5.1: Vocal Types and Ranges
Voice Type
A voice type is a singing voice identified as having certain qualities or characteristics of vocal range, vocal weight, tessitura, vocal timbre, and vocal transition points, such as breaks and lifts within the voice. Voice classification is a tool for singers, composers, venues, and listeners to categorize vocal properties and to associate roles with voices.
Women are typically divided into three groups: soprano, mezzo-soprano, and contralto. Men are usually divided into four groups: countertenor, tenor, baritone, and bass. Some women fall into the tenor or baritone groups, while men identified as countertenors can be grouped as contralto, mezzo-soprano, or soprano. When considering the pre-pubescent voice, an eighth term, treble, is applied. Within each of these major categories, subcategories identify specific vocal qualities such as coloratura facility and vocal weight to differentiate between voices. The vocal range of classical performance covers about five octaves, from a low G1 (in scientific pitch notation) to a high G6. Any individual’s voice can perform over a range of one and a half to more than two octaves. Vocal ranges are grouped into overlapping types that each span about two octaves. Many singers fall between groups and can perform some parts in either type.
Vocal Ranges
A typical choral arrangement divides women into higher and lower voices and men into higher or lower voices. Most voices can be assigned one of these four ranges, and this gives the composer four vocal lines to work with, which is usually enough. The four main vocal ranges are:
- Soprano – A high female (or boy’s) voice
- Alto – A low female (or boy’s) voice
- Tenor – A high (adult) male voice
- Bass – A low (adult) male voice
Arrangements for these four voices are labeled SATB (for Soprano Alto Tenor Bass). The ranges of the four voices overlap, but singers may find themselves straining or getting an unpleasant sound at the top or a weak sound at the bottom of their ranges. So although the full ranges of an alto and a soprano may look quite similar, the soprano gets a strong, clear sound on the higher notes, and the alto a strong, clear sound in the lower part of the range. But there are vocalists whose strong, best-sounding range falls in a distinctly different place from any of these four voices. The names for some of these ranges are:
- Coloratura Soprano – This is not really a different range from the soprano, but a coloratura soprano has a voice that is unusually high, light, and agile, even for a soprano.
- Mezzo-soprano – In between soprano and alto
- Contralto – Contralto and alto originally referred to the same voice. But some people today use “contralto” to refer to a female voice that is even lower than a typical alto
- Countertenor – A male voice that is unusually high, light, and agile, even for a tenor
- Baritone – A male voice that falls in between tenor and bass
Contributors and Attributions
CC licensed content, Shared previously
- Voice type. Provided by : Wikipedia. Located at : http://en.Wikipedia.org/wiki/Voice_type . License : CC BY: Attribution
- Week 6 Presentation. Authored by : Teacher 2 Open High School. Located at : https://vimeo.com/19067177 . License : CC BY-SA: Attribution-ShareAlike
- The operatic war in N. Y.. Provided by : Boston Public Library. Located at : https://www.flickr.com/photos/boston_public_library/19501791605/ . License : CC BY: Attribution


4.5: Monitoring Volcanoes and Predicting Eruptions
In 2005 USGS geologist Chris Newhall made a list of the six most important signs of an imminent volcanic eruption. They are as follows:
- Gas leaks — the release of gases (mostly H 2 O, CO 2 , and SO 2 ) from the magma into the atmosphere through cracks in the overlying rock
- Bit of a bulge — the deformation of part of the volcano, indicating that a magma chamber at depth is swelling or becoming more pressurized
- Getting shaky — many (hundreds to thousands) of small earthquakes, indicating that magma is on the move. The quakes may be the result of the magma forcing the surrounding rocks to crack, or a harmonic vibration that is evidence of magmatic fluids moving underground.
- Dropping fast — a sudden decrease in the rate of seismicity, which may indicate that magma has stalled, which could mean that something is about to give way
- Big bump — a pronounced bulge on the side of the volcano (like the one at Mount St. Helens in 1980), which may indicate that magma has moved close to surface
- Blowing off steam — steam eruptions (a.k.a. phreatic eruptions ) that happen when magma near the surface heats groundwater to the boiling point. The water eventually explodes, sending fragments of the overlying rock far into the air.
With these signs in mind, we can make a list of the equipment we should have and the actions we can take to monitor a volcano and predict when it might erupt.
Assessing Seismicity
The simplest and cheapest way to monitor a volcano is with seismometers. In an area with several volcanoes that have the potential to erupt (e.g., the Squamish-Pemberton area), a few well-placed seismometers can provide us with an early warning that something is changing beneath one of the volcanoes, and that we need to take a closer look. There are currently enough seismometers in the Lower Mainland and on Vancouver Island to provide this information. [1]
If there is seismic evidence that a volcano is coming to life, more seismometers should be placed in locations within a few tens of kilometers of the source of the activity (Figure \(\PageIndex{1}\)). This will allow geologists to determine the exact location and depth of the seismic activity so that they can see where the magma is moving.
Detecting Gases
Water vapor quickly turns into clouds of liquid water droplets and is relatively easy to detect just by looking, but CO 2 and SO 2 are not as obvious. It’s important to be able to monitor changes in the composition of volcanic gases, and we need instruments to do that. Some can be monitored from a distance (from the ground or even from the air) using infrared devices, but to obtain more accurate data, we need to sample the air and do chemical analysis. This can be achieved with instruments placed on the ground close to the source of the gases (see Figure \(\PageIndex{12}\)), or by collecting samples of the air and analyzing them in a lab.
Measuring Deformation
Measurement of deformation allows us to determine if a volcano is expanding or contracting. That can typically be related to the movement of magma into or out of a magma chamber near to surface and so is an indicator of the potential for an eruption. There are two main ways to measure ground deformation. One is known as a tiltmeter , which is a sensitive three-directional level that can sense small changes in the tilt of the ground at a specific location. Another is through the use of GPS (global positioning system) technology (Figure \(\PageIndex{2}\)). Both are effective, but GPS provides more information than a tiltmeter because it can tell us how far the ground has actually moved in the east-west, north-south, and up-down directions.
By combining information from these types of sources, along with careful observations made on the ground and from the air, and a thorough knowledge of how volcanoes work, geologists can get a good idea of the potential for a volcano to erupt in the near future (months to weeks, but not days). They can then make recommendations to authorities about the need for evacuations and restricting transportation corridors. Our ability to predict volcanic eruptions has increased dramatically in recent decades because of advances in our understanding of how volcanoes behave and in monitoring technology. Providing that careful work is done, there is no longer a large risk of surprise eruptions, and providing that public warnings are issued and heeded, it is less and less likely that thousands will die from sector collapse, pyroclastic flows, ash falls, or lahars. Indirect hazards are still very real, however, and we can expect the next eruption like the one at Laki in 1783 to take an even greater toll than it did then, especially since there are now roughly eight times as many people on Earth.
You’re the chief volcanologist for the Geological Survey of Canada (GSC), based in Vancouver. At 10:30 a.m. on a Tuesday, you receive a report from a seismologist at the GSC in Sidney saying that there has been a sudden increase in the number of small earthquakes in the vicinity of Mount Garibaldi. You have two technicians available, access to some monitoring equipment, and a four-wheel-drive vehicle. At noon, you meet with your technicians and a couple of other geologists. By the end of the day, you need to have a plan to implement, starting tomorrow morning, and a statement to release to the press. What should your first day’s fieldwork include? What should you say later today in your press release?
See Appendix 3 for Exercise 4.6 Answers .
Media Attributions
- Figure \(\PageIndex{1}\): Photo by Cathie Hickson. All rights reserved. Used with permission.
- Figure \(\PageIndex{2}\): A Typical GPS Monitoring Station by USGS. Public domain.


8.18: Matlab Script For This Chapter
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I’ve created a script named MMN_artifact_rejection_example.m that shows how to implement the interpolation and artifact detection processes described in this chapter. You can find it in the Chapter_8 folder. It runs on the data from Subjects 1-10 in the ERP CORE MMN experiment. The datasets for these participants are in a subfolder named MMN_Data .
The script demonstrates how you can put subject-specific information in an Excel spreadsheet, such as which channels to interpolate and what artifact detection parameters to use, and then have the script read this information and use it to control the interpolation and artifact detection processes. This is a super useful trick!
I didn’t spend much time customizing the parameters. You can probably do a better job given what you’ve learned in this chapter.
Most of these participants have a lot of blinks and would need to be excluded from the final analyses because they exceed our criterion of 25% rejected trials. As I noted before, this is because we planned to use artifact correction rather than rejection for blinks, and we did nothing to minimize blinking. I should also note that Subject 7 has a ton of low-frequency drift (probably coming from the reference electrodes, because it’s present in all the EEG channels) and was excluded from the final analyses in the ERP CORE paper.


5.2: Bankruptcy
After reading this chapter, you should understand the following:
- A short history of US bankruptcy law
- An overview of key provisions of the 2005 bankruptcy act
- The basic operation of Chapter 7 bankruptcy
- The basic operation of Chapter 11 bankruptcy
- The basic operation of Chapter 13 bankruptcy
- What debtor’s relief is available outside of bankruptcy
Bankruptcy is understood as an aspect of financing, a system that permits creditors to receive an equitable distribution of the bankrupt person’s assets and promises new hope to debtors facing impossible financial burdens. Without such a law, we may reasonably suppose that the level of economic activity would be far less than it is, for few would be willing to risk being personally burdened forever by crushing debt. Bankruptcy gives the honest debtor a fresh start and resolves disputes among creditors.
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2: Polynomial and Rational Functions
In this chapter, we will learn about these concepts and discover how mathematics can be used in such applications.
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- 2.0: Introduction to Polynomial and Rational Functions
- This chapter is dedicated to polynomial and rational functions. We explore their graphs, including the behavior of these curves near their zeros. Vertical, horizontal, and slant asymptotes are detailed when discussing rational functions. Additionally, we spend quite some time working with the Remainder and Factor Theorems in an effort to find all roots (both real- and complex-valued) of polynomials. Synthetic division and the Rational Zeros Theorem are introduced to help with this process.
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- 2.1: Complex Numbers
- This section introduces complex numbers, covering their standard form \(a + bi\), where \(i\) is the imaginary unit. It explains operations with complex numbers, including addition, subtraction, multiplication, division, and finding complex conjugates. The section also introduces the complex plane, where complex numbers are represented graphically, and discusses their magnitude and applications. Examples illustrate these concepts in practice.
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- 2.2: Quadratic Functions
- This section covers quadratic functions, focusing on their general and standard (vertex) forms. It explains how to find and interpret key features such as the vertex, axis of symmetry, and zeros. It also demonstrates graphing parabolas and solving quadratic equations using the Quadratic Formula, completing the square, and factoring. Advanced topics include solving absolute value equations involving quadratic expressions and graphing the absolute value of a quadratic function.
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- 2.3: Power Functions and Polynomial Functions
- This section discusses power and polynomial functions, focusing on their definitions, properties, and graphs. It explains the general form of polynomial functions, the significance of the leading term and degree, and how these influence end behavior. Examples demonstrate graphing polynomial functions and analyzing their key features, including turning points and continuity.
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- 2.4: Graphs of Polynomial Functions
- This section explores the graphs of polynomial functions, focusing on key characteristics such as end behavior, intercepts, and turning points. It discusses how the degree and leading coefficient influence the graph's shape and analyzes multiplicity's role in determining the behavior of the graph at roots. Examples illustrate how to sketch and interpret polynomial graphs effectively.
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- 2.5: Dividing Polynomials
- This section covers methods for dividing polynomials, including long division and synthetic division. It explains how to use these techniques to divide a polynomial by a linear or higher-degree polynomial, interpret the results, and find remainders. Examples illustrate each method step-by-step, helping to solve polynomial division problems efficiently.
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- 2.6: Zeros of Polynomial Functions
- This section explores zeros of polynomial functions, focusing on identifying roots using the Rational Zeros Theorem, the Fundamental Theorem of Algebra, the Complete Factorization Theorem, and the Conjugate Pairs Theorem. It examines how multiplicity impacts the graph of a polynomial at its roots and provides techniques for solving higher-degree polynomial equations through factoring and other algebraic methods.
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- 2.7: Rational Functions
- This section introduces rational functions, exploring their key features such as domain, vertical and horizontal or slant asymptotes, and intercepts. It discusses how to analyze and graph rational functions, focusing on behavior near asymptotes and at infinity. Examples demonstrate the steps to identify these features and interpret their implications for the function's graph.
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- 2.8: Revisiting Inverses
- This section discusses the inverses of polynomial and rational functions, focusing on determining whether a function has an inverse, finding the inverse algebraically, and understanding the domain and range restrictions necessary for invertibility. It provides examples to demonstrate these concepts and explores graphical relationships between functions and their inverses, including symmetry about the line \(y = x\).
Thumbnail: (CC BY-SA; OpenStax).


7.3.3: Conduit_Boxes and Wiring
Conduit
Raceways are defined as enclosed channels of metal or nonmetallic material designed expressly for holding wires or cables. Branch-circuit installation using a raceway (conduit) wiring method is seldom used in residential wiring. However, some areas of the country require that all wiring in a house be installed in a raceway wiring method. Raceways should be installed as a complete system and be securely fastened in place and supported by an approved retainer.
Use individual conductors when installing a circuit in a raceway wiring method. It is common wiring practice to install a green insulated equipment grounding conductor in every raceway. Electric codes have specific requirements for wiring in different types of conduit that include allowable fill rates that vary depending upon wire size and insulation type.
The following conduits are used primarily in light to heavy commercial application and are listed here for your reference:
Rigid metal conduit (RMC) – RMC is generally made of steel with a protective galvanized coating. It is a threadable raceway designed for the physical protection and routing of conductors and cables and for use as an equipment grounding conductor when installed with appropriate fittings. It can be used in all atmospheric conditions and forms of occupancy. Requires pipe and thread cutting specialty tools.
Intermediate metal conduit (IMC) – IMC is a thinner-walled version of rigid metal conduit and can be used in all locations in a house where rigid metal conduit is permitted to be used. It can be used as an equipment grounding conductor when installed with associated couplings and appropriate fittings. Requires pipe and thread cutting specialty tools.
Raceways used in residential wiring include:
An interactive or media element has been excluded from this version of the text. You can view it online here:
EMT Conduit Bending
Bending conduit is a skill that improves with practice. The most common electrical conduit installed in houses is EMT and, for this reason, the discussion that follows on conduit bending will focus on EMT. The bending techniques described may also apply to the other types of circular metal raceways.
EMT is bent in the field using either a hand bender, a hydraulic bender, or an electric bender. Bend sizes 1/2″ through 1-1/4″ are usually formed with a hand bender. A hydraulic or electric power bender is generally used for larger sizes. Since most EMT installed in houses will be 1/2″, 3/4″, or 1″ trade sizes, we will focus on bending with a hand bender.
When making a bend using a hand bender:
- Wear safety glasses and observe all applicable safety rules.
- Bend on a flat surface that is not slippery.
- Mark the locations on the conduit where you wish to make the bends clearly and accurately.
- Apply heavy foot pressure on the foot pedal to keep the conduit tightly in the bender.
- When making multiple bends on the same pipe length, keep all bends in the same plane.
IDEAL Hand Conduit Benders
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IDEAL Benders How To Bend a Stub
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IDEAL Hand Conduit Bender How to Make a Back to Back Bend
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Conduit Bending Basics 3 Bend Saddle
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Boxes
Electrical boxes have many mounting options that range from configurations designed to be nailed or screwed to framing members or blocking, to models for remodeling (called an “old work” box) that attach to the sheetrock that encloses a wall pocket.
Device Boxes- are used to install receptacles or switches at specific locations on an electrical circuit. Standard box openings are approximately 3″ x 2″ with a depth that ranges from 1-1/2″ to 3-1/2″.
Outlet Boxes- are used when installing lighting fixtures in a ceiling or on a wall and when connecting small or large appliances. They are larger than a device box and provide more room for different wiring situations. Outlet boxes are offered in round, octagon, or square shapes.
Junction Boxes (J-Box)- These are used when several conductors are spliced together at a point on the wiring system. The NEC® requires junction boxes to be accessible after installation without the finish of a building having to be altered. Junction boxes must always be covered.
Heavy Load Boxes- Specifically designed and tested to support heavier loads. Used for heavier loads such as ceiling suspended paddle fans. Heavy load boxes can be manufactured with metal or nonmetal material.
Metal Boxes
A metal device box often includes the capability of having the sides of the box removed and the boxes ganged together to make a box that can accommodate multiple devices. The most common metal device box size 3″ x 2″ x 3-1/2″. Another type of metallic device box recognized by the NEC® is the “handy” or “utility” box. This type of box is primarily used for surface mounting and can accommodate one device such as a receptacle or switch.
Nonmetallic Device Boxes
Nonmetallic boxes are usually made of PVC, phenolic, or polycarbonate. The specific advantages of using these boxes include that they are lightweight, strong, very easy to install, and inexpensive. Most all nonmetallic boxes are wired using a nonmetallicsheathed cable wiring method. Nonmetallic boxes are offered in single-gang, two-gang, three-gang device box, and fixture mounting styles.
PVC Conduit Boxes
Although PVC boxes are designed and used for glue-up assembly, some models have female threaded fittings to accommodate a variety of threaded connectors.
Wires (Conductors)
Conductors in residential wiring are usually installed in a cable assembly. They are made of copper, aluminum, and copper-clad aluminum. Copper is preferred because of its great ability to conduct electricity, its strength, and its low instance of problems over the long term.
Conductors are sized according to the American Wire Gauge (AWG). Conductors used in residential wiring typically range in size from 14 AWG to 2/0 copper. The larger the number, the smaller the conductor. The smaller the number, the larger the conductor. Conductor sizes larger than 4/0 are listed in kcmil (1000 circular mils).
Ampacity is the current in amperes that a conductor can carry continuously under the conditions of use without exceeding its temperature rating. A residential electrician or maintenance technician must be able to choose the correct conductor size based on the ampacity needed for each circuit they are working with. The ampacity of a conductor depends not only on the diameter size of the conductor, but also on the length of the conductor, and what insulation type the conductor has.
THHN and THWN are codes for the two most common types of insulated wire used inside conduit. These types of conductors are often used in conjunction with flexible conduit in unfinished areas, such as basements and garages, and for short exposed runs inside the home, such as wiring connections for garbage disposers and hot water heaters. They are also used in solid material conduit branch circuits. The letters indicate specific properties of the wire insulation:
T: thermoplastic
H: heat-resistant; HH means highly heat-resistant
W: rated for wet locations
N: nylon-coated, for added protection
Solid Core VS. Stranded Wire- While solid wire consists of a single metal core, while a stranded wire is composed of numerous thinner wires twisted together into a cohesive bunch. Both types of wire are appropriate for commercial and residential installation, however each has particular advantages and disadvantages that lead to the choice of one over another for each particular application.
Wire Color and Use
Color choice for the insulation of the conductors installed in a raceway depends on the type of circuit it serves.
• For a 120-volt branch circuit, use a white insulated wire and a black insulated wire.
• For a straight 240-volt circuit (like an electric water heater), use two black conductors or a black and a red conductor.

The NEC® requires that each conductor be color coded to indicate the function that it performs in a circuit.
Black– Used as an ungrounded or “hot” conductor and carries the current to the load in 120-volt circuits.
Red– Also used as an ungrounded or “hot” conductor and carries current to the load in 120/240-volt circuits like an electric clothes dryer circuit.
White–
Used as the grounded circuit conductor
– Returns current from the load back to the source
– Called “neutral” conductor, but only true “neutral” when used with black and red wire in multi-wire circuit
Bare– Used as equipment grounding conductor that bonds all non-current carrying metal parts of a circuit together; never carries current.
Green (can be green with yellow stripes)– Used as an insulated equipment grounding conductor; never carries current.
Conductor Installation
Conductors are usually pulled into the conduit, but in shorter runs between electrical boxes conductors they may be pushed through the raceway. Conductors are taken off spools in a way that results in the conductors coming off the spools easily and not becoming tangled with each other. One of the easiest ways to do this is to use a wire cart that allows several spools of wire to be put on at one time.
If the length of conduit between boxes is fairly long, use a fish tape. If the conduit already contains wires, be sure the circuits that supply them are de-energized. Pull the fish tape out of its reel. Insert it into a raceway and push it through until it comes out at a box location. The fish tape will have a hook on the end of it. Attach the conductors to the fish tape end. While one person pulls the conductors slowly off the spools, another person will pull the fish tape with the attached conductors back through the raceway.
Klein Tools Laser-etched Fiberglass Fish Tapes
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See Klein Tools Laser-etched Fiberglass Fish Tapes
If the length of a conduit run is longer than the length of your longest fish tape, another technique can be used.  Once the mouse has been blown or sucked through the conduit, the attached string is removed from the mouse and tied to a stronger pulling rope, which is then pulled though the conduit. The pulling rope is then attached to the wires and they are pulled into the conduit.
Terminations
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Cable Types
Cable wiring methods are easier to install than raceway wiring methods, and this is the main reason why most houses are wired using as little conduit as possible. Cable wire contains all of the conductors needed for the circuit in a single insulated unit.
When purchasing cable wiring system the cable is referred to by two numbers: t he first number specifies the gauge; the second the number of current carrying conductors in the wire. Additionally, there’s usually another wire that is used for grounding (green or bare). “12-2” means 12 gauge, two insulated current carrying wires, and a bare ground. 12-2 wire usually has a black, white and bare ground wire. Black, red, and a ground with no white wire is used for 220V circuits without neutral. 12-3 wire usually has a black, red, white and bare ground wire and is used for 220V with neutral or in three-way switch applications as the traveler between the switches where an additional wire is required.
Nonmetallic-Sheathed Cable (Type NM)- Also known as “Romex”. Least expensive and most used residential wiring method to purchase and install.
Types of Type NM cable:
- Type NM-B (white outer jacket)- Most common type; use in dry locations only. Has a flame-retardant, moisture-resistant, nonmetallic outer jacket.
- Type NMC-B (yellow outer jacket)- Not used often in residential work ; use in dry or damp locations. Has a flame retardant, fungus and corrosion resistant, nonmetallic outer jacket.
- Type NMS-B (orange outer jacket)- Used in new homes with home automation systems. Contains power conductors, telephone wires, coaxial cable for video, and other data conductors all in the same cable. Has moisture-resistant, flame-retardant, nonmetallic outer jacket.
Underground Feeder Cable (Type UF)- Used for underground installation of branch circuits and feeder circuits. Also used in interior installations, but must be installed following the installation requirements for Nonmetallic-Sheathed Cable.
Armored-Clad (Type AC) and Metal-Clad (Type MC) Cable- Certain locations in the United States may not allow Nonmetallic Sheathed Cable in residential construction. Both have a metal outer sheathing and provide very high levels of physical protection for the conductors in the cable. Electricians sometimes find it hard to tell Type AC (also known as “BX” cable) and Type MC apart. Type AC cable has brown paper covering each conductor and Type MC cable has a clear plastic wrap around all of the conductors.


5.3: Linear Independence
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Outcomes
- Determine if a set is linearly independent.
In this section, we will again explore concepts introduced earlier in terms of \(\mathbb{R}^n\) and extend them to apply to abstract vector spaces.
Definition \(\PageIndex{1}\): Linear Independence
Let \(V\) be a vector space. If \(\{\vec{v}_{1},\cdots ,\vec{v}_{n}\} \subseteq V,\) then it is linearly independent if \[\sum_{i=1}^{n}a_{i}\vec{v}_{i}=\vec{0} \;\mbox{implies}\; a_{1}=\cdots =a_{n}=0\nonumber \] where the \(a_i\) are real numbers.
The set of vectors is called linearly dependent if it is not linearly independent.
Example \(\PageIndex{1}\): Linear Independence
Let \(S \subseteq \mathbb{P}_2\) be a set of polynomials given by \[S = \left\{ x^2 + 2x - 1, 2x^2 - x + 3 \right\}\nonumber \] Determine if \(S\) is linearly independent.
Solution
To determine if this set \(S\) is linearly independent, we write \[a ( x^2 + 2x -1 ) + b(2x^2 - x + 3) = 0x^2 + 0x + 0\nonumber \] If it is linearly independent, then \(a=b=0\) will be the only solution. We proceed as follows. \[\begin{aligned} a ( x^2 + 2x -1 ) + b(2x^2 - x + 3) &= 0x^2 + 0x + 0 \\ ax^2 + 2ax - a + 2bx^2 - bx + 3b &= 0x^2 + 0x + 0 \\ (a+2b)x^2 + (2a -b)x - a + 3b &= 0x^2 + 0x + 0\end{aligned}\]
It follows that \[\begin{aligned} a + 2b &= 0 \\ 2a - b &= 0 \\ -a + 3b &= 0\end{aligned}\]
The augmented matrix and resulting reduced row-echelon form are given by \[\left [ \begin{array}{rr|r} 1 & 2 & 0 \\ 2 & -1 & 0 \\ -1 & 3 & 0 \end{array} \right ] \rightarrow \cdots \rightarrow \left [ \begin{array}{rr|r} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 0 \end{array} \right ]\nonumber \]
Hence the solution is \(a=b=0\) and the set is linearly independent.
The next example shows us what it means for a set to be dependent.
Example \(\PageIndex{2}\): Dependent Set
Determine if the set \(S\) given below is independent. \[S=\left\{ \left [\begin{array}{c} -1 \\ 0 \\ 1 \end{array}\right ], \left [\begin{array}{c} 1 \\ 1 \\ 1 \end{array}\right ], \left [\begin{array}{c} 1 \\ 3 \\ 5 \end{array}\right ] \right\}\nonumber \]
Solution
To determine if \(S\) is linearly independent, we look for solutions to \[a\left [\begin{array}{c} -1 \\ 0 \\ 1 \end{array}\right ] +b\left [\begin{array}{c} 1 \\ 1 \\ 1 \end{array}\right ] +c\left [\begin{array}{c} 1 \\ 3 \\ 5 \end{array}\right ] =\left [\begin{array}{c} 0 \\ 0 \\ 0 \end{array}\right ]\nonumber \] Notice that this equation has nontrivial solutions, for example \(a=2\), \(b=3\) and \(c=-1\). Therefore \(S\) is dependent.
The following is an important result regarding dependent sets.
Lemma \(\PageIndex{1}\): Dependent Sets
Let \(V\) be a vector space and suppose \(W = \left\{ \vec{v}_1, \vec{v}_2, \cdots, \vec{v}_k \right\}\) is a subset of \(V\). Then \(W\) is dependent if and only if \(\vec{v}_i\) can be written as a linear combination of \(\left\{ \vec{v}_1, \vec{v}_2, \cdots, \vec{v}_{i-1}, \vec{v}_{i+1}, \cdots, \vec{v}_k \right\}\) for some \(i \leq k\).
Revisit Example \(\PageIndex{2}\) with this in mind. Notice that we can write one of the three vectors as a combination of the others. \[\left [\begin{array}{c} 1 \\ 3 \\ 5 \end{array}\right ] = 2\left [\begin{array}{c} -1 \\ 0 \\ 1 \end{array}\right ] +3\left [\begin{array}{c} 1 \\ 1 \\ 1 \end{array}\right ]\nonumber \]
By Lemma \(\PageIndex{1}\) this set is dependent.
If we know that one particular set is linearly independent, we can use this information to determine if a related set is linearly independent. Consider the following example.
Example \(\PageIndex{3}\): Related Independent Sets
Let \(V\) be a vector space and suppose \(S \subseteq V\) is a set of linearly independent vectors given by \(S = \left\{ \vec{u}, \vec{v}, \vec{w} \right\}\). Let \(R \subseteq V\) be given by \(R = \left\{ 2\vec{u} - \vec{w}, \vec{w} + \vec{v}, 3\vec{v} + \frac{1}{2} \vec{u} \right\}\). Show that \(R\) is also linearly independent.
Solution
To determine if \(R\) is linearly independent, we write \[a(2\vec{u} - \vec{w}) + b(\vec{w} + \vec{v}) + c( 3\vec{v} + \frac{1}{2}\vec{u}) = \vec{0}\nonumber \] If the set is linearly independent, the only solution will be \(a=b=c=0\). We proceed as follows. \[\begin{aligned} a(2\vec{u} - \vec{w}) + b(\vec{w} + \vec{v}) + c( 3\vec{v} + \frac{1}{2} \vec{u}) &= \vec{0} \\ 2a\vec{u} - a\vec{w} + b\vec{w} + b\vec{v} + 3c\vec{v} + \frac{1}{2}c\vec{u} &= \vec{0}\\ (2a + \frac{1}{2}c) \vec{u} + (b+3c)\vec{v} + (-a + b) \vec{w} &= \vec{0}\end{aligned}\]
We know that the set \(S = \left\{ \vec{u}, \vec{v}, \vec{w} \right\}\) is linearly independent, which implies that the coefficients in the last line of this equation must all equal \(0\). In other words: \[\begin{aligned} 2a + \frac{1}{2} c &= 0 \\ b + 3c &= 0 \\ -a + b &= 0 \end{aligned}\]
The augmented matrix and resulting reduced row-echelon form are given by: \[\left [ \begin{array}{rrr|r} 2 & 0 & \frac{1}{2} & 0 \\ 0 & 1 & 3 & 0 \\ -1 & 1 & 0 & 0 \end{array}\right ] \rightarrow \cdots \rightarrow \left [ \begin{array}{rrr|r} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \end{array}\right ]\nonumber \] Hence the solution is \(a=b=c=0\) and the set is linearly independent.
The following theorem was discussed in terms in \(\mathbb{R}^n\). We consider it here in the general case.
Theorem \(\PageIndex{1}\): Unique Representation
Let \(V\) be a vector space and let \(U = \left\{ \vec{v}_1, \cdots, \vec{v}_k \right\} \subseteq V\) be an independent set. If \(\vec{v} \in \mathrm{span} \;U\), then \(\vec{v}\) can be written uniquely as a linear combination of the vectors in \(U\).
Consider the span of a linearly independent set of vectors. Suppose we take a vector which is not in this span and add it to the set. The following lemma claims that the resulting set is still linearly independent.
Lemma \(\PageIndex{2}\): Adding to a Linearly Independent Set
Suppose \(\vec{v}\notin \mathrm{span}\left\{ \vec{u}_{1},\cdots ,\vec{u}_{k}\right\}\) and \(\left\{ \vec{u}_{1},\cdots , \vec{u}_{k}\right\}\) is linearly independent. Then the set \[\left\{ \vec{u}_{1},\cdots ,\vec{u}_{k},\vec{v} \right\}\nonumber \] is also linearly independent.
- Proof
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Suppose \(\sum_{i=1}^{k}c_{i}\vec{u}_{i}+d\vec{v}= \vec{0}.\) It is required to verify that each \(c_{i}=0\) and that \(d=0.\) But if \(d\neq 0,\) then you can solve for \(\vec{v}\) as a linear combination of the vectors, \(\left\{ \vec{u}_{1},\cdots ,\vec{u} _{k}\right\}\), \[\vec{v}=-\sum_{i=1}^{k}\left( \frac{c_{i}}{d}\right) \vec{u}_{i}\nonumber \] contrary to the assumption that \(\vec{v}\) is not in the span of the \(\vec{u}_{i}\). Therefore, \(d=0.\) But then \(\sum_{i=1}^{k}c_{i} \vec{u}_{i}=\vec{0}\) and the linear independence of \(\left\{ \vec{u} _{1},\cdots ,\vec{u}_{k}\right\}\) implies each \(c_{i}=0\) also.
Consider the following example.
Example \(\PageIndex{4}\): Adding to a Linearly Independent Set
Let \(S \subseteq M_{22}\) be a linearly independent set given by \[S = \left\{ \left [ \begin{array}{rr} 1 & 0 \\ 0 & 0 \end{array} \right ], \left [ \begin{array}{rr} 0 & 1 \\ 0 & 0 \end{array} \right ] \right\}\nonumber \] Show that the set \(R \subseteq M_{22}\) given by \[R = \left\{ \left [ \begin{array}{rr} 1 & 0 \\ 0 & 0 \end{array} \right ], \left [ \begin{array}{rr} 0 & 1 \\ 0 & 0 \end{array} \right ], \left [ \begin{array}{rr} 0 & 0 \\ 1 & 0 \end{array} \right ] \right\}\nonumber \] is also linearly independent.
Solution
Instead of writing a linear combination of the matrices which equals \(0\) and showing that the coefficients must equal \(0\), we can instead use Lemma \(\PageIndex{2}\) .
To do so, we show that \[\left [ \begin{array}{rr} 0 & 0 \\ 1 & 0 \end{array} \right ] \notin \mathrm{span}\left\{ \left [ \begin{array}{rr} 1 & 0 \\ 0 & 0 \end{array} \right ], \left [ \begin{array}{rr} 0 & 1 \\ 0 & 0 \end{array} \right ] \right\}\nonumber \]
Write \[\begin{aligned} \left [ \begin{array}{rr} 0 & 0 \\ 1 & 0 \end{array} \right ] &= a\left [ \begin{array}{rr} 1 & 0 \\ 0 & 0 \end{array} \right ] + b\left [ \begin{array}{rr} 0 & 1 \\ 0 & 0 \end{array} \right ] \\ &= \left [ \begin{array}{rr} a & 0 \\ 0 & 0 \end{array} \right ] + \left [ \begin{array}{rr} 0 & b \\ 0 & 0 \end{array} \right ] \\ &= \left [ \begin{array}{rr} a & b \\ 0 & 0 \end{array} \right ]\end{aligned}\]
Clearly there are no possible \(a,b\) to make this equation true. Hence the new matrix does not lie in the span of the matrices in \(S\). By Lemma \(\PageIndex{2}\) , \(R\) is also linearly independent.


Covalent-Network Solids: Semiconductors and Insulators
Skills to Develop
- Explain the properties of some covalent-network solids
- Describe semiconductors and some of their properties
You can read a quick introduction to covalent-network solids in the intro page. The basic idea is that to make a network of covalent bonds, each atom (or many of the atoms) have to make 3 or 4 bonds to other atoms. This means that covalent-network solids usually include carbon, silicon, and their neighbors in the periodic table. Here, we'll focus on simple, orderly structures like diamond, graphite, and pure silicon. There are also covalent-network solid oxides, like the silicates, in which oxygen atoms connect 2 silicon atoms, and each silicon atom connects to 4 oxygens. Partially covalent oxides are what most rocks and ceramics are made of.
Graphite
Carbon has 2 allotropes , or pure elemental forms. The more stable form is graphite, a dark, slippery material used in pencils and lubricants. Remember that carbon typically makes 4 bonds. The structure of graphite is flat hexagonal sheets; a single sheet is called graphene . Each carbon atom makes 3 σ bonds and the leftover p orbitals form a delocalized π-bond network over the whole sheet, very similar to the π-bonding in benzene. The π-bond system actually forms bands, like in a metal, allowing graphite to conduct electricity along the sheets. Weak interactions, like London dispersion forces, (called π-stacking in this case) hold the sheets loosely together. Because they can slide past each other (especially when impurity atoms are trapped in between) graphite is a good lubricant.
Diamond Structure
The other bulk allotrope of carbon is diamond. In diamond, each carbon makes 4 bonds in tetrahedral directions to other carbon atoms. The structure is like the zinc blende ionic structure, except that all the atoms are the same. The properties of diamond (insulator, hard) come from the strong covalent bonds. Remember that C-C bonds are some of the strongest covalent bonds. It's easiest to think about diamond as forming with sp 3 hybrid orbitals on each atom. It's hard to imagine the MO interactions, but the main thing we can know is that because there is good energy match and good overlap between the atoms, the splitting (energy difference) between bonding and anti-bonding MOs will be big (and there won't be any non-bonding MOs, because each atom has 4 orbitals and makes 4 bonds). There will still be bands like in metals, but now there are 2 bands with a big energy gap in the middle. The low-energy, bonding band is called the valence band , and there are exactly enough electrons to fill it. The high-energy, anti-bonding band is called the conduction band , and it is empty.
If it was hard to understand the previous paragraph, let's just imagine making 1 bond between 2 atoms. We use one sp 3 hybrid on each atom. These point right at each other, have exactly the same energy, and have good overlap. We can imagine drawing an MO diagram just like for H 2 , with a big energy gap between the bonding and anti-bonding orbitals. Each atom has 4 electrons total, and makes 4 bonds just like this, so each bond gets 1 electron from each atom: just enough to fill up the bonding MO. When we multiply this over all the bonds in the diamond, we get the full valence band and the empty conduction band. The energy gap between them is called the band gap . In diamond, the band gap is big, and so diamond is an insulator.
Semiconductors
Silicon has a structure just like diamond. (It doesn't make graphite, because mostly π-bonds are weak for the second-row elements.) However, silicon has a smaller band gap than diamond. Germanium, which is below silicon in the periodic table, has the same structure, and an even lower band gap. Generally, as we go down the periodic table, covalent bond strengths get smaller, which is the same as saying that the splitting between bonding and antibonding orbitals gets smaller. It's hard to say why, but if you assume that heavier atoms have worse orbital overlap, you will usually make good predictions.
Semiconductors are materials that conduct electricity just a little bit. They are the basis for all computing and electronics. Semiconductivity comes from having a not-quite-full valence band, a not-quite-empty conduction band, or both. If there are a few electrons in the conduction band, they can conduct electricity just like in a metal (except less, because there aren't very many of them!). If there are a few electrons missing from the valence band, the empty spots are called holes and they can move around, also conducting electricity. If the band gap of a material is not too big compared to the thermal energy, then a few electrons can be in the conduction band even though there is room for them in the valence band (because of thermal energy). For this reason, semiconductors conduct better at higher temperature, because more electrons will be in the conduction band.
Doping Semiconductors
The other way to make a semiconductor, with a material whose band gap is too big at room temperature, is by adding some impurity atoms with different numbers of electrons, which is called doping . Imagine that you have silicon with just a few nitrogen atoms replacing silicon atoms. Each N has an extra electron. Now there will be a few electrons in the conduction band, so it's a semiconductor! And we can control the conductivity by controlling how much N we add. We can do the same thing if we add a little bit of boron, which has 3 electrons. In this case, there would be a few holes in the valence band. These are called p-type (positive, less electrons, like with B) or n-type (negative, extra electrons, like with N) semiconductors. Lots of important devices, like LEDs, solar cells and transistors (the basis of computer chips) are made of layers of p-type and n-type semiconductors.
Compound Semiconductors
We can also make semiconductors that are compounds, like gallium arsenide (formula GaAs). These have an AB formula, and there are always 8 valence electrons in the formula. For example, Ga has 3 and As has 5, so GaAs has 8. Another example is ZnSe, (Zn has 2 valence electrons in 4s, Se has 6 valence electrons just like O). Thus, they have the same number of valence electrons as C or Si. They also have the same structure (zinc blende, just like diamond except that that atoms alternate types). By combining many different elements, we can change various properties, like band gap, to be exactly what we want. Generally, the band gap increases as the 2 elements are farther apart (the bonding becomes more ionic, and ionic solids aren't conductive). We can even mix 3 or more elements, like in CdZnTe (the actual formula would probably be written (Cd,Zn)Te, meaning that the number of Cd + Zn = Te). To make semiconductors with the right properties, we can use different combinations of elements and also dope with many different elements.


5.6: Information Sources- Online
The traditional and media formats may also exist online or in digital formats; these can be found through websites or in library databases. But there are other types of sources unique to the online environment that you might want to consider—or not consider—using. Below are just a few of them.
Wikis
Wikis are a type of website that typically allow a community of users to create pages about different topics. The most popular one, and one that you are probably familiar with, is Wikipedia. These websites are usually very simple in appearance and they are unique because they tend to support the idea of a community contributing to sharing information. With this idea, though, is the possibility for information to be shared without review or checked for reliability. Review the Fact-Checking chapter for further information about how to use Wikipedia effectively .
Blogs
Blogs can house primary source material as they are often like online diaries for individuals. In contrast to wikis, blogs are typically written by a single person, and that individual is typically sharing their perspectives or experiences about a specific topic. These can be insightful, but they are usually very opinion driven. And just because someone has a blog about a topic does not make them an expert about that topic.
Podcasts
Podcasts continue to grow in popularity, and over half of Americans have listened to at least one podcast (Winn). If you have not experienced a podcast, they are similar to radio programs, except that you don’t have to listen to them live to enjoy them—they can be downloaded or streamed at a time convenient to the listener. You can listen to them in your car or from a capable device, like a smartphone. They can be focused on a specific subject area, contain interviews, or be a fictional series show. But just like blogs, podcasts can be hosted by anyone—and can be driven by opinions and biases.
Sources
Image: “ Blog ” by Freepik , adapted by Aloha Sargent, from Flaticon.com
Image: “ Microphone ” by Smashicons , adapted by Aloha Sargent, from Flaticon.com
Image: “ Wikipedia ” by xnimrodx , adapted by Aloha Sargent, from Flaticon.com
Winn, Ross. “ 2020 Podcast Stats & Facts (New Research From Oct 2020) .” Podcast Insights , Quandary Media, 6 Oct. 2020.


3.2: Social Cognition
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The human faculty of Social Cognition
Playing football as a complex social activity
Humans are by far the most talented species in reading the minds of others. That means we are able to successfully predict what other humans perceive, intend, believe, know or desire. Among these abilities, understanding the intention of others is crucial. It allows us to resolve possible ambiguities of physical actions. For example, if you were to see someone breaking a car window, you would probably assume he was trying to steal a stranger's car. He would need to be judged differently if he had lost his car keys and it was his own car that he was trying to break into. Humans also collaborate and interact culturally. We perform complex collaborative activities, like building a house together or playing football as a team. Over time this led to powerful concepts of organizational levels like societies and states. The reason for this intense development can be traced back to the concept of Shared Intentionality .
Shared Intentionality
An intentional action is an organism's intelligent behavioural interaction with its environment towards a certain goal state. This is the concept of Problem Solving , which was already described in the previous chapter.
The social interaction of agents in an environment which understand each other as acting intentionally causes the emergence of Shared Intentionality. This means that the agents work together towards a shared goal in collaborative interaction. They do that in coordinated action roles and mutual knowledge about themselves. The nature of the activity or its complexity is not important, as long as the action is carried out in the described fashion. It is important to mention that the notion of shared goals means that the internal goals of each agent include the intentions of the others. This can easily be misinterpreted. For example, take a group of apes on a hunt. They appear to be acting in a collaborative way, however, it is reasonable to assume that they do not have coordinated action roles or a shared goal – they could just be acting towards the same individual goal. Summing up, the important characteristics of the behaviour in question are that the agents are mutually responsive, have the goal of achieving something together and coordinate their actions with distributed roles and action plans.
The strictly human faculty to participate in collaborative actions that involve shared goals and socially coordinated action plans is also called Joint Intention . This requires an understanding of the goals and perceptions of other involved agents, as well as sharing and communicating these, which again seems to be a strictly human behaviour. Due to our special motivation to share psychological states, we also need certain complex cognitive representations. These representations are called dialogic cognitive representations , because they have as content mostly social engagement. This is especially important for the concept of joint intentions, since we need not only a representation for our own action plan, but also for our partner's plan. Joint Intentions are an essential part of Shared Intentionality.
Dialogic cognitive representations are closely related with the communication and use of linguistic symbols. They allow in some sense a form of collective intentionality , which is important to construct social norms, conceptualize beliefs and, most importantly, share them. In complex social groups the repeated sharing of intentions in a particular interactive context leads to the creation of habitual social practices and beliefs. That may form normative or structural aspects of a society, like government, money, marriage, etc. Society might hence be seen as a product and an indicator of Social Cognition.
The social interaction that builds ground for activities involving Shared Intentionality is proposed to be divided into three groups:
- Dyadic engagement : The simple sharing of emotions and behaviour, by means of interaction and direct mutual response between agents. Dyadic interaction between human infants and adults are called protoconversations . These are turn-taking sequences of touching, face expressions and vocalisations. The exchange of emotions is the most important outcome of this interaction.
- Triadic engagement : Two agents act together towards a shared goal, while monitoring the perception and goal-direction of the other agent. They focus on the same problem and coordinate their actions respectively, which makes it possible to predict following events.
- Collaborative engagement : The combination of Joint Intentions and attention. At this point, the agents share a goal and act in complementary roles with a complex action plan and mutual knowledge about the selective attention and the intentions of one another. The latter aspect allows the agents to assist each other and reverse or take over roles.
These different levels of social engagement require the understanding of different aspects of intentional action, as introduced above, and presuppose the motivation to share psychological states with each other.
Development of Social Cognition during childhood
Children making social experiences
A crucial point for Social Cognition is the comprehension of intentional action. Children's understanding of intentional action can basically be divided into three groups, each representing a more complex level of grasp.
- The first one to be mentioned is the identification of animate action. This means that after a couple of months, babies can differentiate between motion that was caused by some external influence and actions that an organism has performed by itself, as an animate being. At this stage, however, the child has not yet any understanding of potential goals the observed actor might have, so it is still incapable of predicting the behaviour of others.
- The next stage of comprehension includes the understanding that the organism acts with persistence towards achieving a goal. Children can now distinguish accidental incidents from intentional actions and failed from successful attempts. This ability develops after about 9 months. With this new perspective, the child also learns that the person it observes has a certain perception - thus a certain amount of predicting behaviour is possible. This is an essential difference between the first and the second stage.
- After around 14 months of age, children fully comprehend intentional action and the basics of rational decision making. They realise, that an actor pursuing a goal may have a variety of action plans to achieve a goal, and is choosing between them. Furthermore, a certain sense for the selective attention of an agent develops. This allows a broad variety of predictions of behaviour in a certain environment. In addition to that, children acquire the skill of cultural learning: when they observe how an individual successfully reaches a goal, they memorise the procedure. Hence, they can use the methods to reach their own goals. This is called imitative learning, which turns out to be an extremely powerful tool. By applying this technique, children also learn how things are conventionally done in their culture.


4.4: Features of Language
Human language is distinct and unique because there are specific features that distinguish human language from any other form of communication. It is unique from such forms of animal communication because it has linguistic rules that are followed in order to speak, it uses meaningful symbols, and we are continuously creating new ideas.[7] There are some aspects of human language that are features of a true language, meaning humans are the only ones with this ability and is one of the key properties separating human language from the animal language. For example, displacement and productivity are part of "true language", but although they are abilities found only in humans, not all languages have them.[8] The most recognized features of the human language are as follows:
- Duality of patterning : associates sounds with meaning. For Example CAT/TACK/ACT the same phonemes are expressed but organized in a different order to convey different information.
- Productivity : Symbols and rules can be combined for infinite messages. Productivity is also the ability of the native speakers to use certain grammatical processes, mainly in the formation of words.
- Interchangeability : Speakers are able to send and receive messages.
- Arbitrariness: No association with words, and its meaning except for the sounds. For Example, The words "whale" and "microorganism" do not convey any relation to the size or physicality of the word and the physicality of the subject.
- Displacement in time, space, role : Being able to talk about the non-current. This allows people to communicate about the past, future, and distant places.
- Specialization: Language only serves the purpose of communication.
- Cultural transmission : Specifics must be learned by each person.
[7]


6.6: The Internal Environment
- How and why do managers conduct an internal analysis of their firms?
A firm’s internal environment consists of members of the firm itself, investors in the firm, and the assets a firm has. Employees and managers are good examples; they are firm members who have skills and knowledge that are valuable assets to their firms. Evaluating a firm’s internal environment is not just a matter of counting heads, however. Successful firms have a wide range of resources and capabilities that they can use to maintain their success and grow into new ventures. A thorough analysis of a firm’s internal situation provides a manager with an understanding of the resources available to pursue new initiatives, innovate, and plan for future success.
Resources and Capabilities
A firm’s resources and capacities are the unique skills and assets it possesses. Resources are things a firm has to work with, such as equipment, facilities, raw materials, employees, and cash. Capabilities are things a firm can do, such as deliver good customer service or develop innovative products to create value. Both are the building blocks of a firm’s plans and activities, and both are required if a firm is going to compete successfully against its rivals. Firms use their resources and leverage their capabilities to create products and services that have some advantage over competitors’ products. For example, a firm might offer its customers a product with higher quality, better features, or lower prices. Not all resources and capabilities are equally helpful in creating success, though. Internal analysis identifies exactly which assets bring the most value to the firm.
The Value Chain
Before examining the role of resources and capabilities in firm success, let’s take a look at the importance of how a firm uses those factors in its operations. A firm’s value chain is the progression of activities it undertakes to create a product or service that consumers will pay for. A firm should be adding value at each of the chain of steps it follows to create its product. The goal is for the firm to add enough value so that its customers will believe that the product is worth buying for a price that is higher than the costs the firm incurs in making it. As an example, Figure \(\PageIndex{1}\) illustrates a hypothetical value chain for some of Walmart’s activities.
In this example, note that value increases from left to right as Walmart performs more activities. If it adds enough value through its efforts, it will profit when it finally sells its services to customers. By working with product suppliers (procurement), getting those products to store locations efficiently (inbound logistics), and automatically keeping track of sales and inventory (information technology), Walmart is able to offer its customers a wide variety of products in one store at low prices, a service customers value. Primary activities , the ones across the bottom half of the diagram, are the actions a firm takes to directly provide a product or service to customers. Support activities , the ones across the top of the diagram, are actions required to sustain the firm that are not directly part of product or service creation.
Using Resources and Capabilities to Build an Advantage over Rivals
A firm’s resources and capabilities are not just a list of equipment and things it can do. Instead, resources and capabilities are the distinctive assets and activities that separate firms from each other. Firms that can amass critical resources and develop superior capabilities will succeed in competition over rivals in their industry. Strategists evaluate firm resources and capabilities to determine if they are sufficiently special to help the firm succeed in a competitive industry.
Using VRIO
The analytical tool used to assess resources and capabilities is called VRIO . As usual, this is an acronym developed to remind managers of the questions to ask when evaluating their firms’ resources and capabilities. The four questions of VRIO, which focus on value, rarity, imitation, and organization, are illustrated in Figure \(\PageIndex{2}\).
If each question can be answered with a “yes,” then the resource or capability being evaluated can be the source of a competitive advantage for the firm. An example will help you better understand the VRIO process.
Imagine that you are a top manager for Starbucks and you want to understand why you are able to be successful against rivals in the coffee industry. You make a list of some of Starbucks’ resources and capabilities and use VRIO to determine which ones are key to your success. These are shown in Table \(\PageIndex{1}\).
Starbucks' Resources and Capabilities
| Resources | Capabilities |
|---|---|
| Brand name | Making quality coffee drinks |
| Thousands of locations worldwide | Delivering excellent customer service |
| Cash | Training excellent staff |
| Loyal customers | Paying above-average wages |
| Well-trained employees | Retaining quality employees |
Table \(\PageIndex{1}\) (Attribution: Copyright Rice University, OpenStax, under CC-BY 4.0 license)
You look at your list and decide to pick a few of the entries to evaluate with VRIO (Table \(\PageIndex{2}\)):
Evaluating Starbucks' VRIO
| Resource/ Capability | Is it valuable? | Is it rare? | Is it difficult to imitate? | Is Starbucks organized to capture its value? | Can it be a basis for competitive advantage? |
|---|---|---|---|---|---|
| Brand Name | Yes | Yes | Yes | Yes | Yes |
| Delivering excellent customer service | Yes | Yes | Yes | Yes | Yes |
| Thousands of locations worldwide | Yes | No | No | Yes | Yes |
Table \(\PageIndex{2}\): (Attribution: Copyright Rice University, OpenStax, under CC-BY 4.0 license)
According to the evaluation above, Starbucks’ brand helps it compete and succeed against rivals, as does its excellent customer service. However, simply having a lot of locations globally isn’t enough to beat rivals—McDonald’s and Subway also have thousands of worldwide locations, and both serve coffee. Starbucks succeeds against them because of their brand and customer service.
- What are firm resources and capabilities?
- Describe a value chain and what the activities in the chain represent.
- What is VRIO? What questions do the letters stand for, and how does using VRIO help a manager make decisions?
Technology and Innovation: Uber, Lyft, and the Self-Driving Car: The Transportation of the Future Is Coming Soon
Although the ride-sharing industry is still relatively new, it has seen explosive growth, and its two main rivals, Uber and Lyft, are looking for ways to increase their capacity to serve riders. Both firms, and rivals like them, operate in basically the same way. A person needing a ride uses a smartphone app to alert a nearby person with a car of their location. The driver, usually an independent contractor for the service (meaning they are just a person with a car that has signed up to provide rides in exchange for a portion of the fare the customer pays), picks up the customer and drives them to their destination. Paying for the ride is also handled through the app, and the driver receives about 75–80% of the fare, with Uber or Lyft keeping the balance. 1
The popularity of ride-sharing services has soared, and both companies are constantly recruiting more drivers. However, both companies have also explored alternatives to independent drivers: self-driving cars. Uber and Lyft have taken different paths to develop this capability. Uber has worked to internally develop its own software technology and self-driving car technology, while Lyft has focused on software interfaces that can accommodate other companies’ self-driving cars. 2 Lyft’s partnerships with firms such as Google and GM that are already developing self-driving cars has put it ahead of Uber in the race to get driverless vehicles into its ride-sharing network, and it was able to test self-driving cars in Boston by partnering with NuTonomy in 2017. 3 Lyft offered a demonstration to journalists at the Consumer Electronics Show in Las Vegas in 2018, offering rides in self-driving cars developed by Aptiv. 4 Uber had been testing similar technology in Pittsburgh but suspended its self-driving car program after a fatal pedestrian accident in Arizona. 5
Sources: Ridester (2017). “How Much do Uber Drivers Actually Make? The Inside Scoop.”Ridester.com. https://www.ridester.com/how-much-do...-drivers-make/ Accessed July 29, 2017; Bensinger, Greg (2017). “Lyft Shifts Gears With New Driverless-Car Division; San Francisco company to hire hundreds of engineers and open new Silicon Valley office.”The Wall Street Journal. July 21, 2017; Edelstein, Stephen (2017). “Lyft Finally Launches Its Boston Self-Driving Car Pilot Program.”The Drive. Dec. 17, 2017. http://www.thedrive.com/tech/16779/l...-pilot-program ; O’Kane, Sean (2018). “I took a gamble by riding in a self-driving Lyft in Las Vegas.”The Verge. January 8, 2018. https://www.theverge.com/2018/1/8/16...vegas-ces-2018 ; and Korosec, Kristen (2018). “Uber self-driving cars back on public roads, but in manual mode/”Tech Crunch. July 24, 2018. techcrunch.com/2018/07/24/ub...in-manualmode/.
Critical Thinking Questions
- What resource or capability challenges have Uber and Lyft faced because of their fast company growth?
- What PESTEL factors do you think are contributing to the popularity of ride-sharing services?
- What industry challenges (think of Porter’s Five Forces) does the use of self-driving cars address?
References
1. Ridester (2017). “How Much do Uber Drivers Actually Make? The Inside Scoop.”Ridester.com. https://www.ridester.com/how-much-do...-drivers-make/ Accessed July 29, 2017.
2. Bensinger, Greg (2017). “Lyft Shifts Gears With New Driverless-Car Division; San Francisco company to hire hundreds of engineers and open new Silicon Valley office.”The Wall Street Journal. July 21, 2017.
3. Edelstein, Stephen (2017). “Lyft Finally Launches Its Boston Self-Driving Car Pilot Program.”The Drive. Dec. 17, 2017. http://www.thedrive.com/tech/16779/l...-pilot-program
4. O’Kane, Sean (2018). “I took a gamble by riding in a self-driving Lyft in Las Vegas.”The Verge. January 8, 2018. https://www.theverge.com/2018/1/8/16...vegas-ces-2018
5. Korosec, Kristen (2018). “Uber self-driving cars back on public roads, but in manual mode/”Tech Crunch. July 24, 2018. techcrunch.com/2018/07/24/ub...in-manualmode/


6.4: Case Study 3- Pregnant Adult Client (continued)
1. Which blood pressure do you record?
The blood pressure readings that were taken after the woman rested for five minutes should be recorded. Record both the right arm and left arm reading in the narrative notes and the highest blood pressure reading on the vital sign record (e.g., the right arm reading of 132/90). Whenever a reading is elevated, consider repeating the measurement for confirmation.
2. Is the variation between the arms of concern?
The difference between the two arms is not significant. A difference below 10 mm Hg between arms is normal.
1430 hrs, August 14, 2018
- T 37.1°C axilla
- RR 14 (shallow breathing)
- P 92 radial in sitting position, regular rhythm, 2+ force, Sp02 97%
- BP 134/90
1435 hrs, August 14, 2018
- BP 132/90 mm Hg right arm, P 92
- BP 128/88 mm Hg left arm, P 88
Print the blank vital sign record and document the woman’s vital signs. Then, go to the next page to see accurate documentation of vital signs.


30.22: Plant Sensory Systems and Responses - Abscisic Acid, Ethylene, and Nontraditional Hormones
- Describe the roles played by ethylene and nontraditional hormones in plant development
Growth Responses
In addition to the growth hormones auxins, cytokinins, gibberellins, there are two more major types of plant hormones, abscisic acid and ethylene, as well as several other less-studied compounds that control plant physiology.
Abscisic Acid
The plant hormone abscisic acid (ABA) was first discovered as the agent that causes the abscission or dropping of cotton bolls. However, more-recent studies indicate that ABA plays only a minor role in the abscission process. ABA accumulates as a response to stressful environmental conditions, such as dehydration, cold temperatures, or shortened day lengths. Its activity counters many of the growth-promoting effects of GAs and auxins. ABA inhibits stem elongation and induces dormancy in lateral buds.
ABA induces dormancy in seeds by blocking germination and promoting the synthesis of storage proteins. Plants adapted to temperate climates require a long period of cold temperature before seeds germinate. This mechanism protects young plants from sprouting too early during unseasonably warm weather in winter. As the hormone gradually breaks down over winter, the seed is released from dormancy and germinates when conditions are favorable in spring. Another effect of ABA is to promote the development of winter buds; it mediates the conversion of the apical meristem into a dormant bud. Low soil moisture causes an increase in ABA, which causes stomata to close, reducing water loss in winter buds.
Ethylene
Ethylene is associated with fruit ripening, flower wilting, and leaf fall. Ethylene is unusual because it is a volatile gas (C 2 H 4 ). Hundreds of years ago, when gas street lamps were installed in city streets, trees that grew close to lamp posts developed twisted, thickened trunks, shedding their leaves earlier than expected. These effects were caused by ethylene volatilizing from the lamps.
Aging tissues (especially senescing leaves) and nodes of stems produce ethylene. The best-known effect of the hormone, however, is the promotion of fruit ripening. Ethylene stimulates the conversion of starch and acids to sugars. Some people store unripe fruit, such as avocados, in a sealed paper bag to accelerate ripening; the gas released by the first fruit to mature will speed up the maturation of the remaining fruit. Ethylene also triggers leaf and fruit abscission, flower fading and dropping, and promotes germination in some cereals and sprouting of bulbs and potatoes.
Ethylene is widely used in agriculture. Commercial fruit growers control the timing of fruit ripening with application of the gas. Horticulturalists inhibit leaf dropping in ornamental plants by removing ethylene from greenhouses using fans and ventilation.
Nontraditional Hormones
Recent research has discovered a number of compounds that also influence plant development. Their roles are less understood than the effects of the major hormones described so far.
Jasmonates play a major role in defense responses to herbivory. Their levels increase when a plant is wounded by a predator, resulting in an increase in toxic secondary metabolites. They contribute to the production of volatile compounds that attract natural enemies of predators. For example, chewing of tomato plants by caterpillars leads to an increase in jasmonic acid levels, which in turn triggers the release of volatile compounds that attract predators of the pest.
Oligosaccharins also play a role in plant defense against bacterial and fungal infections. They act locally at the site of injury; they can also be transported to other tissues. Strigolactones promote seed germination in some species and inhibit lateral apical development in the absence of auxins. Strigolactones also play a role in the establishment of mycorrhizae, a mutualistic association of plant roots and fungi. Brassinosteroids are important to many developmental and physiological processes. Signals between these compounds and other hormones, notably auxin and GAs, amplify their physiological effect. Apical dominance, seed germination, gravitropism, and resistance to freezing are all positively influenced by hormones. Root growth and fruit dropping are inhibited by steroids.
Key Points
- Under stress, abscisic acid accumulates in plants, inhibiting stem elongation and inducing bud dormancy.
- The plant hormone ethylene controls fruit ripening, flower wilting, and leaf fall by stimulating the conversion of starch and acids to sugars.
- Other nontraditional hormones such as jasmonates and oligosaccharins control defense responses from herbivores and bacterial/fungal infections, respectively.
Key Terms
- abscisic acid : a plant hormone that functions in many plant developmental processes, including bud dormancy, inhibition of seed germination, and plant stress tolerance.
- jasmonate : any of several esters of jasmonic acid that act as plant hormones
- ethylene : a plant hormone that is involved in fruit ripening, flower wilting, and leaf fall


12.5: Conclusion
In summary, definitions of the terms rural and/or rurality and delineation of rural from urban areas have been long debated topics in many academic works. Rural space comes into existence in certain areas, typified by a series of factors such as land use (especially for agriculture), population density, agricultural employment, and built areas. Generally, rural areas are considered to be synonymous with more extensive land use activities in agriculture and forestry, low population density, small settlements, and an agrarian way of life. Rural space is divided into territorial entities, with variable scales, covering the local or regional economy, and each unit includes both agricultural and non-agricultural activities. Different countries have varying definitions of rural for statistical and administrative purposes. Although urbanization is a global phenomenon, today about 45.5 percent of the world’s population still lives in rural areas. 8
There are many types of rural settlements. Early villages had to be near a reliable water supply, be defensible, and have sufficient land nearby for cultivation, to name but a few concerns. They also had to adapt to local physical and environmental conditions, conditions that can be identified with a practiced eye. Villages in the Netherlands are linear, crowded on the dikes surrounding land reclaimed from the sea. Circular villages in parts of Africa indicate a need for a safe haven for livestock at night. A careful examination of the rural settlement of a region reveals much about its culture, history and traditions.
Most people can agree that cities are places where large numbers of people live and work, and are hubs of government, commerce, and transportation. But how best to define the geographical limits of a city is a matter of some debate. So far, no standardized international criteria exist for determining the boundaries of a city. Often, different boundary definitions are available for any given city. The “city proper,” for example, describes a city according to an administrative boundary, while “urban agglomeration,” considers the extent of the built-up area, to delineate the city’s boundaries. A third concept of the city, the “metropolitan area,” defines its boundaries according to the degree of economic and social interconnectedness of nearby areas.
The United Nations, the most comprehensive source of statistics regarding urbanization, emphasizes the fact that more than one half of the world population now lives in urban areas (54.5 percent in 2016) 9 , and virtually all countries of the world are becoming increasingly urbanized. Yet, given the fact that different countries use different definitions, it is difficult to know exactly how urbanized the world has become. Canada and Australia consider urban any settlements of 1,000 inhabitants or more, for example, while a settlement of 2,000 is a significant urban center in Peru. Other countries consider other limits for urban settlements such as 5,000 inhabitants in Romania and 50,000 in Japan. Consequently, in 2016, the percentage of urban population by continent was as follows: North America, 81 percent, the most urbanized continent in the world; Latin America, 80 percent; Europe, 74 percent; Oceania, 70 percent; Asia, 48 percent; and Africa, 41 percent. 10


7.1: Introduction
The Biomedical Model asserts that diseases have a cause or causes based in human biology. Additionally, risk factors and protective factors may exist as well which increase or decrease a person’s likelihood of developing a disease. This model is very useful in helping to identify, diagnose, and develop treatments for different diseases - whether they are transmissible between humans or not. The more we discover about these causes and factors, the more we can take steps to discover and treat diseases earlier, as well as take steps to prevent these diseases from occurring or progressing. In this chapter, we will go over different types of diseases, and some that are emerging or current concerns. We’ll also discuss how public health is working to address these diseases with detection and prevention efforts.


Builds confidence and higher levels of self-esteem
Allows free exploration of the environment
Fosters learning through hands-on and sensory exploration
It is now understood that moments often discounted as “just play” or as “fiddling around” are actually moments in which children are actively learning (Hirsh-Pasek et al. 2009; Jones and Reynolds 2011; Zigler, Singer, and Bishop-Josef 2004; Elkind 2007.) While engaged in play, children explore the physical properties of materials and the possibilities for action, transformation, or representation. Children try out a variety of ways to act on objects and materials and, in so doing, experiment with and build concepts and ideas. This active engagement with the world of people and objects starts from the moment of birth.
This description of the young child as an active participant in learning informs the role of the teacher who works with young children birth to five. Early childhood teaching and learning begins with teachers watching and listening to discover how infants and young children actively engage in making sense of their everyday encounters with people and objects. When teachers observe and listen with care, infants and young children reveal clues about their thinking, their feelings, or their intentions. Children’s actions, gestures, and words illuminate what they are trying to figure out or how they attempt to make sense of the attributes, actions, and responses of people and objects. Effective early childhood teaching requires teachers to recognize how infants and young children actively search for meaning, making sense of ideas and feelings.
When teaching is viewed in this light, children become active participants alongside teachers in negotiating the course of the curriculum. Families who entrust their children to the care and guidance of early childhood teachers also become active participants in this process. Shared participation by everyone in the work of creating lively encounters with learning allows a dynamic exchange of information and ideas—from child to adult, from adult to child, from adult to adult, and from child to child. The perspective of each (child, family, teacher) informs the other, and each learns from the other. Each relationship (child with family, child with teacher, child with child, and family with teacher) is reciprocal, with each participant giving and receiving from the other, and each adding to the other’s learning and understanding.
[2]
The
Educators’ Guide to the Framework For School Age Care In Australia
discusses the benefits of play:
Play is a valued process, not only for enjoyment and leisure, but also for learning. Through play, children develop a sense of identity and an understanding of their social and cultural worlds. Children use play to explore and understand cultures, communities and friendships. We gain a lot through playing, not just as children, but also as adults.
Recent brain research has heralded the benefits of a stimulating play-based environment in encouraging the brain to grow and develop (Diamond 1988). Low stress levels and high engagement combine to nourish neural development. Research by Vandell and others (2005) demonstrates how school-aged care environments achieve this through the combination of high intrinsic motivation and challenge, effort and enjoyment. Lester and Russell (2009) identified the flexibility and plasticity of the brain, which develops through play and increases potential for learning later in life.
The intellectual and cognitive benefits of playing have been well documented. Children who engage in quality play experiences are more likely to:
Have well developed memory skills and language development,
Have the ability to regulate their behavior, leading to enhanced adjustment to school and academic learning.
Play also provides children with an opportunity to just ‘be’.
[4]
Pause to Reflect
What does it mean to just be?  What facilitated the opportunity? What feelings did you experience? What might this mean for young children?
Educators observe stages of play experiences children navigate in their programs. Educators use these observations of children to plan for environments, set individual objectives and create appropriate curricular experiences.
Exploring, inspecting, and learning through repetitive physical activity.
[6]
Symbolic Play
The ability to use objects, actions, or ideas to represent other objects, actions, or ideas and may include taking on roles.
[7]
Constructive Play
Involves experimenting with objects to build things; learning things that were previously unknown with hands on manipulations of materials.
[8]
Games with Rules
Imposes rules that must be followed by everyone that is playing; the logic and order involved forms that the foundations for developing game playing strategy.
[9]
In addition to the stages of play described by Piaget, there are also a variety of types of play children use when interacting within our ECE Programs.
[4]
Australian Government Department of Education (n.d.) Educator My Time, Our Place. Retrieved from files.acecqa.gov.au/files/National-Quality-Framework-Resources-Kit/educators_my_time_our_place.pdf


18.13: Trust across Cultures
- Describe how leaders can build trust across cultures
Why Does Trust Matter?
Without trust we don’t truly collaborate; we merely coordinate or, at best, cooperate. It is trust that transforms a group of people into a team.
—Stephen R. Covey from his book, The Speed of Trust
Trust is an essential part of a successful team. Without trust, it is impossible for a company to reach its maximum potential. Building trust requires time and patience but is definitely worth the effort. Many teams that work together every day can build trust organically. However, when working with countries and cultures from around the world, building trust may require more effort. Since many international companies operate remotely, and meet with their teams through virtual communication platforms, leaders may not have daily interactions with their team. Therefore, building trust may take a long time. Trust must be earned over time through genuine and supportive words and actions. Most importantly, once trust has been established, it is essential for leaders to continue to nurture and develop trust in their relationships with their team.
How to Build Trust across Cultures
First and foremost, to successfully earn trust, managers must believe in the importance of building trust. If managers do not value trust, they will never put forth enough effort to establish it. There are multiple ways to establish and earn trust. It is important to understand that trust building looks different from one relationship to the next and may require differing amounts of time and energy to establish it. Building trust requires patience and understanding and is not something that can be built overnight. Understanding your employees’ and colleagues’ cultures and backgrounds can help managers gain insight into how others build trust. A 2019 article from the Harvard Business Review suggests asking the following questions to gain insight into the trust cultures of other countries: [1]
- How trusting is it?
- How performance oriented is it?
- How hierarchical and autocratic is it?
- How do people in that culture build trust themselves?
Having an open dialogue around trust can help managers to better understand how to establish trust on their teams. However, it is important to know when and where to have these conversations. In some cultures, these types of conversations should be held in a private, one-on-one setting. In other cultures, employees are not comfortable discussing their supervisors, as they follow a hierarchical approach to business.
There are two key foundations to building trust across cultures: results and character. For example, when someone performs their job duties well and yields great results, people are more trusting of them. In other cultures, a person’s character is valued above their performance. Understanding different cultures, and their definition and understanding of trust, is the first step in building it.
Additional Strategies
Recognition
It is important to give people credit for their work. Managers who recognize their team for their efforts are able to build rapport and trust with their teams. However, it is important to understand how other cultures receive recognition. For example, some people may not be comfortable getting recognized in a group setting. To avoid making people feel uncomfortable in these cases, managers can praise groups for their efforts in a public setting but provide individual recognition in private.
Respect
Respect is a key component to trust and should be highly valued. Managers can foster respect through transparency and strong expectations. To promote a respectful work environment, managers should prohibit disrespectful behavior and help to bridge the gap between cultural misunderstandings.
Consistency
Trust takes a long time to establish and only a moment to break. Consistency is key to maintaining and nurturing trust. Managers should handle similar situations in similar ways. Consistency helps to build trust and respect because it allows employees to predict the actions of their managers.
Sources
Solomon, Charlene. “ 10 Practical Tips to Build Trust as a Global Leader .” RW3, April 19, 2019.
-
Javidan, Mansour, and Aks Zaheer. “
How Leaders Around the World Build Trust Across Cultures
.” Harvard Business Review, May 27, 2019. ↵
Contributors and Attributions
- Trust across Cultures. Authored by : Freedom Learning Group. Provided by : Lumen Learning. License : CC BY: Attribution
- Authored by : rawpixel. Provided by : Pix. Located at : Pixabay. License : CC0: No Rights Reserved . License Terms : Pixabay License
- Authored by : rawpixel. Provided by : Pixabay. Located at : pixabay.com/photos/business-adu /. License : CC0: No Rights Reserved . License Terms : Pixabay License


22.3: Shock Drugs
By the end of this section, you should be able to:
- 22.3.1 Identify the characteristics of drugs used to treat anaphylactic, hypovolemic, and cardiogenic shock.
- 22.3.2 Explain the indications, actions, adverse reactions, and interactions of drugs used to treat anaphylactic, hypovolemic, and cardiogenic shock.
- 22.3.3 Describe nursing implications of drugs used to treat anaphylactic, hypovolemic, and cardiogenic shock.
- 22.3.4 Explain the client education related to drugs used to treat anaphylactic, hypovolemic, and cardiogenic shock.
Shock is a state of medical emergency in which tissues are not receiving enough oxygenated blood to sustain life. If not treated rapidly, decreased perfusion will cause hypoxia and eventually cell and tissue death. Because many different cells and tissues are at risk, cell and tissue death can lead to multiorgan failure and, eventually, death.
Anaphylactic Shock Drugs
Anaphylactic shock is a severe and life-threatening response to an allergen to which the body has a hypersensitivity. Typically, systemic vasodilation occurs, which causes shock and bronchoconstriction (often severe). Drugs are used to reverse bronchoconstriction and support hemodynamic stability.
Epinephrine
Epinephrine , a nonselective adrenergic agonist, is the most important drug used to treat anaphylactic shock. It causes sympathetic nervous system stimulation, which dilates the pulmonary bronchioles to open up airways and constricts blood vessels to increase blood pressure. Epinephrine acts very quickly and can decrease bronchoconstriction within 3–5 minutes. Epinephrine can be administered intramuscularly or intravenously depending on the acuteness of the situation. Table 22.8 earlier in the chapter is a drug prototype table for epinephrine use in emergency situations.
Nursing Implications
The nurse should do the following for clients receiving epinephrine intramuscularly or intravenously for anaphylactic shock:
- Place the client on continuous cardiac monitoring.
- Assess lung sounds prior to administration and frequently after administration.
- Monitor blood pressure frequently. (Blood pressure is often measured continuously when a client is in shock.)
- Monitor respiratory rate frequently.
- Monitor oxygen saturation continuously.
- Monitor level of consciousness.
- Have resuscitative equipment and drugs available.
- Provide client teaching regarding the drug. See below for client teaching guidelines.
Client Teaching Guidelines
In ventricular fibrillation, pulseless ventricular tachycardia, asystole, or pulseless electrical activity, the client will be unconscious. In anaphylaxis, the client may be unconscious.
If alert and oriented, the client receiving epinephrine should:
- Inform the health care team if they have a change in status (better or worse) after medication administration.
- Inform the health care team if they notice a change in their breathing.
Albuterol
Albuterol is a beta - adrenergic receptor agonist that causes bronchiole smooth muscle dilation, which opens up the bronchiole airways. Albuterol may be used in anaphylaxis if epinephrine does not fully open the airways. In anaphylaxis, it is administered as an inhaled nebulizer treatment.
Adverse Effects and Contraindications
Albuterol can cause paradoxical bronchospasm, tachycardia, and an immediate hypersensitivity reaction.
Hypersensitivity is the only contraindication to albuterol.
Table 22.14 is a drug prototype table for albuterol. It lists drug class, mechanism of action, adult dosage, indications, therapeutic effects, drug and food interactions, adverse effects, and contraindications.
|
Drug Class
Beta-adrenergic receptor agonist Mechanism of Action Directly stimulates beta receptors in the lungs, which causes smooth muscle dilation and opens airways |
Drug Dosage
For acute/severe bronchospasm: 2.5–5 mg via nebulizer every 20 minutes for 3 cycles; may repeat treatments every 1–4 hours as needed. |
|
Indications
Relief of bronchospasm Therapeutic Effects Causes bronchodilation |
Drug Interactions
Other short-acting sympathomimetic aerosol bronchodilators Epinephrine Monoamine oxidase inhibitors Tricyclic antidepressants Beta blockers Food Interactions No significant interactions |
|
Adverse Effects
Paradoxical bronchospasm Tachycardia Immediate hypersensitivity reaction |
Contraindications
Hypersensitivity |
Nursing Implications
The nurse should do the following for clients receiving albuterol via nebulizer for anaphylaxis:
- Assess lung sounds prior to administration and frequently after administration.
- Monitor blood pressure frequently. (Blood pressure is often measured continuously when a client is in shock.)
- Monitor respiratory rate frequently.
- Monitor oxygen saturation continuously.
- Monitor level of consciousness.
- Have resuscitative equipment and drugs available.
- Provide client teaching regarding nebulizer treatment.
- Provide client teaching regarding the drug. See below for client teaching guidelines.
Client Teaching Guidelines
The client receiving albuterol should:
- Hold the nebulizer mouthpiece between their teeth with their lips closed around it.
- Hold the nebulizer in an upright position.
- Understand that treatment often lasts 10–15 minutes.
- Inform the health care provider of chest pain or pressure or a feeling of rapid heart rate.
Isotonic Intravenous Solution
Anaphylactic shock causes fluids to shift from within the blood vessels (intravascular) to the tissues (extravascular). This can occur very rapidly and is the primary cause of the shock. Isotonic IV solutions have the same amount of sodium concentration as blood does.
Because fluid has shifted to the extravascular space in anaphylactic shock, there is not enough volume in the intravascular space to maintain blood pressure and tissue perfusion. Isotonic intravenous solution will increase volume, which then increases blood pressure.
In anaphylactic shock, 1–2 L of an isotonic IV solution such as normal saline should be administered rapidly (at the highest flow rate possible) as soon as an IV is established. After the initial IV fluid bolus, the client may need continuous IV fluids at a rapid rate to maintain blood pressure. Examples of isotonic IV solutions are normal saline and lactated Ringer’s.
Hypovolemic Shock Drugs
Hypovolemic shock occurs when the circulating volume of fluid has decreased so much that it affects tissue perfusion. The first priority in hypovolemic shock is to correct the underlying cause; for example, if the hypovolemia is caused by blood loss, measures should be taken to stop the blood loss, and the client should receive a blood transfusion as soon as possible. Intravenous fluid resuscitation is also used to increase cardiac output and stabilize blood pressure. The use of vasopressors (drugs that increase blood pressure) in hypovolemic shock is controversial and will not be included in this section.
In hypovolemic shock, 2 L of an isotonic IV solution should be administered as quickly as possible. After the initial fluid bolus, additional IV solution may be ordered to maintain blood pressure.
Cardiogenic Shock Drugs
Cardiogenic shock occurs when the myocardium is not able to pump effectively enough to maintain cardiac output. This can be due to ischemia, infarction, or other causes. Cardiogenic shock is treated with vasopressors and SNS stimulation. Cardiac output must be increased in order to restore adequate tissue perfusion. Medications used in cardiogenic shock include dopamine, dobutamine, and norepinephrine. Dopamine and dobutamine are covered in a previous section in this chapter. Norepinephrine can be used for other types of shock, but it is included here because of its effects on the heart.
Norepinephrine
Norepinephrine is an alpha-1 receptor agonist and a moderate beta-1 receptor agonist . Alpha-1 receptors are located in the smooth muscle around blood vessels. When these receptors are stimulated, they cause muscle contraction, which causes vasoconstriction. Beta-1 receptors are located in the heart; when they are stimulated, they cause increased heart rate and force of contraction.
Adverse Effects and Contraindications
Norepinephrine can cause cardiac arrhythmias, severe peripheral ischemia in clients who are hypovolemic, gangrene in clients with occlusive or thrombotic vascular disease (in high doses), and rebound hypotension after discontinuation. Norepinephrine may cause decreased sensitivity to insulin, so clients with diabetes may need their glucose levels monitored more frequently as well as increased doses of antidiabetic medications.
Extravasation of norepinephrine at the IV site can cause tissue necrosis.
There are no contraindications for norepinephrine.
Table 22.15 is a drug prototype table for norepinephrine. It lists drug class, mechanism of action, adult dosage, indications, therapeutic effects, drug and food interactions, adverse effects, and contraindications.
|
Drug Class
Alpha/beta antagonist Mechanism of Action Stimulates alpha- and beta-adrenergic receptors, thereby increasing blood pressure, heart rate, and force of contraction |
Drug Dosage
For profound hypotension or shock: Initial dose: 8–12 mcg/min, titrated to blood pressure. Typical maintenance dose: 2–4 mcg/min. Hypovolemia must be corrected before initiating norepinephrine infusion. |
|
Indications
Severe acute hypotension Shock Therapeutic Effects Increased blood pressure Increased heart rate and force of contraction |
Drug Interactions
Monoamine oxidase inhibitors (can lead to profound hypertension) Tricyclic antidepressants (can lead to profound hypertension) Halogenated anesthetics (can cause ventricular tachycardia or fibrillation) Food Interactions Caffeine |
|
Adverse Effects
Tissue ischemia in clients who are hypovolemic (severe peripheral ischemia) Gangrene in clients with occlusive or thrombotic vascular disease (in high doses) Rebound hypotension after discontinuation Cardiac arrhythmias |
Contraindications
None |
Nursing Implications
The nurse should do the following for clients receiving norepinephrine:
- Place the client on continuous cardiac monitoring.
- Monitor heart rate frequently.
- Monitor level of consciousness.
- Have resuscitative equipment and drugs available.
- Assess the IV site frequently.
- Correct hypovolemia before giving norepinephrine.
- Provide client teaching regarding the drug. See below for client teaching guidelines.
Client Teaching Guidelines
The client receiving norepinephrine should:
- Inform the health care team if they have a change in status (better or worse) after medication administration.
- Inform the health care team if they have discomfort or pain at the IV site.