examples, or other potentially extraneous information to remove to shorten other sections. Remember, you don’t need to cut an entire topic out of your presentation if you can shorten it instead. With time and practice, you will learn how to make fine adjustments to the different topics in your presentation.


9.12: Outcome- Brand Development Strategies
What you’ll learn to do: explain key strategies for developing brands including brand ownership, brand and line extensions, co-branding, and licensing
Up to this point, this module has explored the important ingredients of creating brands. But once you’ve combined the ingredients and you have a fledgling brand, then what?
You need a branding strategy.
Branding strategies are different approaches for expanding the reach of a brand, reinforcing its value, and finding advantageous ways to coexist with other brands. It’s a crowded marketplace for brands today, and in the future it will only grow more crowded. As you’ll discover, carefully selected and wisely executed branding strategies can multiply the benefits of the brands you build.
Learning Activities
The learning activities for this section include the following:
- Reading: Brand Development Strategies
- Self Check: Brand Development Strategies
Contributors and Attributions
- Outcome: Brand Development Strategies. Provided by : Lumen Learning. License : CC BY: Attribution


2.3: The Measure of Matter
- Describe the names and abbreviations of the SI base units and the SI decimal prefixes .
- Define the liter and the metric ton in these units.
- Explain the meaning and use of unit dimensions ; state the dimensions of volume .
- State the quantities that are needed to define a temperature scale , and show how these apply to the Celsius, Kelvin, and Fahrenheit temperature scales.
- Explain how a Torricellian barometer works.
The natural sciences begin with observation , and this usually involves numerical measurements of quantities such as length, volume, density, and temperature. Most of these quantities have units of some kind associated with them, and these units must be retained when you use them in calculations. All measuring units can be defined in terms of a very small number of fundamental ones that, through "dimensional analysis", provide insight into their derivation and meaning, and must be understood when converting between different unit systems.
Units of Measure
Have you ever estimated a distance by “stepping it off”— that is, by counting the number of steps required to take you a certain distance? Or perhaps you have used the width of your hand, or the distance from your elbow to a fingertip to compare two dimensions. If so, you have engaged in what is probably the first kind of measurement ever undertaken by primitive mankind.
Leonardo da Vinci - Vitruvian Man
The results of a measurement are always expressed on some kind of a scale that is defined in terms of a particular kind of unit . The first scales of distance were likely related to the human body, either directly (the length of a limb) or indirectly (the distance a man could walk in a day). As civilization developed, a wide variety of measuring scales came into existence, many for the same quantity (such as length), but adapted to particular activities or trades. Eventually, it became apparent that in order for trade and commerce to be possible, these scales had to be defined in terms of standards that would allow measures to be verified, and, when expressed in different units (bushels and pecks, for example), to be correlated or converted.
Over the centuries, hundreds of measurement units and scales have developed in the many civilizations that achieved some literate means of recording them. Some, such as those used by the Aztecs, fell out of use and were largely forgotten as these civilizations died out. Other units, such as the various systems of measurement that developed in England, achieved prominence through extension of the Empire and widespread trade; many of these were confined to specific trades or industries. The examples shown here are only some of those that have been used to measure length or distance. The history of measuring units provides a fascinating reflection on the history of industrial development.
The most influential event in the history of measurement was undoubtedly the French Revolution and the Age of Enlightenment that followed. This led directly to the metric system that attempted to do away with the confusing multiplicity of measurement scales by reducing them to a few fundamental ones that could be combined in order to express any kind of quantity. The metric system spread rapidly over much of the world, and eventually even to England and the rest of the U.K. when that country established closer economic ties with Europe in the latter part of the 20th Century. The United States is presently the only major country in which “metrication” has made little progress within its own society, probably because of its relative geographical isolation and its vibrant internal economy.
The SI Units
Science, being a truly international endeavor, adopted metric measurement very early on; engineering and related technologies have been slower to make this change, but are gradually doing so. Even the within the metric system, however, a variety of units were employed to measure the same fundamental quantity; for example, energy could be expressed within the metric system in units of ergs, electron-volts, joules, and two kinds of calories. This led, in the mid-1960s, to the adoption of a more basic set of units, the Systeme Internationale ( SI ) units that are now recognized as the standard for science and, increasingly, for technology of all kinds.
In principle, any physical quantity can be expressed in terms of only seven base units . Each base unit is defined by a standard which is described in the NIST Web site.
kelvin| Observable | Base Unit | Abbreviation |
|---|---|---|
| length | meter | m |
| mass | kilogram | kg |
| time | second | s |
| temperature (absolute) | Kelvin | K |
| amount of substance | mole | mol |
| electric current | ampere | A |
| luminous intensity | candela | cd |
A few special points about some of these units are worth noting
- The base unit of mass is unique in that a decimal prefix (see below) is built-in to it; that is, it is not the gram , as you might expect.
- The base unit of time is the only one that is not metric. Numerous attempts to make it so have never garnered any success; we are still stuck with the 24:60:60 system that we inherited from ancient times. (The ancient Egyptians of around 1500 BC invented the 12-hour day, and the 60:60 part is a remnant of the base-60 system that the Sumerians used for their astronomical calculations around 100 BCE.)
- Of special interest to Chemistry is the mole , the base unit for expressing the quantity of matter . The number is also known as Avogadro’s number and is exactly \(6.02214076 \times 10^{23}\) of anything.
Owing to the wide range of values that quantities can have, it has long been the practice to employ prefixes such as milli and mega to indicate decimal fractions and multiples of metric units. As part of the SI standard, this system has been extended and formalized.
deci| prefix | abbreviation | multiplier | -- | prefix | abbreviation | multiplier |
|---|---|---|---|---|---|---|
| peta | P | 10 15 | deca | d | 10 –1 | |
| tera | T | 10 12 | centi | c | 10 –2 | |
| giga | G | 10 9 | milli | m | 10 –3 | |
| mega | M | 10 6 | micro | μ | 10 –6 | |
| kilo | k | 10 3 | nano | n | 10 –9 | |
| hecto | h | 10 2 | pico | p | 10 –12 | |
| deca | da | 10 | femto | f | 10 –15 |
There is a category of units that are “honorary” members of the SI in the sense that it is acceptable to use them along with the base units defined above. These include such mundane units as the hour, minute, and degree (of angle), etc., but the three shown here are of particular interest to chemistry, and you will need to know them.
| liter (litre) | L | 1 L = 1 dm 3 = 10 –3 m 3 |
| metric ton | t | 1 t = 10 3 kg |
| united atomic mass unit | u | 1 u = 1.66054×10 –27 kg |
SI-Derived Units and Dimensional Analysis
Most of the physical quantities we actually deal with in science and also in our daily lives, have units of their own: volume, pressure, energy and electrical resistance are only a few of hundreds of possible examples. It is important to understand, however, that all of these can be expressed in terms of the SI base units; they are consequently known as derived units. In fact, most physical quantities can be expressed in terms of one or more of the following five fundamental units:
| mass | length | time | electric charge | temperature |
|---|---|---|---|---|
| M | L | T | Q | Θ (theta) |
Dimensional analysis is an important tool in working with and converting units in calculations. Consider, for example, the unit of volume , which we denote as \(V\). To measure the volume of a rectangular box, we need to multiply the lengths as measured along the three coordinates:
\[V = x · y · z \label{eq20}\]
We say, therefore, that volume has the dimensions of length-cubed:
\[dim.V = L^3\]
Thus the units of volume will be m 3 (in the SI) or cm 3 , ft 3 (English), etc. Moreover, any formula that calculates a volume must contain within it the L 3 dimension; thus the volume of a sphere is 4/3 π r 3 .
Units and their Ranges in Chemistry
In this section, we will look at some of the quantities that are widely encountered in Chemistry, and at the units in which they are commonly expressed. In doing so, we will also consider the actual range of values these quantities can assume, both in nature in general, and also within the subset of nature that chemistry normally addresses. In looking over the various units of measure, it is interesting to note that their unit values are set close to those encountered in everyday human experience
Ranges of Mass and Weight in Chemistry
These two quantities are widely confused. Although they are often used synonymously in informal speech and writing, they have different dimensions: weight is the force exerted on a mass by the local gravitational field:
\[f = m a = m g\]
where g is the acceleration of gravity. While the nominal value of the latter quantity is 9.80 m s –2 at the Earth’s surface, its exact value varies locally. Because it is a force, the proper SI unit of weight is the newton , but it is common practice (except in physics classes!) to use the terms "weight" and "mass" interchangeably, so the units kilograms and grams are acceptable in almost all ordinary laboratory contexts.
Please note that in this diagram and in those that follow, the numeric scale represents the logarithm of the number shown. For example, the mass of the electron is 10 –30 kg.
The range of masses spans 90 orders of magnitude, more than any other unit. The range that chemistry ordinarily deals with has greatly expanded since the days when a microgram was an almost inconceivably small amount of material to handle in the laboratory; this lower limit has now fallen to the atomic level with the development of tools for directly manipulating these particles. The upper level reflects the largest masses that are handled in industrial operations, but in the recently developed fields of geochemistry and environmental chemistry, the range can be extended indefinitely. Flows of elements between the various regions of the environment (atmosphere to oceans, for example) are often quoted in t
Range of Distances Encountered in Chemistry
Chemists tend to work mostly in the moderately-small part of the distance range. Those who live in the lilliputian world of crystal- and molecular structures and atomic radii find the picometer a convenient currency, but one still sees the older non-SI unit called the Ångstrom used in this context;
\[1\,\unicode{x212B} = 10^{–10}\,\text{m} = 100\,\text{pm}. \]
Nanotechnology, the rage of the present era, also resides in this realm. The largest polymeric molecules and colloids define the top end of the particulate range; beyond that, in the normal world of doing things in the lab, the centimeter and occasionally the millimeter commonly rule.
For humans, time moves by the heartbeat; beyond that, it is the motions of our planet that count out the hours, days, and years that eventually define our lifetimes. Beyond the few thousands of years of history behind us, those years-to-the-powers-of-tens that are the fare for such fields as evolutionary biology, geology, and cosmology, cease to convey any real meaning to us. Perhaps this is why so many people are not very inclined to accept the validity of these sciences.
Most of what actually takes place in the chemist’s test tube operates on a far shorter time scale, although there is no limit to how slow a reaction can be; the upper limits of those we can directly study in the lab are in part determined by how long a graduate student can wait around before moving on to gainful employment.
Looking at the microscopic world of atoms and molecules themselves, the time scale again shifts us into an unreal world where numbers tend to lose their meaning. You can gain some appreciation of the duration of a nanosecond by noting that this is about how long it takes a beam of light to travel between your two outstretched hands. In a sense, the material foundations of chemistry itself are defined by time: neither a new element nor a molecule can be recognized as such unless it lasts around sufficiently long enough to have its “picture” taken through measurement of its distinguishing properties.
Range of Temperatures in Chemistry
Temperature, the measure of thermal intensity, spans the narrowest range of any of the base units of the chemist’s measure. The reason for this is tied into temperature’s meaning as an indicator of the intensity of thermal kinetic energy. Chemical change occurs when atoms are jostled into new arrangements, and the increasing weakness of these motions brings most chemistry to a halt as absolute zero is approached. At the upper end of the scale, thermal motions become sufficiently vigorous to shake molecules into atoms, and eventually, as in stars, strip off the electrons, leaving an essentially reaction-less gaseous fluid, or plasma, of bare nuclei (ions) and electrons.
We all know that temperature is expressed in degrees. What we frequently forget is that the degree is really an increment of temperature, a fixed fraction of the distance between two defined reference points on a temperature scale .
Range of Pressures in Chemistry
Pressure is the measure of the force exerted on a unit area of surface. Its SI units are therefore newtons per square meter, but we make such frequent use of pressure that a derived SI unit, the pascal , is commonly used:
\[1\, \text{Pa} = 1\, \text{N}\, \text{m}^{–2}\]
Pressure of the Atmosphere
The concept of pressure first developed in connection with studies relating to the atmosphere and vacuum that were first carried out in the 17th century. The molecules of a gas are in a state of constant thermal motion, moving in straight lines until experiencing a collision that exchanges momentum between pairs of molecules and sends them bouncing off in other directions.
This leads to a completely random distribution of the molecular velocities both in speed and direction— or it would in the absence of the Earth’s gravitational field which exerts a tiny downward force on each molecule, giving motions in that direction a very slight advantage. In an ordinary container this effect is too small to be noticeable, but in a very tall column of air the effect adds up: the molecules in each vertical layer experience more downward-directed hits from those above it. The resulting force is quickly randomized, resulting in an increased pressure in that layer which is then propagated downward into the layers below.
At sea level, the total mass of the sea of air pressing down on each 1 m 2 of surface is about 1034 g, or 10340 kg m –2 . The force (weight) that the Earth’s gravitational acceleration \(g\) exerts on this mass is:
\[\begin{align} f &= ma \nonumber \\[4pt] &= mg \nonumber \\[4pt] &= (10340\text{ kg})(9.81\text{ m s}^{–2}) \nonumber \\[4pt] &= 1.013 \times 10^5\text{ kg m s}^{–2} \nonumber \\[4pt] &= 1.013 \times 10^5 \text{ newtons} \end{align}\]
resulting in a pressure of
\[1.013 \times 10^5\, \text{N}\, \text{m}^{–2} = 1.013 \times 10^5 \text{ Pa}.\]
The actual pressure at sea level varies with atmospheric conditions, so it is customary to define standard atmospheric pressure as 1 atm = 1.013 × 10 5 Pa or 101 kPa.
Although the standard atmosphere (atm) is not an SI unit, it is still widely employed. In meteorology, the bar , exactly 1.000 × 10 5 = 0.967 atm, is often used.
The Barometer
In the early 17th century, the Italian physicist and mathematician Evangalisto Torricelli invented a device to measure atmospheric pressure. The Torricellian barometer consists of a vertical glass tube closed at the top and open at the bottom. It is filled with a liquid, traditionally mercury, and is then inverted, with its open end immersed in the container of the same liquid. The liquid level in the tube will fall under its own weight until the downward force is balanced by the vertical force transmitted hydrostatically to the column by the downward force of the atmosphere acting on the liquid surface in the open container. Torricelli was also the first to recognize that the space above the mercury constituted a vacuum, and is credited with being the first to create a vacuum.
One standard atmosphere will support a column of mercury that is 76 cm high, so the “millimeter of mercury”, now more commonly known as the torr , has long been a common pressure unit in the sciences: 1 atm = 760 torr.


16.5: Lecture- Computer Security
Access lectures from the “ Understanding Computers and the Internet: Computer Science E-1 ” course offered through the Harvard Extension School.
- In the right-column of the screen, click on the lecture you would like to watch, then click “Video” and select “MP4” or “download.”
For this assignment, please watch the following lectures:
- Lecture 6: Security
- Lecture 7: Security, Continued
CC licensed content, Shared previously
- Computer Science E-1 is a course at . Authored by : Dan Armendariz and David J. Malan. Provided by : Harvard University. Located at : http://computerscience1.tv/2011/spring/#lectures,license . License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike


6.1: Introduction
Astronomy Laboratory 6 – Optics and Simple Telescopes
Module Introduction
Optics is the study of light and its interaction with various materials, called medium. We are all familiar with optics in the world around us. Whether you wear glasses or not, your eyes are a splendid example of optics.
In order to better understand modern optics such as binoculars, cameras, and telescopes, and how lenses and mirrors work, you will conduct specified experiments with lenses and mirrors in this lab. With the supplied lab kit resource, you will assemble a simple refracting telescope. You will take the telescope outdoors and conduct a series of observations with the simple telescope. (1)
Objectives
At the end of this module, students will be able to:
- Describe types of mirrors and lenses, along with their functions
- Compare and contrast types of mirrors and lenses
- Assemble a Simple Refracting Telescope
- Utilize a Simple Refracting Telescope (1)
Outcomes
The material in this module includes content designed to meet the following course outcomes:
- Communicate scientific ideas through oral or written assignments.
- Interpret scientific models such as formulas, graphs, tables and schematics, draw inferences from them and recognize their limitations.
- Demonstrate the ability to think critically.
- Demonstrate the ability to use scientific and quantitative reasoning. (1)
Assigned Readings
Learning Unit 6
Assignments
- Optics and Simple Telescopes Activity
- Lab 6 Quiz (1)
- Authored by : Florida State College at Jacksonville. License : CC BY: Attribution


15.4: Assignment- The Future of Unions
Scenario
In the 1900s, union organizers and union members played a critical role in establishing the basic rights of working people: negotiating better (if not equitable) wages, reasonable work hours and safer working conditions for laborers who had previously been considered expendable. However, we live in very different times. Although some industries and business models are still exploitative, our current labor markets and socio-political dynamics are significantly different than those of the 1900s. Are unions still relevant? What is the future of unions?
Your Task
In your next rotation, you have been assigned to the firm’s Employee Relations practice. This practice provides research and advisory services, including benefit and wage benchmarking. One of the sub-specialties is tracking union organization efforts, public sentiment and legislation and—in a departure from the usual practice—advising both unions and management on how to develop employee value propositions and collaborative management practices.
Your task is to develop a 1 to 2-page draft position statement for the firm’s Employee Relations principal, distilling what you’ve learned in this module. Your position statement must reflect current realities, including additional research as needed.
Additional Information: Read James Sherk’s “ Unions need to reinvent themselves ” (cited in the module) commentary for perspective on what the principal is looking for in substance and tone.Grading Rubric
| Criteria | Inadequate (40%) | Minimal (60%) | Adequate (80%) | Exemplary (100%) | Total Points |
|---|---|---|---|---|---|
| Organization and format |
2 pts
Writing lacks logical organization. It may show some coherence but ideas lack unity. Serious errors and generally is an unorganized format and information. |
3 pts
Writing is coherent and logically organized, using a format suitable for the material presented. Some points may be contextually misplaced and/or stray from the topic. Transitions may be evident but not used throughout the essay. Organization and format used may detract from understanding the material presented. |
4 pts
Writing is coherent and logically organized, using a format suitable for the material presented. Transitions between ideas and paragraphs create coherence. Overall unity of ideas is supported by the format and organization of the material presented. |
5 pts
Writing shows high degree of attention to details and presentation of points. Format used enhances understanding of material presented. Unity clearly leads the reader to the writer’s conclusion and the format and information could be used independently. |
5 pts |
| Content |
8 pts
Some but not all required questions are addressed. Content and/or terminology is not properly used or referenced. Little or no original thought is present in the writing. Concepts presented are merely restated from the source, or ideas presented do not follow the logic and reasoning presented throughout the writing. |
12 pts
All required questions are addressed but may not be addressed with thoughtful consideration and/or may not reflect proper use of content terminology or additional original thought. Additional concepts may not be present and/or may not be properly cited sources. |
16 pts
All required questions are addressed with thoughtful consideration reflecting both proper use of content terminology and additional original thought. Some additional concepts may be presented from other properly cited sources, or originated by the author following logic and reasoning they’ve clearly presented throughout the writing. |
20 pts
All required questions are addressed with thoughtful in-depth consideration reflecting both proper use of content terminology and additional original thought. Additional concepts are clearly presented from properly cited sources, or originated by the author following logic and reasoning they’ve clearly presented throughout the writing. |
20 pts |
| Development—Critical Thinking |
8 pts
Shows some thinking and reasoning but most ideas are underdeveloped, unoriginal, and/or do not address the questions asked. Conclusions drawn may be unsupported, illogical or merely the author’s opinion with no supporting evidence presented. |
12 pts
Content indicates thinking and reasoning applied with original thought on a few ideas, but may repeat information provided and/ or does not address all of the questions asked. The author presents no original ideas, or ideas do not follow clear logic and reasoning. The evidence presented may not support conclusions drawn. |
16 pts
Content indicates original thinking, cohesive conclusions, and developed ideas with sufficient and firm evidence. Clearly addresses all of the questions or requirements asked. The evidence presented supports conclusions drawn. |
20 pts
Content indicates synthesis of ideas, in-depth analysis and evidence beyond the questions or requirements asked. Original thought supports the topic, and is clearly a well-constructed response to the questions asked. The evidence presented makes a compelling case for any conclusions drawn. |
20 pts |
| Grammar, Mechanics, Style |
2 pts
Writing contains many spelling, punctuation, and grammatical errors, making it difficult for the reader to follow ideas clearly. There may be sentence fragments and run-ons. The style of writing, tone, and use of rhetorical devices disrupts the content. Additional information may be presented but in an unsuitable style, detracting from its understanding. |
3 pts
Some spelling, punctuation, and grammatical errors are present, interrupting the reader from following the ideas presented clearly. There may be sentence fragments and run-ons. The style of writing, tone, and use of rhetorical devices may detract from the content. Additional information may be presented, but in a style of writing that does not support understanding of the content. |
4 pts
Writing is free of most spelling, punctuation, and grammatical errors, allowing the reader to follow ideas clearly. There are no sentence fragments and run-ons. The style of writing, tone, and use of rhetorical devices enhance the content. Additional information is presented in a cohesive style that supports understanding of the content. |
5 pts
Writing is free of all spelling, punctuation, and grammatical errors and written in a style that enhances the reader’s ability to follow ideas clearly. There are no sentence fragments and run-ons. The style of writing, tone, and use of rhetorical devices enhance the content. Additional information is presented to encourage and enhance understanding of the content. |
5 pts |
| Total: | 50 pts |


Liquids
Skills to Develop
- Explain some of the properties of liquids
- Distinguish cohesive and adhesive forces
In general, liquids are harder to describe than gases (in which interactions between particles are simple collisions) and solids, in which particles stay mostly still in an organized arrangement. So we will only describe some properties here. Certain properties of liquids also depend on the intermolecular forces, like the viscosity and surface tension . These roughly describe the shapes liquids take when poured, or as droplets, etc.
Viscosity
Viscosity means how thick or sticky a liquid is. For instance, water pours easily and quickly, so it is pretty low viscosity. Honey is a thick, sticky liquid that pours slowly, so it has higher viscosity. Viscosity depends on how easily the molecules can flow past each other. The smaller they are, and the weaker the forces between them, the easier they flow. If the molecules are big and flexible, they might be able to get a bit tangled together, and that could make them flow more slowly.
Surface Tension
Surface tension means how much the liquid wants to minimize its surface area. If the intermolecular forces are big, then molecules would rather be inside the liquid where they have favorable intermolecular interactions instead of being on the surface. This could make the liquid pull itself into rounded shapes to make the surface area smaller. You've probably seen water do this, like on a non-stick pan, because water has strong hydrogen-bonds. In this case, they are called cohesive forces , which means forces that pull the material together. (A cohesive team is very close and works well together.) On the other hand, water can have good interactions with glass surfaces, so it doesn't mind so much spreading out on glass. In fact, the forces that make water stick to glass, called adhesive forces are bigger than the cohesive forces in water, which is why the water in a glass tube is higher around the edges.
In contrast, mercury doesn't spread out over glass, and in a glass tube, it is higher in the middle. This means that mercury has bigger cohesive forces than adhesive forces toward glass.


12.5.3: Nail, Hand and Foot Care
Procedure: Nail Care
Providing nail care for a patient allows Home Health Aides/Personal Care Aides an opportunity to assess the health of their patient’s skin, nails, and the strength of their hands and feet. It also provides a sense of comfort and promotes self-esteem for the patient. While many patients may enjoy having their hands and feet cared for, take special care with patients who do not find this a pleasurable experience. Some patients have very sensitive feet and may be ticklish. Home Health Aides/Personal Care Aides should always tell a patient when they are going to touch their feet and inform them of what they are doing so that they expect the touch.
Make sure to follow directions from a supervisor and those written in the Care Plan for nail care performed. Never use a nail clipper to clip finger or toe nails. Use an emery board to smooth nail edges. Home Health Aides/Personal Care Aides should inform their supervisor if advanced nail care needs to be performed. Never perform toenail care on a patient who has diabetes. These patients require special care from a podiatrist . It is acceptable to cleanse and inspect these patient’s feet, but never clip their toenails
Procedure: Hand Care
- Explain the procedure to the patient.
- Wash and dry your hands. Put on gloves as necessary.
- Gather equipment and supplies as needed.
- Use proper working height by raising the bed to waist level if the patient is bed bound. If the patient is sitting in a chair or wheelchair, Home Health Aides/Personal Care Aides may sit next to them to avoid bending their back. Keep the back straight, feet planted on the floor and face the direction you are working.
- Soak patient’s hands in warm (not hot) water. Temperature should be no greater than 105 degrees Fahrenheit. Soak hands for at least five minutes, or according to patient preferences. Clean under nails with a soft nail brush or nail stick, or do as directed in the Care Plan.
- Remove the patient’s hands from the water and wash with a soapy wash cloth. Rinse and dry well. Be sure to rinse and dry between fingers.
- Remove basin from the patient area.
- File nails as necessary and as requested with an emery board or nail file to keep edges smooth and free of rough edges or hangnails.
- Massage hands with lotion.
- Apply nail polish as the patient requests.
- Discard the water and rinse the basin. Put away equipment and supplies.
- Lower the bed to its lowest level and ensure side rails are up.
- Remove your gloves. Wash and dry your hands.
- Document completion of task and record any changes in condition or behavior. Report any skin conditions observed.
Procedure: Foot Care
- Fill a basin with warm water. Do not exceed 105 degrees Fahrenheit. Have the patient test the water for comfort.
- If providing foot care in bed, soak and work with one foot at a time. Place the basin of water over a waterproof pad or towel at the foot of the patient’s bed. If the patient is sitting, place the basin on the floor with a towel or waterproof pad underneath. Ensure the patient’s feet and ankles are supported. Feet should be flat against the bottom of the basin.
- Soak the patient’s feet in warm (not hot) water for at least 10 minutes. Add warm water to the basin as needed. Clean under their toenails with a soft nail brush.
- Working with one foot at a time, remove a foot from the basin and wash with a soapy wash cloth. Take care to clean between toes. Rinse their foot well. Make sure no soap is left between the toes.
- Dry the patient’s foot. Take special care to dry well in between toes.
- Repeat for the other foot.
- File toenails as needed. Do not cut patient ‘ s toe nails . Discuss any needed advanced toe nail or foot care with a supervisor.
- If applying lotion on feet, take care to not apply lotion between the toes. Place socks and/or other footwear on patient once done.
- Apply nail polish as the patient requests.
- Discard the water and rinse the basin. Put away equipment and supplies.
- Lower bed to its lowest level and ensure side rails are up.
- Remove your gloves. Wash and dry your hands.
- Document completion of task and record any changes in condition or behavior. Report any skin conditions observed. Report and document any discoloration of the feet, blood, drainage, ingrown toenails, thickened toenails, reddened heels, or foot/ankle swelling.


3.0: Introduction
Public/community health nurses act as change agents in their communities, working to support health outcomes for clients and the broader population. They play a pivotal role in advancing the health of clients, communities, and families and in achieving population health objectives. The actions of public/community health nurses align with the principles and functions of public health: assessment, assurance, and policy development. This chapter will explore historical perspectives on public/community health nursing, the foundation and functions of professional practice, and how public/community health nurses lead and deliver care across levels of prevention to show how the connection between nursing practice and public health supports population health.
As Foundations of Public/Community Health notes, the term “public/community health” is fairly common as the goals and functions of these closely related disciplines are interconnected. In nursing, community health has long been viewed as indistinguishable from public health (American Nurses Association [ANA], 2022, p.3.)
This chapter will continue to refer to Alexandra Lee and her family, whom the text has been following since What Is Population Health? to explore how population, public, and community health impact their well-being. Remember that the Lee family members include parents Alexandra, a daycare teacher who is pregnant, and Christopher, who has hypertension and is currently without a job or health plan coverage, and their children Sunshine, a full-time school student with a life-threatening allergy, and Woody, a generally healthy toddler.