8.9: The Break-Even Point and the Sales Mix
Learning Outcomes
- Analyze the break-even point data for a company that wants to adjust its sales mix
What if your company sells more than one product (which most companies do!). How do we go about figuring the break even point when we decide to adjust our sales mix? This is a complex question.
After watching the video, take a look at an additional example, with three products in the mix.
Let’s say your company makes three products:
- Product 1: Sells for $40 with variable costs of $20 each.
- Product 2: Sells for $10 with variable costs of $2 each
- Product 3: Sells for $20 with variable costs of $15 each.
Note the difference in contribution margin for each product.
- Product 1 contributes $20 to cover fixed expenses per item sold.
- Product 2 contributes $8 to cover fixed expenses per item sold.
- Product 3 contributes $5 to cover fixed expenses per item sold.
So, let’s look at the current sales mix, contribution margins and fixed costs.
| Product Type | Product #1 | Product #2 | Product #3 | Total |
|---|---|---|---|---|
| Quantity | 500 | 1500 | 750 | 2750 |
| Total Sales | $20,000 | $15,000 | $15,000 | 50000 |
| Variable Costs | $10,000 | $3,000 | $11,250 | 24250 |
| Contribution Margin | $10,000 | $12,000 | $3,750 | 25750 |
| Fixed Costs | $19,000 | |||
| Net Profit | $6,750 |
Now, let’s also assume that this mix uses all of the manufacturing space, all of the time!! What happens if we suddenly have a huge demand for product #3, the one contributing the least to the contribution margin? We look at reallocating space to produce more of product #3, but that means we need to produce less of products #1 and #2 that contribute more to our contribution margin
Let’s take a look at what happens if our sales mix shifts. We are making a couple of assumptions
- We have production space and labor for 2750 products total.
- Variable costs remain the same per item, regardless of quantity.
So, if we shift our production to making more of product #3
| Product Type | Product #1 | Product #2 | Product #3 | Total |
|---|---|---|---|---|
| Quantity | 125 | 1000 | 1625 | 2750 |
| Total Sales | $5,000 | $10,000 | $32,500 | 47500 |
| Variable Costs | $2,500 | $2,000 | $24,375 | 28875 |
| Contribution Margin | $2,500 | $8,000 | $8,125 | 18625 |
| Fixed Costs | $19,000 | |||
| Net Profit | $375 |
We are still making the exact same number of products, but due to the contribution margin being lower on product #3, we are now showing a net loss rather than a profit!
Companies make these kinds of decisions on a daily basis. As a manager, you may be asked to determine a product mix that is profitable for your company. Keep the contribution margin, manufacturing space and labor in mind as you work through this process.
Practice Questions


5.11: Citric Acid Cycle
- Describe the reactions of the citric acid cycle.
- Describe the function of the citric acid cycle and identify the products produced.
Citric Acid Cycle
Acetyl-CoA is a two-carbon molecule that enters a circular pathway of reactions known collectively as the citric acid cycle (or Krebs cycle). The cycle brings about the oxidation of the two carbons of acetyl-CoA to carbon dioxide and water. It was first proposed by Hans Krebs in 1937. He was awarded the 1953 Nobel Prize in Physiology or Medicine. Acetyl-CoA’s entrance into the citric acid cycle is the beginning of stage III of catabolism. The citric acid cycle produces guanosine triphosphate (GTP), three reduced nicotinamide adenine dinucleotide (NADH), reduced flavin adenine dinucleotide (FADH 2 ), and metabolic intermediates required for the synthesis of more ATP molecules.
At first glance, the citric acid cycle appears rather complex. All the reactions, however, are familiar types in organic chemistry: hydration, oxidation, decarboxylation, and hydrolysis. Each reaction of the citric acid cycle is numbered. The two carbon atoms of Acetyl-CoA are highlighted in red. Each intermediate in the cycle is a carboxylic acid, existing as an anion at physiological pH of around 7. All the reactions occur within the mitochondria, which are small organelles within the cells of plants and animals. This part of the cell is known as the powerhouse of the cell since this is where most of the ATP is produced.
Figure \(\PageIndex{1}\): The Citric Acid Cycle
Step 1
In the first reaction, acetyl-CoA enters the citric acid cycle, and the two-carbons of the acetyl group reacts with a four-carbon anion called oxaloacetate, yielding a six-carbon anion called citrate. This step also involves addition of water. Note that this step releases coenzyme A. The reaction is catalyzed by citrate synthase .
Step 2
In this step, aconitase catalyzes the isomerization of citrate to isocitrate. In this reaction, a tertiary alcohol, which cannot be oxidized, is converted to a secondary alcohol, which can be oxidized in the next step. Citrate and isocitrate are isomers.
Step 3
Isocitrate then undergoes a reaction known as oxidative decarboxylation because the 2 o -alcohol is oxidized and the molecule is shortened by one carbon atom with the release of carbon dioxide (decarboxylation). The reaction is catalyzed by isocitrate dehydrogenase , and the product of the reaction is α-ketoglutarate. The oxidizing agent of the 2 o -alcohol is the coenzyme nicotinamide adenine dinucleotide (NAD + ) which is reduced to NADH.
Step 4
The fourth step is another oxidative decarboxylation. This time α-ketoglutarate is converted to succinyl-CoA, and another molecule of NAD + is reduced to NADH. The α-ketoglutarate dehydrogenase catalyzes this reaction.
So far, in the first four steps, two carbon atoms have entered the cycle as an acetyl group, and two carbon atoms have been released as molecules of carbon dioxide. The remaining reactions of the citric acid cycle use the four carbon atoms of the succinyl group to resynthesize a molecule of oxaloacetate, which is the compound needed to combine with an incoming acetyl group and begin another round of the cycle.
Step 5
In the fifth reaction, the energy released by the hydrolysis of the high-energy thioester bond of succinyl-CoA is used to make guanosine triphosphate (GTP) from guanosine diphosphate (GDP) and inorganic phosphate (P i ) in a reaction catalyzed by succinyl-CoA synthetase . This step is the only reaction in the citric acid cycle that directly forms a high-energy phosphate compound GTP. GTP is considered equivalent in energy to ATP.
Step 6
Succinate dehydrogenase then catalyzes the removal of two hydrogen atoms from succinate, forming fumarate. This oxidation-reduction reaction uses flavin adenine dinucleotide (FAD), rather than NAD + , as the oxidizing agent.
Step 7
In step 7, a molecule of water is added to the double bond of fumarate to form malate in a hydration reaction catalyzed by fumarase .
Step 8
One cycle is completed with the oxidation of malate to oxaloacetate, catalyzed by malate dehydrogenase . This is the third oxidation-reduction reaction. It uses NAD + as the oxidizing agent to oxidize the 2 o alcohol in malate to a ketone.
Oxaloacetate can accept two carbons from the reaction with acetyl-CoA, allowing the cycle to begin again.
Summary
The citric acid cycle consists of eight step and are made of familiar types of reactions in organic chemistry: hydration, oxidation, decarboxylation, and hydrolysis. The harvest of the citric acid cycle consists of 3NADH, FADH 2 , and GTP.


4: Probability and Counting
Probability theory is concerned with probability, the analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion.
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- 4.2: Independent and Mutually Exclusive Events
- Two events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs. If they are not independent, then they are dependent. In sampling with replacement, with selecting each member with the possibility of being chosen more than once, and the events are considered to be independent. In sampling without replacement, each member may be chosen only once, and the events are considered not to be independent. When events do not share outcomes, they are mutu
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- 4.3: The Addition and Multiplication Rules of Probability
- The multiplication rule and the addition rule are used for computing the probability of A and B, and the probability of A or B for two given events A, B. In sampling with replacement each member has the possibility of being chosen more than once, and the events are considered to be independent. In sampling without replacement, each member may be chosen only once, and the events are not independent. The events A and B are mutually exclusive events when they have no common outcomes.
Contributors and Attributions
-
Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>.


18.1: Environmental Ethics and Justice
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Environmental Ethics
The concept of ethics involves standards of conduct. These standards help to distinguish between behavior that is considered right and that which is considered wrong. As we all know, it is not always easy to distinguish between right and wrong, as there is no universal code of ethics. For example, a poor farmer clears an area of rainforest in order to grow crops. Some would not oppose this action, because the act allows the farmer to provide a livelihood for his family. Others would oppose the action, claiming that the deforestation will contribute to soil erosion and global warming. Right and wrong are usually determined by an individual's morals, and to change the ethics of an entire society, it is necessary to change the individual ethics of a majority of the people in that society.
Moral extensionism defines how far a persons values extend outside of themselves (Figure \(\PageIndex{1}\)). There are many variables that can influence where the limit lies for each individual person. For example: religion, culture, education, and personal interests (just to name a few).
Frontier Ethic
The ways in which humans interact with the land and its natural resources are determined by ethical attitudes and behaviors. Early European settlers in North America rapidly consumed the natural resources of the land. After they depleted one area, they moved westward to new frontiers. Their attitude towards the land was that of a frontier ethic . A frontier ethic assumes that the earth has an unlimited supply of resources. If resources run out in one area, more can be found elsewhere or alternatively human ingenuity will find substitutes.  The frontier ethic is completely anthropocentric (human-centered), for only the needs of humans are considered.
Most industrialized societies experience population and economic growth that are based upon this frontier ethic, assuming that infinite resources exist to support continued growth indefinitely. In fact, economic growth is considered a measure of how well a society is doing. The late economist Julian Simon pointed out that life on earth has never been better, and that population growth means more creative minds to solve future problems and give us an even better standard of living. However, now that the human population has passed seven billion and few frontiers are left, many are beginning to question the frontier ethic. Such people are moving toward an environmental ethic, which includes humans as part of the natural community rather than managers of it. Such an ethic places limits on human activities (e.g., uncontrolled resource use), that may adversely affect the natural community.
Some of those still subscribing to the frontier ethic suggest that outer space may be the new frontier. If we run out of resources (or space) on earth, they argue, we can simply populate other planets. This seems an unlikely solution, as even the most aggressive colonization plan would be incapable of transferring people to extraterrestrial colonies at a significant rate. Natural population growth on earth would outpace the colonization effort. A more likely scenario would be that space could provide the resources (e.g. from asteroid mining) that might help to sustain human existence on earth.
Sustainable Ethic
A sustainable ethic is an environmental ethic by which people treat the earth as if its resources are limited. This ethic assumes that the earth’s resources are not unlimited and that humans must use and conserve resources in a manner that allows their continued use in the future. A sustainable ethic also assumes that humans are a part of the natural environment and that we suffer when the health of a natural ecosystem is impaired. A sustainable ethic includes the following tenets:
- The earth has a limited supply of resources.
- Humans must conserve resources.
- Humans share the earth’s resources with other living things.
- Growth is not sustainable.
- Humans are a part of nature.
- Humans are affected by natural laws.
- Humans succeed best when they maintain the integrity of natural processes sand cooperate with nature.
For example, if a fuel shortage occurs, how can the problem be solved in a way that is consistent with a sustainable ethic? The solutions might include finding new ways to conserve oil or developing renewable energy alternatives. A sustainable ethic attitude in the face of such a problem would be that if drilling for oil damages the ecosystem, then that damage will affect the human population as well. A sustainable ethic can be either anthropocentric or biocentric (life-centered). An advocate for conserving oil resources may consider all oil resources as the property of humans. Using oil resources wisely so that future generations have access to them is an attitude consistent with an anthropocentric ethic. Using resources wisely to prevent ecological damage is in accord with a biocentric ethic.
Land Ethic
Aldo Leopold, an American wildlife natural historian and philosopher, advocated a biocentric ethic in his book, A Sand County Almanac . He suggested that humans had always considered land as property, just as ancient Greeks considered slaves as property. He believed that mistreatment of land (or of slaves) makes little economic or moral sense, much as today the concept of slavery is considered immoral. All humans are merely one component of an ethical framework. Leopold suggested that land be included in an ethical framework, calling this the land ethic.
“The land ethic simply enlarges the boundary of the community to include soils, waters, plants and animals; or collectively, the land. In short, a land ethic changes the role of Homo sapiens from conqueror of the land-community to plain member and citizen of it. It implies respect for his fellow members, and also respect for the community as such.” (Aldo Leopold, 1949)
Leopold divided conservationists into two groups: one group that regards the soil as a commodity and the other that regards the land as biota, with a broad interpretation of its function. If we apply this idea to the field of forestry, the first group of conservationists would grow trees like cabbages, while the second group would strive to maintain a natural ecosystem. Leopold maintained that the conservation movement must be based upon more than just economic necessity. Species with no discernible economic value to humans may be an integral part of a functioning ecosystem. The land ethic respects all parts of the natural world regardless of their utility, and decisions based upon that ethic result in more stable biological communities.
“Anything is right when it tends to preserve the integrity, stability and beauty of the biotic community. It is wrong when it tends to do otherwise.” (Aldo Leopold, 1949)
Hetch Hetchy Valley
In 1913, the Hetch Hetchy Valley – located in Yosemite National Park in California – was the site of a conflict between two factions, one with an anthropocentric ethic and the other, a biocentric ethic. As the last American frontiers were settled, the rate of forest destruction started to concern the public.
The conservation movement gained momentum, but quickly broke into two factions. One faction, led by Gifford Pinchot, Chief Forester under Teddy Roosevelt, advocated utilitarian conservation (i.e., conservation of resources for the good of the public). The other faction, led by John Muir, advocated preservation of forests and other wilderness for their inherent value. Both groups rejected the first tenet of frontier ethics, the assumption that resources are limitless. However, the conservationists agreed with the rest of the tenets of frontier ethics, while the preservationists agreed with the tenets of the sustainable ethic.
The Hetch Hetchy Valley was part of a protected National Park, but after the devastating fires of the 1906 San Francisco earthquake, residents of San Francisco wanted to dam the valley to provide their city with a stable supply of water. Gifford Pinchot favored the dam.
“As to my attitude regarding the proposed use of Hetch Hetchy by the city of San Francisco…I am fully persuaded that… the injury…by substituting a lake for the present swampy floor of the valley…is altogether unimportant compared with the benefits to be derived from it’s use as a reservoir.
“The fundamental principle of the whole conservation policy is that of use, to take every part of the land and its resources and put it to that use in which it will serve the most people.” (Gifford Pinchot, 1913)
John Muir, the founder of the Sierra Club and a great lover of wilderness, led the fight against the dam. He saw wilderness as having an intrinsic value, separate from its utilitarian value to people. He advocated preservation of wild places for their inherent beauty and for the sake of the creatures that live there. The issue aroused the American public, who were becoming increasingly alarmed at the growth of cities and the destruction of the landscape for the sake of commercial enterprises. Key senators received thousands of letters of protest.
“These temple destroyers, devotees of ravaging commercialism, seem to have a perfect contempt for Nature, and instead of lifting their eyes to the God of the Mountains, lift them to the Almighty Dollar.” (John Muir, 1912)
Despite public protest, Congress voted to dam the valley. The preservationists lost the fight for the Hetch Hetchy Valley, but their questioning of traditional American values had some lasting effects. In 1916, Congress passed the “National Park System Organic Act,” which declared that parks were to be maintained in a manner that left them unimpaired for future generations. As we use our public lands, we continue to debate whether we should be guided by preservationism or conservationism.
Environmental Justice
Environmental Justice is defined as the fair treatment and meaningful involvement of all people regardless of race, color, national origin, or income with respect to the development, implementation, and enforcement of environmental laws, regulations, and policies. It will be achieved when everyone enjoys the same degree of protection from environmental and health hazards and equal access to the decision-making process to have a healthy environment in which to live, learn, and work.
Whenever a community is faced with the potential of an environmentally undesirable facility, such as the placement of a hazardous waste dump in its midst, the usual response from residents is: "Not in my back yard!" Such a response is known as the NIMBY principle. Such reactions are usually reactions to visions of previous environmental irresponsibility: uncontrolled dumping of noxious industrial wastes and rusty steel drums oozing hazardous chemicals into the environment. Such occurrences were all too real in the past and some are still taking place. It is now possible -- and much more common -- to build environmentally sound, state-of-the-art disposal facilities. However, the NIMBY principle usually prevents the construction of such new facilities. Instead, hazardous waste facilities tend to be built upon pre-existing, already contaminated sites, even though the geology of such locations may be less favorable for containment than potential new sites.
During the 1980’s minority groups protested that hazardous waste sites were preferentially sited in minority neighborhoods. In 1987, Benjamin Chavis of the United Church of Christ Commission for Racism and Justice coined the term environmental racism to describe such a practice. The charges generally failed to consider whether the facility or the demography of the area came first. Most hazardous waste sites are located on property that was used as disposal sites long before modern facilities and disposal methods were available. Areas around such sites are typically depressed economically, often as a result of past disposal activities. Persons with low incomes are often constrained to live in such undesirable, but affordable, areas. The problem more likely resulted from one of insensitivity rather than racism. Indeed, the ethnic makeup of potential disposal facilities was most likely not considered when the sites were chosen.
Decisions in citing hazardous waste facilities are generally made on the basis of economics, geological suitability and the political climate. For example, a site must have a soil type and geological profile that prevents hazardous materials from moving into local aquifers. The cost of land is also an important consideration. The high cost of buying land would make it economically unfeasible to build a hazardous waste site in Beverly Hills. Some communities have seen a hazardous waste facility as a way of improving their local economy and quality of life. Emelle County, Alabama had illiteracy and infant mortality rates that were among the highest in the nation. A landfill constructed there provided jobs and revenue that ultimately helped to reduce both figures.
In an ideal world, there would be no hazardous waste facilities, but we do not live in an ideal world. Unfortunately, we live in a world plagued by rampant pollution and dumping of hazardous waste. Our industrialized society has necessarily produced wastes during the manufacture of products for our basic needs. Until technology can find a way to manage (or eliminate) hazardous waste, disposal facilities will be necessary to protect both humans and the environment. By the same token, this problem must be addressed. Industry and society must become more socially sensitive in the selection of future hazardous waste sites. All humans who help produce hazardous wastes must share the burden of dealing with those wastes, not just the poor and minorities.
Indigenous People
Since the end of the 15th century, most of the world’s frontiers have been claimed and colonized by established nations. Invariably, these conquered frontiers were home to people indigenous to those regions. Some were wiped out or assimilated by the invaders, while others survived while trying to maintain their unique cultures and way of life. The United Nations officially classifies indigenous people as those “having an historical continuity with pre-invasion and pre-colonial societies,” and “consider themselves distinct from other sectors of the societies now prevailing in those territories or parts of them.” Furthermore, indigenous people are “determined to preserve, develop and transmit to future generations, their ancestral territories, and their ethnic identity, as the basis of their continued existence as peoples in accordance with their own cultural patterns, social institutions and legal systems.” A few of the many groups of indigenous people around the world are: the many tribes of Native Americans (i.e., Navajo, Sioux) in the contiguous 48 states, the Inuit of the arctic region from Siberia to Canada, the rainforest tribes in Brazil, and the Ainu of northern Japan.
Many problems face indigenous people including the lack of human rights, exploitation of their traditional lands and themselves, and degradation of their culture. In response to the problems faced by these people, the United Nations proclaimed an “International Decade of the World’s Indigenous People” beginning in 1994. The main objective of this proclamation, according to the United Nations, is “the strengthening of international cooperation for the solution of problems faced by indigenous people in such areas as human rights, the environment, development, health, culture and education.” Its major goal is to protect the rights of indigenous people. Such protection would enable them to retain their cultural identity, such as their language and social customs, while participating in the political, economic and social activities of the region in which they reside.
Despite the lofty U.N. goals, the rights and feelings of indigenous people are often ignored or minimized, even by supposedly culturally sensitive developed countries. In the United States many of those in the federal government are pushing to exploit oil resources in the Arctic National Wildlife Refuge on the northern coast of Alaska. The “Gwich’in,” an indigenous people who rely culturally and spiritually on the herds of caribou that live in the region, claim that drilling in the region would devastate their way of life. Thousands of years of culture would be destroyed for a few months’ supply of oil. Drilling efforts have been stymied in the past, but mostly out of concern for environmental factors and not necessarily the needs of the indigenous people. Curiously, another group of indigenous people, the “Inupiat Eskimo,” favor oil drilling in the Arctic National Wildlife Refuge. Because they own considerable amounts of land adjacent to the refuge, they would potentially reap economic benefits from the development of the region.
The heart of most environmental conflicts faced by governments usually involves what constitutes proper and sustainable levels of development. For many indigenous peoples, sustainable development constitutes an integrated wholeness, where no single action is separate from others. They believe that sustainable development requires the maintenance and continuity of life, from generation to generation and that humans are not isolated entities, but are part of larger communities, which include the seas, rivers, mountains, trees, fish, animals and ancestral spirits. These, along with the sun, moon and cosmos, constitute a whole. From the point of view of indigenous people, sustainable development is a process that must integrate spiritual, cultural, economic, social, political, territorial and philosophical ideals.
Contributors and Attributions
- Kyle Whittinghill (University of Pittsburgh)
- Essentials of Environmental Science by Kamala Doršner is licensed under CC BY 4.0. Modified from the original by Matthew R. Fisher.
- Modified by Rachel Schleiger from Sustainability: A Comprehensive Foundation by Openstax (licensed under CC-BY )


14.1: Impulse-Momentum Equations for a Rigid Body
The concepts of impulse and momentum provide a third method of solving kinetics problems in dynamics. Generally this method is called the Impulse-Momentum Method , and it can be boiled down to the idea that the impulse exerted on a body over a given time will be equal to the change in that body's momentum. In a rigid body we will be concerned with not only linear impulse and momentum, but also angular impulse and momentum. The linear and angular impulse momentum equations are below, with the new term for angular impulse \((\vec{K})\) starting out the angular impulse momentum equation.
\[ \vec{J} = m \vec{v}_f - m \vec{v}_i \]
\[ \vec{K} = I_G \vec{\omega}_f - I_G \vec{\omega}_i \]
For two-dimensional problems, we can break the linear impulse equation down into two scalar components to solve. In the case of planar problems, we simply need to break all forces and velocities into \(x\) and \(y\) components - since all rotation will be about the \(z\)-axis, the angular impulse momentum equation remains a single equation. Notice, however, that we will need to take the mass moment of inertia about the center of mass of the body into account; similarly, we will use the velocity of the center of mass when discussing the velocity in the linear impulse momentum equations.
\[ J_x = m v_{f,x} - m v_{i,x} \]
\[ J_y = m v_{f,y} - m v_{i,y} \]
\[ K_z = I_G \omega_f - I_G \omega_i \]
Impulse:
As discussed with particles, a linear impulse in its most basic form is a force integrated over a time. For a force with a constant magnitude, we can find the magnitude of the impulse by multiplying the magnitude of the force by the time that force is exerted. If the force is not constant, we simply integrate the force function over the set time period. The direction of the impulse vector will be the direction of the force vector, and the units will be a force multiplied by a time (Newton-seconds or pound-seconds, for example).
\begin{align} \text{Constant magnitude force:} \quad &\, \vec{J} = \vec{F} * t \\ \text{Non-constant magnitude force:} \quad &\, \vec{J} = \int \vec{F}(t) \ dt \end{align}
An angular impulse is similar to a linear impulse, except it is the moment exerted over time instead of the force exerted over time.
\begin{align} \text{Constant magnitude moment:} \quad &\, \vec{K} = \vec{M} * t \\ \text{Non-constant magnitude moment:} \quad &\, \vec{K} = \int \vec{M}(t) \ dt \end{align}
This moment can come either in the form of a torque directly applied to a body, or an off-center force causing a linear and angular impulse at the same time. All moments should be taken about the center of mass of the body.
Momentum:
As discussed with particles, the linear momentum of a body will be equal to the mass of the body times its current velocity. Since velocity is a vector, the momentum will also be a vector, having both magnitude and a direction. Unlike the impulse, which happens over some set time, the momentum is captured as a snapshot of a specific instant in time (usually right before and after some impulse is exerted). The units for linear momentum will be mass times unit distance per unit time. This is usually kilogram-meters per second in metric, or slug-feet per second in English units.
Angular momentum, on the other hand, will be equal to the body's mass moment of inertia (about its center of mass) times its current angular velocity. It's important to note that while the mass moment of inertia remains constant if the body does not change shape, a shape that does change shape will likely have changes in mass moments of inertia along with changes in angular velocity.
Practice \(\PageIndex{1}\)
A miter saw has an operating speed of 1500 rpm. The blade and motor armature have a combined weight of 3 lbs and a radius of gyration of 1 inch.
- What is the time required for the bearing friction alone (torque=0.015 inch-lbs) to stop the blade?
- What is the torque a braking system would need to apply to stop the blade in just 0.25 seconds?
- Solution (not yet available):
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Not yet available.
Practice \(\PageIndex{2}\)
A bowling ball is modeled as a 7-kilogram uniform sphere, 300 mm in diameter. The ball is released with an initial velocity of 6 m/s on a horizontal wooden floor (\(\mu_k\) = 0.1) with zero angular velocity.
- How long does it take before the ball begins to roll without slipping?
- What is the linear velocity of the ball at this time?
- Solution (not yet available):
-
Not yet available.


11.2.1: Medical Importance of Viruses
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Learning Objectives
- Describe the fundamental characteristics of viruses
Viruses are extremely diverse and have evolved to infect nearly all life forms. Amid this diversity, viruses with similar genome organizations exhibit major conserved themes in their replication strategies. Once inside a cell, all viruses must uncoat, replicate, and transcribe their genomes, and then repackage their genomes into viral progeny that are released from cells. RNA viruses in particular must coordinate the switch between plus and minus strand synthesis and between replication and transcription while protecting their genomes from cellular nucleases. Because of the conserved nature of a virus ‘s intracellular life cycle, fundamental advances in our understanding of replication have come from viruses that infect both animal and non-animal hosts.
The devastating effects of viral diseases such as AIDs, smallpox, polio, influenza, diarrhea, and hepatitis are well known, and studies of viral pathogens are easily justified from a world health perspective. Sobering examples of emerging viral diseases have occurred. Among these are the sudden emergence of the coronavirus that causes severe acute respiratory syndrome (SARS), the continued transmission of an avian influenza virus to humans (“bird flu”), and the isolation of poliovirus vaccine -wild type recombinants that have hampered poliovirus eradication efforts. In addition, the threat of bioterrorism became a reality on U.S. soil, creating an obligation for scientists to respond with aggressive countermeasures. Vaccination remains the preferred strategy for controlling viral diseases because the intimate association of viruses with the host cellular machinery complicates the development of safe drugs. However, certain viruses have proven difficult targets for vaccines, and antiviral drugs provide the only option for controlling disease.
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- OpenStax College, Organizing Life on Earth. November 9, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44588/latest/#fig-ch20_01_01 . License : CC BY: Attribution
- Severe acute respiratory syndrome. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Severe_...atory_syndrome . License : CC BY-SA: Attribution-ShareAlike
- Poliovirus. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Poliovirus . License : CC BY-SA: Attribution-ShareAlike
- vaccination. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/vaccination . License : CC BY-SA: Attribution-ShareAlike
- eradication. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/eradication . License : CC BY-SA: Attribution-ShareAlike
- Biological classification L Pengo vflip. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/File:Bi...engo_vflip.svg . License : CC BY-SA: Attribution-ShareAlike
- File:VirusBaltimoreClassification.svg - Wikipedia, the free encyclopedia. Provided by : Wikipedia. Located at : en.Wikipedia.org/w/index.php?...ion.svg&page=1 . License : CC BY-SA: Attribution-ShareAlike
- OpenStax College, Organizing Life on Earth. November 9, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44588/latest/#fig-ch20_01_01 . License : CC BY: Attribution
- SARS xray. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/File:SARS_xray.jpg . License : CC BY-SA: Attribution-ShareAlike
Key Points
- Viruses multiply by taking control of the host cell’s genetic material and regulating the synthesis and assembly of new viruses.
- Viruses are able to infect a host cell and cause acute diseases or alter its genetic material to cause chronic diseases such as cancer.
- Most viral infections can resolve in weeks but others are the cause of more serious, debilitating and sometimes fatal diseases.
Key Terms
- vaccination : inoculation with a vaccine in order to protect a particular disease or strain of disease.
- eradication : the act of plucking up by the roots; a rooting out; extirpation; utter destruction.


6: The Workplace
In the career research chapter, you learned how to discover facts about potential careers including educational requirements, skills and abilities needed, typical work tasks and salary estimates. As you researched potential careers, you may have seen details about “job outlook” or employment projections. The outlook for a career or employment projection means whether that occupation is changing in some way, perhaps growing or declining or even transitioning into new work tasks and descriptions. In this chapter, we will investigate several workplace trends that could affect outlook and employment projections including the changing labor market and recent developments affecting how people work.
Thumbnail: Image of job announcement for social media manager. (Pixabay License via Pixabay )


4.4: Annotated Sample Reading- from Life on the Mississippi by Mark Twain
By the end of this section, you will be able to:
- Read for understanding, showing that genre conventions are shaped by purpose, culture, and expectation.
- Analyze relationships between ideas and patterns of organization in a nonfiction text
Introduction
Figure \(4.5\) Mark Twain, 1907 (credit: “Mark Twain” by A.F. Bradley/Wikimedia Commons, Public Domain)
An image in literature is a description that engages one of the five senses. Details rich in imagery appeal to readers’ emotions, create new meaning, and draw an audience into the story. Sensory images—what the narrator sees, hears, tastes, feels, and smells—should be specific and contain emotional content that enhances your writing.
In the text excerpt you are about to read, Mark Twain (1835–1910) uses imagery to place readers with him aboard a steamboat on the Mississippi River as Mr. Bixby trains him to pilot it. As you read, put yourself in the shoes of the narrator—Mark Twain. Notice how vividly he describes sensory experiences and how they enhance your understanding of his purpose.
Twain lived in a pre–Civil War America in which slavery was accepted and prevalent. He used his literature to criticize slavery and hierarchical social codes of the American South, though he wasn’t necessarily an outspoken opponent in his public life. Twain provides an example of the ways in which literature can subtly influence the beliefs and identities of generations of readers. Visit Project Gutenberg ( https://openstax.org/r/ projectgutenberg) for the full text of Life on the Mississippi .
Living By Their Own Words
The Storyteller's World: Entering through Imagery
Figure \(4.6\) In this illustration, appearing in Life on the Mississippi, the steamboat is an older vessel but is similar to the one in Twain’s memoir. (credit: “MISSISSIPPI STEAMBOAT - FIFTY YEARS AGO” by Samuel Langhorne Clemens/ Wikimedia Commons, Public Domain)
Mr. Bixby served me in this fashion once, and for years afterward I used to blush even in my sleep when I thought of it. I had become a good steersman [a person steering a boat or ship]; so good, indeed, that I had all the work to do on our watch, night and day; Mr. Bixby seldom made a suggestion to me; all he ever did was to take the wheel on particularly bad nights or in particularly bad crossings, land the boat when she needed to be landed, play gentleman of leisure nine-tenths of the watch, and collect the wages. The lower river was about bank-full, and if anybody had questioned my ability to run any crossing between Cairo and New Orleans without help or instruction, I should have felt irreparably hurt. The idea of being afraid of any crossing in the lot, in the day-time, was a thing too preposterous for contemplation. Well, one matchless summer’s day I was bowling down the bend above island 66, brimful of self-conceit and carrying my nose as high as a giraffe’s, when Mr. Bixby said,—
Point of view. Twain writes in first person, using the pronouns I and me.
Exposition. Though the excerpt starts in the middle of a chapter of a larger work, this paragraph begins an anecdote that Twain relates about a specific incident in his time in training. The paragraph acts as the exposition, establishing the setting, characters, and lead-in to the conflict related in the anecdote.
Reflection. Twain’s reflection of the memory, saying he would “blush even in my sleep,” reveals his embarrassment in a way that readers can relate to.
“I am going below a while. I suppose you know the next crossing?”
This was almost an affront. It was about the plainest and simplest crossing in the whole river. One couldn’t come to any harm, whether he ran it right or not; and as for depth, there never had been any bottom there. I knew all this, perfectly well.
“Know how to run it? Why, I can run it with my eyes shut.”
Tone. In this dialogue, the narrator takes on a tone of confidence, which helps develop his own voice and character.
Dialogue. Twain uses dialogue to recreate the scene and reveal characters.
“How much water is there in it?”
“Well, that is an odd question. I couldn’t get bottom there with a church steeple.”
“You think so, do you?”
The very tone of the question shook my confidence. That was what Mr. Bixby was expecting. He left, without saying anything more. I began to imagine all sorts of things. Mr. Bixby, unknown to me, of course, sent somebody down to the forecastle [forward part of the ship, below the deck] with some mysterious instructions to the leadsmen, another messenger was sent to whisper among the officers, and then Mr. Bixby went into hiding behind a smoke-stack where he could observe results. Presently the captain stepped out on the hurricane deck [an upper deck on a ship]; next the chief mate appeared; then a clerk. Every moment or two a straggler was added to my audience; and before I got to the head of the island I had fifteen or twenty people assembled down there under my nose. I began to wonder what the trouble was. As I started across, the captain glanced aloft at me and said, with a sham uneasiness in his voice,—
Vivid Details and Imagery. Twain builds tension through vivid detail and imagery that recreates the sounds and paints a picture of his experience. From the whispers of the messengers to the sight of more and more people appearing on the deck to observe the narrator, readers can almost feel the narrator becoming more nervous.
Rising Action. The reader begins to understand the conflict through the sequence of events. This rising action builds tension by contrasting Twain’s earlier stated confidence with his increasing anxiety.
“Where is Mr. Bixby?”
“Gone below, sir.”
Dialogue. Twain employs dialogue to advance the plot and simultaneously increase tension, thus defining the conflict. The dialogue here signals the narrator’s move from confidence to anxiety, the next line indicating that the captain’s questioning “did the business” for him. Dialogue also helps establish authenticity and recreate “reality” for readers, allowing them an opportunity to “witness” the scene and the characters directly.
But that did the business for me. My imagination began to construct dangers out of nothing, and they multiplied faster than I could keep the run of them. All at once I imagined I saw shoal [shallow] water ahead! The wave of coward agony that surged through me then came near dislocating every joint in me. All my confidence in that crossing vanished. I seized the bell-rope; dropped it, ashamed; seized it again; dropped it once more; clutched it tremblingly once again, and pulled it so feebly that I could hardly hear the stroke myself. Captain and mate sang out instantly, and both together,—
Vivid Description. Twain moves the plot toward the climax in this paragraph, particularly with his description of the dangers multiplying and the peril he imagines.
Mood. In this section, Twain creates a frazzled and frantic mood through not only the details and description but also the sentence structure. Particularly in the sentence “I seized the bell-rope; dropped it, ashamed; seized it again; dropped it once more . . . ,” the short, connected clauses and phrases and the repetition of the words dropped and seized all add to the sense of panic.
“Starboard lead there! and quick about it!”
This was another shock. I began to climb the wheel like a squirrel; but I would hardly get the boat started to port [the left side of the ship when a person on board is facing forward] before I would see new dangers on that side, and away I would spin to the other; only to find perils accumulating to starboard [the right side of the ship when a person on board is facing forward], and be crazy to get to port again. Then came the leadsman’s sepulchral [bleak, morbid] cry:—
Organization. After the introduction in which Twain writes in the present tense to indicate he will tell an embarrassing story from the past, the rest of the passage follows a chronological organization, recounting the event from beginning to end.
D-e-e-p four!”
Deep four in a bottomless crossing! The terror of it took my breath away.
“M-a-r-k three! . . . M-a-r-k three . . . Quarter less three! . . . Half twain!”
This was frightful! I seized the bell-ropes and stopped the engines.
“Quarter twain! Quarter twain! Mark twain!”
Dialogue. Here, the dialogue emphasizes the narrator’s terror and leads to the climax.
I was helpless. I did not know what in the world to do. I was quaking from head to foot, and I could have hung my hat on my eyes, they stuck out so far.
Hyperbole. Twain uses a combination of sensory detail and hyperbole, or exaggeration, to emphasize how panicked he feels in the moment.
“Quarter less twain! Nine and a half !”
We were drawing nine! My hands were in a nerveless flutter. I could not ring a bell intelligibly with them. I flew to the speaking-tube and shouted to the engineer,—
“Oh, Ben, if you love me, back her! Quick, Ben! Oh, back the immortal soul out of her!”
Climax. In this part of the story the narrator calls out for help as the tension reaches its peak.
I heard the door close gently. I looked around, and there stood Mr. Bixby, smiling a bland, sweet smile. Then the audience on the hurricane deck sent up a thundergust [roar] of humiliating laughter. I saw it all, now, and I felt meaner than the meanest man in human history. I laid in the lead, set the boat in her marks, came ahead on the engines, and said:—
Vivid Details. The narrator describes Mr. Bixby’s “bland” smile, contrasted with the uproarious laughter of the rest of the group. He also uses vivid details to describe his own reaction: he “felt meaner than the meanest man in human history.”
Falling Action. After it is revealed that the group was tricking Twain, the tension begins to dissipate.
“It was a fine trick to play on an orphan, wasn’t it?  In fact I hope you won’t; for I want you to learn something by that experience. Didn’t you know there was no bottom in that crossing?”
“Yes, sir, I did.”
“Very well, then. You shouldn’t have allowed me or anybody else to shake your confidence in that knowledge. Try to remember that. And another thing: when you get into a dangerous place, don’t turn coward. That isn’t going to help matters any.”
Theme. Through this dialogue, Twain introduces the message of the story. More than providing an amusing recollection about a time he was embarrassed, his purpose is to convey the message that it is important to rely on your knowledge and training rather than allow fear to rule.
It was a good enough lesson, but pretty hardly learned. Yet about the hardest part of it was that for months I so often had to hear a phrase which I had conceived a particular distaste for. It was, “Oh, Ben, if you love me, back her!”
Resolution. The narrator explicitly states his lesson learned at the end of the story and adds a detail about his continuing humiliation.
Discussion Questions
- For what reason might Twain have chosen to tell this anecdote in his memoir?
- How does telling this story help Twain reveal his experience of learning to be a riverboat pilot?
- How does Twain build tension to support the conflict in the anecdote?
- How does the narrator pull the reader into the action in the paragraph beginning “But that did the business for me”?
- How do the narrator’s word choices in the story shape the tone and mood?
- How does Twain’s use of vivid details and descriptions help the reader connect to the text?


7.2.2: Transpiration
The principal way in which water enters the air is through evaporation. Plants are another important source of atmospheric moisture. Plants contribute water to the atmosphere by transpiration. Transpiration is the transfer of water into the air via leaf pores or stomata . Interestingly, the same three requirements for evaporation apply to transpiration. Approximately 600 cal/gm of energy is required to transpire water from leaves. The transfer of water into the air removes heat from the plant and so transpiration, like evaporation, is a cooling process. Thus transpiration is an important means of transporting heat between the surface and air above.
Water for transpiration comes from that which is stored in the soil and then extracted by plant roots. The amount of water that is held in the soil moisture zone is dependent on the texture and structure of the soil. Coarse textured soil dominated by sand-size particles holds less moisture than a finer textured soil.
How important is plant transpiration? Consider this, one mature oak tree can transpire as much as 100 gallons of water in a day. An acre of corn can transpire as much as 4000 gallons of water per day ( EPA ). The problem that many countries face is an ever dwindling resource of groundwater to promote agriculture in regions too dry to do so. Far too often, groundwater resources are extracted faster than they can naturally replenish themselves. Over pumping depletes groundwater reserves in aquifers and ultimately leads to their collapse. This is happening in the semiarid and arid regions of the United States. One aquifer in particular, the Ogallala Aquifer, is at risk of being depleted . The recharge area where water enters the aquifer is in the Rocky Mountains. The aquifer extends underground for hundreds of miles into the Great Plains. The aquifer is used to support agriculture and municipal water supplies on the Great Plains. Unfortunately, water is being pumped out of the aquifer much faster than the rate of replenishment. The fear is that over pumping will lead to the aquifer running dry causing severe stress on the Great Plains agricultural economy.


13.12: Case Questions
The Big University football team, a member of the Southeastern Conference (SEC), brings in over $100 million a year in revenue, including TV rights, ticket sales, and bowl games. Seats to a game cost well over $100, and coaches are paid millions of dollars (more than anyone else at Big U, including the president). However, despite enormous revenues, universities and their football teams are considered not-for-profit organizations and pay no taxes on the $100+ million their football programs bring in. Should a university football program be allowed to exist as a not-for-profit organization?
2 .Jen started a new sustainability-oriented business six years ago, making single-serve coffee pods out of recyclable paper, rather than plastic. Her company, Jen’s Pod, is now experiencing rapid growth. Jen started her company as an LLC but has been considering making a decision to incorporate. What are some of the advantages of changing to a C corporation?
3 .You are headed off to college. Some close family members decide it would be a good idea to buy a house in the college town and then rent it out to students, with you also living there and actively managing it. Assuming you and your family buy it, what form of business would you select?
4 .Jackson owns and runs a small computer repair business, a sole proprietorship, out of his home, with one employee. He also goes to small businesses at their locations, mostly cleaning viruses and doing other small maintenance tasks and repairs. A family physician’s office calls him in for a repair. He sends his employee to do the repair. Unknown to him, his employee makes a copy of patients’ personal information and sells it on the dark web. Jackson ends up being sued, and the plaintiffs ask the court to allow them to access Jackson’s personal, nonbusiness bank account that also has his spouse’s funds in the account. Can the plaintiffs take that money?


4.1: Graphs
Back in the 18 th century in the Prussian city of Königsberg, a river ran through the city and seven bridges crossed the forks of the river. The river and the bridges are highlighted in the picture to the right[1].
As a weekend amusement, townsfolk would see if they could find a route that would take them across every bridge once and return them to where they started.
Solution
Leonard Euler (pronounced OY-lur), one of the most prolific mathematicians ever, looked at this problem in 1735, laying the foundation for graph theory as a field in mathematics. To analyze this problem, Euler introduced edges representing the bridges:
Since the size of each land mass it is not relevant to the question of bridge crossings, each can be shrunk down to a vertex representing the location:
Notice that in this graph there are two edges connecting the north bank and island, corresponding to the two bridges in the original drawing. Depending upon the interpretation of edges and vertices appropriate to a scenario, it is entirely possible and reasonable to have more than one edge connecting two vertices.
While we haven’t answered the actual question yet of whether or not there is a route which crosses every bridge once and returns to the starting location, the graph provides the foundation for exploring this question.
Definitions
While we loosely defined some terminology earlier, we now will try to be more specific.
A vertex is a dot in the graph that could represent an intersection of streets, a land mass, or a general location, like “work” or “school”. Vertices are often connected by edges. Note that vertices only occur when a dot is explicitly placed, not whenever two edges cross. Imagine a freeway overpass – the freeway and side street cross, but it is not possible to change from the side street to the freeway at that point, so there is no intersection and no vertex would be placed.
Edges connect pairs of vertices. An edge can represent a physical connection between locations, like a street, or simply that a route connecting the two locations exists, like an airline flight.
A loop is a special type of edge that connects a vertex to itself. Loops are not used much in street network graphs.
The degree of a vertex is the number of edges meeting at that vertex. It is possible for a vertex to have a degree of zero or larger.
A path is a sequence of vertices using the edges. Usually we are interested in a path between two vertices. For example, a path from vertex A to vertex M is shown below. It is one of many possible paths in this graph.
A circuit is a path that begins and ends at the same vertex. A circuit starting and ending at vertex A is shown below.
A graph is connected if there is a path from any vertex to any other vertex. Every graph drawn so far has been connected. The graph below is disconnected ; there is no way to get from the vertices on the left to the vertices on the right.
Here is a portion of a housing development from Missoula, Montana[2]. As part of her job, the development’s lawn inspector has to walk down every street in the development making sure homeowners’ landscaping conforms to the community requirements.
Solution
Naturally, she wants to minimize the amount of walking she has to do. Is it possible for her to walk down every street in this development without having to do any backtracking? While you might be able to answer that question just by looking at the picture for a while, it would be ideal to be able to answer the question for any picture regardless of its complexity.
To do that, we first need to simplify the picture into a form that is easier to work with. We can do that by drawing a simple line for each street. Where streets intersect, we will place a dot.
This type of simplified picture is called a graph .
While we drew our original graph to correspond with the picture we had, there is nothing particularly important about the layout when we analyze a graph. Both of the graphs below are equivalent to the one drawn above since they show the same edge connections between the same vertices as the original graph.
In the first section, we created a graph of the Königsberg bridges and asked whether it was possible to walk across every bridge once. Because Euler first studied this question, these types of paths are named after him.
An Euler path is a path that uses every edge in a graph with no repeats. Being a path, it does not have to return to the starting vertex.
In the graph shown below, there are several Euler paths.
Solution
One such path is CABDCB. The path is shown in arrows to the right, with the order of edges numbered.
An Euler circuit is a circuit that uses every edge in a graph with no repeats. Being a circuit, it must start and end at the same vertex.
The graph below has several possible Euler circuits.
Solution
Here’s a couple, starting and ending at vertex A: ADEACEFCBA and AECABCFEDA. The second is shown in arrows.
Look back at the example used for Euler paths – does that graph have an Euler circuit? A few tries will tell you no; that graph does not have an Euler circuit. When we were working with shortest paths, we were interested in the optimal path. With Euler paths and circuits, we’re primarily interested in whether an Euler path or circuit exists .
Why do we care if an Euler circuit exists? Think back to our housing development lawn inspector from the beginning of the chapter. The lawn inspector is interested in walking as little as possible. The ideal situation would be a circuit that covers every street with no repeats. That’s an Euler circuit! Luckily, Euler solved the question of whether or not an Euler path or circuit will exist.
A graph will contain an Euler path if it contains at most two vertices of odd degree.
A graph will contain an Euler circuit if all vertices have even degree
In the graph below, vertices A and C have degree 4, since there are 4 edges leading into each vertex. B is degree 2, D is degree 3, and E is degree 1. This graph contains two vertices with odd degree (D and E) and three vertices with even degree (A, B, and C), so Euler’s theorems tell us this graph has an Euler path, but not an Euler circuit.
Now we know how to determine if a graph has an Euler circuit, but if it does, how do we find one? While it usually is possible to find an Euler circuit just by pulling out your pencil and trying to find one, the more formal method is Fleury’s algorithm.
- Start at any vertex if finding an Euler circuit. If finding an Euler path, start at one of the two vertices with odd degree.
- Choose any edge leaving your current vertex, provided deleting that edge will not separate the graph into two disconnected sets of edges.
- Add that edge to your circuit, and delete it from the graph.
- Continue until you’re done.
Let’s find an Euler Circuit on this graph using Fleury’s algorithm, starting at vertex A.
Solution
Step 1:
Original Graph. Choosing edge AD.
Circuit so far: AD
Step 2:
AD deleted. D is current. Can’t choose DC since that would disconnect graph. Choosing DE
Circuit so far: ADE
Step 3:
E is current. From here, there is only one option, so the rest of the circuit is determined.
Circuit: ADEBDCA
Does the graph below have an Euler Circuit? If so, find one.
- Answer
-
Yes, all vertices have even degree so this graph has an Euler Circuit. There are several possibilities. One is: ABEGFCDFEDBCA
Not every graph has an Euler path or circuit, yet our lawn inspector still needs to do her inspections. Her goal is to minimize the amount of walking she has to do. In order to do that, she will have to duplicate some edges in the graph until an Euler circuit exists.
Eulerization is the process of adding edges to a graph to create an Euler circuit on a graph. To eulerize a graph, edges are duplicated to connect pairs of vertices with odd degree. Connecting two odd degree vertices increases the degree of each, giving them both even degree. When two odd degree vertices are not directly connected, we can duplicate all edges in a path connecting the two.
Note that we can only duplicate edges, not create edges where there wasn’t one before. Duplicating edges would mean walking or driving down a road twice, while creating an edge where there wasn’t one before is akin to installing a new road!
For the rectangular graph shown, three possible eulerizations are shown. Notice in each of these cases the vertices that started with odd degrees have even degrees after eulerization, allowing for an Euler circuit.
In the example above, you’ll notice that the last eulerization required duplicating seven edges, while the first two only required duplicating five edges. If we were eulerizing the graph to find a walking path, we would want the eulerization with minimal duplications.
Eulerize the graph shown, then find an Euler circuit on the eulerized graph.
- Answer
-
This graph can be eulerized by duplicating the edge BC, as shown. One possible Euler circuit on the eulerized graph is ACDBCBA
Looking again at the graph for our lawn inspector, the vertices with odd degree are shown highlighted. With eight vertices, we will always have to duplicate at least four edges.
Solution
In this case, we need to duplicate five edges since two odd degree vertices are not directly connected. Without weights we can’t be certain this is the eulerization that minimizes walking distance, but it looks pretty good.
The problem of finding the optimal eulerization is called the Chinese Postman Problem, a name given by an American in honor of the Chinese mathematician Mei-Ko Kwan who first studied the problem in 1962 while trying to find optimal delivery routes for postal carriers. This problem is important in determining efficient routes for garbage trucks, school buses, parking meter checkers, street sweepers, and more.
Unfortunately, algorithms to solve this problem are fairly complex.
[1] Bogdan Giuşcă. http://en.Wikipedia.org/wiki/File:Ko...rg_bridges.png
[2] Sam Beebe. http://www.flickr.com/photos/sbeebe/2850476641/ , CC-BY


12.17: Putting It Together- Geological Resources
Summary
In this section, we used almost all of the concepts we have learned so far. While plate tectonics may not have been mentioned directly, we know the role it plays in the formation of rock, minerals and mineral resources. In this section, we focused on these items:
- How mineral resources and fossil fuels are formed
- How these resources are mined
- Nonrenewable and renewable resources
- What type and amount of resources we use in our everyday life
Synthesis
Hopefully, having a better understanding of the material and resources we use will give you a better understanding of current issues including the importance of resource conservation, alternative resource use, and what it means to live sustainably.
Contributors and Attributions
CC licensed content, Original
- Authored by : Kimberly Schulte and Lumen Learning. Provided by : Lumen Learning. License : CC BY: Attribution


3.1.7: Summary
3.1.2 Overview of the Entrepreneurial Journey
As you prepare for your journey into entrepreneurship, it is critical to consider the multiple aspects associated with preparing for, experiencing, and completing a journey unique to you. The key is an honest and introspective assessment of how you can make a journey that brings your desired outcomes and results. The seven steps outlined in this section will provide you with a perspective of what you might encounter on your entrepreneurial venture.
3.1.3 The Process of Becoming an Entrepreneur
The entrepreneurial process provides a flexible guideline for launching a venture with an individualized approach. This process should be a fluid, not static, exercise that adjusts to market needs and demands until you achieve an appropriate fit to reap the rewards of your investment. The material in this section will be covered in greater depth as you progress through the rest of the chapters. For now, gaining a perspective on the entire process provides you with a background understanding of what an entrepreneurial venture involves, from ideation through creating the venture to harvesting the venture with the potential to begin the process all over again with a new idea.
3.1.4 Entrepreneurial Pathways
Your pathway to entrepreneurship might arise out of necessity, opportunity, or a combination of situations. Being open to the idea of becoming an entrepreneur provides you with the potential to identify a unique opportunity that fits your interests and goals. Entrepreneurs learn to recognize when an opportunity presents itself and how and when it fits with their goals and dreams.
3.1.5 Frameworks to Inform Your Entrepreneurial Path
You can connect your background, training, and discipline with your entrepreneurial pathway by using frameworks that capture your developmental activities. To achieve your goals, you need some type of plan that outlines the steps you need to take to reach them. Just as there are many types of ventures, there are many versions and types of plans and tools that can assist you in developing the plan that best fits you. As more global issues and opportunities continue to arise, many different types of entrepreneurs have emerged, offering innovative solutions. The diversity of entrepreneurial types provides unique niches for opportunities that might not fit the mainstream or traditional route to entrepreneurial success.


20.1: Introduction
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- Miranda Banks & David Hesmondhalgh
- University of California Press
Across the world, trade unions have played a major role in efforts by workers to improve their conditions, defend their rights, and promote social justice in people’s working lives. Yet in the recent “turn to labor” in media and cultural studies, there has been little sustained consideration of unions. 1 The collective action and bargaining offered by unions are crucial in providing a means of limiting the problematic working conditions that, as a number of researchers have shown, are apparent in much media work, in spite of easy and flawed assumptions that the media industries provide high-quality or “easy” jobs. 2 The labor precariousness that is the subject of this collection would be much less likely to prevail in a situation where strong unions were able to negotiate collectively on behalf of workers. In addition, the best trade unions strive to counter inequalities and exclusions based on gender, class, ethnicity, and other dimensions of social power, and these too are real problems in the media industries. Yet many media workers feel uncertain about the value of trade unions, or anxious that affiliation or identification with them will lead to the loss of work. This chapter concerns efforts by professional and trade organizations to defend and improve the rights and conditions of writers as a community of workers in the media industries, both within particular nations and internationally. It explores these issues via a case study of the Writers Guild of America (WGA).
However, our concerns are not confined to the borders of the United States. We begin by discussing various obstacles and tensions facing organized labor in the media industries. Although here we focus on the United States and the United Kingdom, many of these issues can be found internationally. We then discuss some of the ways these issues have played out historically in the specific example of the WGA, before turning to a recent significant development that raises crucial questions about media labor in an era of internationalization or, as some would have it, “globalization”: increasing efforts by the WGA to work with other writers’ labor organizations abroad, not only to prevent outsourcing of work to cheaper locations (of course a problem in many industries, media and otherwise, in the global era), but also to build solidarity. Yet some of the same problems regarding tensions between solidarity and exclusion, fairness and privilege, can be found in the context of international media labor organization, though with intriguing new dynamics that we explore below. Those new dynamics can be properly understood only when explained in the context of problems facing organized labor in the media industries, and we begin this chapter with a historical perspective on these issues.


1.8: Chapter 1 Review
Chapter 1 Review
- Answers
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Which of the following is a characteristic of people with a growth mindset?
A. They feel challenges help them grow.
B. They fear failure.
C. They feel ability is predetermined.
D. They give up easily.
Which of the following is a characteristic of people with a fixed mindset?
A. They liked to be challenged.
B. They embrace change.
C. When things get hard, they give up.
D. They believe you can always improve yourself.
Grit involves:
A. Passion
B. Perseverance
C. Determination
D. All of the above
The SMART Decision Making Process can help you to:
A. Systematically think through each decision
B. Set goals
C. Evaluate your progress in school
D. Determine if you have a growth or fixed mindset
The last step in the SMART Decision Making Process is:
A. Reflect
B. Take Action
C. Measure
D. Assess
Answer Key: 1, A: 2, C: 3,D: 4, A: 5, B