13.1: What Is a Database?
By the end of this section, you will be able to:
- Discuss how databases are used in organizations
- Compare and contrast the features of a relational database system with other types of databases and data storage
- Describe the objects in a relational database
- Evaluate applications of relational database management systems in organizations
Data—bits of information about people, places, and things—is a key part of the world of business and technology. It can take the form of words or numbers and is frequently collected without active individual involvement. For example, the internet is constantly collecting information on what consumers look at, click on, and read. This information is then often passed on to a database or even parsed out to several databases. Other technology, including sensors and the so-called Internet of Things, is also constantly recording and storing data for businesses to use in a myriad of ways.
One of the challenges of managing and analyzing data is understanding what data is, what it can be, and how it can transform the world around us. Data on its own is not valuable or actionable. To make a difference, data needs to be processed and organized to give it context. When this occurs, we have information. Then, knowledge is generated from data that has been transformed into information and then finally analyzed in a way to give meaning and draw conclusions about the data.
No matter how much data is collected, it is useless without organization and structure.  If those things were collected but had no structure (imagine bits of paper with single words or numbers thrown into a pile), you would not be able to make sense of them. Since the value of data lies in its ability to inform decisions and help us understand the world, both past and present, the structure and storage of data are critical.
A database stores a large amount of data in an effective way that will allow for efficient retrieval in a computerized environment. Databases may be physical objects, such as address books or file folders, each of which provides a place to keep data in an organized fashion so we can quickly locate what we need. Physical storage has limits, however, because its structure is easily overwhelmed when datasets get too large, and retrieval of meaningful information becomes impossible.
A digital database is a computerized file that not only stores data in a structured or organized way but also allows users to make changes to transform data. Digital databases are often contained within a program such as Access on a desktop computer or Microsoft Azure or an structured query language (SQL) server at the companywide level. Digital databases add new features and capabilities to business decision-making by combining the power of analytics with the structure of tables and rows.
Mac Tip
Access is only available on desktops and laptops with a Windows operating system. It is not available on Mac, Chrome, or Linux devices. Mac has a comparable desktop/laptop database called FileMaker.
Digital databases provide structure, organization, and access. But unlike physical objects, they provide a flexible structure that enables us to capture, store, and organize large, complicated sets of data, and that also gives us options for retrieving and using information. Using digital databases enables users to transform data, creating new ways of informing decisions. Because businesses must make decisions based on data every day, the key to good decision-making is creating a database that contains accessible, organized, actionable data.
The Role of Databases in an Organization
Databases drive nearly all business functions in organizations throughout the world. Any business that uses the internet has a digital platform or foundational technology that is built on databases. A digital platform is a place where users can interact with and explore the products and services offered by a company. Digital platforms often come in the form of an app, website, or social media. The term database is ubiquitous in organizations, where you can assume that every function and every employee or customer are interacting with many databases.
Organizations use databases to store information about customers, employees, vendors, products, supply chain, transportation, maintenance, sales, inventory, and much more. Anywhere an organization is working with data, some type of database will be involved. Often the database is the foundation for the work, and the people who interact with the database may not even be aware that it is there.
Data in organizations comes from a variety of inputs, such as from direct input by employees or customers. Some examples include entering new customer information, recording human resources information, creating maintenance requests, purchasing goods for company use, and engaging in sales transactions. Data can also come from technology that records information related to the business—for example, technology that tracks items such as inventory levels, building management (temperature, air quality, occupancy), traffic patterns (employee use of resources), resource use by customers, and customer contact (frequency and method of contact, as well as the results).
Sales and marketing departments collect a great deal of data about their operations and customers. In addition to typical customer information and sales history, a business is also likely to look at daily performance data on marketing and sales operations. This can include sales force performance, customer service, and experience data; social media promotion; and web platform performance. Automatic data collection tends to generate a very large quantity of data that needs to be connected (or related) and then aggregated (or summarized) to be understandable and useful.
Businesses also capture public data from other sources. For example, sales and marketing departments need to look at public data, which is available from the government and other organizations. Public data includes demographics and financial information and may even include climate change and environmental data that affects how businesses work. These datasets are free, very large, constantly changing, and challenging to locate and use. A clear plan for identifying and using this data benefits a sales and marketing department.
All of this data has to go somewhere, and that is the digital platform and the databases it comprises. It is not enough to have data—data needs to be organized to be useful. Since data is key to decision-making and action in most organizations, the digital platform is mission critical.
Data Collection and Storage in Organizations
In a typical business, a production database contains live data that the business uses to produce transactions such as customer requests, inventory management, and sales transactions. Because production databases are in constant use, they should not be used for testing or analysis. Any change to a production database makes the system unavailable for some period of time, which is not desirable when the database is the interface between the company and its customers, suppliers, and other important people outside the company. Instead, when an organization needs to work with a production database, it moves its data to either a development database (used for testing) or an analytical database (used for analysis).
One of the best practices for working with databases is that users do not work directly with the production system—that is, the production database containing the live data that actively run the business. But why? It seems that working directly with the production system would be the most efficient choice. In this case, however, following best practices prevents users from making mistakes that can seriously compromise the business. “Don’t work with the production system” is an ethical issue—part of the code of conduct that all analysts are expected to follow. Watch this video using a case study to discuss this problem to learn more about why this has become a standard in database work.
Access is a desktop-based relational database program that can be used to work with a wide variety of data quickly and easily, regardless of its source. Users can request data from the department in charge of the data warehouse, which is a type of data management system that businesses use, then download the dataset to work with to provide actionable information. Let’s see how this might look at WorldCorp.
John works as a data analyst for WorldCorp. The company has a robust data warehouse that stores vast amounts of customer data, sales records, and inventory information. The data warehouse is managed by the Data Management Department (DMD) within WorldCorp. (Other companies may choose to contract out their data management department to a third party.)
John is tasked with analyzing the sales trends of a particular product category to identify potential areas for improvement. To do so, he needs access to a specific dataset from the data warehouse. John follows the established procedure and sends a formal request to the DMD, specifying the dataset he requires and providing relevant details about his analysis objectives. The request outlines the specific parameters, such as the time frame, region, and product category of interest.
Upon receiving the request, the DMD acknowledges John’s inquiry and begins processing it. They retrieve the requested dataset from the data warehouse, ensuring that it contains the relevant information needed by John to perform his analysis. After completing the data retrieval process, the DMD notifies John that the dataset is ready for download. John receives an email with a link to access the dataset securely.
John clicks on the provided link, which directs him to a secure portal where he can download the dataset. He verifies his credentials and proceeds to download the dataset onto his local machine. With the dataset now available on his computer, John starts working with the data using specialized analysis tools. He cleans the dataset, performs statistical analyses, and generates insightful visualizations to gain a better understanding of the sales trends in the specified product category.
After extensive analysis, John identifies certain regions where the product category is underperforming. He also discovers opportunities for strategic marketing campaigns and potential adjustments to the product assortment. John compiles his findings into a comprehensive report, highlighting actionable insights and recommendations based on the analysis of the downloaded dataset. He presents this report to the company’s management team, enabling them to make informed decisions to improve the performance of the product category.
In this example, the user (John) requests data from the department in charge of the data warehouse (DMD), downloads the dataset, and uses it to generate actionable information through analysis.
Data can come in a variety of formats and configurations. The way in which data is stored can affect how the data can be used, so it is important that a business carefully consider how its data will be stored. There are advantages and disadvantages to each storage medium, but based on the type and volume of data being stored, some storage formats are more suitable than others.
Data Warehouses
When we discuss data storage, we are typically talking about the data warehouse —a data management system that stores and manages data, especially data related to business intelligence operations and activities. Data warehouses are built for storage, accessibility, and retrieval, as Figure 13.2 illustrates, and often integrate data from a variety of sources within the organization. You may also hear the term data mart , which is a subset of the data warehouse that is optimized for specific workgroups or functions. Typically, data flows into the warehouse on a predetermined schedule, adding to the existing data available for analytical work.
A data warehouse is also a type of database, but it differs from the type of database you will use in Access. As an organization’s central data repositories, data warehouses hold a lot of information and use a complex structure. Typically, a department or team will include someone who is trained to interact with the data warehouse, using business intelligence tools or other analytics technology. That employee can then use Microsoft products such as an Access database or an Excel spreadsheet for analysis and preparation for management to aid in decision-making.
Flat Files
Many businesses store their data in flat files —individual files that have a tabular structure, including single spreadsheets, other tables, and stand-alone lists of information. Flat files have no set links to other information. In fact, if there are any links, they will be obvious to employees but typically not in documents or parts of the file itself. Flat files tend to look like tables, with headers at the top and a row representing each record, as Figure 13.3 shows.
Flat files are easiest to use when datasets are small and when the individual using them understands the data well. But even flat files that are quite large, containing thousands or hundreds of thousands of records, can be usable if all records follow a consistent pattern. Flat files are typically created by departments and individual employees in the course of their work, and most organizations have a huge number of these files, which are stored on personal computers and may not be updated or even available beyond the person who created them. In this way, they are a form of dark data —data that is not used or actionable for the organization.
Flat-file databases are also used in other ways, including the transfer of information from one system to another. For example, suppose a sales organization wants to examine inventory records from a warehouse. In this case, the warehouse may send them a flat-file database that follows a uniform pattern, with columns for fields and rows for records. This type of flat file merely stores information; it does not have an indexed system or any links to other systems, and it is typically in a text format. Common examples of file formats that contain plain text include CSV (comma-separated values, where data items are separated by commas), txt (text, where items are separated by space in the file), or tsv (tab-separated values, where items are separated by tabs). Often businesses must consider the other systems that their database will interact with before deciding on a data format. Plain text is one of the most universally supported formats for data, making it simple to move data between business systems.
Relational Database Management Systems
The power in a digital database comes from the ability to connect data from one area to another. A relational database management system (RDBMS) is software that houses, manages, accesses, and retrieves data in its database. The term relational refers to the way that data links together by creating relationships between the tables that hold the data itself. In this way, relational databases can hold much more information that is complex and yet easily accessible.
There are many different types of RDBMS in use today. Access is a desktop system that holds information that is typically generated in other, larger database systems running on dedicated database infrastructure servers. For example, a data analyst might use Access at their computer at their desk at headquarters but will pull the data from the more powerful relational database systems running in WorldCorp’s dedicated data center. Still, Access is also an RDBMS, with the power to manage relationships between tables, making it possible to create complex reports.
A relational database is a type of database that stores and provides access to data. Relational databases hold a collection of items, with preset relationships between them. Sometimes people use data, database, and relational databases interchangeably, though you may need to pay attention to context to understand if a person is talking about the data, the database, or the system itself.
A relational database and RDBMS are designed to give structure to data and to ensure that data is stored and used effectively. Examples of large-scale RDBMS include MySQL , IBM DB2 , Oracle DB , and Microsoft SQL Server . Although each of these larger databases support querying and generating reports, in many small to medium-sized businesses, data is often exported and brought into an Access relational database for further refinement, analysis, and reporting or brought into Microsoft Excel for more complex statistical analysis.
Relational databases, running in an RDBMS, allow us to join or connect tables, perform complex analysis, and run reports efficiently. A join is a function within an RDBMS that sets up the relationship between records in two tables. In a data warehouse environment, relationships (or joins) that connect tables make it possible to store vast quantities of data and still be able to retrieve them quickly and efficiently.
Access, as a desktop RDBMS, uses the same idea of connecting tables through joins to make data retrieval quick and efficient and has the added benefit of using a graphical user interface. To work with data in Access, you do not need to know a language such as Java, Python, R, or SQL. Since we often need to analyze information from a larger data store, like the data warehouse, being able to work with relationships makes it possible to efficiently access information from multiple parts of the database.
Storing Data in an RDBMS
An RDBMS stores data in a database, which is a series of connected tables. The RDBMS provides the software and system structure for the data; the database is the holding area of the data. In practice, the term database is usually used for both of these, but it is important to understand that the data is separate from the program housing it. As a result, you can move data from one software to another program, such as from Access to Outlook or Word for communication distribution.
A database can hold a variety of data types in its data tables. A relational database that uses structured data can recognize and process data based on its type; for example, it can understand the difference between text and numbers and process them accordingly. Data types in Access are shown in Table 13.1.
| Data Type | Description |
|---|---|
| Text | Alphanumeric data (in either short or long format) |
| Number | Numerical data |
| Date/time | Date and time |
| Currency | Monetary data with four decimal places |
| Aut\nonumber | Unique value set by Access |
| Yes/No | Data stored as yes/no (true/false) |
| OLE object | Pictures, graphics, or other files that are stored |
| Hyperlink | Link to a document (online, local computer, or network) |
| Attachment | Full file attachment stored in the database |
| Calculated | Mathematical expression (or calculation) |
| Lookup Wizard | Field that uses the contents of another table to populate the field |
Data Manipulation
One of the strengths of a database is that it enables users to manipulate data, changing it in a way that makes the data more useful and actionable. An example of data manipulation is the creation of new fields based on combining and calculating existing fields within the database. WorldCorp often manipulates its data as new products are added to its portfolio or old products are updated with new features. Data manipulation allows users to set up the data in a way that helps them and their audience make sense of it and transform it into business intelligence.
Objects and Relationships
Objects and relationships are key concepts in a database. Objects are the items that make up a database, including tables, queries, forms, and reports. Relationships link objects together in the database, as Figure 13.4 illustrates, which in turn improves the performance of the database itself.
A database object is used to store, reference, or interact with the database. There are four main types of objects in an Access database:
- Tables: the structures that hold individual data records
- Queries: structured data requests
- Forms: formatted screens for inputting or viewing data
- Reports: formatted summaries of specific information in the database
A relationship (also known as a join ) tells the database that two records have a connection. This means we can break up a table into many tables, which in turn keeps screens manageable and speeds up processing. Relationships are created by using a key field , which is a field in a table that serves as a unique identifier for an individual record in a table. For example, in a database about employees, an employee ID number would be a key field and would act as the link between tables that hold employee information, payroll information, and even performance information in a sales department. Instead of trying to hold all this data in one extremely large table, we can have many smaller tables, each specializing in a particular type of data and linked to other tables by key fields, such as primary or foreign keys.
Tables
Tables hold the data within a database organized into rows and columns in two dimensions. A table consists of columns, each of which is a field, and rows, each of which is a record. The column or field names apply to each record in the table and create the structure the database uses to organize information. A database can include many tables that are joined together by relationships between fields. This structure makes relational databases fast and efficient when retrieving data.
Each table typically contains a key field. A primary key field is a unique field in the table, which serves as a unique identifier for the individual record you are looking at. A table can also have a foreign key field , which refers to the primary key field in another table. For example, an invoice number for a sales record is a primary key field—it is unique—but it can also appear as a foreign key field in other tables. In this way, the primary key field prevents duplication in a sales invoice table and also provides a link to the sales invoice list as a foreign key when it appears elsewhere in the database. In Access, primary key fields have an image of a key next to them when viewed in Design View, as shown in Figure 13.5.
Key fields make it simple to gather useful information about a single data point from multiple tables. WorldCorp might use a model number as a key field in a database that stores the features, availability, and price of their products. In another database, WorldCorp can use a customer identification number to track various customer metrics such as location, purchase history, and contact information across various tables.
Queries
In a large database, it can be difficult or even impossible to find the information you need by simply scrolling through the records. It is even more difficult when a database contains many tables linked by joins. Instead, you can design or build a query , a structured request that allows you to set up criteria instructing the database to return what you are looking for.
For example, suppose your boss at WorldCorp asks you to gather sales transactions on a specific date or all transactions for a certain dollar amount. Or you might want to be more specific, asking for all sales of a specific product in a specified time period that exceeded a certain dollar amount. In each case, you can use queries to ask the database to provide the information you need. In many relational databases, structured query language (SQL) is used to create and run queries. SQL is a system of written commands used to manipulate data in a database; it was developed by IBM in the 1970s to allow its engineers to interface with database systems more efficiently. SQL is in Access; however, users can create queries without knowing SQL.
Forms
A form is a database object that simplifies the use of information within the database. A form creates a user interface—a way for individuals to interact with the database—without directly using the table, which can be slow, overwhelming, and risky (because data in the table can be inadvertently changed). A form can be used to input information into a database (e.g., new customer information that customers enter themselves). A form can also be used to retrieve information (e.g., when a customer service representative needs to look up a specific customer record to resolve an issue). Examples of sales forms include customer information, sales invoices, and sales records.
Reports
A report is a formatted output of a database, ready for use and action. A report summarizes data in a way that matches the needs of the audience. For example, a product listing on a website or in print is a format ready for presentation to a customer or someone else who needs to see all products at a glance. A listing of sales, summarized by month, is also ready for presentation if the audience needs to know monthly sales figures for a decision or action. Reports are typically one of the final outputs of a database, as they are directly linked to the actionable goal or business intelligence activities of a specific workgroup, team, or project. An example of a sales report may cover sales by product or sales over a time period, such as a month or year.
Applications of RDBMS
Databases offer unique functionality that goes beyond the calculations and statistics provided by other programs such as Excel. This is because of the RDBMS functionality. A relational database provides structure for data, includes relationships that connect pieces of data in meaningful ways, and allows controlled access through queries, forms, and reports. Because of this advanced functionality, RDBMSs are used in a variety of use cases across multiple industries.
As organizations work to transform themselves to meet the needs of the twenty-first century, companies are shifting how they view customers, employees, and work in general. Databases play an integral role in this shift. Digital transformation relies on data, and for companies to transform, they need not only good data but actionable data, available when they need it, where they need it. The core of this change is the data management system, and an organization’s data landscape is a constantly growing and evolving part of the business plan. Since the digital transformation of a business or organization is about leveraging technology to change the way a business is run, an organization’s collection and use of data is an ongoing process, with the focus on people—not technology—and how we enable people to be more innovative, responsive, and successful.
Large organizations typically collect data through transactions and sensors, which then store the data. Eventually, data is transferred to a data warehouse, which stores data for historical purposes. From the data warehouse, organizations can bring datasets to a relational database such as Access for analytics and use. Data warehouses and Access are built on relational database models, which provide benefits, including the following:
- Data accuracy: The use of primary and foreign keys improves accuracy.
- Easy access to data: Data is held in tables that are easily accessed through queries, improving speed and efficiency.
- Flexibility: A RDBMS easily scales to include more data and tables as needed by the organization, without affecting the existing structure or the data in the database.
- Security: Because data is held in separate tables, it is possible to create a variety of user roles and permissions, allowing individuals to access some data without needing full system access.
- Adaptability: Databases can be easily modified as business requirements change.
Because data in an organization is created in production systems and then brought to the analytical system for work, an RDBMS focuses on keeping the data organized and ready for retrieval. The RDBMS also allows the analyst to create database objects that make working with the data more accurate, effective, and efficient.
Examples of Database Use
How do companies apply the information they get from databases? They do so in many ways, most commonly through their marketing and customer service initiatives, for example. WorldCorp’s Sales and Marketing Department depends on databases to inform marketing strategy and customer service processes and procedures and to understand sales trends and future opportunities.
Example: Marketing Strategy
Recall that WorldCorp manufactures health-care products. Its leadership has been looking at their online promotion of allergy medications. They have a variety of advertisements online, served by social media platforms. While they can easily look at the data to see the click-through rate (which is the number of times a consumer clicks an online ad in relation to how many times the ad is shown) and the purchase rate on specific partner sites, they also want to know if they can better understand the customers who are considering purchasing but have not yet done so.
Using the data warehouse, you as the WorldCorp employee can request a report of all shopping carts that were populated with a particular medication from an online shopping site partner. Since the data warehouse stores both the WorldCorp information and key information on sales from major partners, you are able to ask for a year’s worth of sales data, with customer demographics including location, family structure, and other related purchase information such as, say, other antihistamine and allergy comfort items. You receive the data, import it into Access, analyze it to identify who was likely to add the item to the cart and what they did after placing it in the cart (purchase the item, purchase something else, or another action), and prepare this data for the strategy meeting.
Example: Customer Service
WorldCorp supplies medication to its vendor partners, including online distributors (both over-the-counter and online pharmacies) and physical distributors, as well as health-care organizations. They are looking to improve the customer experience for their vendors. Now you are the analyst working with the customer service team in the Sales and Marketing Department. You need to understand where vendor needs pain points are to prepare a report for the leadership team. You request a list of all vendor support contacts, which includes the vendor name and contact information, the request itself (including date, time, and method of request), and the resolution. You analyze them to determine the most common types of questions and requests, where these requests originate from, and how they were resolved. You use the dataset to create a report for the leadership team that summarizes and highlights the top issues over the past eighteen months.
Example: Sales Trends
Next, the sales team at WorldCorp is looking at where to focus their attention for the upcoming year in terms of promoting their medication for obstructive airway diseases such as chronic obstructive pulmonary disease. The team wants to identify areas in the world where their medications may be needed and prepare for the demand. Working with their public health experts, they know that obstructive airway diseases are more common in people who smoke or breathe in secondhand smoke or who live in areas with high pollution. They also learn that people are often over age 40 years when symptoms appear, that asthma increases the chances of developing these diseases, and that they occur more commonly in individuals with certain jobs or who have had a high number of respiratory infections in childhood.
You, again as the business analyst, want to identify the geographic areas that are most likely to increase the risk of obstructive airway diseases and look at sales trends in these areas over the past five years. You work with the Data Science Department to ensure that the public data that WorldCorp has available and the internal sales data (including the data from the vendor) are available. You then create reports that show specific geographic areas and risks and the sales trends for these areas over the past five years.
NoSQL Databases
In addition to Microsoft Access and other databases that define the relationships between data stored in them, which are the main topics of this chapter, there are other ways that organizations can capture and store data: nonrelational database s. A NoSQL database (NoSQL stands for “not only SQL”) stores data in a different way than the databases we are discussing in this chapter. A NoSQL database, also known as a nonrelational database, is a type of database management system that provides a mechanism for storing and retrieving data that is different from traditional relational databases. Unlike relational databases, which store data in structured tables with predefined schemas, NoSQL databases store data in a variety of ways and are designed to handle large volumes of unstructured or semistructured data. NoSQL databases have gained popularity due to their flexibility, scalability, and high performance.
NoSQL databases often store documents and images and manage large amounts of data in their original formats, rather than in tables; this is also known as unstructured data. NoSQL tends to be used when an organization needs to store huge volumes of both structured and unstructured data and also needs the ability to quickly develop and scale data initiatives. Scaling data initiatives is the process of expanding and advancing data-related projects, strategies, and operations to handle larger volumes of data, accommodate increased complexity, and support the growing needs of an organization. It involves implementing measures and techniques to effectively manage, process, and analyze data on a larger scale, often in terms of volume, velocity, and variety. For example, WorldCorp uses a NoSQL database to record logistics for shipping its products. Because the data involved with logistics has unique structure and is greatly varied, a NoSQL database is an ideal candidate for managing this data.
Data Lakes
You may also hear about data lakes in your organization. A data lake is a centralized repository that allows for the storage and analysis of vast amounts of diverse data in its original, raw, unprocessed format. A data lake can store both structured and unstructured data and make it available for use and analysis as needed. In a data lake, data is collected from various sources, such as databases, applications, sensors, social media feeds, and more, without the need for up-front structuring or transformation. This raw data is stored as is, preserving its original format and granularity. This includes structured data (e.g., relational tables), semistructured data (e.g., JSON, XML), and unstructured data (e.g., text documents, images, videos). Data lakes offer several advantages, including the ability to store and analyze large volumes of diverse data, support for flexible data exploration and discovery, and the potential to uncover valuable insights and patterns. However, they also present challenges related to data quality, data integration, and ensuring proper governance practices, as the raw, unstructured data may require additional effort for data preparation and cleansing.
Although many organizations use NoSQL databases and data lakes, RDBMSs are still the most common type of databases used to power transactional systems, such as managing and tracking customer profiles at WorldCorp. At present, Access does not have a built-in mechanism to directly interface with NoSQL systems or data lakes, although data that comes from a NoSQL database or data lake can be formatted and sent to you for analysis.


1.4.1: Introduction to Hazards of Chemistry
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Hazards Introduction
What we as a population must realize is that no substance in and of itself is a poison or a remedy. It is the dosage that defines the activity of the substance. For example, let’s look at the concept of “hormesis” as a precursor to the concept of poison/remedy by dosage.
We all have heard at one time or another the phrase, “What doesn't kill you makes you stronger”. This phrase contains truth and contains at its essence the theory of hormesis: when organisms are exposed to low levels of stressors or toxins, they become more resistant to larger levels of stressors or toxins. This theory has been met with skepticism. Recently, however, biologists have put together a molecular explanation of its function and it has finally been accepted as a fundamental principle of biomedicine.
For example, exposing mice to low levels of gamma ray radiation before irradiating them with high levels actually decreases their likelihood of cancer. Similarly, when dioxin is given to rats we find the same situation. However, the biochemical mechanisms are not well understood. It is believed that a low dose of a toxin can trigger repair mechanisms that are efficient enough to not only neutralize the toxin, but repair other defects not caused by the toxin.
Thus, hormesis is nature’s way of dealing with harmful agents; in fact, antibodies are a natural consequence of hormesis. However, the toxins/poisons that were once absolute, are NO LONGER. For example, thalidomide was found to be a very dangerous chemical for embryo development, but has recently found great promise in a number of ailments according to the Mayo Clinic including HIV, skin lesions, and multiple myeloma (please see: http://www.mayoclinic.org/diseasesco...e/art-20046534 ). Such a fact is outstanding considering the horrific aftermath (a few photographs shown below(Figure \(\PageIndex{1}\)) of its use in the middle part of last century:
In fact, the list of former “pure” toxins is extremely interesting: snake venom, bacteria (botulin), fungi (penicillin), leeches (Hirudin), maggots (gangrene), etc. The toxic aspect notwithstanding, we all live in the wake of a world and society that is rife with potential hazards.
Types of hazards
A hazard is “threat” to life, health, property, or environment. These can come in many forms, but they are classified according to their modalities or nature of operation. The modalities of hazards are the following:
- Dormant: Has the potential, but nothing currently can be affected. This modality is typified by the “volcano” scenario – a volcano that is no longer showing any signs of activity or imminent threat but is lying “dormant”. There is no immediate and pressing issue based on human perception.
- Armed: Has the potential, and something can be affected. This modality is given by a person holding a gun in the midst of a war or other aggressive situation. The gun has the potential to affect life, limb, or other vital function, but it is not yet doing so, although the intention is there
- Active: Currently on-going event (something is being affected). Finally, this is the modality that is actually affecting life, limb, or some other vital function. A volcano that is spewing, a gun that is being fired, a fire that is consuming a building, radiation that is leaking, etc. These are the situations that are causing harm.
Within these modalities of hazards, hazards can be further refined as to their types. The following types of hazards classify the threats to life:
- Physical: Condition or situations that cause the body physical harm, e.g., a bullet that is entering into a human being.
- Chemical: Substances that cause harm or damage to the body, property or the environment, e.g., liquid oxygen converting to gaseous oxygen within a closed container (bomb).
- Biological: Biological agents that cause harm to the body, e.g., anthrax bacteria.
- Psychological: Stress affecting the mental state, e.g., the knowledge that the trajectory of a fivemile wide asteroid coincides with earth.
- Radiation: Electromagnetic radiation that harms or damages biological organisms.


27.3.5: Lvalue and Rvalue
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Overview
Some programming languages use the idea of l-values and r-values , deriving from the typical mode of evaluation on the left and right hand side of an assignment statement. An lvalue refers to an object that persists beyond a single expression. An rvalue is a temporary value that does not persist beyond the expression that uses it. [1] .
Discussion
Lvalue and Rvalue refer to the left and right side of the assignment operator. The Lvalue (pronounced: L value) concept refers to the requirement that the operand on the left side of the assignment operator is modifiable, usually a variable. Rvalue concept pulls or fetches the value of the expression or operand on the right side of the assignment operator. Some examples:
age = 39
The value 39 is pulled or fetched (Rvalue) and stored into the variable named age (Lvalue); destroying the value previously stored in that variable.
voting_age = 18 age = voting_age
If the expression has a variable or named constant on the right side of the assignment operator, it would pull or fetch the value stored in the variable or constant. The value 18 is pulled or fetched from the variable named voting_age and stored into the variable named age.
age < 17
If the expression is a test expression or Boolean expression, the concept is still an Rvalue one. The value in the identifier named age is pulled or fetched and used in the relational comparison of less than.
JACK_BENNYS_AGE = 39 JACK_BENNYS_AGE = 65;
This is illegal because the identifier JACK_BENNYS_AGE does not have Lvalue properties. It is not a modifiable data object, because it is a constant.
Some uses of the Lvalue and Rvalue can be confusing in languages that support increment and decrement operators. Consider:
oldest = 55 age = oldest++
Postfix increment says to use my existing value then when you are done with the other operators; increment me. Thus, the first use of the oldest variable is an Rvalue context where the existing value of 55 is pulled or fetched and then assigned to the variable age; an Lvalue context. The second use of the oldest variable is an Lvalue context wherein the value of the oldest is incremented from 55 to 56.
Key Terms
- Lvalue
- The requirement that the operand on the left side of the assignment operator is modifiable, usually a variable.
- Rvalue
- Pulls or fetches the value stored in a variable or constant.


7.8: Use of Force During Arrest
Police officers have the power to use force if deemed necessary. If an officer uses more force than required for the situation, this brings up many red flags. The Violent Crime Control and Law Enforcement Act of 1994 authorized the Civil Rights Division of the U.S. Department of Justice (DOJ) to initiate civil actions against policing agencies if the use of force utilized is excessive or constitutes a pattern of depriving individuals of their rights.
One additional issue in police use of force situations is that it is difficult to measure. There are many types of force police can use. The force utilized varies from going hands-on to pepper spray, taser, ASP baton, control holds or takedowns, to deadly force. Every situation is different because it involves human beings and can be interpreted differently from those involved to those standing on the sidelines.
Vehicle Pursuits
Vehicle pursuits have dramatically changed over the last decade. It used to be commonplace for officers to engage in several vehicle pursuits during one shift. Officers would get in a vehicle pursuit for many reasons, stemming from locating a rolling stolen vehicle to a driver failing to stop after running a stop sign. Vehicle pursuits have at a minimum, two four-to-five thousand-pound deadly weapons (a.k.a., the vehicles) that are driven recklessly (most times), chasing one another. The morgue has seen large numbers of fatalities due to vehicle pursuits. Victims range from an innocent person in a crosswalk at the wrong time when the vehicle police were pursuing hit the victim, or the innocent person driving across an intersection with a green traffic light struck while the pursuing vehicle runs a red traffic light. There are many sad stories of the innocent victim killed because the police decided to pursue a vehicle with lights and sirens when the vehicle being pursued refused to pull over.
Because of the many senseless fatalities, many police departments have updated their vehicle pursuit policies and procedures. Although the policies of each department do differ in minor areas, most departments have chosen to only approve a vehicle pursuit in dire situations. Such a situation fitting that description would be if the driver of the fleeing vehicle were actively engaging in behavior that was placing other citizens in immediate dire harm.


2.5: The Transpose
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Another important operation on matrices is that of taking the transpose . For a matrix \(A\), we denote the transpose of \(A\) by \(A^T\). Before formally defining the transpose, we explore this operation on the following matrix.
\[\left[ \begin{array}{cc} 1 & 4 \\ 3 & 1 \\ 2 & 6 \end{array} \right] ^{T}= \ \ \left[ \begin{array}{ccc} 1 & 3 & 2 \\ 4 & 1 & 6 \end{array} \right] \nonumber\]
What happened? The first column became the first row and the second column became the second row. Thus the \(3\times 2\) matrix became a \(2\times 3\) matrix. The number \(4\) was in the first row and the second column and it ended up in the second row and first column.
The definition of the transpose is as follows.
Definition \(\PageIndex{1}\): The Transpose of a Matrix
Let \(A\) be an \(m\times n\) matrix. Then \(A^{T}\), the transpose of \(A\), denotes the \(n\times m\) matrix given by
\[A^{T} = \left[ a _{ij}\right] ^{T}= \left[ a_{ji} \right]\nonumber \]
The \(\left( i, j \right)\)-entry of \(A\) becomes the \(\left( j,i \right)\)-entry of \(A^T\).
Consider the following example.
Example \(\PageIndex{1}\): The Transpose of a Matrix
Calculate \(A^T\) for the following matrix
\[A = \left[ \begin{array}{rrr} 1 & 2 & -6 \\ 3 & 5 & 4 \end{array} \right] \nonumber\]
Solution
By Definition \(\PageIndex{1}\) , we know that for \(A = \left[ a_{ij} \right]\), \(A^T = \left[ a_{ji} \right]\). In other words, we switch the row and column location of each entry. The \(\left( 1, 2 \right)\)-entry becomes the \(\left( 2,1 \right)\)-entry.
Thus, \[A^T = \left[ \begin{array}{rr} 1 & 3 \\ 2 & 5 \\ -6 & 4 \end{array} \right] \nonumber\]
Notice that \(A\) is a \(2 \times 3\) matrix, while \(A^T\) is a \(3 \times 2\) matrix.
The transpose of a matrix has the following important properties.
Lemma \(\PageIndex{1}\): Properties of the Transpose of a Matrix
Let \(A\) be an \(m\times n\) matrix, \(B\) an \(n\times p\) matrix, and \(r\) and \(s\) scalars. Then
- \[\left(A^{T}\right)^{T} = A\nonumber \]
- \[\left( AB\right) ^{T}=B^{T}A^{T} \nonumber\]
- \[\left( rA+ sB\right) ^{T}=rA^{T}+ sB^{T} \nonumber\]
- Proof
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First we prove 2. From Definition \(\PageIndex{1}\) ,
\[ \begin{aligned} \left(AB\right)^{T} &= \left[ (AB) _{ij} \right] ^{T}=\left[ (AB)_{ji} \right]=\sum_{k}a_{jk}b_{ki}= \sum_{k}b_{ki}a_{jk} \\[4pt] &= \sum_{k}\left[ b_{ik}\right]^{T}\left[ a_{kj}\right]^{T}=\left[ b_{ij}\right] ^{T} \left[ a_{ij}\right]^{T} = B^{T}A^{T} \end{aligned}\]
The proof of Formula 3 is left as an exercise.
The transpose of a matrix is related to other important topics. Consider the following definition.
We will explore these definitions in the following examples.
Example \(\PageIndex{2}\): Symmetric Matrices
Let
\[A=\left[ \begin{array}{rrr} 2 & 1 & 3 \\ 1 & 5 & -3 \\ 3 & -3 & 7 \end{array} \right] \nonumber\]
Use Definition \(\PageIndex{2}\) to show that \(A\) is symmetric.
Solution
By Definition \(\PageIndex{2}\) , we need to show that \(A = A^T\). Now, using Definition \(\PageIndex{1}\) ,
\[A^{T} = \left[ \begin{array}{rrr} 2 & 1 & 3 \\ 1 & 5 & -3 \\ 3 & -3 & 7 \end{array} \right]\nonumber\]
Hence, \(A = A^{T}\), so \(A\) is symmetric.
Example \(\PageIndex{3}\): A Skew Symmetric Matrix
Let
\[A=\left[ \begin{array}{rrr} 0 & 1 & 3 \\ -1 & 0 & 2 \\ -3 & -2 & 0 \end{array} \right] \nonumber \]
Show that \(A\) is skew symmetric.
Solution
By Definition \(\PageIndex{2}\) ,
\[A^{T} = \left[ \begin{array}{rrr} 0 & -1 & -3\\ 1 & 0 & -2\\ 3 & 2 & 0 \end{array} \right] \nonumber\]
You can see that each entry of \(A^T\) is equal to \(-1\) times the same entry of \(A\). Hence, \(A^{T} = - A\) and so by Definition \(\PageIndex{2}\) , \(A\) is skew symmetric.


2.1: Ball Toss Project
Purpose of the project: get familiar with the idea of creating a velocity function based on position data
Above are frames from a video of a simple ball toss. Every other frame from the 30 frames per second video is shown, so the time between the frames is approximately of a second.
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Fill in the position data for each time in the table below. Velocity is usually defined as \(\frac{\text{Position}}{\text{Time}}\). How could you calculate velocities for each data point? Fill these in as well.
Time (s) Position (cm) Velocity (cm/s) \(0\) \(\frac{1}{15}\) \(\frac{2}{15}\) \(\frac{3}{15}\) \(\frac{4}{15}\) -
Create two graphs, either by hand or with graphing software: position versus time, and velocity versus time. In each case, time is the \(x\)-axis, while the \(y\)-axis is position in the first graph and velocity in the second graph. How are the two graphs related?
Going from a position graph to a velocity graph like this is called a derivative , which we’ll talk a lot more about in upcoming chapters.
- While your velocity graph is probably not a perfect line, imagine that it is linear for a second. What is the slope of the velocity graph? This is the rate of acceleration due to gravity, an important quantity in physics.


24.3: Carbohydrate Metabolism
By the end of this section, you will be able to:
- Explain the processes of glycolysis
- Describe the pathway of a pyruvate molecule through the Krebs cycle
- Explain the transport of electrons through the electron transport chain
- Describe the process of ATP production through oxidative phosphorylation
- Summarize the process of gluconeogenesis
Carbohydrates are organic molecules composed of carbon, hydrogen, and oxygen atoms. The family of carbohydrates includes both simple and complex sugars. Glucose and fructose are examples of simple sugars, and starch, glycogen, and cellulose are all examples of complex sugars. The complex sugars are also called polysaccharides and are made of multiple monosaccharide molecules. Polysaccharides serve as energy storage (e.g., starch and glycogen) and as structural components (e.g., chitin in insects and cellulose in plants).
During digestion, carbohydrates are broken down into simple, soluble sugars that can be transported across the intestinal wall into the circulatory system to be transported throughout the body. Carbohydrate digestion begins in the mouth with the action of salivary amylase on starches and ends with monosaccharides being absorbed across the epithelium of the small intestine. Once the absorbed monosaccharides are transported to the tissues, the process of cellular respiration begins (Figure \(\PageIndex{1}\)). This section will focus first on glycolysis, a process where the monosaccharide glucose is oxidized, releasing the energy stored in its bonds to produce ATP.
Glycolysis
Glucose is the body’s most readily available source of energy. After digestive processes break polysaccharides down into monosaccharides, including glucose, the monosaccharides are transported across the wall of the small intestine and into the circulatory system, which transports them to the liver. In the liver, hepatocytes either pass the glucose on through the circulatory system or store excess glucose as glycogen. Cells in the body take up the circulating glucose in response to insulin and, through a series of reactions called glycolysis , transfer some of the energy in glucose to ADP to form ATP (Figure \(\PageIndex{2}\)). The last step in glycolysis produces the product pyruvate .
Glycolysis begins with the phosphorylation of glucose by hexokinase to form glucose-6-phosphate. This step uses one ATP, which is the donor of the phosphate group. Under the action of phosphofructokinase, glucose-6-phosphate is converted into fructose-6-phosphate. At this point, a second ATP donates its phosphate group, forming fructose-1,6-bisphosphate. This six-carbon sugar is split to form two phosphorylated three-carbon molecules, glyceraldehyde-3-phosphate and dihydroxyacetone phosphate, which are both converted into glyceraldehyde-3-phosphate. The glyceraldehyde-3-phosphate is further phosphorylated with groups donated by dihydrogen phosphate present in the cell to form the three-carbon molecule 1,3-bisphosphoglycerate. The energy of this reaction comes from the oxidation of (removal of electrons from) glyceraldehyde-3-phosphate. In a series of reactions leading to pyruvate, the two phosphate groups are then transferred to two ADPs to form two ATPs. Thus, glycolysis uses two ATPs but generates four ATPs, yielding a net gain of two ATPs and two molecules of pyruvate. In the presence of oxygen, pyruvate continues on to the Krebs cycle (also called the citric acid cycle or tricarboxylic acid cycle (TCA) , where additional energy is extracted and passed on.
Interactive Link
Watch this video to learn about glycolysis.
Glycolysis can be divided into two phases: energy consuming (also called chemical priming) and energy yielding. The first phase is the energy-consuming phase , so it requires two ATP molecules to start the reaction for each molecule of glucose. However, the end of the reaction produces four ATPs, resulting in a net gain of two ATP energy molecules.
Glycolysis can be expressed as the following equation:
\[Glucose + 2ATP + 2NAD^{+} + 4ADP + 2P_{i} \rightarrow 2 Pyruvate + 4ATP + 2NADH + 2H^{+} \]
This equation states that glucose, in combination with ATP (the energy source), NAD
The following discussions of glycolysis include the enzymes responsible for the reactions. When glucose enters a cell, the enzyme hexokinase (or glucokinase, in the liver) rapidly adds a phosphate to convert it into glucose-6-phosphate . A kinase is a type of enzyme that adds a phosphate molecule to a substrate (in this case, glucose, but it can be true of other molecules also). This conversion step requires one ATP and essentially traps the glucose in the cell, preventing it from passing back through the plasma membrane, thus allowing glycolysis to proceed. It also functions to maintain a concentration gradient with higher glucose levels in the blood than in the tissues. By establishing this concentration gradient, the glucose in the blood will be able to flow from an area of high concentration (the blood) into an area of low concentration (the tissues) to be either used or stored. Hexokinase is found in nearly every tissue in the body. Glucokinase , on the other hand, is expressed in tissues that are active when blood glucose levels are high, such as the liver. Hexokinase has a higher affinity for glucose than glucokinase and therefore is able to convert glucose at a faster rate than glucokinase. This is important when levels of glucose are very low in the body, as it allows glucose to travel preferentially to those tissues that require it more.
In the next step of the first phase of glycolysis, the enzyme glucose-6-phosphate isomerase converts glucose-6-phosphate into fructose-6-phosphate. Like glucose, fructose is also a six carbon-containing sugar. The enzyme phosphofructokinase-1 then adds one more phosphate to convert fructose-6-phosphate into fructose-1-6-bisphosphate, another six-carbon sugar, using another ATP molecule. Aldolase then breaks down this fructose-1-6-bisphosphate into two three-carbon molecules, glyceraldehyde-3-phosphate and dihydroxyacetone phosphate. The triosephosphate isomerase enzyme then converts dihydroxyacetone phosphate into a second glyceraldehyde-3-phosphate molecule. Therefore, by the end of this chemical-priming or energy-consuming phase, one glucose molecule is broken down into two glyceraldehyde-3-phosphate molecules.
The second phase of glycolysis, the energy-yielding phase , creates the energy that is the product of glycolysis. Glyceraldehyde-3-phosphate dehydrogenase converts each three-carbon glyceraldehyde-3-phosphate produced during the energy-consuming phase into 1,3-bisphosphoglycerate. This reaction releases an electron that is then picked up by NAD + to create an NADH molecule. NADH is a high-energy molecule, like ATP, but unlike ATP, it is not used as energy currency by the cell. Because there are two glyceraldehyde-3-phosphate molecules, two NADH molecules are synthesized during this step. Each 1,3-bisphosphoglycerate is subsequently dephosphorylated (i.e., a phosphate is removed) by phosphoglycerate kinase into 3-phosphoglycerate. Each phosphate released in this reaction can convert one molecule of ADP into one high-energy ATP molecule, resulting in a gain of two ATP molecules.
The enzyme phosphoglycerate mutase then converts the 3-phosphoglycerate molecules into 2-phosphoglycerate. The enolase enzyme then acts upon the 2-phosphoglycerate molecules to convert them into phosphoenolpyruvate molecules. The last step of glycolysis involves the dephosphorylation of the two phosphoenolpyruvate molecules by pyruvate kinase to create two pyruvate molecules and two ATP molecules.
In summary, one glucose molecule breaks down into two pyruvate molecules, and creates two net ATP molecules and two NADH molecules by glycolysis. Therefore, glycolysis generates energy for the cell and creates pyruvate molecules that can be processed further through the aerobic Krebs cycle (also called the citric acid cycle or tricarboxylic acid cycle); converted into lactic acid or alcohol (in yeast) by fermentation; or used later for the synthesis of glucose through gluconeogenesis.
Anaerobic Respiration
When oxygen is limited or absent, pyruvate enters an anaerobic pathway called fermentation. In these reactions, pyruvate can be converted into lactic acid. In addition to generating an additional ATP, this pathway serves to keep the pyruvate concentration low so glycolysis continues, and it oxidizes NADH into the NAD + needed by glycolysis. In this reaction, lactic acid replaces oxygen as the final electron acceptor. Anaerobic respiration occurs in most cells of the body when oxygen is limited or mitochondria are absent or nonfunctional. For example, because erythrocytes (red blood cells) lack mitochondria, they must produce their ATP from anaerobic respiration. This is an effective pathway of ATP production for short periods of time, ranging from seconds to a few minutes. The lactic acid produced diffuses into the plasma and is carried to the liver, where it is converted back into pyruvate or glucose via the Cori cycle. Similarly, when a person exercises, muscles use ATP faster than oxygen can be delivered to them. They depend on glycolysis and lactic acid production for rapid ATP production.
Aerobic Respiration
In the presence of oxygen, pyruvate can enter the Krebs cycle where additional energy is extracted as electrons are transferred from the pyruvate to the receptors NAD + , GDP, and FAD, with carbon dioxide being a “waste product” (Figure \(\PageIndex{3}\)). The NADH and FADH 2 pass electrons on to the electron transport chain, which uses the transferred energy to produce ATP. As the terminal step in the electron transport chain, oxygen is the terminal electron acceptor and creates water inside the mitochondria.
Krebs Cycle/Citric Acid Cycle/Tricarboxylic Acid Cycle
The pyruvate molecules generated during glycolysis are transported across the mitochondrial membrane into the inner mitochondrial matrix, where they are metabolized by enzymes in a pathway called the Krebs cycle (Figure \(\PageIndex{4}\)). The Krebs cycle is also commonly called the citric acid cycle or the tricarboxylic acid (TCA) cycle. During the Krebs cycle, high-energy molecules, including ATP, NADH, and FADH 2 , are created. NADH and FADH 2 then pass electrons through the electron transport chain in the mitochondria to generate more ATP molecules.
Interactive Link
Watch this animation to observe the Krebs cycle.
The three-carbon pyruvate molecule generated during glycolysis moves from the cytoplasm into the mitochondrial matrix, where it is converted by the enzyme pyruvate dehydrogenase into a two-carbon acetyl coenzyme A (acetyl CoA) molecule. This reaction is an oxidative decarboxylation reaction. It converts the three-carbon pyruvate into a two-carbon acetyl CoA molecule, releasing carbon dioxide and transferring two electrons that combine with NAD + to form NADH. Acetyl CoA enters the Krebs cycle by combining with a four-carbon molecule, oxaloacetate, to form the six-carbon molecule citrate, or citric acid, at the same time releasing the coenzyme A molecule.
The six-carbon citrate molecule is systematically converted to a five-carbon molecule and then a four-carbon molecule, ending with oxaloacetate, the beginning of the cycle. Along the way, each citrate molecule will produce one ATP, one FADH 2 , and three NADH. The FADH 2 and NADH will enter the oxidative phosphorylation system located in the inner mitochondrial membrane. In addition, the Krebs cycle supplies the starting materials to process and break down proteins and fats.
To start the Krebs cycle, citrate synthase combines acetyl CoA and oxaloacetate to form a six-carbon citrate molecule; CoA is subsequently released and can combine with another pyruvate molecule to begin the cycle again. The aconitase enzyme converts citrate into isocitrate. In two successive steps of oxidative decarboxylation, two molecules of CO 2 and two NADH molecules are produced when isocitrate dehydrogenase converts isocitrate into the five-carbon α-ketoglutarate, which is then catalyzed and converted into the four-carbon succinyl CoA by α-ketoglutarate dehydrogenase. The enzyme succinyl CoA dehydrogenase then converts succinyl CoA into succinate and forms the high-energy molecule GTP, which transfers its energy to ADP to produce ATP. Succinate dehydrogenase then converts succinate into fumarate, forming a molecule of FADH 2 . Fumarase then converts fumarate into malate, which malate dehydrogenase then converts back into oxaloacetate while reducing NAD + to NADH. Oxaloacetate is then ready to combine with the next acetyl CoA to start the Krebs cycle again (see Figure \(\PageIndex{4}\)). For each turn of the cycle, three NADH, one ATP (through GTP), and one FADH 2 are created. Each carbon of pyruvate is converted into CO 2 , which is released as a byproduct of oxidative (aerobic) respiration.
Oxidative Phosphorylation and the Electron Transport Chain
The electron transport chain (ETC) uses the NADH and FADH 2 produced by the Krebs cycle to generate ATP. Electrons from NADH and FADH 2 are transferred through protein complexes embedded in the inner mitochondrial membrane by a series of enzymatic reactions. The electron transport chain consists of a series of four enzyme complexes (Complex I – Complex IV) and two coenzymes (ubiquinone and Cytochrome c), which act as electron carriers and proton pumps used to transfer H + ions into the space between the inner and outer mitochondrial membranes (Figure \(\PageIndex{5}\)). The ETC couples the transfer of electrons between a donor (like NADH) and an electron acceptor (like O 2 ) with the transfer of protons (H + ions) across the inner mitochondrial membrane, enabling the process of oxidative phosphorylation . In the presence of oxygen, energy is passed, stepwise, through the electron carriers to collect gradually the energy needed to attach a phosphate to ADP and produce ATP. The role of molecular oxygen, O 2 , is as the terminal electron acceptor for the ETC. This means that once the electrons have passed through the entire ETC, they must be passed to another, separate molecule. These electrons, O 2 , and H + ions from the matrix combine to form new water molecules. This is the basis for your need to breathe in oxygen. Without oxygen, electron flow through the ETC ceases.
Interactive Link
Watch this video to learn about the electron transport chain.
The electrons released from NADH and FADH 2 are passed along the chain by each of the carriers, which are reduced when they receive the electron and oxidized when passing it on to the next carrier. Each of these reactions releases a small amount of energy, which is used to pump H + ions across the inner membrane. The accumulation of these protons in the space between the membranes creates a proton gradient with respect to the mitochondrial matrix.
Also embedded in the inner mitochondrial membrane is an amazing protein pore complex called ATP synthase . Effectively, it is a turbine that is powered by the flow of H + ions across the inner membrane down a gradient and into the mitochondrial matrix. As the H + ions traverse the complex, the shaft of the complex rotates. This rotation enables other portions of ATP synthase to encourage ADP and P i to create ATP. In accounting for the total number of ATP produced per glucose molecule through aerobic respiration, it is important to remember the following points:
- A net of two ATP are produced through glycolysis (four produced and two consumed during the energy-consuming stage). However, these two ATP are used for transporting the NADH produced during glycolysis from the cytoplasm into the mitochondria. Therefore, the net production of ATP during glycolysis is zero.
- In all phases after glycolysis, the number of ATP, NADH, and FADH 2 produced must be multiplied by two to reflect how each glucose molecule produces two pyruvate molecules.
- In the ETC, about three ATP are produced for every oxidized NADH. However, only about two ATP are produced for every oxidized FADH 2 . The electrons from FADH 2 produce less ATP, because they start at a lower point in the ETC (Complex II) compared to the electrons from NADH (Complex I) (see Figure \(\PageIndex{5}\)).
Therefore, for every glucose molecule that enters aerobic respiration, a net total of 36 ATPs are produced (Figure \(\PageIndex{6}\)).
Gluconeogenesis
Gluconeogenesis is the synthesis of new glucose molecules from pyruvate, lactate, glycerol, or the amino acids alanine or glutamine. This process takes place primarily in the liver during periods of low glucose, that is, under conditions of fasting, starvation, and low carbohydrate diets. So, the question can be raised as to why the body would create something it has just spent a fair amount of effort to break down? Certain key organs, including the brain, can use only glucose as an energy source; therefore, it is essential that the body maintain a minimum blood glucose concentration. When the blood glucose concentration falls below that certain point, new glucose is synthesized by the liver to raise the blood concentration to normal.
Gluconeogenesis is not simply the reverse of glycolysis. There are some important differences (Figure \(\PageIndex{7}\)). Pyruvate is a common starting material for gluconeogenesis. First, the pyruvate is converted into oxaloacetate. Oxaloacetate then serves as a substrate for the enzyme phosphoenolpyruvate carboxykinase (PEPCK), which transforms oxaloacetate into phosphoenolpyruvate (PEP). From this step, gluconeogenesis is nearly the reverse of glycolysis. PEP is converted back into 2-phosphoglycerate, which is converted into 3-phosphoglycerate. Then, 3-phosphoglycerate is converted into 1,3 bisphosphoglycerate and then into glyceraldehyde-3-phosphate. Two molecules of glyceraldehyde-3-phosphate then combine to form fructose-1-6-bisphosphate, which is converted into fructose 6-phosphate and then into glucose-6-phosphate. Finally, a series of reactions generates glucose itself. In gluconeogenesis (as compared to glycolysis), the enzyme hexokinase is replaced by glucose-6-phosphatase, and the enzyme phosphofructokinase-1 is replaced by fructose-1,6-bisphosphatase. This helps the cell to regulate glycolysis and gluconeogenesis independently of each other.
As will be discussed as part of lipolysis, fats can be broken down into glycerol, which can be phosphorylated to form dihydroxyacetone phosphate or DHAP. DHAP can either enter the glycolytic pathway or be used by the liver as a substrate for gluconeogenesis.
Aging and the...
Body’s Metabolic Rate
The human body’s metabolic rate decreases nearly 2 percent per decade after age 30. Changes in body composition, including reduced lean muscle mass, are mostly responsible for this decrease. The most dramatic loss of muscle mass, and consequential decline in metabolic rate, occurs between 50 and 70 years of age. Loss of muscle mass is the equivalent of reduced strength, which tends to inhibit seniors from engaging in sufficient physical activity. This results in a positive-feedback system where the reduced physical activity leads to even more muscle loss, further reducing metabolism.
There are several things that can be done to help prevent general declines in metabolism and to fight back against the cyclic nature of these declines. These include eating breakfast, eating small meals frequently, consuming plenty of lean protein, drinking water to remain hydrated, exercising (including strength training), and getting enough sleep. These measures can help keep energy levels from dropping and curb the urge for increased calorie consumption from excessive snacking. While these strategies are not guaranteed to maintain metabolism, they do help prevent muscle loss and may increase energy levels. Some experts also suggest avoiding sugar, which can lead to excess fat storage. Spicy foods and green tea might also be beneficial. Because stress activates cortisol release, and cortisol slows metabolism, avoiding stress, or at least practicing relaxation techniques, can also help.


11: The Giant Planets
“What do we learn about the Earth by studying the planets? Humility.”—Andrew Ingersoll discussing the results of the Voyager mission in 1986.
Beyond Mars and the asteroid belt, we encounter a new region of the solar system: the realm of the giants. Temperatures here are lower, permitting water and other volatiles to condense as ice. The planets are much larger, distances between them are much greater, and each giant world is accompanied by an extensive system of moons and rings.
From many perspectives, the outer solar system is where the action is, and the giant planets are the most important members of the Sun’s family. When compared to these outer giants, the little cinders of rock and metal that orbit closer to the Sun can seem insignificant. These four giant worlds—Jupiter, Saturn, Uranus, Neptune—are the subjects of this chapter. Their rings, moons, and the dwarf planet Pluto are discussed in a later chapter.
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- 11.1: Exploring the Outer Planets
- The outer solar system contains the four giant planets: Jupiter, Saturn, Uranus, and Neptune. The gas giants Jupiter and Saturn have overall compositions similar to that of the Sun and have been explored by the Pioneer, Voyager, Galileo, and Cassini spacecraft. Voyager 2 explored Jupiter (1979), Saturn (1981), Uranus (1986), and Neptune (1989)—a grand tour of the giant planets—and these flybys have been the only explorations to date of the ice giants Uranus and Neptune.
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- 11.2: The Giant Planets
- Jupiter is 318 times more massive than Earth. Saturn is about 25% as massive as Jupiter, and Uranus and Neptune are only 5% as massive. All four have deep atmospheres and opaque clouds, and all rotate quickly with periods from 10 to 17 hours. Jupiter and Saturn have extensive mantles of liquid hydrogen. Uranus and Neptune are depleted in hydrogen and helium relative to Jupiter and Saturn (and the Sun). Each giant planet has a core of “ice” and “rock” of about 10 Earth masses.
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- 11.3: Atmosphere of the Giant Planets
- The four giant planets have generally similar atmospheres, composed mostly of hydrogen and helium. Their atmospheres contain small quantities of methane and ammonia gas, both of which also condense to form clouds. Deeper (invisible) cloud layers consist of water and possibly ammonium hydrosulfide (Jupiter and Saturn) and hydrogen sulfide (Neptune). In the upper atmospheres, hydrocarbons and other trace compounds are produced by photochemistry. We do not know the origin of Jupiter's cloud colors.
Thumbnail: The four giant planets in our solar system all have hydrogen atmospheres, but the warm gas giants, Jupiter and Saturn, have tan, beige, red, and white clouds that are thought to be composed of ammonia ice particles with various colorants called “chromophores.” The blue-tinted ice giants, Uranus and Neptune, are much colder and covered in methane ice clouds. (credit: modification of work by Lunar and Planetary Institute, NASA)


13.8.4: Multiply Square Roots
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Learning Objectives
By the end of this section, you will be able to:
- Multiply square roots
- Use polynomial multiplication to multiply square roots
Note
Before you get started, take this readiness quiz.
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Simplify: (3u)(8v).
If you missed this problem, review Example 6.2.31 . -
Simplify: 6(12−7n).
If you missed this problem, review Example 6.3.1 . -
Simplify: (2+a)(4−a).
If you missed this problem, review Example 6.3.34 .
Multiply Square Roots
We have used the Product Property of Square Roots to simplify square roots by removing the perfect square factors. The Product Property of Square Roots says
\[\sqrt{ab}=\sqrt{a}·\sqrt{b} \nonumber\]
We can use the Product Property of Square Roots ‘in reverse’ to multiply square roots.
\[\sqrt{a}·\sqrt{b}=\sqrt{ab} \nonumber\]
Remember, we assume all variables are greater than or equal to zero.
We will rewrite the Product Property of Square Roots so we see both ways together.
Definition: PRODUCT PROPERTY OF SQUARE ROOTS
If a , b are nonnegative real numbers, then
\(\sqrt{ab}=\sqrt{a}·\sqrt{b}\) and \(\sqrt{a}·\sqrt{b}=\sqrt{ab}\).
So we can multiply \(\sqrt{3}·\sqrt{5}\) in this way:
\[\begin{array}{l} {\sqrt{3}·\sqrt{5}}\\ {\sqrt{3·5}}\\ {\sqrt{15}}\\ \nonumber \end{array}\]
Sometimes the product gives us a perfect square:
\[\begin{array}{l} {\sqrt{2}·\sqrt{8}}\\ {\sqrt{2·8}}\\ {\sqrt{16}}\\ {4}\\ \nonumber \end{array}\]
Even when the product is not a perfect square, we must look for perfect-square factors and simplify the radical whenever possible.
Multiplying radicals with coefficients is much like multiplying variables with coefficients. To multiply 4x·3y we multiply the coefficients together and then the variables. The result is 12xy. Keep this in mind as you do these examples.
Example \(\PageIndex{1}\)
Simplify:
- \(\sqrt{2}·\sqrt{6}\)
- \((4\sqrt{3})(2\sqrt{12})\).
- Answer
-
1. \(\sqrt{2}·\sqrt{6}\) Multiply using the Product Property. \(\sqrt{12}\) Simplify the radical. \(\sqrt{4}·\sqrt{3}\) Simplify. \(2\sqrt{3}\) 2. \((4\sqrt{3})(2\sqrt{12})\) Multiply using the Product Property. \(8\sqrt{36}\) Simplify the radical. \(8·6\) Simplify. \(48\)
Example \(\PageIndex{2}\)
Simplify:
- \(\sqrt{3}·\sqrt{6}\)
- \((2\sqrt{6})(3\sqrt{12})\).
- Answer
-
- \(3\sqrt{2}\)
- \(36\sqrt{2}\)
Example \(\PageIndex{3}\)
Simplify:
- \(\sqrt{5}·\sqrt{10}\)
- \((6\sqrt{3})(5\sqrt{6})\)
- Answer
-
- \(5\sqrt{2}\)
- \(90\sqrt{2}\)
Example \(\PageIndex{4}\)
Simplify: \((6\sqrt{2})(3\sqrt{10})\)
- Answer
-
\((6\sqrt{2})(3\sqrt{10})\) Multiply using the Product Property. \(18\sqrt{20}\) Simplify the radical. \(18\sqrt{4}·\sqrt{5}\) Simplify. \(18·2·\sqrt{5}\) \(36\sqrt{5}\)
Example \(\PageIndex{5}\)
Simplify: \((3\sqrt{2})(2\sqrt{30})\)
- Answer
-
\(12\sqrt{15}\)
Example \(\PageIndex{6}\)
Simplify: \((3\sqrt{3})(3\sqrt{6})\).
- Answer
-
\(27\sqrt{2}\)
When we have to multiply square roots, we first find the product and then remove any perfect square factors.
Example \(\PageIndex{7}\)
Simplify:
- \((\sqrt{8x^3})(\sqrt{3x})\)
- \((\sqrt{20y^2})(\sqrt{5y^3})\)
- Answer
-
1. \((\sqrt{8x^3})(\sqrt{3x})\) Multiply using the Product Property. \(\sqrt{24x^4}\) Simplify the radical. \(\sqrt{4x^4}·\sqrt{6}\) Simplify. \(2x^2\sqrt{6}\) 2. \((\sqrt{20y^2})(\sqrt{5y^3})\) Multiply using the Product Property. \(\sqrt{100y^5}\) Simplify the radical. \(10y^2\sqrt{y}\)
Example \(\PageIndex{8}\)
Simplify:
- \((\sqrt{6x^3})(\sqrt{3x})\)
- \((\sqrt{2y^3})(\sqrt{50y^2})\).
- Answer
-
- \(3x^2\sqrt{2}\)
- \(10y^2\sqrt{y}\)
Example \(\PageIndex{9}\)
Simplify:
- \((\sqrt{6x^5})(\sqrt{2x})\)
- \((\sqrt{12y^2})(\sqrt{3y^5})\)
- Answer
-
- \(2x^3\sqrt{3}\)
- \(6y^2\sqrt{y}\)
Example \(\PageIndex{10}\)
Simplify: \((10\sqrt{6p^3})(3\sqrt{18p})\)
- Answer
-
\((10\sqrt{6p^3})(3\sqrt{18p})\) Multiply. \(30\sqrt{108p^4}\) Simplify the radical. \(30\sqrt{36p^4}·\sqrt{3}\) \(30·6p^2·\sqrt{3}\) \(180p^2\sqrt{3}\)
Example \(\PageIndex{11}\)
Simplify: \((\sqrt{62x^2})(8\sqrt{45x^4})\)
- Answer
-
\(144x^3\sqrt{10}\)
Example \(\PageIndex{12}\)
Simplify: \((2\sqrt{6y^4})(12\sqrt{30y})\).
- Answer
-
\(144y^2\sqrt{5y}\)
Example \(\PageIndex{13}\)
Simplify:
- \((\sqrt{2})^2\)
- \((−\sqrt{11})^2\).
- Answer
-
1. \((\sqrt{2})^2\) Rewrite as a product. \((\sqrt{2})(\sqrt{2})\) Multiply. \(\sqrt{4}\) Simplify. 2 2. \((−\sqrt{11})^2\) Rewrite as a product. \((−\sqrt{11})(−\sqrt{11})\) Multiply. \(\sqrt{121}\) Simplify. 11
Example \(\PageIndex{14}\)
Simplify:
- \((\sqrt{12})^2\)
- \((−\sqrt{15})^2\).
- Answer
-
- 12
- 15
Example \(\PageIndex{15}\)
Simplify:
- \((\sqrt{16})^2\)
- \((−\sqrt{20})^2\).
- Answer
-
- 16
- 20
The results of the previous example lead us to this property.
Definition: SQUARING A SQUARE ROOT
If a is a nonnegative real number, then
\((\sqrt{a})^2=a\)
By realizing that squaring and taking a square root are ‘opposite’ operations, we can simplify \((\sqrt{2})^2\) and get 2 right away. When we multiply the two like square roots in part (a) of the next example, it is the same as squaring.
Example \(\PageIndex{16}\)
Simplify:
- \((2\sqrt{3})(8\sqrt{3})\)
- \((3\sqrt{6})^2\).
- Answer
-
1. \((2\sqrt{3})(8\sqrt{3})\) Multiply. Remember, \((\sqrt{3}^2)\) 16·3 Simplify. 48 2. \((3\sqrt{6})^2\) Multiply. 9·6 Simplify. 54
Example \(\PageIndex{17}\)
Simplify:
- \((6\sqrt{11})(5\sqrt{11})\)
- \((5\sqrt{8})^2\).
- Answer
-
- 330
- 200
Example \(\PageIndex{18}\)
Simplify:
- \((3\sqrt{7})(10\sqrt{7})\)
- \((−4\sqrt{6})^2\).
- Answer
-
- 210
- 96
Use Polynomial Multiplication to Multiply Square Roots
In the next few examples, we will use the Distributive Property to multiply expressions with square roots.
We will first distribute and then simplify the square roots when possible.
Example \(\PageIndex{19}\)
Simplify:
- \(3(5−\sqrt{2})\)
- \(\sqrt{2}(4−\sqrt{10})\).
- Answer
-
1. \(3(5−\sqrt{2})\) Distribute. \(15−3\sqrt{2})\) 2. \(\sqrt{2}(4−\sqrt{10})\) Distribute. \(4\sqrt{2}−\sqrt{20}\) Simplify. \(4\sqrt{2}−2\sqrt{5}\)
Example \(\PageIndex{20}\)
Simplify:
- \(2(3−\sqrt{5})\)
- \(\sqrt{3}(2−\sqrt{18})\).
- Answer
-
- \(6−2\sqrt{5}\)
- \(2\sqrt{3}−3\sqrt{6}\)
Example \(\PageIndex{21}\)
Simplify:
- \(6(2+\sqrt{6})\)
- \(\sqrt{7}(1+\sqrt{14})\).
- Answer
-
- \(12+\sqrt{6}\)
- \(\sqrt{7}+7\sqrt{2}\)
Example \(\PageIndex{22}\)
Simplify:
- \(\sqrt{5}(7+2\sqrt{5})\)
- \(\sqrt{6}(\sqrt{2}+\sqrt{18})\).
- Answer
-
1. \(\sqrt{5}(7+2\sqrt{5})\) Distribute. \(7\sqrt{5}+2·5\) Simplify. \(7\sqrt{5}+10\) \(10+7\sqrt{5}\) 2. \(\sqrt{6}(\sqrt{2}+\sqrt{18})\) Multiply. \(\sqrt{12}+\sqrt{108}\) Simplify. \((\sqrt{4}·\sqrt{3}+\sqrt{36}·\sqrt{3})\) \(2\sqrt{3}+6\sqrt{3}\) Combine like radicals. \(8\sqrt{3}\)
Example \(\PageIndex{23}\)
Simplify:
- \(\sqrt{6}(1+3\sqrt{6})\)
- \(\sqrt{12}(\sqrt{3}+\sqrt{24})\)
- Answer
-
- \(18+\sqrt{6}\)
- \(6+12\sqrt{2}\)
Example \(\PageIndex{24}\)
Simplify:
- \(\sqrt{8}(2−5\sqrt{8})\)
- \(\sqrt{14}(\sqrt{2}+\sqrt{42})\)
- Answer
-
- \(−40+4\sqrt{2}\)
- \(2\sqrt{7}+14\sqrt{3}\)
When we worked with polynomials, we multiplied binomials by binomials. Remember, this gave us four products before we combined any like terms. To be sure to get all four products, we organized our work—usually by the FOIL method.
Example \(\PageIndex{25}\)
Simplify: \((2+\sqrt{3})(4−\sqrt{3})\)
- Answer
-
\((2+\sqrt{3})(4−\sqrt{3})\) Multiply. \(8−2\sqrt{3}+4\sqrt{3}−3\) Combine like terms. \(5+2\sqrt{3}\)
Example \(\PageIndex{26}\)
Simplify: \((1+\sqrt{6})(3−\sqrt{6})\).
- Answer
-
\(−3+2\sqrt{6}\)
Example \(\PageIndex{27}\)
Simplify: \((4−\sqrt{10})(2+\sqrt{10})\).
- Answer
-
\(−2+2\sqrt{10}\)
Example \(\PageIndex{28}\)
Simplify: \((3−2\sqrt{7})(4−2\sqrt{7})\).
- Answer
-
\((3−2\sqrt{7})(4−2\sqrt{7})\) Multiply. \(12−6\sqrt{7}−8\sqrt{7}+4·7\) Simplify. \(12−6\sqrt{7}−8\sqrt{7}+28\) Combine like terms. \(40−14\sqrt{7}\)
Example \(\PageIndex{29}\)
Simplify: \((6−3\sqrt{7})(3+4\sqrt{7})\).
- Answer
-
\(−66+15\sqrt{7}\)
Example \(\PageIndex{30}\)
Simplify: \((2−3\sqrt{11})(4−\sqrt{11})\)
- Answer
-
\(41+14\sqrt{11}\)
Example \(\PageIndex{31}\)
Simplify: \((3\sqrt{2}−\sqrt{5})(\sqrt{2}+4\sqrt{5})\).
- Answer
-
\(3\sqrt{2}−\sqrt{5})(\sqrt{2}+4\sqrt{5})\) Multiply. \(3·2+12\sqrt{10}−\sqrt{10}−4·5\) Simplify. \(6+12\sqrt{10}−\sqrt{10}−20\) Combine like terms. \(−14+11\sqrt{10}\)
Example \(\PageIndex{32}\)
Simplify: \((5\sqrt{3}−\sqrt{7})(\sqrt{3}+2\sqrt{7})\)
- Answer
-
\(1+9\sqrt{21}\)
Example \(\PageIndex{33}\)
Simplify: \((\sqrt{6}−3\sqrt{8})(2\sqrt{6}+\sqrt{8})\)
- Answer
-
\(−12−20\sqrt{3}\)
Example \(\PageIndex{34}\)
Simplify: \((4−2\sqrt{x})(1+3\sqrt{x})\).
- Answer
-
\((4−2\sqrt{x})(1+3\sqrt{x})\). Multiply. \(4+12\sqrt{x}−2\sqrt{x}−6x\) Combine like terms. \(4+10\sqrt{x}−6x\)
Example \(\PageIndex{35}\)
Simplify: \((6−5\sqrt{m})(2+3\sqrt{m})\).
- Answer
-
\(12+8\sqrt{m}−15m\)
Example \(\PageIndex{36}\)
Simplify: \((10+3\sqrt{n})(1−5\sqrt{n})\)
- Answer
-
\(10−47\sqrt{n}−15n\)
Note that some special products made our work easier when we multiplied binomials earlier. This is true when we multiply square roots, too. The special product formulas we used are shown below.
Definition: SPECIAL PRODUCT FORMULAS
\[\begin{array}{ll} {\textbf{Binomial Squares}}&{\textbf{Product of Conjugates}}\\ {(a+b)^2=a^2+2ab+b^2}&{(a−b)(a+b)=a^2−b^2}\\ {(a−b)^2=a^2−2ab+b^2}&{}\\ \nonumber \end{array}\]
We will use the special product formulas in the next few examples. We will start with the Binomial Squares formula.
Example \(\PageIndex{37}\)
Simplify:
- \((2+\sqrt{3})^2\)
- \((4−2\sqrt{5})^2\).
- Answer
-
Be sure to include the 2ab term when squaring a binomial.
1.
2.Multiply using the binomial square pattern. Simplify. Combine like terms. Multiply using the binomial square pattern. Simplify. Combine like terms.
Example \(\PageIndex{38}\)
Simplify:
- \((10+\sqrt{2})^2\)
- \((1+3\sqrt{6})^2\).
- Answer
-
- \(102+20\sqrt{2}\)
- \(55+6\sqrt{6}\)
Exercise \(\PageIndex{39}\)
Simplify:
- \((6-\sqrt{5})^2\)
- \((9-2\sqrt{10})^2\).
- Answer
-
- \(41-12\sqrt{5}\)
- \(121-36\sqrt{10}\)
Example \(\PageIndex{40}\)
Simplify: \((1+3\sqrt{x})^2\).
- Answer
-
Multiply using the binomial square pattern. Simplify.
Example \(\PageIndex{41}\)
Simplify: \((2+5\sqrt{m})^2\).
- Answer
-
\(4+20\sqrt{m}+25m\)
Example \(\PageIndex{42}\)
Simplify: \((3−4\sqrt{n})^2\).
- Answer
-
\(9−24\sqrt{n}+16n\)
In the next two examples, we will find the product of conjugates.
Example \(\PageIndex{43}\)
Simplify: \((4−\sqrt{2})(4+\sqrt{2})\).
- Answer
-
Multiply using the binomial square pattern. Simplify.
Example \(\PageIndex{44}\)
Simplify: \((2−\sqrt{3})(2+\sqrt{3})\)
- Answer
-
1
ExAMPLe \(\PageIndex{45}\)
Simplify: \((1+\sqrt{5})(1−\sqrt{5})\)
- Answer
-
−4
Example \(\PageIndex{46}\)
Simplify: \((5−2\sqrt{3})(5+2\sqrt{3})\)
- Answer
-
Multiply using the binomial square pattern. Simplify.
Example \(\PageIndex{47}\)
Simplify: \((3−2\sqrt{5})(3+2\sqrt{5})\).
- Answer
-
−11
Example \(\PageIndex{48}\)
Simplify: \((4+5\sqrt{7})(4−5\sqrt{7})\).
- Answer
-
−159
Access these online resources for additional instruction and practice with multiplying square roots.
- Product Property
- Multiply Binomials with Square Roots
Key Concepts
-
Product Property of Square Roots
If
a
,
b
are nonnegative real numbers, then
\(\sqrt{ab}=\sqrt{a·b}\) and \(\sqrt{a}·\sqrt{b}=\sqrt{ab}\)
-
Special formulas
for multiplying binomials and conjugates:
\[\begin{array}{ll} {(a+b)^2=a^2+2ab+b^2}&{(a−b)(a+b)=a^2−b^2}\\ {(a−b)^2=a^2−2ab+b^2 }&{}\\ \nonumber \end{array}\]
- The FOIL method can be used to multiply binomials containing radicals.