26.2: Physical Assessment
By the end of this section, you will be able to:
- Perform a comprehensive neurological assessment
- Understand abnormalities identified during the assessment of the neurological system
- Recall proper documentation of neurological assessment
The neurological exam is a clinical assessment of the functioning of the CNS and PNS. Routine neurological exams performed by registered nurses during their daily clinical practice include assessing mental status and level of consciousness, pupillary response , motor strength, sensation , and gait. The Glasgow Coma Scale (GCS) is also frequently used to objectively monitor level of consciousness in patients with neurological damage such as a head injury or cerebrovascular accident, or stroke (Figure 26.7). Periodic reevaluations are performed when the patient has experienced an acute injury or illness causing neurological deficits, such as a stroke, which require frequent monitoring for change in condition.
Comprehensive Neurological Assessment
The comprehensive neurological assessment requires the nurse to collect both subjective and objective data through an interview as well as a detailed physical exam . This exam is more extensive and performed on patients with a neurological concern. In addition to the components included in a routine neurological exam, the examiner may also assess cranial nerves, detailed cerebellar function, deep tendon reflexes, and complete a Mini-Mental State Exam (MMSE).
Subjective Data
The subjective data are collected during an interview and guide the focus of a physical exam. It is crucial that the nurse collects a complete health history using effective communication to identify any current or potential issues, because some issues may only be identified through precise questioning during the interview. For example, the nurse will want to ask questions regarding loss of sensation, loss of concentration, or dizziness to identify potential problems (Table 26.5). Follow-up questions may also be required to identify when a patient’s symptoms started and any associated signs. The nurse may also ask about other signs and symptoms such as headaches, seizures, confusion, vertigo, recent injury, numbness, tingling, weakness, dysphagia (difficulty swallowing), dysphasia (difficulty speaking), or loss or coordination.
| Interview Questions | Follow-up |
|---|---|
|
Are you experiencing any current neurological concerns such as headache, dizziness, weakness, numbness, tingling, tremors, loss of balance, or decreased coordination?
Have you experienced any difficulty swallowing or speaking? Have you experienced any recent falls? |
If the patient is seeking care for an acute neurological problem, use the PQRSTU method to further evaluate their chief complaint.
Note: If critical findings of an acute neurological event are actively occurring, such as signs of a stroke, obtain emergency assistance according to agency policy. |
| Have you ever experienced a neurological condition such as a stroke, transient ischemic attack, seizure, or head injury? | Describe the condition(s), date(s), and treatment(s). |
| Are you currently taking any medications, herbs, or supplements for a neurological condition? | Please describe. |
Scenario: A nurse is collecting subjective data about a 79-year-old male in the clinic.
Nurse: Hi. My name is Suzie, and I’m the nurse who will be taking care of you today. May I have your name and date of birth?
Patient: My name is Fred Reid, date of birth January 21, 1944.
Nurse: Great, thank you. What brings you in today?
Patient: I am just here for a check-up. I have been feeling off lately.
Nurse: Okay, can you describe for me what that means?
Patient: Well, I have just been dizzy some.
Nurse: Do you feel light-headed also, and do you notice if it occurs with a particular activity or when you change positions?
Patient: Mainly when I stand up. I start to lose my balance some.
Nurse: When did this start?
Patient: Oh, maybe a week or so ago.
Nurse: Have you experienced any recent falls or medication changes?
Patient: No falls yet. That is why I am here, so I can try to figure this out and not fall. I did get started on Lasix about 10 days ago.
Nurse: Okay, a common side effect of Lasix is called orthostatic hypotension. It is a condition where your blood pressure can lower suddenly when standing from a seated or lying position. It can cause light-headedness or a loss of balance. It is important for you to change positions slowly. So, for example, when you are getting out of bed, you’ll want to sit up on the side of the bed and wait a minute or so before standing up to give your body time to adjust to the position changes. You will want to make sure you feel steady before moving, so even if it takes you a few minutes to get your bearings, that is okay.
Patient: Oh, that makes sense.
Nurse: Yes sir. I will let Dr. Caldwell know, and he may order additional testing regarding this while you are here.
Patient: Okay.
Nurse: Have you experienced any other neurological signs or symptoms, like difficulty swallowing or speaking, seizures, headaches, numbness, tingling, or tremors?
Patient: No ma’am.
Nurse: Okay, we will review your other body systems and then move into a physical exam if you are ready.
Scenario follow-up: Now that the nurse has completed the nervous system assessment, they can move on to the other body systems.
Objective Data
The objective data collected during an exam are used to assess the patient’s mental status as well as motor and sensory function, cranial nerve function, and deep tendon reflexes. In addition, this part of the comprehensive exam will require the nurse to observe the patient’s posture, ability to walk, and personal hygiene, as well. Table 26.6 describes common objective exams used to evaluate various components of the nervous system.
| Test | What It Assesses | How to Perform |
|---|---|---|
| Glasgow Coma Scale | Mental status/level of consciousness | Scoring tool that assesses eye opening response, verbal response, and motor response (Figure 26.7). |
| National Institutes of Health Stroke Scale | Neurological function (mental status, ability to communicate, motor function) |
Tool used to assess for suspected cerebrovascular accident. Uses the mnemonic “BEFAST”:
B : Balance (Is there a sudden loss of balance?) E : Eyes (Any loss of vision in one or both eyes?) F : Face (Does the face appear uneven, is there any drooping?) A : Arm (Any weakness or numbness in either arm?) S : Speech test (Any slurred speech or trouble speaking? Does patient appear confused?) T : Time to call for immediate assistance |
| Mini-Mental State Exam | Cognitive status | 30-point test used to assess for dementia (chronic, irreversible confusion) or delirium (acute, reversible confusion that may be due to an infection, fever, or lack of oxygen). Scoring is as follows: 24–30, no impairment; 18–23, mild cognitive impairment; and <18, severe cognitive impairment. |
You can see the full text of the MMSE and see the types of questions for which patients earns points for each correct response. For example, the first question asks five things, so the patient would get a point for each correct answer.
Cranial Nerves
Cranial nerve assessment is also a part of an objective assessment. The nurse should remember to compare each side of the face when assessing each cranial nerve. The cranial nerves can be assessed as followed in Table 26.7.
| Cranial Nerve | How to Assess |
|---|---|
| I (olfactory) | Ask the patient to identify a smell with their eyes closed, such as an alcohol swab or coffee. |
| II (optic) | The Snellen chart assesses far vision. The patient should cover one eye and read the letters from the lowest line they can from 20 feet away. The patient may use glasses or contact lenses. The nurse will need to document the results as “corrected vision.” |
| III, IV, and V (oculomotor, trochlear, and abducens) |
These nerves are tested together using the acronym PERRLA (pupils are equal, round, and reactive to light and accommodation). This is done as follows:
|
| V (trigeminal) | Test the patient’s sensory function by lightly touching their face, forehead, and chin with a wisp of a cotton ball while the patient’s eyes are closed. The patient should feel each touch. Test the patient’s motor function by palpating the temporalis of the masseter muscles for strength while the patient is clenching their teeth. The patient should be able to symmetrically open and close their mouth as well as clench their teeth. |
| VII (facial) | Test motor function and assess for symmetry and facial muscle strength while the patient smiles, shows teeth, closes both eyes, puffs their cheeks, frowns, and raises eyebrows. Test sensory function by having the patient taste separate cotton applicators that are moistened with salt, sugar, and lemon. The patient should identify each correctly. |
| VIII (vestibulocochlear) | Test auditory function by whispering at an arm length’s away. Each ear should be tested individually while the patient occludes the ear not being tested. The nurse should exhale and use as quiet of a voice as possible while whispering a combination of letters and numbers (e.g., 3-R-5). The patient should be asked to repeat what they heard. A patient is considered passing if they answer three of the six correctly. If the patient does not respond correctly, the nurse should test again but using a different sequence of letters and numbers. The opposite ear should be testing using a different sequence also. Test balance by using the Romberg test. This test is used to assess balance by having the patient stand with their feet together and eyes closed. The nurse must stand by in case the patient begins to fall. The patient should be able to stand erect and maintain their balance. A positive test occurs if the patient sways or loses their balance. |
| IX (glossopharyngeal) | This nerve is assessed by asking the patient to open their mouth and saying “Ah.” The nurse assesses the symmetry of the upper palate. The tongue and uvula should be midline, and the uvula should symmetrically rise as the patient says “Ah.” |
| X (vagus) | This nerve is assessed by using a cotton swab or tongue blade to touch the posterior pharynx and observe for a gag reflex, followed by swallowing. |
| XI (spinal accessory) |
|
| XII (hypoglossal) | The hypoglossal nerve is assessed by examining any unilateral weakness while the patient protrudes their tongue or by having the patient touch their cheek with their tongue while the nurse provides resistance on the outside of the cheek. |
Nurses should be aware of normal age-related changes that can affect a neurological exam. Part of the normal age-related changes is changes to the senses: vision, hearing, tasting, smelling, and touch. As individuals age, the vision becomes slower due to the elasticity loss of the lens. Older adults also have trouble focusing their eyes and their pupils get smaller. The change in pupil size leads to the lens thickening and becoming less transparent, which ultimately results in a reduction of light reaching the retina. Another common visual a change is the loss of near-vision. Cataracts and glaucoma are common in older adults as well. Hearing loss may occur due to injury, genetics, medications, or exposure to repetitive loud noises or other damaging factors over time. Taste and smell are affected due to less saliva being produced, a decrease in the number of taste buds, mouth diseases, and the overall less ability to differentiate sweet and sour tastes. The sense of touch may be altered due to a condition, lack of blood flow, arthritis, or sedentary lifestyle.
Deep Tendon Reflex
Assessment of reflexes is not typically performed by registered nurses as part of a routine nursing neurological assessment of adult patients, but it is used in nursing specialty units and in advanced practice. Spinal cord injuries, neuromuscular diseases, or diseases of the lower motor neuron tract can cause weak or absent reflexes. To perform deep reflex tendon testing, place the patient in a seated position. Use a reflex hammer in a quick striking motion by the wrist on various tendons to produce an involuntary response . Before classifying a reflex as absent or weak, the test should be repeated after the patient is encouraged to relax, because voluntary tensing of the muscles can prevent an involuntary reflexive action.
Reflexes are graded from 0 to 4+, with “2+” considered normal:
- 0: absent
- 1+: hypoactive
- 2+: normal
- 3+: hyperactive without clonus
- 4+: hyperactive with clonus (involuntary muscle contraction)
Sensory Response
Testing of peripheral sensation begins with examining the response to light touch according to regions of the skin known as dermatomes. A dermatome is an area of the skin that is supplied by a single spinal nerve that sends information to the brain for processing. To test the sensory fields, ask the patient to close their eyes and then gently touch the soft end of a cotton-tipped applicator on random locations of the skin according to the dermatome region. Instruct the patient to report “Now” when feeling the placement of the applicator. If a patient is unable to feel the sensation of a cotton applicator, an advanced technique applied to comatose patients is to use ice or even the prick of a pin.
It is not necessary to test every part of the skin’s surface during a routine neurological exam; testing a few distal areas with light touch is usually sufficient. In-depth testing is performed when the patient is exhibiting neurological signs or symptoms such as motor deficits, numbness, tingling, and weakness.
Cortical processing that occurs in the cerebral cortex of the parietal lobe is assessed using stereognosis , which is the ability to perceive the physical form and identity of a familiar object such as a key or paper clip, on the basis of tactile stimuli alone. Often this is called a monofilament testing, and it is routinely done in primary care. As shown in Figure 26.8, the nurse performs this test by asking the patient to close their eyes and then placing the object in their hand. The patient can use their finger to move the object around. The nurse will ask the patient to name the object. A different object should be tested in each hand. To perform the stereognosis test, ask the patient to close their eyes; then place a familiar object in their hand and ask them to name it. Each hand should be tested with a different object.
Motor Strength
Motor and coordination functions are also part of the objective assessment. Motor strength is assessed by performing a brief musculoskeletal assessment of the upper and lower extremities. This testing may include hand grasps, upper body strength, and lower body strength. Expected findings of a motor function test is that the patient will have equal strength bilaterally. For the hand grasp test, the nurse should extend two fingers of each hand and have the patient squeeze both hands at the same time. Upper body strength is assessed by having the patient extend their forearms with palms facing upward. The nurse then places their hands on the patient’s inner forearms. The nurse asks the patient to pull their arms toward them while the nurse provides resistance.
Lower body strength is assessed while the patient is in a seated position and can be done in multiple ways. The first way is for the nurse to place their hands behind the patient’s calves. The nurse will then ask the patient to pull backward with their lower legs while the nurse is providing resistance in the opposite direction. Other tests assess the strength of the patient’s lower thighs by having them to lift their legs upward while the nurse provides resistance downward, or the nurse can place their hands on the top of the patient’s feet and ask them to pull their toes upward while providing resistance. The feet can also be assessed by the nurse placing their hands on the dorsal part of the patient’s feet and asking them to press downward while the nurse provides resistance.
Cerebellar Function
Tests used to evaluate cerebellar function (coordination) include assessment of gait and balance, the finger-to-nose test, and the heel-to-shin test. When assessing gait and balance, as shown in Figure 26.9, the nurse will ask the patient to perform the following actions (using an assistive device if needed): ambulate 10 feet, pivot, and walk back; walk heel to toe while looking straight ahead; walk on their tiptoes; and walk on their heels. An abnormal result occurs if the patient demonstrates any change in gait, shuffling, weakness, jerky movements, loss of balance, or uncoordinated arm swinging.
The finger-to-nose test, as shown in Figure 26.10, evaluates equilibrium and coordination. The patient can be in a seated or standing position. The nurse will ask the patient to close their eyes and instruct them to extend their arms outward from the sides of their body. The nurse will then instruct the patient to touch the tip of their nose with their right index finger and return their arm to the extended position. The nurse will then instruct the patient to repeat this motion on the left side. The nurse will also have the patient repeat these steps by alternating arms.
For the heel-to-shin test, as shown in Figure 26.11, the nurse will place the patient in a supine position. The nurse will then instruct the patient to place the heel of their right foot just below their left kneecap. The next step is to have the patient slide their right heel in a straight line down to the ankle. The nurse will instruct the patient to repeat this motion on the left leg. An abnormal finding is if the patient is not able to perform the steps in smooth, straight motion or if the heel falls off the lower leg.
Abnormalities of the Neurological Assessment
There are many abnormalities that can affect the neurological assessment. The most common alterations are altered mental status , altered language, altered nerve function, alterations in sensory function, and alterations in motor and coordination function. The nurse should have a foundation in what is an expected versus an unexpected finding, as well as how to properly perform the assessment to ensure a finding is accurate.
There are various abnormalities of the neurological system that can exist and affect a patient’s safety. It is essential that the nurse performs a thorough assessment of the patient’s cognitive, behavioral, and motor functionality to determine safety risks. Individuals are at risk for falls due to any dysfunction in their neurological status, such as a loss of balance or coordination, dysfunctions with gait , confusion related to cognitive impairments, or any impaired sense of position. The nurse should identify risks and implement interventions to promote a safe environment for patients and reduce their risk of falls. For example, a nurse may identify a patient as a fall risk due to an altered mental status and so activate a bed alarm to alert the nurse’s station if the patient tries to get up by themselves.
Altered Mental Status
An altered mental status or an altered level of consciousness is present when a patient experiences a change in mental function as a result of a disease or condition affecting the brain. The GCS, as previously described, is the standard tool to assess a person’s mental state. This allows the nurse to obtain a baseline to compare against future assessments as well as develop appropriate nursing interventions. Mental status changes can be described as depression, dementia , delirium , and coma.
- Depression: poor cognition test results, slowed speech, personal withdrawal
- Dementia: slow, progressive loss of mental capacity.  Vascular dementia is more fluctuating, with the addition of motor changes along with cognitive decline (Patti & Gupta, 2023).
- Delirium: an acute condition of confusion that can fluctuate from hyperactive to hypoactive states, with periods of lucidity (Patti & Gupta, 2023). Sundowning, or worse delirium at night, is a common phenomenon.
- Coma: inability to respond to normal stimuli but may retain brain stem reflexes (e.g., cough, gag, corneal, pain stimulus, oculovestibular reflexes) (Patti & Gupta, 2023).
The Alzheimer’s Society provides information on the difference between dementia and delirium . Families and caregivers sometimes worry that a change in a mental status automatically means dementia. This is a great resource to provide aid in differentiating between the two.
Altered Language
The term aphasia refers to a brain disorder in which an individual has difficulty with all forms of communication: expression, understanding, reading, and writing (National Institutes of Health [NIH], 2017). Aphasia can be caused by various conditions but most commonly from traumatic brain injury and stroke . To ensure accurate findings, the nurse should be aware of any devices the patient may need for communication, such as hearing aids or glasses, before performing an assessment.
An altered finding includes speech that is garbled or slurred, the patient struggling to find the right term or word, problems comprehending written or spoken words, or using words that do not make sense in the context of the conversation. If the nurse is unsure of whether altered language is a new change, the nurse should ask the patients family or caregiver about the patient’s baseline, if available. New changes could be indicative of a stroke and require early intervention.
Scenario: A nurse is assessing a patient who had a stroke 1 week ago.
Nurse: Hi. My name is Kai. May I have your name and date of birth?
Patient: My name is R-r-r-ob Gome. [looks at wife]
Patient’s wife: His name is Robert Gomes, date of birth is February 10, 1951. He has been having trouble speaking ever since his stroke.
Patient: [nods his head]
Nurse: Okay, that is actually a common finding. It lasts different lengths for every individual but can take a few weeks to months to see improvement. Mr. Gomes, do you mind if I perform an assessment?
Patient: You can.
Nurse: Okay, can you tell me where you are?
Patient: [garbled] Eagle R-r-ranch.
Nurse: Very good.
[Nurse arranges a pen, her cell phone, and a watch on the table.]
Nurse: Mr. Gomes, I have a few things on the table here. Will you point to the item that is the pen?
[Patient correctly points at the pen.]
Nurse: Very good. Will you describe a hamburger to me?
Patient: [garbled] Yes, there is a patty and bread with ve-veg-tables and must or ma-mayonnaise.
[Nurse holds up a paper with the following sentence: It may rain today.]
Nurse: Will you read this sentence for me?
Patient: [garbled] It m-may r-rain today.
Nurse: Very good. Thank you. Your provider will be in soon to discuss your recent hospital stay, the testing that was performed there, and the review of your assessment.
Patient’s wife: Great, thank you. [patient nods his head]
Altered Nerve Function
Cranial nerve deficits can cause pain, numbness, tingling, weakness, or paralysis of the face or eyes. This can be due to nerve damage, poorly controlled diabetes, head injuries, poorly controlled blood pressure, infections, stroke, or tumors affecting the area. Table 26.8 outlines expected versus unexpected findings from a cranial nerve assessment.
| Cranial Nerve | Expected Findings | Unexpected Findings |
|---|---|---|
| I (olfactory) | Patient is able to identify or describe odor. | Anosmia (inability to identify odors) |
| II (optic) | Patient has 20/20 vision (near and far). | Decreased visual acuity or visual fields |
| III (oculomotor) | PERRLA (pupils are equal, round, and reactive to light and accommodation) | Pupil sizes are not equal or reactive bilaterally. |
| IV (trochlear) | Both eyes follow the examiner’s penlight in the appropriate direction. | Patient is unable to follow the penlight with their eyes in the various directions or demonstrates ptosis (eyelid drooping). |
| V (trigeminal) | Patient is able to feel touch and chew without struggle. | Weakened chewing muscle responses or decreased sensations to touch |
| VI (abducens) | Eyes move in coordination bilaterally. | Patient is unable to look laterally or has diplopia (double vision). |
| VII (facial) | Patient is able to smile, raise eyebrows, puff checks, and close eyes without struggle and is also able to differentiate tastes. | Decreased taste sensations, facial paralysis or symmetry (facial drooping) |
| VIII (vestibulocochlear) | Patient is able to hear whispered words in both ears and is able to walk upright and/or maintain balance. | Decreased hearing in one or both ears; decreased ability to walk upright and/or maintain balance. |
| IX (glossopharyngeal) | Present gag reflex | Absent gag reflex or dysphagia (difficulty swallowing) |
| X (vagus) | Patient is able to speak and swallow without struggle. | Slurred speech or dysphagia |
| XI (spinal accessory) | Patient is able to turn head side to side and shrug shoulders against resistance. | Patient is unable to turn head side to side and shrug shoulders against resistance. |
| XII (hypoglossal) | Patient’s tongue is midline and able to move without struggle. | Patient’s tongue is weak or is not midline. |
Alterations in Sensory Function
Alterations in sensory function can be caused by a direct insult to the brain or due to aberrant stress responses, such as trauma, severe illness, acute changes in the environment, and surgery, that cause alterations in neurotransmission. Biochemical imbalances, decreased cholinergic functions, or changes in neurotransmitter levels may contribute to such changes. Age-related changes in neurotransmission and intracellular signaling may also occur and lead to sensory alterations (Khan & Khan, 2022).
Damage to the PNS can cause weakness, numbness, or pain from nerve damage also known as peripheral neuropathy . Disorders that may contribute to this sensory alteration include diabetes, autoimmune disorders, metabolic imbalances, smoking, atherosclerosis, nutritional imbalances, kidney or liver disorders, infection, chemotherapy , cancer, and lupus. Types of neuropathies include Guillain-Barre syndrome, diabetic neuropathy, carpal tunnel syndrome, and complex regional pain syndrome.
Alterations in Motor and Coordination Function
Similar to other alterations discussed, there are various reasons for alterations in motor and coordination function. Abnormalities like unsteady gait , abnormal muscle movement, or abnormal posturing can be due to damage to a particular area of the brain, CNS, or PNS in addition to neurodegenerative disorders or neurodevelopmental abnormalities.
When unexpected findings are noted during the motor and coordination function assessment, the nurse should verify any conditions in the patient history that could contribute to the alteration or if this is a new finding. Decreased muscle tone, or hypotonia , can occur on its own or is an underlying medical condition, such as muscular dystrophy or cerebral palsy. Hypotonia is often detected at infancy. Increased muscle tone, or hypertonia , is caused by damage to the CNS, upper motor neuron lesions, or conditions such as stroke , brain tumors, toxins, neurodevelopmental abnormalities, such as cerebral palsy, and neurodegenerative disorders, including multiple sclerosis or Parkinson disease.
There are common motor changes in the aging adult that the nurse should be aware of when performing an assessment to determine what may be normal versus a sign of a neurological dysfunction. The following are changes that may be common among the aging adult population:
- A reduction in muscle mass and function can make movements slower or less coordinated, and so may also contribute to a risk of falls.
- A reduction in velocity of contraction and movement can be due to smaller muscle fibers in older adults versus younger adults.
- Abnormal gait may be due to the deterioration of proprioception mechanisms, visual changes, and osteoarthritis.
- Arthritis is common among older adults and can affect all tissues of the joint. This may be painful and have swelling, both of which may lead to the patient having an abnormal gait or reduced movement in the joint.
- Degradation of the synapses of motor nerve and neuromuscular junction is common with aging and causes muscle fiber alterations.
Additionally, older adults may be taking medications that can affect a patient’s sense of awareness as well as contribute to dizziness. The nurse should be aware of the medications and supplements the patient takes daily to be aware of any potential side effects or risks.
Validating and Documenting Findings
Documentation is a crucial component to any nursing assessment. This is the baseline information against which future assessments will be compared for evaluation of improving or worsening signs and symptoms. Nursing documentation should include:
- assessment tools used to perform the exam
- detailed findings of each assessment, including any subjective and objective data
- if the practitioner was notified of any abnormal findings, include the name of the practitioner, date and time of notification, and any interventions performed
- any teaching provided to the patient and family, including understanding of the teaching and any follow up teaching needed
Consider the following example. The nurse needs to use a combination of tools to gather subjective and objective data about a patient in the emergency department. The nurse documents that the patient reports “numb feeling” on the left side of their body and that their left arm “feels weak.” The nurse notes during the conversation that the patient is struggling to talk, and their speech is difficult to understand. On the motor and sensory components of the exam, the nurse notes the patient’s left arm is weak and they have decreased sensation. They note the time of the exam as well as the time that the patient reported their symptoms began. The nurse also assesses and documents the patient’s MMSE and GCS scores. In the patient’s chart, the nurse documents both the subjective data provided by the patient and the objective data gathered from the exam. Based on what the nurse has observed, they decide the stroke protocol needs to be initiated. The nurse’s assessment and documentation are key steps in the diagnostic workflow. From here, the medical team can quickly take next steps to determine if the patient is having a stroke (e.g., ordering a computed tomography scan of the head; laboratory tests) and start treatment (e.g., administering an anticoagulant) as soon as possible. When assessing a patient for a stroke, swift action on the part of the nurse can be critical. Timing is key for stroke diagnosis and treatment, and the nurse’s role in conducting a prompt but accurate and thorough neurological assessment is essential.


3.3: The Rock Cycle
INTRODUCTION
There are three types of rocks: igneous, sedimentary and metamorphic. Each of these types is part of the rock cycle. Through changes in conditions one rock type can become another rock type. Or it can become a different rock of the same type.
Figure 1. The different colors and textures seen in this rock are caused by the presence of different minerals.
WHAT ARE ROCKS?
A rock is a naturally formed, non-living earth material. Rocks are made of collections of mineral grains that are held together in a firm, solid mass (figure 1).
How is a rock different from a mineral? Rocks are made of minerals. The mineral grains in a rock may be so tiny that you can only see them with a microscope, or they may be as big as your fingernail or even your finger (figure 1).
Figure 2. A pegmatite from South Dakota with crystals of lepidolite, tourmaline, and quartz (1 cm scale on the upper left).
Rocks are identified primarily by the minerals they contain and by their texture. Each type of rock has a distinctive set of minerals. A rock may be made of grains of all one mineral type, such as quartzite. Much more commonly, rocks are made of a mixture of different minerals. Texture is a description of the size, shape, and arrangement of mineral grains. Are the two samples in figure 2 the same rock type? Do they have the same minerals? The same texture?
Figure 3. Rock samples.
| Sample | Minerals | Texture | Formation | Rock Type |
| Sample 1 | plagioclase, quartz, hornblende, pyroxene | Crystals, visible to the naked eye | Magma cooled slowly | Diorite |
| Sample 2 | plagioclase, hornblende, pyroxene | Crystals are tiny or microscopic | Magma erupted and cooled quickly | Andesite |
Table 1
As seen in table 1, these two rocks have the same chemical composition and contain mostly the same minerals, but they do not have the same texture. Sample 1 has visible mineral grains, but Sample 2 has very tiny or invisible grains. The two different textures indicate different histories. Sample 1 is a diorite, a rock that cooled slowly from magma (molten rock) underground. Sample 2 is an andesite , a rock that cooled rapidly from a very similar magma that erupted onto Earth’s surface.
THREE MAIN CATEGORIES OF ROCKS
Rocks are classified into three major groups according to how they form. Rocks can be studied in hand samples that can be moved from their original location. Rocks can also be studied in outcrop , exposed rock formations that are attached to the ground, at the location where they are found.
Igneous Rocks
Igneous rocks form from cooling magma. Magma that erupts onto Earth’s surface is lava, as seen in figure 4. The chemical composition of the magma and the rate at which it cools determine what rock forms as the minerals cool and crystallize.
Figure 4. This flowing lava is molten rock that will harden into an igneous rock.
Sedimentary Rocks
Sedimentary rocks form by the compaction and cementing together of sediments , broken pieces of rock-like gravel, sand, silt, or clay (figure 5). Those sediments can be formed from the weathering and erosion of preexisting rocks. Sedimentary rocks also include chemical precipitates , the solid materials left behind after a liquid evaporates.
Figure 5. This sedimentary rock is made of sand that is cemented together to form a sandstone.
Metamorphic Rocks
Metamorphic rocks form when the minerals in an existing rock are changed by heat or pressure within the Earth. See figure 6 for an example of a metamorphic rock.
Figure 6. Quartzite is a metamorphic rock formed when quartz sandstone is exposed to heat and pressure within the Earth.
A simple explanation of the three rock types and how to identify them can be seen in this video:
This video discusses how to identify igneous rocks:
This video discusses how to identify a metamorphic rocks:
This Science Made Fun video discusses the conditions under which the three main rock types form:
THE ROCK CYCLE
Rocks change as a result of natural processes that are taking place all the time. Most changes happen very slowly; many take place below the Earth’s surface, so we may not even notice the changes. Although we may not see the changes, the physical and chemical properties of rocks are constantly changing in a natural, never-ending cycle called the rock cycle .
Figure 7. James Hutton is considered the Father of Geology
The concept of the rock cycle was first developed by James Hutton, an eighteenth century scientist often called the “Father of Geology” (shown in figure 7). Hutton recognized that geologic processes have “no [sign] of a beginning, and no prospect of an end.” The processes involved in the rock cycle often take place over millions of years. So on the scale of a human lifetime, rocks appear to be “rock solid” and unchanging, but in the longer term, change is always taking place.
In the rock cycle, illustrated in figure 8, the three main rock types—igneous, sedimentary, and metamorphic—are shown. Arrows connecting the three rock types show the processes that change one rock type into another. The cycle has no beginning and no end. Rocks deep within the Earth are right now becoming other types of rocks. Rocks at the surface are lying in place before they are next exposed to a process that will change them.
Figure 8. The Rock Cycle.
PROCESSES OF THE ROCK CYCLE
Several processes can turn one type of rock into another type of rock. The key processes of the rock cycle are crystallization, erosion and sedimentation, and metamorphism.
Crystallization
Magma cools either underground or on the surface and hardens into an igneous rock. As the magma cools, different crystals form at different temperatures, undergoing crystallization . For example, the mineral olivine crystallizes out of magma at much higher temperatures than quartz. The rate of cooling determines how much time the crystals will have to form. Slow cooling produces larger crystals.
Erosion and Sedimentation
Weathering wears rocks at the Earth’s surface down into smaller pieces. The small fragments are called sediments. Running water, ice, and gravity all transport these sediments from one place to another by erosion . During sedimentation , the sediments are laid down or deposited. In order to form a sedimentary rock, the accumulated sediment must become compacted and cemented together.
Metamorphism
When a rock is exposed to extreme heat and pressure within the Earth but does not melt, the rock becomes metamorphosed. Metamorphism may change the mineral composition and the texture of the rock. For that reason, a metamorphic rock may have a new mineral composition and/or texture.
LESSON SUMMARY
- Rocks are collections of minerals of various sizes and types.
- The three main rock types are igneous, sedimentary, and metamorphic.
- Crystallization, erosion and sedimentation, and metamorphism transform one rock type into another or change sediments into rock.
- The rock cycle describes the transformations of one type of rock to another.
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Contributors and Attributions
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Original content from Kimberly Schulte (Columbia Basin College) and supplemented by Lumen Learning . The content on this page is copyrighted under a Creative Commons Attribution 4.0 International license.


5.6: Remedies Available for the Misappropriation of Trade Secrets
After completing this section, you will be able to
- Describe how injunctions are used to enjoin actual and threatened misappropriations of trade secrets.
- Explain how remedies are awarded under the Uniform Trade Secrets Act.
The UTSA provides a full array of remedies, including statutory damages , injunctive relief , attorneys’ fees , and exemplary damages . xxviii The remedy or remedies will depend on the extent of trade secrets involved, the manner of misappropriation or conversion, and the type of damage sustained by the owner.
Injunctive Relief
As discussed above, under the UTSA, injunctive relief is available to enjoin actual, as well as threatened, misappropriation. Injunctive relief allows the owner of a trade secret to obtain a court order prohibiting the actual or threatened misappropriation of a trade secret. The ability to enjoin threatened misappropriation is very important because it enables the owner of the trade secret to prevent public disclosure of the trade secret. xxix Injunctive relief may take many forms. The scope of an injunction may vary from a broad prohibition on any use of material found to be a trade secret, to a more limited prohibition on the scope of an employee’s work with a new employer. xxx Both the scope and subject matter of an injunction vary depending upon the specific facts of the case and the nature of the trade secret in question. The UTSA provides that an injunction shall terminate once the trade secret ceases to exist, but may be continued for a reasonable period of time to extinguish any commercial advantage that otherwise would be derived from the misappropriation. This is especially important where, at the time of the action, the information or knowledge is no longer a trade secret. In such a case, the court may still award the owner injunctive relief that is narrowly crafted to deprive the defendant of the benefit of time saved by improper use of the owner’s trade secret. xxxi
| Definition | Injunctive relief allows the owner of a trade secret to legally prohibit a former employee, for example, from misappropriating, publicly disclosing, or otherwise profiting from knowledge of the trade secret. |
| Scope | The scope of an injunction varies based on the on the nature of the potential misappropriator’s knowledge of the trade secret, and on the potential competitive advantage that knowledge might grant. |
| Duration and Termination | The duration of an injunction is determined based on the amount of time it would take a competitor to reveal the trade secret by proper means. An injunction can be terminated when the trade secret ceases to exist. |
| Permanent Injunctions | To determine the appropriate length of time, courts may rely on the opinions/experience of experts and competitors. They may impose permanent injunctions or rely on other considerations seen as important by the court. |
Table 5.2 Injunctive Relief
Where the information has not been publicly disclosed, the issue becomes more difficult. The duration of the injunction is often calculated according to the time that would be required for independent development of the information or knowledge that was misappropriated. These “head start” injunctions assume that the information could be properly obtained through reverse engineering or independent development. xxxii
To determine what length of time is appropriate, courts may rely on the opinions of experts and the experience of other competitors. xxxiii However, a court may also opt to impose a permanent injunction that can later be modified, or in some circumstance rely on other considerations deemed important by the court. xxxiv
Courts also exhibit broad flexibility in the nature and duration of relief in cases dealing with former employees. When an injunction is issued in these cases, it usually will not be an outright ban on employment. Rather, it will be a more limited injunction for a more limited duration. xxxv Most courts are willing to allow continued employment, but will restrict the employee from working with a particular product line or area of the new employer’s business. xxxvi However, if the role the employee will assume would inevitably lead to the disclosure of trade secrets, the employment may be prohibited altogether. xxxvii
Damages Awarded
Damages are often awarded in addition to an injunction and are not an exclusive remedy. xxxviii For example, in Seagate Tech., LLC v. Western Digital Corp. , 834 N.W.2d 555 (Minn. App. 2013), the Minnesota Court of Appeals affirmed a judgment of $630 million in favor of the plaintiffs against the defendants stemming from a trade secret misappropriation dispute. Under the UTSA, damages are measured by the actual loss caused by the misappropriation as well as any resulting unjust enrichment of the misappropriator. Where the amount of actual loss or unjust enrichment cannot be accurately calculated, the UTSA provides that damages may also be measured by the imposition of a reasonable royalty for the misappropriator’s unauthorized disclosure or use of the trade secret. Exemplary or punitive damages may be awarded where the court finds that the misappropriation was willful and malicious. xxxix For example, in Mattel, Inc. v. MGA Entm’t, Inc. , 801 F. Supp. 2d 950 (C.D. Cal 2011), Mattel was found to have engaged in a prolonged practice of encouraging employees to use false pretenses to acquire competitive information from the defendant. As a result of this conduct, the jury awarded, and the court affirmed a verdict of $85 million dollars in exemplary damages. A punitive or exemplary award may not exceed twice the amount of the damage award. xl However, some states have modified this cap on punitive damages, and allow for punitive damages greater than two times the amount of actual damages. xli
Case Studies
| Case | Description of Damages |
|---|---|
| Seagate Tech., LLC v. Western Digital Corp. | In this case, the Minnesota Court of Appeals affirmed a judgment of $630 million in favor of the plaintiff stemming from a trade secret misappropriation. Under the UTSA, damages are measured by the actual loss caused by the misappropriation and any resulting unjust enrichment of the misappropriator. |
| Mattel, Inc. v. MGA Entm’t. Inc. | In this case, Mattel was found to have encouraged employees to use false pretenses to acquire competitive information from the defendant. As a result of this conduct, $85 million dollars in exemplary damages was awarded. A punitive or exemplary award may not exceed twice the amount of the damage award. xlii However, some states have modified this cap. xliii |
Table 5.3
In exceptional circumstances, an injunction may entitle the owner of the trade secret to a royalty for the period of time during which the use of the trade secret was prohibited. For example, the Supreme Court of Georgia has affirmed a trial court’s reliance on a seldom-used provision of the UTSA to impose a “royalty injunction” instead of an injunction prohibiting the use of the plaintiff’s trade secret. xliv
A court may also award attorneys’ fees to a prevailing party in exceptional circumstances. A bad faith claim of misappropriation, a bad faith resistance to a motion to terminate an injunction, or a finding of willful and malicious appropriation are exceptional circumstances in which an award of attorneys’ fees may be appropriate. However, courts are generally disinclined to award attorneys’ fees. xlv The attorney fee provision is included to dissuade parties from filing malicious misappropriation actions in bad faith, and considered along with the need for exemplary damages. xlvi
Footnotes
- xxviii See Unif. Trade Secrets Act §§ 2-5, U.L.A (1985).
- xxix Standard Brands, Inc. v. Zumpe , 264 F. Supp. 254, 269 (E.D. La. 1967).
- xxx See 3M v. Pribyl , 259 F.3d 587, 598 (7th Cir 2001) (upholding broad injunction on use of material in employee handbook, as overly specific injunctions may invite evasion).
- xxxi See Cherne Indus., Inc. v. Grounds & Associates , 278 N.W.2d 81 (Minn. 1979).
- xxxii See, e.g., Surgidev Corp. v. Eye Technology, Inc. , 828 F.2d 452, 456-457 (8th Cir. 1987) (affirming 15-month injunction based on the period of time that would be required for independent development of the protected information).
- xxxiii See, Restatement (Third) of Unfair Competition Section 44, comment f.
- xxxiv See e.g., General Electric Co. v. Sung , 843 F. Supp. 776, 780-781 (D. Mass. 1994) (seven-year product injunction, taking into account the willfulness of the misappropriation).
- xxxv See, e.g., Doubleclick v. Henderson , No. 116914/97 (N.Y. Sup. Ct. Nov. 5, 1997) (granting an injunction restraining two former employees from competing with their former employer for a period of six months).
- xxxvi See, Merck & Co. Inc v. Lyon , 941 F. Supp. 1443 (M.D.N.C. 1996). See also Allis Chalmers Manf. Co. v. Continental Aviation and Eng. Corp., 255 F. Supp. 645 (E.D. Mich. 1966) (injunction limited to research as to a particular type of pump); but see Union Carbide Corp. v. UGI Corp. , 731 F.2d 1186 (5th Cir. 1984) (affirming injunction against use of information in 14 broad areas).
- xxxvii PepsiCo , Inc. v. Redmond , 54 F.3d 1262, 1272 (7th Cir 1995).
- xxxviii See e.g., Mikes Train House, Inc. v. Lionel, L.L.C. , 472 F.3d 398, 413-15 (6th Cir. 2006).
- xxxix See, e.g., Aries Information Sys., Inc. v. Pacific Management Sys. Corp. , 366 N.W.2d 366 (Minn. Ct. App. 1985).
- xl See Unif. Trade Secrets Act § 3(b), U.L.A (1985).
- xli Reingold v. Swiftships, Inc. , 210 F.3d 320, 323 (5th Cir. 2000).
- xlii Reingold v. Swiftships , Inc., 210 F.3d 320, 323 (5th Cir. 2000).
- xliii See Unif. Trade Secrets Act § 3(b), U.L.A (1985).
- xliv See Electronic Data Systems Corp. v. Heinemann , 493 S.E.2d 132 (Ga. Sup. Ct. 1997).
- xlv See, e.g., Gordon Employment, Inc. v. Jewe1 , 356 N.W.2d 738 (Minn. Ct. App. 1984).
- xlvi See Unif. Trade Secrets Act § 4 (comment), U.L.A(1985).


10.4: Mental Health
Mental health is a broad category that covers over 200 potential illnesses of varying severity. The mental health spectrum includes emotional, psychological, and social well-being. Mental health is influenced by genetics, biological factors like diseases or injuries, neurochemistry (chemical messengers in the brain), as well as environmental factors such as stress, adverse childhood experiences (like abuse, neglect, etc.), trauma, isolation and loneliness, and the use of drugs and alcohol. Life changes significantly impact mental health - particularly significant changes such as the death of a loved one, the end of a relationship, the birth of a child, a change in living situation, and physiological changes that occur across the lifespan such as maturation and aging. When certain symptoms of psychological distress or problematic thinking are severe or long lasting, they may be diagnosed as a mental illness. The CDC reports that over 20% of U.S. adults currently live with a mental illness, and over 20% of youth between the ages of 13-18 have experienced a debilitating mental health issue. The most serious mental illnesses include bipolar disorder, schizophrenia, and major depression, affecting about 1 in 25 adults (CDC/National Center for Injury Prevention and Control, 2024).
Mental illnesses or mental disorders cannot be diagnosed with blood tests or X-rays. Instead, these disorders are diagnosed by a cluster of symptoms - usually by a licensed psychologist or psychiatrist (the difference being only the latter type of doctor provides any prescriptions for psychiatric medications). As research continues to expand our knowledge of mental health disorders, these diagnoses are updated into a manual used by mental health professionals. The Diagnostic and Statistical Manual of Mental Disorders - Fifth Edition (DSM-5) is the most recent iteration, published by the American Psychiatric Association. This manual includes symptoms and diagnoses for different types of psychological disorders, including:
- Neurodevelopmental disorders - such as autism spectrum disorder (ASD), attention deficit hyperactivity disorder (ADHD)
- Schizophrenia spectrum and other psychoses
- Bipolar disorders (also known as manic-depression)
- Anxiety disorders - such as generalized anxiety disorder (GAD), panic disorders, and specific phobias
- Obsessive-compulsive disorders - such as OCD, hoarding, body dysmorphic disorder
- Depressive disorders - such as major depression, dysthymic disorder, premenstrual dysphoric disorder
- Trauma and stress-related disorders - such as post-traumatic stress disorder (PTSD) or acute stress disorder
- Eating disorders - such as anorexia nervosa, bulimia nervosa, and binge-eating disorder
- Neurocognitive disorders - such as Alzheimer’s disease or cognitive impairment
- Personality disorders - such as narcissistic, antisocial, paranoid, or borderline personality disorder
- Sexual dysfunctions
- Substance-related disorders - such as addiction to alcohol, cannabis, pills, or gambling
- Other disorders such as dissociative, somatic, and impulse-control disorders (Seabert et al., 2021).
Mental disorders can occur together, and the interpretation of symptoms (and therefore diagnosis) is complicated. Accurate diagnosis and treatment is also dependent on the cultural competency of the provider to differentiate between behavioral differences that are due to socio-cultural factors vs. those caused by a mental disorder (Seabert et al., 2021). Historically, the DSM has been revised in favor of emerging evidence-based criteria in diagnostics, and to reflect the evolving understanding of socio-cultural influences on the interpretation of mental health. For example, up until the 1980s (when it was removed), homosexuality - or a reference to “sexual orientation disturbance” - was present in the DSM. And prior to the 1980s, PTSD, bipolar disorder, and acute stress disorders were not included. In the DSM-5, the term “hysteria” was replaced with “somatic symptom disorder”, and Asperger’s was removed as an independent diagnosis and instead included within the Autism spectrum (Surís et al., 2016). Further advances in the medical understanding of mental health and diagnostic procedures for psychiatric disorders will likely prompt continued evolution of this manual, as well as psychiatric and psychological practices.
Even for those without a diagnosed mental illness, mental and emotional health are highly influenced by stress. Each year the American Psychological Association (APA) conducts a survey on Stress in America to get a snapshot of the amount of stress Americans are experiencing and the most common stressors (sources of stress). The data for 2023 indicate increased stress in America due to recovery from the COVID-19 pandemic, as well as global conflict, inflation, racism and racial injustice, and climate disasters (such as drought, wildfires, floods, and severe storms). Collective traumatic stress from the pandemic may be impacting the psychological and physical health of individuals and communities in the U.S., where COVID-19 has claimed the lives of over 1 million people, caused huge job losses and economic impacts, and strained social cohesion. According to this latest analysis, self-reported mental illness diagnoses have increased from 32% of adults in 2019 to 37% of adults in 2023 (though 81% of those surveyed reported their own mental health as good or better). Those reporting a stress level of 8/10 or higher rose from 19% in 2019 to 24% in 2023. The increase was especially pronounced for those aged 35-44 (American Psychological Association, 2023).
Mental health issues are particularly concerning for adolescents. Over half of all mental illness cases will start showing symptoms by age 14, and 75% of them develop symptoms before 24 ((CDC/National Center for Injury Prevention and Control, 2024). The top 3 leading causes of death for adolescents are unintentional injuries (accidents), homicides, and suicides (Elflein, 2024), all of which may have poor mental health as a factor.  The Youth Risk Behavior Surveillance Survey in 2021 reported that persistent feelings of sadness and hopelessness (symptoms of depression) affected 42% of high school students, and this rate was significantly higher for female students and LGBTQ+ youth. Overall, rates of poor mental health for high schoolers had increased since 2011 (CDC/DASH, 2023).
College students are also struggling with increasing rates of mental health issues, particularly during the recovery from the COVID-19 pandemic. According to one study, in 2020-2021, over 60% of college students met the criteria for a mental health disorder - a 50% increase from 2013 (Lipson et al., 2022). High levels of stress are often reported by college students, as well as depression, anxiety, panic attacks, and substance abuse problems. In fact, college may be where many students first begin experiencing symptoms of mental disorders, and/or begin using stimulants or prescription substances to get high or help with studying. Having a supportive network of family and friends as well as access to mental health services on campus may help to help students find balance and prevent them from dropping out early. Common barriers to getting help include social stigma of seeking help for mental health, as well as cost and access to counselors (Johnson et al., 2023).


5.11: Nursing Process Considerations
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- Ernstmeyer & Christman (Eds.)
- Chippewa Valley Technical College via OpenRN
Nursing Process Related to Respiratory Medications
Now that we have reviewed the respiratory system and common respiratory disorders, let’s apply the nursing process to the administration of respiratory medications.
Nursing Process: Assessment
Although there are numerous details to consider when administering medications, it is always important to first think about what you are giving and why?
First, let’s think of why?
Respiratory medications are often given to alleviate allergies, cold symptoms, or to decrease/eliminate shortness of breath (SOB). An important piece of your nursing assessment should be to assess the patient’s respiratory status. The respiratory assessment includes observing the respiratory rate and quality of respirations (shallow, deep), obtaining a pulse oximetry reading, and auscultating lung sounds. Other pieces of the assessment include inspecting skin color, such as observing for pallor , or cyanosis, and determining if there is a cough or sputum present. If sputum is present, it should be assessed for color, odor, consistency, and amount (COCA).
Additional baseline information to collect prior to the administration of any respiratory medication includes any history of allergy or previous adverse drug response.
Nursing Process: Implementation of Interventions
Respiratory medications are available in many different formulations, such as nasal spray, inhalations, oral tablets or liquids, injections, or intravenous route, so it is always important to verify the correct route and anticipate the associated side effects. For example, inhalations deliver the required medicine or medicines directly to the lungs, which means the medicine(s) can act directly on the lung tissues, minimizing systemic side effects. On the other hand, intravenous medications are administered to act quickly, but can cause systemic side effects. Additionally, some products contain more than one medicine with different dosages (for example, inhalers that combine a long-acting bronchodilator with a glucocorticoid).
During the administration of respiratory medications, it is important to anticipate the expected outcome of the medication and any common side effects. For example, albuterol is a short acting Beta-2 agonist that is given for bronchodilation. The nurse should plan to perform a respiratory assessment before and after administration of albuterol to document the effectiveness of the medication, as well as monitor for tachycardia, a common side effect.
Additionally, the nurse should also ensure the proper use of the inhalers by the patient. Observe the patient self-administering the medication, and further instruct the patient in proper use. [1]
Nursing Process: Evaluation
Finally, it is important to always evaluate the patient’s response to a medication. With respiratory medications, the nurse should assess decrease in allergy symptoms (cough, runny nose, tearing eyes) and any decrease in shortness of breath. The nurse should complete a respiratory assessment (respirations, pulse oximetry, and lung auscultation) before and after the medications have been administered and compare the results. If the symptoms are not improving or the clinical assessment is worsening, prompt intervention is required (such as notification of the health care provider for further orders) to prevent further clinical deterioration.
- Drugs.com. (n.d.). Respiratory agents. https://www.drugs.com/drug-class/respiratory-agents.html ↵


13.6: The Helium-Neon Laser
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The He-Ne laser was the first continuous-wave (cw) laser invented. A few months after Maiman announced his invention of the pulsed ruby laser, Ali Javan and his associates W. R. Bennet and D. R. Herriott announced their creation of a cw He-Ne laser. This gas laser is a four-level laser that uses helium atoms to excite neon atoms. The atomic transitions in the neon produce the laser light. The most commonly used neon transition in these lasers produces red light at 632.8 nm. These lasers can also produce green and yellow light in the visible region, as well as several UV and IR wavelengths (Javan's first He-Ne operated in the IR at 1152.3 nm). By using highly reflective mirrors designed for one of these many possible lasing transitions, a given He-Ne's output is made to operate at a single wavelength.
He-Ne lasers are not sources of high-power laser light, typically producing a few to tens of mW (milli-Watt, or \(10^{-3}\) W) of power. Probably one of the most important features of these lasers is that they are highly stable, both in terms of their wavelength (mode stability) and intensity of their output light (low jitter in power level). For these reasons, He-Ne lasers are often used to stabilize other lasers. They are also used in applications, such as holography, where mode stability is important. Until the mid-1990's, He-Ne lasers were the dominant type of lasers produced for low-power applications - from range finding to scanning to optical transmission, to laser pointers, etc. Recently, however, other types of lasers, most notably the semiconductor lasers, seem to have won the competition because of reduced costs.
The energy level diagram in figure \(\PageIndex{1}\) shows the two excited states of a helium atom, the 2 3 S and 2 1 S, that get populated as a result of electromagnetic pumping. Both of these states are metastable and do not allow de-excitations via radiative transitions. Instead, the helium atoms give off their energy to neon atoms through collisional excitation. In this way, the 4s and 5s levels in neon get populated.
\[He^* (2s^3 \, S_1) + Ne(g) \rightarrow He(g) + Ne^*(2p^54s) \nonumber \]
\[He^* (2s^1 \, S_0) + Ne(g) \rightarrow He(g) + Ne^*(2p^55s) \nonumber \]
These are the two upper lasing levels, each for a separate set of lasing transitions. Each of these upper lasing levels contains 4 states ( 3 P 2 , 3 P 1 , 3 P 0 , 1 P 1 ). Radiative decay from the 5s to the 4s levels is forbidden. So, ten states associated with the 4p and 3p levels serve as the lower lasing levels and rapidly decay into the metastable 3s level. In this way, population inversion is easily achieved in the He-Ne mixture. The 632.8 nm laser transition, for example, involves the 5s and 3p levels, as shown above. Table \(\PageIndex{1}\) lists parameters of several of the Ne transitions.
| Transition | \(\lambda\) (nm) | Einstein Coefficient A (s -1 ) | Relative Intensity |
|---|---|---|---|
| 5s 1 P 1 → 3p 3 P 1 | 640.1 | 0.60 x 10 6 | 100 |
| 5s 1 P 1 → 3p 3 P0 | 635.2 | 0.70 x 10 6 | 100 |
| 5s 1 P 1 → 3p 3 P2 | 632.8 | 6.56 x 10 6 | 300 |
| 5s 1 P 1 → 3p 1 P 1 | 629.4 | 1.35 x 10 6 | 100 |
| 5s 1 P 1 → 3p 1 D 2 | 611.8 | 1.28 x 10 6 | 100 |
In most He-Ne lasers the gas, a mixture of 5 parts helium to 1 part neon, is contained in a sealed glass tube with a narrow (2 to 3 mm diameter) bore as shown above in figure \(\PageIndex{2}\). Typically the laser's optical cavity mirrors, the high reflector and the output coupler form the two sealing caps for the narrow bore tube. High voltage electrodes create a narrow electric discharge along the length of this tube, which then leads to the narrow beam of laser light.
Many He-Ne lasers also contain a ballast which serves to maintain the desired gas mixture. Since some of the atoms may get embedded in the glass and/or the electrodes as they accelerate within the discharge, in the absence of a ballast the lasing mixture would not last very long. To further prolong the useable life of the laser, some of these lasers also use "getters", often metals such as titanium, that absorb impurities in the gas. Figure \(\PageIndex{3}\) below shows a He-Ne laser with a ballast.
A typical commercially available He-Ne produces about a few mW of 632.8 nm light with a beam width of a few millimeters at an overall efficiency of near 0.1%. This means that for every 1 Watt of input power from the power supply, 1 mW of laser light is produced. Still, because of their long operating lifetime of 20,000 hours or more and their relatively low manufacturing cost, He-Ne lasers are among the most popular gas lasers.


33.3: Advocacy and Coalition Building
By the end of this section, you should be able to:
- Examine the benefits of uniting to create change.
- Identify situations in which forming a coalition of groups and individuals would be beneficial.
- Explain how to start a community coalition.
- Describe the challenges and barriers to starting a community coalition.
A coalition is a group of people with shared vision or concerns, such as nurses or nursing associations and other groups that join forces to support a cause. Nurses may form coalitions to maximize resources to improve the chances of successfully achieving these goals. Coalitions may emerge from loose-knit networks of groups that are created to share resources and information. Coalitions may develop from groups formed by a task force, advisory committee, or commission. They may develop into a consortia , which consists of organizations with a particular goal. By creating a collective voice and sharing interprofessional expertise and resources, coalitions can have an impact on improving health outcomes by addressing inequities. To maximize their impact, coalitions require formal governance, strong leadership, participation, diversity, cohesiveness among the members, and collaboration with other agencies (Crowder et al., 2022).
The Essential Steps in Forming a Coalition
Coalitions can advance a cause more effectively than independent work as resources are shared and credibility is enhanced. This approach offers a more widespread reach than any single organization could achieve. For example, a parent-teacher association (PTA) is a coalition that may work toward improving student safety by requiring bike helmets for children riding their bikes to school. Members of this coalition may be from several organizations, such as retail stores, the department of public health, local government, parents, and others. These members may attend specific conferences or write letters to legislators and local news outlets to advocate for their cause. The cause’s credibility is enhanced as the coalition may represent several organizations rather than a single special interest group. This dynamic often fosters trust and cooperation among several grassroots organizations.
The decision to form a coalition may be spontaneous or may be the result of a detailed analysis of a community’s need (Figure 33.4). In some cases, receipt of a community-based grant may necessitate the formation of a coalition to fulfill the objectives specified in the grant award. The first step in deciding to form a coalition involves clarifying the objectives and appropriateness of the activities planned. A community assessment of the existing strengths and weaknesses is an essential element in forming a coalition as this identifies potential barriers and support systems in place, which guides the development of the best strategies to implement. An analysis of the strategy to employ must include the cost of the resources required. See Assessment, Analysis, and Diagnosis for more information on conducting a community assessment .
The coalition then decides how members are recruited, how many are needed, and what type of members are essential to meet the coalition’s goals. While individual members may be recruited, existing member organizations may already be in place that are working toward a similar objective and may be willing to collaborate. Identifying competitors and adversaries who could impede the coalition’s objectives is also important.
When forming a coalition, a leadership team is essential. It is often composed of a chairperson, facilitator, individual members, staff, a steering committee, a lead agency, and member organizations. While the chairperson is the organization’s spokesperson, this individual is often responsible for signing letters, testifying in court, or serving in other roles to represent the coalition. The facilitator plays a key role as this individual will lead discussions and activities of the coalition and must possess the knowledge and skills of managing group dynamics. The facilitator will serve in a key role to resolve any disagreements, working in concert with the chairperson. The facilitator and chairperson may or may not be from the lead agency.
The coalition’s activities will be developed, discussed, and defined at the meetings, conferences, or workshops by lead members of the coalition. The necessary resources will be identified in terms of the time commitment of the members and lead agency as well as financial considerations. Local service clubs and foundations may be essential in providing additional resources, and student trainees and volunteers may also support the coalition’s activities.
The parameters of the membership agreement are critical to the organization’s success and must be established and agreed upon. The location, frequency, and length of the meetings, as well as the members’ expectations, is another important step when organizing membership. Also, there may be limitations to the duration of the coalition’s existence. For example, the coalition’s objective may be set to be achieved within 2 years, and a plan may be in place to disband the coalition when the objective has been met. Setting time limits for a coalition may help members decide their involvement level.
The meeting structure and the method of making decisions should also be well communicated to all members. Members may also be expected to participate between structured meetings, and this commitment should be carefully outlined. After successfully forming the coalition, maintaining the energy and vision of the objective for each of the members requires skillful vision and attention to detail when problems arise. Leaders of the coalition must anticipate these difficulties, such as power sharing, group dynamics, individual disagreements, and the process for acceptance of new members.
Leaders must also actively engage steps to renew the objectives through ongoing education and training. Leaders will also embrace the challenge of bringing new issues to the group. An important step in maintaining a coalition is to focus on celebrating the group’s successes, both large and small, and acknowledge key individuals who have gone above and beyond to support the cause. Evaluating the achievements will also lead to additional improvements in the strategies, enhancing the ability to continue moving forward. Evaluations may be formative (evaluating the process) and summative (evaluating the outcome).
Leaders and members of a coalition often serve to enhance visibility within a community to increase public awareness and influence the perception of the problem at hand. This may lead to additional organizations and individuals becoming interested in providing support. Lastly, while coalitions do not last forever, the mutual trust in relationships that are formed may last a lifetime, whether the objectives were met or not.
This video depicts how one community coalition was launched in Tulsa, Oklahoma, to address the social determinants of health.
Watch the video, and then respond to the following questions.
- How did the idea for the North Tulsa Community Coalition begin?
- What are the mission and goals of the North Tulsa Community Coalition?
- What are some positive outcomes of this coalition?
Nurses and Coalitions
Many nurses hesitate to become involved in coalitions to support public health causes until they or someone they care about is personally affected by structural inequities in health care. Sometimes, a university professor or a client may have inspired one’s interest in activism. Faculty in academic settings and nurse educators within the practice environment teach students and new nurses about safety and civility. They can ignite an interest in advocacy through mentoring and role modeling. In many ways, nurse educators are responsible for forming the professional identity of novice nurses to further the profession in an ever-changing health care environment (ANA, 2023a).
The ANA has developed a nursing advocacy coalition called RNaction that is available to help nurses act in groups on important issues in the United States that affect persons, nurses, and public health (ANA, 2023a). The Campaign for Action is another example of a coalition that has brought nurses, health care providers, consumers, educators, and businesses in almost every state together to ensure the health of all people by strengthening nursing (Campaign for Action, 2023). These state-level action coalitions build on the Future of Nursing Report to unite schools, fire and emergency services, and local businesses, clubs, and social justice organizations such as the Robert Wood Johnson Foundation to promote healthy communities by transforming health care. As a result of the Campaign for Action coalition, significant work is being conducted at the state level to address issues that impact health as a result of nursing care, such as access to health care, transforming nursing education, fostering interprofessional collaboration, the need for diversity in the nursing profession, and building healthy communities (Campaign for Action, 2023). For example, in 2022, 26 states improved access to health care by adopting full practice authority for all APRNs so they can practice to the full extent of their education and training. Several local and statewide programs have been launched to increase diversity in the nursing workforce due to this coalition. In Brandywine, Delaware, as part of the 2021 Nursing Innovations Fund project, the school district piloted an afterschool program called BSD’s Lifesavers to increase the awareness of nursing as a career to communities that are underrepresented in the nursing workforce (Campaign for Action, 2022). The program’s success will be measured by identifying the percentage of participants pursuing a career in nursing.
The Future of Nursing: Campaign for Action, funded by the AARP Foundation, AARP, and the Robert Wood Johnson Foundation, collaborates nationally with nurses and other health care professionals, consumers, educators, and industry to improve health and health equity by strengthening nursing. The Campaign has action coalitions in every U.S. state.
Visit the Campaign for Action website, scroll to the bottom of the page, select your state or another state of interest, and read about the latest news from that state’s coalition. Then respond to the following questions.
- Which state did you select?
- What current actions is that state taking to increase health equity for its communities?
Nurses also advocate for health care of populations by seeking appointments or elected positions on various trustee boards for businesses and organizations that impact health care, whether in nursing, business, or education. The Nurses on Boards Coalition (NOBC) was formed in 2014 in response to the 2011 Future of Nursing Report, which called for nurses to lead change and advance health (Institute of Medicine, 2011). The NOBC collaborates with its member associations, partners in health care, and businesses to provide nursing leadership as members on the boards of directors for over 10,000 organizations (NOBC, 2021). Nurses interested in serving on boards may register on the Nurses on Boards Coalition website to find an organization that matches their skills and expertise or seek resources to build leadership skills. Many national organizations such as specialty nursing organizations have local chapters. Becoming a local chapter member is a great way to stay up to date on the latest science and network with other nurses with similar interests. Leadership opportunities often become available within a specialty organization, and most are elected positions. The Nursing on Boards Coalition offers web-based and one-on-one advisement with a mentor to develop the skills to gain leadership skills and build to higher-level positions in these or other organizations congruent with an area of interest to advocate for populations of clients and nurses.
Read the following scenario, and then answer the questions that follow based on all the case information provided in the chapter thus far. This case study is a follow-up to Case Study Part A.
Tanesha has been staying at the homeless shelter for the past 2 days. She was placed on antibiotics for lower lobe pneumonia, and her blood glucose level and blood pressure have stabilized. She has been able to shower and obtain shoes that fit her feet. She has a small diabetic ulcer at the base of her right great toe that has been cleaned and bandaged. Her car was moved to a safe place in the parking lot. She expresses concern about staying in the shelter; she fears that she will be assaulted and will be unable to protect herself as men have been seen sneaking into the women’s ward. She said that she left home because she was assaulted and admits that she still feels afraid. She mentioned that she couldn’t sleep well at the shelter because babies were crying all night. She said that she plans to return to her car to live soon if the conditions do not improve in the shelter.
3. What would the nurse consider a priority for clients like Tanesha?
- Suicide precautions
- Mental health evaluation
- Nutritional assessment
- Sleep assessment
4. What health policies might the nurse advocate for to best serve homeless individuals like Tanesha?
- Early childhood health education
- Safe housing programs for families with children
- Free mental health screening for veterans
- Education on how to access health care
Student Involvement in Coalitions
Universities have historically been centers for igniting social changes that improve health. At one college of nursing, senior-level nursing students were concerned about the lack of a mandate for the COVID-19 vaccination in the workplace. Under the direction of their public health faculty member, more than 100 students formed a coalition. They wrote letters to their respective legislators with their concerns, which launched a wide range discussion in the state, resulting in a meeting to discuss the issue with the state’s health commissioner. The box below shows an example of the letter the students developed. Student nurses have many avenues to become involved in advocating for the health of the communities they serve.
Date
Name/affiliation/contact info
The Honorable _______
Dear State Senator _____
My name is____, and I reside at______. I am currently a nursing student at _____ University, in ( town ), ( State ). I am writing to you in hopes that you will support our stance on the recommendation to endorse a mandate on the COVID-19 vaccination in the workplace. According to the CDC’s reported data about the state of ____, “95% of the state’s total population has received at least one vaccine dose, 83% are fully vaccinated and only 24.4% have the latest bivalent booster” ( cite ). In examining this data, most residents in our state are hesitant toward receiving a COVID-19 booster. As we move away from the height of the pandemic and into the future, it is necessary that action is taken to prevent any loss of progress. COVID-19 vaccines have been proven to fight against the virus and prevent hospitalizations. The CDC adds that moreover, “public health experts see reduced protection over time against mild and moderate disease, especially among certain populations. For the best protection, everyone 6 months and older is recommended to stay up to date with their COVID-19 vaccines, which includes getting boosters (CDC, ___).”
If the COVID-19 vaccination were to be mandated within the workplace, we would see an upward trend in ( state __) residents staying up to date with CDC recommendations, which would influence others to follow suit. In addition, the workplace specifically must be accounted for as a place for greater risk of COVID-19 spread. Individuals working together in close quarters for many hours each week provides a breeding ground for infection spread. Studies have shown that “many private-sector employers want their employees to be vaccinated against COVID-19 to prevent the spread of the virus, reassure employees and customers that the premises are safe, avoid potential liability for transmission of the virus, and advance public health” (Rothstein et al., 2021, p. 1062). A mandate in the workplace would promote adequate protection of the individuals of ( state ). By keeping in line with the CDC recommendations, we can continue to move away from some of the darkest times in our world’s history. Prevention is our biggest strength in continuing to fight against COVID-19. A mandate would only further promote this. This is a prevalent and dire time in our nation’s history. With proper legislation, we can continue to move forward and keep on track for a healthy environment for all.
Thank you for your time and for considering this request.
Sincerely,
Name
In this video, a father and son discuss the challenges of finding full-time support professionals to assist Nicholas, who has autism, intellectual disabilities, and several health issues. Visit The Arc website to learn about family perspectives regarding medically complex and fragile children.
Watch the video, review the website, and then respond to the following questions.
- What are the financial and career challenges that parents of medically complex children face?
- How does Medicaid support families of children that are medically complex?
- How can nurses advocate to protect children that are ventilator dependent or have other medically complex needs?


10.10: Development and Regeneration of Muscle Tissue
By the end of this section, you will be able to:
- Describe the function of satellite cells
- Define fibrosis
- Explain which muscle has the greatest regeneration ability
Most muscle tissue of the body arises from embryonic mesoderm. Paraxial mesodermal cells adjacent to the neural tube form blocks of cells called somites . Skeletal muscles, excluding those of the head and limbs, develop from mesodermal somites, whereas skeletal muscle in the head and limbs develop from general mesoderm. Somites give rise to myoblasts. A myoblast is a muscle-forming stem cell that migrates to different regions in the body and then fuse(s) to form a syncytium, or myotube . As a myotube is formed from many different myoblast cells, it contains many nuclei, but has a continuous cytoplasm. This is why skeletal muscle cells are multinucleate, as the nucleus of each contributing myoblast remains intact in the mature skeletal muscle cell. However, cardiac and smooth muscle cells are not multinucleate because the myoblasts that form their cells do not fuse.
Gap junctions develop in the cardiac and single-unit smooth muscle in the early stages of development. In skeletal muscles, ACh receptors are initially present along most of the surface of the myoblasts, but spinal nerve innervation causes the release of growth factors that stimulate the formation of motor end-plates and NMJs. As neurons become active, electrical signals that are sent through the muscle influence the distribution of slow and fast fibers in the muscle.
Although the number of muscle cells is set during development, satellite cells help to repair skeletal muscle cells. A satellite cell is similar to a myoblast because it is a type of stem cell; however, satellite cells are incorporated into muscle cells and facilitate the protein synthesis required for repair and growth. These cells are located outside the sarcolemma and are stimulated to grow and fuse with muscle cells by growth factors that are released by muscle fibers under certain forms of stress. Satellite cells can regenerate muscle fibers to a very limited extent, but they primarily help to repair damage in living cells. If a cell is damaged to a greater extent than can be repaired by satellite cells, the muscle fibers are replaced by scar tissue in a process called fibrosis . Because scar tissue cannot contract, muscle that has sustained significant damage loses strength and cannot produce the same amount of power or endurance as it could before being damaged.
Smooth muscle tissue can regenerate from a type of stem cell called a pericyte , which is found in some small blood vessels. Pericytes allow smooth muscle cells to regenerate and repair much more readily than skeletal and cardiac muscle tissue. Similar to skeletal muscle tissue, cardiac muscle does not regenerate to a great extent. Dead cardiac muscle tissue is replaced by scar tissue, which cannot contract. As scar tissue accumulates, the heart loses its ability to pump because of the loss of contractile power. However, some minor regeneration may occur due to stem cells found in the blood that occasionally enter cardiac tissue.
Career Connection
Physical Therapist
As muscle cells die, they are not regenerated but instead are replaced by connective tissue and adipose tissue, which do not possess the contractile abilities of muscle tissue. Muscles atrophy when they are not used, and over time if atrophy is prolonged, muscle cells die. It is therefore important that those who are susceptible to muscle atrophy exercise to maintain muscle function and prevent the complete loss of muscle tissue. In extreme cases, when movement is not possible, electrical stimulation can be introduced to a muscle from an external source. This acts as a substitute for endogenous neural stimulation, stimulating the muscle to contract and preventing the loss of proteins that occurs with a lack of use.
Physiotherapists work with patients to maintain muscles. They are trained to target muscles susceptible to atrophy, and to prescribe and monitor exercises designed to stimulate those muscles. There are various causes of atrophy, including mechanical injury, disease, and age. After breaking a limb or undergoing surgery, muscle use is impaired and can lead to disuse atrophy. If the muscles are not exercised, this atrophy can lead to long-term muscle weakness. A stroke can also cause muscle impairment by interrupting neural stimulation to certain muscles. Without neural inputs, these muscles do not contract and thus begin to lose structural proteins. Exercising these muscles can help to restore muscle function and minimize functional impairments. Age-related muscle loss is also a target of physical therapy, as exercise can reduce the effects of age-related atrophy and improve muscle function.
The goal of a physiotherapist is to improve physical functioning and reduce functional impairments; this is achieved by understanding the cause of muscle impairment and assessing the capabilities of a patient, after which a program to enhance these capabilities is designed. Some factors that are assessed include strength, balance, and endurance, which are continually monitored as exercises are introduced to track improvements in muscle function. Physiotherapists can also instruct patients on the proper use of equipment, such as crutches, and assess whether someone has sufficient strength to use the equipment and when they can function without it.


11.8: How Do You Respond to Criticism?
- Discuss key points to a professional response to criticism.
How you respond to correction, criticism, and negative feedback demonstrates who you are. Thus, it is essential to learn how to take criticism gracefully, and treat these instances as opportunities to grow. If you immediately shut-down and act defensively, you’re unlikely to learn and grow from past mistakes. Receiving correction is pivotal to your development.
Positive Responses
The first step in receiving criticism is to listen actively and make a concerted effort not to be defensive. Remember that giving criticism can be almost as hard as receiving it, so neither you nor your critic are likely to be entirely comfortable. Once your reviewer/critic has said their piece—whether in person or in writing—the following effective tools can help you respond:
- Gratitude. Avoid extremes: don’t get gushy or pretend it doesn’t hurt. Just say thanks for your feedback.
- Questions. Avoid statements until you’ve asked clarifying questions.
- Restatements. “I hear you saying…”
- Request for solutions. Ask for suggested solutions. Simple is essential; one or two is enough.
- Happiness. Do corrective behaviors make sense and feel good? If the path forward isn’t inviting, you’ll avoid it.
- Follow-up. Ask for a check-in meeting in two weeks for a progress report. Four weeks is too long. If your behaviors elicit negative feedback, solve them quickly.
- Gratitude again.
Time
Sometimes it’s worth taking a pause and delaying your response, rather than responding with your first reaction (which could likely end up being an overreaction). Correction is tough to hear. Listen, and if necessary, ask for some time to think it over. Be honest in your responses, and don’t be afraid to ask for time: “This is hard to hear. Could I have an hour to digest your feedback?”
Transparency
Include those who were impacted by negative behaviors. Explain what you’re working on and corrective actions. You go further when others know where you’re going. In a few days, ask them how you’re doing.
Open up don’t push away.
Drop it and move on.
Ask for affirmation when you achieved goals. Reject nitpicking. Move on.
Responding well to negative feedback, toughens character, increases influence, and strengthens connections.
According to communications expert Jack Griffin, there is a six step process that you can use to respond to negative feedback in a constructive manner. Here are excerpts from his guidelines. [1]
Step 1: Accept criticism as an opportunity. All criticism, even unmerited criticism is useful to you. Criticism, after all, may actually point out things that you are doing ineffectively or poorly—things you could do better.
Step 2 : Fight the impulse to respond defensively. Listen and learn.
Step 3: Realize that the criticism is a perception, nothing more.
Step 4 : Do not meekly accept unjust or unfounded criticism, but don’t reject it. Learn from it. Learn about creating more positive impressions.
Step 5: Seize the opportunity to respond to criticism, to communicate in a way that can strengthen and enhance your relationship with your boss.
Step 6 : While listening to criticism, demonstrate that you are hearing the criticism.
Negative Responses
Of course, while there are a variety of good ways to respond, there are poor or unproductive ways to respond to criticism. Here are examples of how not to respond.
- “It’s your fault too.”
- Making it personal.
- Standing aloof
- Minimizing.
- Arguing.
- Feeling attacked.
- Finger pointing.
- Excuse making.
- Denial.
- “I’ll never be good enough.”
Negative responses to negative feedback delay growth, destroy progress, and lose respect.
- Jack Griffin, “How To Say It At Work”, 1998.
Contributors and Attributions
- How Do You Respond to Criticism?. Authored by : Robert Danielson. Provided by : Lumen Learning. License : CC BY: Attribution
- Seven Positive Responses to Negative Feedback. Provided by : Leadership Freak. Located at : https://leadershipfreak.blog/2013/11/13/seven-positive-responses-to-negative-feedback/ . License : CC BY: Attribution


13.6: Math Models
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- 13.6.1: Use a Problem-Solving Strategy
- We have reviewed translating English phrases into algebraic expressions, using some basic mathematical vocabulary and symbols. We have also translated English sentences into algebraic equations and solved some word problems. The word problems applied math to everyday situations. We restated the situation in one sentence, assigned a variable, and then wrote an equation to solve the problem. This method works as long as the situation is familiar and the math is not too complicated.
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- 13.6.2: Solve Percent Applications
- We will solve percent equations using the methods we used to solve equations with fractions or decimals. Without the tools of algebra, the best method available to solve percent problems was by setting them up as proportions. Now as an algebra student, you can just translate English sentences into algebraic equations and then solve the equations.
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- 13.6.3: Solve Mixture Applications
- In mixture problems, we will have two or more items with different values to combine together. The mixture model is used by grocers and bartenders to make sure they set fair prices for the products they sell. Many other professionals, like chemists, investment bankers, and landscapers also use the mixture model.
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- 13.6.4: Triangles, Rectangles, and the Pythagorean Theorem
- In this section we will use some common geometry formulas. We will adapt our problem-solving strategy so that we can solve geometry applications. The geometry formula will name the variables and give us the equation to solve. In addition, since these applications will all involve shapes of some sort, most people find it helpful to draw a figure and label it with the given information. We will include this in the first step of the problem solving strategy for geometry applications.
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- 13.6.5: Solve Uniform Motion Applications
- In this section, we will use this formula in situations that require a little more algebra to solve than the ones we saw earlier. Generally, we will be looking at comparing two scenarios, such as two vehicles traveling at different rates or in opposite directions. When the speed of each vehicle is constant, we call applications like this uniform motion problems.
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- 13.6.6: Solve Applications with Linear Inequalities
- Many real-life situations require us to solve inequalities. In fact, inequality applications are so common that we often do not even realize we are doing algebra. The method we will use to solve applications with linear inequalities is very much like the one we used when we solved applications with equations.
Thumbnail: https://www.wikihow.com/Make-a-Mathematical-Model


6.5: Statements Involving Disjunction
First, let's consider a conditional statement with a disjunction on the hypothesis side. To prove a statement of the form \((P_1 \lor P_2) \Rightarrow Q\text{,}\) we can use Fact 6.4.1 to decompose into two conditionals:
Appealing to the properties of conjunction, as in our discussion of reduction to cases, we see that we can prove \(P_1 \Rightarrow Q\) and \(P_2 \Rightarrow Q\) by separate proofs.
What about a conditional with a disjunction on the conclusion side? To prove a statement of the form \(P \Rightarrow (Q_1 \lor Q_2)\text{,}\) we can again reduce to cases, but in a sort of tricky way. For any statement, there are only two possibilities — either the statement is true or it is false. (See Basic Tautology 3 in Example 1.4.1 . Apply this fact to one of the statements we are trying to prove.
To prove a statement of the form \(P \Rightarrow (Q_1 \lor Q_2)\text{,}\) start by assuming that \(P\) is true and \(Q_1\) is false . Try to show that these assumptions lead to \(Q_2\) being true.
There are only two possibilities for \(Q_1\text{:}\) either it is true or it is false. If \(Q_1\) is true, then \(Q_1 \lor Q_2\) is already true, regardless of the truth values of \(P\) and \(Q_2\text{,}\) so there is nothing to prove in this case. On the other hand, if \(Q_1\) is false, the only way \(Q_1 \lor Q_2\) could be true is if \(Q_2\) is true.
- Also see Exercise 2.5.3 .
- Of course, you can swap the roles of \(Q_1\) and \(Q_2\) above: you could also start by assuming that \(P\) is true and \(Q_2\) is false, then try to show that this leads to \(Q_1\) being true.
- Another strategy is to attempt a proof by contradiction (discussed in Section 6.9 below). By DeMorgan, \(\neg(Q_1 \lor Q_2) \Leftrightarrow \neg Q_1 \land \neg Q_2\text{,}\) so for this strategy, you should start by assuming that \(P\) is true and both \(Q_1\) and \(Q_2\) are false. Then, try to arrive at a contradiction.
Prove: Every odd number is either \(1\) more or \(3\) more than a multiple of \(4\text{.}\)
Solution
Let \(P(n)\) represent the predicate “\(n\) is odd”, let \(Q_1(n)\) represent the predicate “\(n\) is \(1\) more than a multiple of \(4\)”, and let \(Q_2(n)\) represent the predicate “\(n\) is \(3\) more than a multiple of \(4\)”, each with domain the integers.
Start by assuming that \(n\) is an odd number that is not \(1\) more than a multiple of \(4\text{.}\) We must now try to show that \(n\) is \(3\) more than a multiple of \(4\text{.}\) We know that \(n\) is odd, so there exists a number \(m\) such that \(n = 2m + 1\text{.}\) However, since \(n\) is not \(1\) more than a multiple of \(4\text{,}\) \(2m\) cannot be a multiple of \(4\text{,}\) and so \(m\) cannot be a multiple of \(2\text{.}\) Therefore, \(m\) is also odd, and so there exists another number \(\ell\) such that \(m = 2\ell + 1\text{.}\) Then
which says that \(n\) is \(3\) more than a multiple of \(4\text{,}\) as desired.


8.7: Types of Jails
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- Last updated
- Save as PDF
- Alison S. Burke, David Carter, Brian Fedorek, Tiffany Morey, Lore Rutz-Burri, & Shanell Sanchez
- Southern Oregon University via OpenOregon
Jails vary greatly in function and size. For example, the vast majority of jails hold less than 50 jail detainees each (roughly 2,000 jails). Yet, the 50 biggest jails hold over half of the total number of detainees, more than 350,000 in the 50 biggest jails. [1] For example, Los Angeles County Jail is actually a system of buildings spread across LA County, which includes the Inmate Reception Center, North Facility, South Facility, LOMA, Twin Towers, Men’s Central, just to name a few of the facilities. For a more detailed description of the jail facilities in L.A. County Jail, please see http://shq.lasdnews.net/pages/tgen1.aspx?id=as1 .
While most jails are run by County Sheriff, there are some jails that are managed by cities or jurisdictions. For example, Chicago, New York, Philadelphia, and Washington D.C. all have their own jails, which are not managed directly by the county in which they reside.
Jails also vary by how they are designed. While there are others, jails can be separated into two broad types, the older generation, and the new generation. Older generation jails are jails that are typically linear in design, with cell doors separating rooms or sections down long corridors. Many jails operate with this design. Newer generation jails are more podular in design, where multiple cells face a central area. Additionally, when these podular designs are used, a direct supervision approach is also often used. Direct supervision is where there are no particular barriers between the deputies and the detainees within a facility. For example, the image below depicts what a direct supervision jail may look like.
New Generation Jail Design
As you can see in the image, the operational booth (immediate left) is open to access the day area or common area, and the doors of the cells for this jail section open to this space. Below is an image of the older generation, linear style of jail. This typically uses the indirect supervision approach.
Older Generation Jail Design
- Minton, T. D. (2012). Jail inmates at midyear, statistical tables. U.S. Department of Justice. https://www.bjs.gov/content/pub/pdf/jim11st.pdf ↵