17.2: Basic Concepts of Enteral Tubes
Gastrointestinal Function
It is important to understand the anatomy and functioning of the gastrointestinal system before administering feedings or medications through an enteral tube. See Figure \(\PageIndex{1}\) [1] for an illustration of the anatomy of the gastrointestinal system.
For more information about the digestive function of the gastrointestinal system, visit the “ Gastrointestinal System ” chapter in Open RN Nursing Pharmacology .
Enteral Nutrition
Enteral nutrition is indicated for patients who need nutritional supplementation and have a functioning gastrointestinal tract, but cannot swallow food safely. Feedings can be administered via enteral tubes placed into the stomach or into the small intestine (usually the jejunum). For example, enteral feeding is commonly used for patients with the following conditions:
- Impaired swallowing (such as from a stroke or Parkinson’s disease)
- Decreased level of consciousness
- Respiratory distress requiring mechanical ventilation
- Oropharyngeal or esophageal obstruction (such as in head or neck cancer)
- Hypercatabolic states (such as in severe burns) [2]
For short-term feeding, NG tubes are used. If the duration of feeding is longer than four weeks or if access through the nose is contraindicated, a surgery is performed to place the tube directly through the gastrointestinal wall (for example, PEG or PEJ tubes).
Patients who are not candidates for enteral nutrition are prescribed parenteral nutrition. Parenteral nutrition is a concentrated intravenous solution containing glucose, amino acids, minerals, electrolytes, and vitamins. A lipid solution is typically administered as a separate infusion. This combination of solutions is called total parenteral nutrition because it supplies complete nutritional support. Parenteral nutrition is administered via a large central intravenous line, typically the subclavian or internal jugular vein, because it is irritating to the blood vessels.
Types of Enteral Tubes
There are several different types of enteral tubes based on their location in the gastrointestinal system, as well as their function. Three commonly used enteral tubes are the nasogastric tube, the percutaneous endoscopic gastrostomy (PEG) tube, and the percutaneous endoscopic jejunostomy (PEJ) tube. See Figure \(\PageIndex{2}\) [3] for an illustration of common enteral tubes. NG tubes are typically used for a short period of time (less than four weeks), whereas PEG and PEJ tubes are inserted for long-term enteral nutrition. Some institutions also place nasoduodenal (ND) tubes to provide long-term enteral nutrition. [4]
A nasogastric (NG) tube is a single- or double-lumen tube that is inserted into the nasopharynx through the esophagus and into the stomach. NG tubes can be used for feeding, medication administration, and suctioning. NG tubes used for feeding and medication administration are small and flexible, whereas NG tubes used for suctioning are larger and more rigid. NG tubes are secured externally on the patient’s nose or cheek by adhesive tape or a fixation device, so this area should be assessed daily for signs of pressure damage. See Figure \(\PageIndex{3}\) [5] for an image of a small bore feeding tube.
An example of a large bore nasogastric tube is the Salem Sump. Large bore nasogastric tubes, such as the Salem Sump, are used for gastric decompression. The Salem Sump has a double lumen that includes a venting system. One lumen is used to empty the stomach, and the other lumen is used to provide a continuous flow of air. The continuous flow of air reduces negative pressure and prevents gastric mucosa from being drawn into the catheter, which causes mucosal damage. This terminal end also has an anti-reflux valve to prevent gastric secretions from traveling through the wrong lumen. See Figure \(\PageIndex{4}\) [6] for an example of a double-lumen enteral tube.
Other types of tubes are placed through the patient’s abdominal wall and are used for long-term enteral feeding. A percutaneous endoscopic gastrostomy (PEG) tube is placed via an endoscopic procedure into the stomach. Alternatively, a percutaneous endoscopic jejunostomy (PEJ) tube is placed in the jejunum of the small intestine for patients who cannot tolerate the administration of enteral formula or medications into the stomach due to medical conditions such as delayed gastric emptying. See Figure \(\PageIndex{5}\) [7] for an image of a PEG tube insertion kit and the appearance of an enteral tube as it exits from a patient’s abdomen.
Assessing Tube Placement
Feedings or medications administered into an incorrectly placed enteral tube result in life-threatening aspiration pneumonia. The placement of an enteral tube is immediately verified after insertion by an X-ray to ensure it has not been inadvertently placed into the trachea and down into the bronchi. See Figure \(\PageIndex{6}\) [8] for an image of an X-ray demonstrating correct placement of an enteral tube in the stomach as indicated by the lower red arrow. (This X-ray also demonstrates an endotracheal tube correctly placed in the trachea as indicated by the top arrow.) After X-ray verification, the tube should be marked with adhesive tape and/or a permanent marker to indicate the point on the tube where the feeding tube enters the nares or penetrates the abdominal wall. This number on the tube at the entry point should be documented in the medical record and communicated during handoff reports. At the start of every shift, nurses evaluate if the incremental marking or external tube length has changed. If a change is observed, bedside tests such as visualization or pH testing of tube aspirate can help determine if the tube has become dislocated. If in doubt, a radiograph should be obtained to determine tube location. [9]
After the initial verification of tube placement by X-ray, it is possible for the tube to migrate out of position due to the patient coughing, vomiting, and moving. For this reason, the nurse must routinely check tube placement before every use. The American Association of Critical‐Care Nursing recommends that the position of a feeding tube should be checked and documented every four hours and prior to the administration of enteral feedings and medications by measuring the visible tube length and comparing it to the length documented during X-ray verification. [10] , [11] , [12]
Older methods of checking tube placement included observing aspirated GI contents or the administration of air with a syringe while auscultating (commonly referred to as the “whoosh test”). However, research has determined these methods are unreliable and should no longer be used to verify placement. [13] , [14]
Checking the pH of aspirated gastric contents is an alternative method to verify placement that may be used in some agencies. Gastric aspirate should have a pH of less than or equal to 5.5 using pH indicator paper that is marked for use with human aspirate. However, caution should be used with this method because enteral formula and some medications alter the gastric pH. [15]
Follow agency policy for assessing and documenting tube placement. Additionally, if the patient develops respiratory symptoms that indicate potential aspiration, immediately notify the provider and withhold enteral feedings and medications until the placement is verified.
Assessing and Cleaning the Tube Insertion Site
The area of tube insertion should be assessed daily for signs of pressure damage. For NG tubes, the adhesive used to secure the tube can be irritating and cause skin breakdown. PEG and PEJ tubes may have fluid seepage around the insertion point that can cause skin breakdown if not cleaned regularly. Follow agency policy for cleansing the external insertion site for PEG and PEJ tubes. Cleansing is typically performed using gauze moistened with water or saline and then allowed to air dry before the fixation plate is repositioned. Because skin surrounding the insertion site is prone to breakdown, barrier cream or dressings may be prescribed to prevent breakdown. [16] , [17]
Tube Feeding
Enteral Nutrition (EN) refers to nutrition provided directly into the gastrointestinal (GI) tract through an enteral tube that bypasses the oral cavity. Each year in the United States, over 250,000 hospitalized patients from infants to older adults receive EN. It is also used widely in rehabilitation, long‐term care, and home settings. EN requires a multidisciplinary team approach, including a registered dietician, health care provider, pharmacist, and bedside nurses. The registered dietician performs a nutrition assessment and determines what type of enteral nutrition is appropriate to promote improved patient outcomes. The health care provider writes the order for the enteral nutrition. Prescriptions for enteral nutrition should be reviewed by the nurse for the following components: type of enteral nutrition formula, amount and frequency of free water flushes, route of administration, administration method, and rate. Any concerns about the components of the prescription should be verified with the provider before tube feeding is administered. [18]
Tube feeding can be administered using gravity to provide a bolus feeding or via a pump to provide continuous or intermittent feeding. Feedings via a pump are set up in mL/hr, with the rate prescribed by the health care provider. See Figure \(\PageIndex{7}\) [19] for an image of an enteral tube feeding pump and the associated tubing. Note that tubing used for enteral feeding is indicated by specific colors (such as purple in Figure \(\PageIndex{7}\)). A global safety initiative, referred to as “EnFit,” is in progress to ensure all devices used with enteral feeding, such as extension sets, syringes, PEG tubes, and NG tubes have specific EnFit ends that can only be used with tube feeding sets. This new safety design will avoid inadvertent administration of enteral feeding into intravenous tubing that can cause life-threatening adverse effects.
Review the “ Checklist for NG Tube Enteral Feeding by Gravity with Irrigation ” section for additional information regarding administering bolus feedings by gravity.
Life Span Considerations
Enteral feeding is administered to infants and children via a syringe, gravity feeding set, or feeding pump. The method selected is dependent on the nature of the feeding and clinical status of the child. [20]
Complications of Enteral Feeding
The most serious complication of enteral feeding is inadvertent respiratory aspiration of gastric contents, causing life-threatening aspiration pneumonia. Other complications include tube clogging, tubing misconnections, and patient intolerance of enteral feeding. [21]
Reducing Risk of Aspiration
In addition to verifying tube placement as discussed in an earlier section, nurses perform additional interventions to prevent aspiration. The American Association of Critical‐Care Nurses recommends the following guidelines to reduce the risk for aspiration:
- Maintain the head of the bed at 30°-45° unless contraindicated
- Use sedatives as sparingly as possible
- Assess feeding tube placement at four‐hour intervals
- Observe for change in the amount of external length of the tube
- Assess for gastrointestinal intolerance at four‐hour intervals [22]
Measurement of gastric residual volume (GRV) is performed by using a 60-mL syringe to aspirate stomach contents through the tube. It has traditionally been used to assess aspiration risk with associated interventions such as slowing or stopping the enteral feeding. GRVs in the range of 200–500 mL cause interventions such as slowing or stopping the feeding to reduce risk of aspiration. However, according to recent research, it is not appropriate to stop enteral nutrition for GRVs less than 500 mL in the absence of other signs of intolerance because of the impact on the patient’s overall nutritional status. Additionally, the aspiration of gastric residual volumes can contribute to tube clogging. [23] Follow agency policy regarding measuring gastric residual volume and implementing interventions to prevent aspiration.
Managing Tube Clogging
Feeding tubes are prone to clogging for a variety of reasons. The risk of clogging may result from tube properties (such as narrow tube diameter), the tube tip location (stomach vs. small intestine), insufficient water flushes, aspiration for gastric residual volume (GRV), contaminated formula, and incorrect medication preparation and administration. A clogged feeding tube can result in decreased nutrient delivery or delayed administration of medication, and, if not corrected, the patient may require additional surgical intervention to replace the tube. [24]
Research supports using water as the best choice for initial declogging efforts. Instill warm water into the tube using a 60‐mL syringe, and apply a gentle back‐and‐forth motion with the plunger of the syringe. Research shows that the use of cranberry juice and carbonated beverages to flush the tube can worsen tube occlusions because the acidic pH of these fluids can cause proteins in the enteral formula to precipitate within the tube. If water does not work, a pancreatic enzyme solution, an enzymatic declogging kit, or mechanical devices for clearing feeding tubes are the best second‐line options. [25]
To prevent enteral tubes from clogging, it is important to follow these guidelines:
- Flush feeding tubes at a minimum of once a shift.
- Flush feeding tubes immediately before and after intermittent feedings. During continuous feedings, flush at standardized, scheduled intervals.
- Flush feeding tubes before and after medication administration and follow appropriate medication administration practices.
- Limit gastric residual volume checks because the acidic gastric contents may cause protein in enteral formulas to precipitate within the lumen of the tube. [26]
Preventing Tubing Misconnections
In April 2006, The Joint Commission issued a Sentinel Event Alert on tubing misconnections due to enteral feedings being inadvertently infused into intravenous lines with life-threatening results. A color-coded enteral tubing connection design was developed to visually communicate the difference between enteral tubing and intravenous tubing. In addition to tubing design, follow these guidelines to prevent tubing misconnection errors:
- Make tubing connections under proper lighting.
- Do not modify or adapt IV or feeding devices because doing so may compromise the safety features incorporated into their design.
- When making a reconnection, routinely trace lines back to their origins and then ensure that they are secure.
- As part of a hand‐off process, recheck connections and trace all tubes back to their origins. [27]
Managing Intolerances and Imbalances
Patients should be monitored daily for signs of tube feeding intolerance, such as abdominal bloating, nausea, vomiting, diarrhea, cramping, and constipation. If cramping occurs during bolus feedings, it can be helpful to administer the enteral nutritional formula at room temperature to prevent symptoms. [28] Notify the provider of signs of intolerance with anticipated changes in the prescription regarding the type of formula or the rate of administration. Electrolytes and blood glucose levels should also be monitored, as ordered, for signs of imbalances. [29] , [30]
Tube Irrigation
Enteral tubes are routinely flushed to maintain patency. Follow agency policy when flushing a tube. Typically, tap water and a 60-mL syringe are used to flush enteral tubes. [31] See Figure \(\PageIndex{8}\) [32] for an image of a nurse irrigating an NG tube.
The steps for irrigating enteral tubes are typically the following:
- Draw the required amount of water into the 60-mL syringe and dispel excess air.
- If the tube has a clamp, close it.
- Open the distal end of the tube and connect the syringe.
- Open the clamp.
- Administer the water.
- Close the clamp.
- Remove the syringe and refill it with water if indicated.
- Repeat as needed to obtain the desired flushing volume.
- Once completed, remove the syringe, close the tube cap, and reopen the clamp. [33]
Tube Suctioning
NG tubes may be used to remove gastric content, referred to as gastric decompression. In these situations, the stomach is drained by gravity or by connection to a suction pump to prevent nausea, vomiting, gastric distension, or to wash the stomach of toxins. This procedure is commonly used for post-operative patients who have not yet regained peristalsis or for patients with a small bowel obstruction to remove the accumulation of stomach bile. It is also used in the emergency department for patients with some types of poisonings or overdoses and is commonly referred to as “pumping out the stomach.”
For patients receiving suctioning via enteral tubes, the drainage amount and color should be documented every shift.
- “abdomen-intestine-large-small-1698565” by bodymybody is licenced under CCO ↵
- Wireko, B. M., & Bowling, T. (2010). Enteral tube feeding. Clinical Medicine, 10 (6), 616–619. https://doi.org/10.7861/clinmedicine.10-6-616 ↵
- “Types and Placement of Enteral Tubes.png” by Meredith Pomietlo for Chippewa Valley Technical College is licensed under CC BY 4.0 ↵
- Best, C. (2019). Selection and management of commonly used enteral feeding tubes. Nursing Times, 15 (3), 43-47. https://www.nursingtimes.net/clinical-archive/nutrition/selection-and-management-of-commonly-used-enteral-feeding-tubes-18-02-2019/ ↵
- “ Enteral_feeding_tube_stylet_retracted.png ” by Tenbergen is licensed under CC BY-SA 4.0 ↵
- “ Silicone_dual_lumen_stomach_tube_with_plug_removed.png ” by Tenbergen is licensed under CC BY-SA 4.0 ↵
- “ PEG_tube_kit.jpg ” by Gilo1969 and “Percutaneous_endoscopic_gastrostomy-tube.jpg” by Pflegewiki-User HoRaMi are licensed under CC BY-SA 3.0 ↵
- "ETTubeandNGtubeMarked.png" by James Heilman, MD is licensed under CC BY-SA 4.0 ↵
- Boullata, J. I., Carrera, A. L., Harvey, L., Escuro, A. A., Hudson, L., Mays, A., McGinnis, C., Wessel, J. J., Bajpai, S., Beebe, M. L., Kinn, T. J., Klang, M. G., Lord, L., Martin, K., Pompeii‐Wolfe, C., Sullivan, J., Wood, A., Malone, A., & Guenter, P. (2017). ASPEN safe practices for enteral nutrition therapy. Journal of Parenteral and Enteral Nutrition, 41 (1), 15-103. doi.org/10.1177/0148607116673053. ↵
- Lemyze, M. (2010). The placement of nasogastric tubes. CMAJ : Canadian Medical Association Journal , 182 (8), 802. https://doi.org/10.1503/cmaj.091099 ↵
- Simons, S. R., & Abdallah, L. M. (2012). Bedside assessment of enteral tube placement: Aligning practice with evidence. American Journal of Nursing, 112 (2), 40-46. https://doi.org/10.1097/01.naj.0000411178.07179.68 ↵
- Boullata, J. I., Carrera, A. L., Harvey, L., Escuro, A. A., Hudson, L., Mays, A., McGinnis, C., Wessel, J. J., Bajpai, S., Beebe, M. L., Kinn, T. J., Klang, M. G., Lord, L., Martin, K., Pompeii‐Wolfe, C., Sullivan, J., Wood, A., Malone, A., & Guenter, P. (2017). ASPEN safe practices for enteral nutrition therapy. Journal of Parenteral and Enteral Nutrition, 41 (1), 15-103. doi.org/10.1177/0148607116673053. ↵
- Simons, S. R., & Abdallah, L. M. (2012). Bedside assessment of enteral tube placement: Aligning practice with evidence. American Journal of Nursing, 112 (2), 40-46. https://doi.org/10.1097/01.naj.0000411178.07179.68 ↵
- Boullata, J. I., Carrera, A. L., Harvey, L., Escuro, A. A., Hudson, L., Mays, A., McGinnis, C., Wessel, J. J., Bajpai, S., Beebe, M. L., Kinn, T. J., Klang, M. G., Lord, L., Martin, K., Pompeii‐Wolfe, C., Sullivan, J., Wood, A., Malone, A., & Guenter, P. (2017). ASPEN safe practices for enteral nutrition therapy. Journal of Parenteral and Enteral Nutrition, 41( 1), 15-103. doi.org/10.1177/0148607116673053.↵
- Best, C. (2019). Selection and management of commonly used enteral feeding tubes. Nursing Times, 15 (3), 43-47. https://www.nursingtimes.net/clinical-archive/nutrition/selection-and-management-of-commonly-used-enteral-feeding-tubes-18-02-2019/ ↵
- Blumenstein, I., Shastri, Y. M., & Stein, J. (2014). Gastroenteric tube feeding: Techniques, problems and solutions. World Journal of Gastroenterology, 20 (26), 8505–8524. https://doi.org/10.3748/wjg.v20.i26.8505 ↵
- Best, C.(2019). Selection and management of commonly used enteral feeding tubes. Nursing Times, 15 (3), 43-47. https://www.nursingtimes.net/clinical-archive/nutrition/selection-and-management-of-commonly-used-enteral-feeding-tubes-18-02-2019/ ↵
- Boullata, J. I., Carrera, A. L., Harvey, L., Escuro, A. A., Hudson, L., Mays, A., McGinnis, C., Wessel, J. J., Bajpai, S., Beebe, M. L., Kinn, T. J., Klang, M. G., Lord, L., Martin, K., Pompeii‐Wolfe, C., Sullivan, J., Wood, A., Malone, A., & Guenter, P. (2017). ASPEN safe practices for enteral nutrition therapy. Journal of Parenteral and Enteral Nutrition, 41 (1), 15-103. doi.org/10.1177/0148607116673053. ↵
- “ Open_system_enteral_feeding.jpg ” by Ashashyou is licensed under CC BY-SA 3.0 ↵
- The Royal Children’s Hospital Melbourne. (2017, December). Enteral feeding and medication administration . https://www.rch.org.au/rchcpg/hospital_clinical_guideline_index/Enteral_feeding_and_medication_administration/ ↵
- Blumenstein, I., Shastri, Y. M., & Stein, J. (2014). Gastroenteric tube feeding: Techniques, problems and solutions. World Journal of Gastroenterology, 20 (26), 8505–8524. https://doi.org/10.3748/wjg.v20.i26.8505 ↵
- Boullata, J. I., Carrera, A. L., Harvey, L., Escuro, A. A., Hudson, L., Mays, A., McGinnis, C., Wessel, J. J., Bajpai, S., Beebe, M. L., Kinn, T. J., Klang, M. G., Lord, L., Martin, K., Pompeii‐Wolfe, C., Sullivan, J., Wood, A., Malone, A., & Guenter, P. (2017). ASPEN safe practices for enteral nutrition therapy. Journal of Parenteral and Enteral Nutrition, 41 (1), 15-103. doi.org/10.1177/0148607116673053. ↵
- Boullata, J. I., Carrera, A. L., Harvey, L., Escuro, A. A., Hudson, L., Mays, A., McGinnis, C., Wessel, J. J., Bajpai, S., Beebe, M. L., Kinn, T. J., Klang, M. G., Lord, L., Martin, K., Pompeii‐Wolfe, C., Sullivan, J., Wood, A., Malone, A., & Guenter, P. (2017). ASPEN safe practices for enteral nutrition therapy. Journal of Parenteral and Enteral Nutrition, 41 (1), 15-103. doi.org/10.1177/0148607116673053.↵
- Boullata, J. I., Carrera, A. L., Harvey, L., Escuro, A. A., Hudson, L., Mays, A., McGinnis, C., Wessel, J. J., Bajpai, S., Beebe, M. L., Kinn, T. J., Klang, M. G., Lord, L., Martin, K., Pompeii‐Wolfe, C., Sullivan, J., Wood, A., Malone, A., & Guenter, P. (2017). ASPEN safe practices for enteral nutrition therapy. Journal of Parenteral and Enteral Nutrition, 41 (1), 15-103. doi.org/10.1177/0148607116673053.↵
- Boullata, J. I., Carrera, A. L., Harvey, L., Escuro, A. A., Hudson, L., Mays, A., McGinnis, C., Wessel, J. J., Bajpai, S., Beebe, M. L., Kinn, T. J., Klang, M. G., Lord, L., Martin, K., Pompeii‐Wolfe, C., Sullivan, J., Wood, A., Malone, A., & Guenter, P. (2017). ASPEN safe practices for enteral nutrition therapy. Journal of Parenteral and Enteral Nutrition, 41 (1), 15-103. doi.org/10.1177/0148607116673053. ↵
- Boullata, J. I., Carrera, A. L., Harvey, L., Escuro, A. A., Hudson, L., Mays, A., McGinnis, C., Wessel, J. J., Bajpai, S., Beebe, M. L., Kinn, T. J., Klang, M. G., Lord, L., Martin, K., Pompeii‐Wolfe, C., Sullivan, J., Wood, A., Malone, A., & Guenter, P. (2017). ASPEN safe practices for enteral nutrition therapy. Journal of Parenteral and Enteral Nutrition, 41 (1), 15-103. doi.org/10.1177/0148607116673053.↵
- Boullata, J. I., Carrera, A. L., Harvey, L., Escuro, A. A., Hudson, L., Mays, A., McGinnis, C., Wessel, J. J., Bajpai, S., Beebe, M. L., Kinn, T. J., Klang, M. G., Lord, L., Martin, K., Pompeii‐Wolfe, C., Sullivan, J., Wood, A., Malone, A., & Guenter, P. (2017). ASPEN safe practices for enteral nutrition therapy. J ournal of Parenteral and Enteral Nutrition, 41 (1), 15-103. doi.org/10.1177/0148607116673053. ↵
- The Royal Children’s Hospital Melbourne. (2017, December). Enteral feeding and medication administration. https://www.rch.org.au/rchcpg/hospital_clinical_guideline_index/Enteral_feeding_and_medication_administration/ ↵
- Blumenstein, I., Shastri, Y. M., & Stein, J. (2014). Gastroenteric tube feeding: Techniques, problems and solutions. World Journal of Gastroenterology, 20 (26), 8505–8524. https://doi.org/10.3748/wjg.v20.i26.8505 ↵
- Boullata, J. I., Carrera, A. L., Harvey, L., Escuro, A. A., Hudson, L., Mays, A., McGinnis, C., Wessel, J. J., Bajpai, S., Beebe, M. L., Kinn, T. J., Klang, M. G., Lord, L., Martin, K., Pompeii‐Wolfe, C., Sullivan, J., Wood, A., Malone, A., & Guenter, P. (2017). ASPEN safe practices for enteral nutrition therapy. Journal of Parenteral and Enteral Nutrition, 41 (1), 15-103. doi.org/10.1177/0148607116673053. ↵
- Best, C. (2019). Selection and management of commonly used enteral feeding tubes. Nursing Times, 15( 3), 43-47. https://www.nursingtimes.net/clinical-archive/nutrition/selection-and-management-of-commonly-used-enteral-feeding-tubes-18-02-2019/ ↵
- “ DSC_1667.jpg ” by British Columbia Institute of Technology is licensed under CC BY 4.0. Access for free at https://opentextbc.ca/clinicalskills/chapter/10-2-nasogastric-tubes ↵
- Best, C. (2019). Selection and management of commonly used enteral feeding tubes. Nursing Times, 15 (3), 43-47. https://www.nursingtimes.net/clinical-archive/nutrition/selection-and-management-of-commonly-used-enteral-feeding-tubes-18-02-2019/ ↵


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7.9: Collaborative Group Activities
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Discuss and make a list of the reasons why we humans might want to explore the other worlds in the solar system. Does your group think such missions of exploration are worth the investment? Why?
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Your instructor will assign each group a world. Your task is to think about what it would be like to be there. (Feel free to look ahead in the book to the relevant chapters.) Discuss where on or around your world we would establish a foothold and what we would need to survive there.
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In the There’s No Place Like Home feature, we discuss briefly how human activity is transforming our planet’s overall environment. Can you think of other ways that this is happening?
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Some scientists criticized Carl Sagan for “wasting his research time” popularizing astronomy. To what extent do you think scientists should spend their time interpreting their field of research for the public? Why or why not? Are there ways that scientists who are not as eloquent or charismatic as Carl Sagan or Neil deGrasse Tyson can still contribute to the public understanding of science?
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Your group has been named to a special committee by the International Astronomical Union to suggest names of features (such as craters, trenches, and so on) on a newly explored asteroid. Given the restriction that any people after whom features are named must no longer be alive, what names or types of names would you suggest? (Keep in mind that you are not restricted to names of people, by the way.)
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A member of your group has been kidnapped by a little-known religious cult that worships the planets. They will release him only if your group can tell which of the planets are currently visible in the sky during the evening and morning. You are forbidden from getting your instructor involved. How and where else could you find out the information you need? (Be as specific as you can. If your instructor says it’s okay, feel free to answer this question using online or library resources.)
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In the Carl Sagan: Solar System Advocate feature, you learned that science fiction helped spark and sustain his interest in astronomy. Did any of the members of your group get interested in astronomy as a result of a science fiction story, movie, or TV show? Did any of the stories or films you or your group members saw take place on the planets of our solar system? Can you remember any specific ones that inspired you? If no one in the group is into science fiction, perhaps you can interview some friends or classmates who are and report back to the group.
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A list of NASA solar system spacecraft missions can be found at
http://www.nasa.gov/content/solar-missions-list
. Your instructor will assign each group a mission. Look up when the mission was launched and executed, and describe the mission goals, the basic characteristics of the spacecraft (type of instruments, propellant, size, and so on), and what was learned from the mission. If time allows, each group should present its findings to the rest of the class.
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What would be some of the costs or risks of developing a human colony or base on another planetary body? What technologies would need to be developed? What would people need to give up to live on a different world in our solar system?


The
hidden curriculum
is a phrase used to cover a wide variety of circumstances at school that can influence learning and affect your experience. Sometimes called the invisible curriculum, it varies by institution and can be thought of as a set of unwritten rules or expectations.
Situation:
According to your syllabus, your history professor is lecturing on the chapter that covers the stock market crash of 1929 on Tuesday of next week.
Sounds pretty straightforward and common. Your professor lectures on a topic and you will be there to hear it. However, there are some unwritten rules, or hidden curriculum, that are not likely to be communicated. Can you guess what they may be?
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What is an unwritten rule about what you should be doing before attending class?
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What is an unwritten rule about what you should be doing in class?
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What is an unwritten rule about what you should be doing after class?
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What is an unwritten rule if you are not able to attend that class?
Some of your answers could have included the following:
Table 3.6
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Before class:
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read the assigned chapter, take notes, record any questions you have about the reading
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During class:
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take detailed notes, ask critical thinking or clarifying questions, avoid distractions, bring your
book and your reading notes
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After class:
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reorganize your notes in relation to your other notes, start the studying process by testing
yourself on the material, make an appointment with your professor if you are not clear on a concept
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Absent:
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communicate with the professor, get notes from a classmate, make sure you did not miss
anything important in your notes
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The expectations before, during, and after class, as well as what you should do if you miss class, are often unspoken because many professors assume you already know and do these things or because they feel you should figure them out on your own. Nonetheless, some students struggle at first because they don’t know about these habits, behaviors, and strategies. But once they learn them, they are able to meet them with ease.
While the previous example may seem obvious once they’ve been pointed out, most instances of the invisible curriculum are complex and require a bit of critical thinking to uncover. What follows are some common but often overlooked examples of this invisible curriculum.
One example of a hidden curriculum could be found in the beliefs of your professor. Some professors may refuse to reveal their personal beliefs to avoid your writing toward their bias rather than presenting a cogent argument of your own. Other professors may be outspoken about their beliefs to force you to consider and possibly defend your own position. As a result, you may be influenced by those opinions which can then influence your learning, but not as an official part of your study.
Other examples of how this hidden curriculum might not always be so easily identified can be found in classroom arrangements or even scheduling. To better understand this, imagine two different classes on the exact same subject and taught by the same instructor. One class is held in a large lecture hall and has over 100 students in it, while the other meets in a small classroom and has fewer than 20 students. In the smaller class, there is time for all of the students to participate in discussions as a learning activity, and they receive the benefit of being able to talk about their ideas and the lessons through direct interaction with each other and the professor. In the larger class, there is simply not enough time for all 100 students to each discuss their thoughts. On the flip side, most professors who teach lecture classes use technology to give them constant feedback on how well students understand a given subject. If the data suggests more time should be spent, these professors discover this in real time and can adapt the class accordingly.
Another instance where class circumstances might heavily influence student learning could be found in the class schedule. If the class was scheduled to meet on Mondays and Wednesdays and the due date for assignments was always on Monday, those students would benefit from having the weekend to finalize their work before handing it in. If the class met on a different day, students might not have as much free time just before handing in the assignment. The obvious solution would be better planning and time management to complete assignments in advance of due dates, but nonetheless, conditions caused by scheduling may still impact student learning.
Working Within the Hidden Curriculum
The first step in dealing with the hidden curriculum is to recognize it and understand how it can influence your learning. After any specific situation has been identified, the next step is to figure out how to work around the circumstances to either take advantage of any benefits or to remove any roadblocks.
To illustrate this, here are some possible solutions to the situations given as examples earlier in this section:
Prevailing Opinions—Simply put, you are going to encounter instructors and learning activities that you sometimes agree with and sometimes do not. The key is to learn from them regardless. In either case, take ownership of your learning and even make an effort to learn about other perspectives, even if it is only for your own education on the matter. There is no better time to expose yourself to other opinions and philosophies than in college. In fact, many would say that this is a significant part of the college experience. With a growth mindset, it is easy to view everything as a learning opportunity.
Classroom Circumstances—These kinds of circumstances often require a more structured approach to turn the situation to your advantage, but they also usually have the most obvious solutions. In the example of the large class, you might find yourself limited in the ability to participate in classroom discussions because of so many other students. The way around that would be to speak to several classmates and create your own discussion group. You could set up a time to meet, or you could take a different route by using technology such as an online discussion board, a Skype session, or even a group text. Several of the technologically based solutions might even be better than an in-class discussion since you do not all have to be present at the same time. The discussion can be something that occurs all week long, giving everyone the time to think through their ideas and responses.
Again, the main point is to first spot those things in the hidden curriculum that might put your learning at a disadvantage and devise a solution that either reduces the negative impact or even becomes a learning advantage.


1.6: Drills and Accessories
Drills
Drills are used to bore holes, tighten and loosen fasteners, and, with some models and accessories, mix paint, mortar, and similar materials, and to chisel and chip mortar, concrete, and other dense or hard materials. The selection of the proper dill for a job requires knowledge of the material being worked, the types and models of drills and their purposes, and the accessories that are appropriate for the task. Tool makers offer all of the types of drills in corded models and the majority of them are also available in variable speed and battery powered models that offer greater portability and reduced tool weight with lighter weight DC brushless motor technology.
Basic Drill Parts Identification
Drill Safety
- Wear safety glasses when operating with portable electric drill.
- Disconnect the drill from the electrical supply when installing bits.
- Clamp stock so it will not move during the drilling operation.
- Before drilling, turn the drill on to see if the bit is centered and running true.
- Align the bit with the desired hole location before turning the drill on.
- Hold the drill firmly with both hands while drilling.
- When drilling deep holes with a twist drill, move the bit up and down several times while drilling to remove cuttings and reduce overheating in the bit.
- Do not allow the cord to become wrapped around the drill when working.
- If the electrical cord becomes frayed or starts to separate from the drill housing, repair it immediately!
- Remove the bit from the drill as soon as the work is completed.
- Select the correct bit for the finish and material being drilled. Make sure the bit is securely tightened in the drill chuck.
- Be extremely careful when using larger portable electric drills (3/8″ and 1/2″). If the bit should hang or get caught the drill will twist in the operator’s hands causing a sprain or bruised fingers.
- Always remove the key from the chuck before drilling.
- To prevent seizing, reduce the feed pressure when the drill bit is about to come through the material.
Drill Operating Procedures
- Always center punch or make a starting indentation in the material being drilled to get an accurate starting point for the drill bit.
- Tighten the drill bit by rotating the chuck key to all three holes in the chuck. This will help to keep the drill bit centered.
- Apply moderate even pressure to the drill during the drilling operation. If excessive pressure is required to make the bit cut then the bit is dull and needs to be sharpened.
- Maintain good balance at all times when drilling.
- Use slow drill speeds for drilling metal and fast speeds for drilling wood.
- To obtain holes that are placed accurately, drill a small pilot first then drill the final hole.
Drill Types
Query \(\PageIndex{1}\)
The interactive or media element is excluded from the print version of the text. You can view it online here:
Interactive media drills
Bits & Accessories
Along with using the driver bits for various fasteners discussed in the previous chapter, drills can be accessorized to perform a variety of functions.
Query \(\PageIndex{1}\)
The interactive or media element is excluded from the print version of the text. You can view it online here:
Interactive media drill bits


16.0: Introduction
According to the International Association for the Study of Pain (2021b), pain is defined as “an unpleasant sensory and emotional experience associated with, or resembling that associated with, actual or potential tissue damage.” Pain can be acute or chronic, mild or severe, and expressed in many different ways. Pain is triggered by a perceived danger or stress and tells the body to withdraw from threatening stimuli. Most pain resolves after the painful stimulus is removed and the body has healed, but sometimes pain persists despite removal of the stimulus and apparent healing of the body.
Pain is a subjective experience and can be influenced by biological, psychological, and social factors. Pain affects people in every aspect of health care, requiring nurses to be able to assess, manage, and treat it. Pain is subjective, meaning the patient defines the pain (ANA Center for Ethics and Human Rights, 2018). Patients can express pain through verbal and nonverbal behaviors. Some patients may rate their pain on a pain scale while other patients can only exhibit nonverbal cues such as grimacing, crying, and vital sign changes.
Because the experience of pain has so many variables, pain assessment and management must be comprehensive to be effective. Nurses must perform frequent comprehensive pain assessments to determine what pain interventions would be most effective for each patient. Pain management plans must be individualized and involve the patient and healthcare team. Pain is one of the most common reasons for patients seeking care, and treating pain must be a top priority for healthcare providers in all settings.


8.1: Conclusion
Three forces combined to shape the course of Central Asian history: the Turkic migrations, expansion of Islam, and the Mongol conquest. Beginning in the second century BCE, waves of Turkic migrations entered the region. Turkic tribes occupied the great steppe, Turkifying the region and endowing it with a more nomadic character. They also populated the agricultural basin of Transoxiana, displacing the original Iranian inhabitants of the area. Many of these Turks slowly settled down over time, and displayed a unique ability to absorb the Islamic faith and internalize the Mongol conquest.
Islam transformed the religious adherence of Central Asia and left a lasting mark on the region as well. Transoxiana gradually Islamicized, but Turkic and Persian cultures persisted. As Islam spread through the area, the faith demonstrated an extraordinary capacity to incorporate local traditions, permitting some customs to linger so long as doing so accelerated conversion. Sufi missionaries made some compromises with the Turkic nomadic culture in order to establish the religion in the area. Sufism’s inherent flexibility helped to promote conversion, and the blend of orthodox Islam and Turkic pastoral nomadism created a uniquely Central Asian brand of the faith.
The Mongol conquest of Central Asia had the most immediate impact on the history of the region. Although the Mongols eventually Turkified over time, the legacy of Genghis-Khanid legitimacy remained. Genghis Khan had developed a secure and dependable means of transferring power. The Genghis-Khanid legitimacy reduced the number of contenders vying for the throne, and the Mongols did not collapse as a “nation” following the death of their founder. Genghis Khan bequeathed a legacy of political legitimacy to the region that would last until 1920.


3.8: III Glossary
Adaptive coping strategies: Coping strategies, including problem-focused coping and emotion-focused coping.

Coping: Cognitive and behavioral efforts made to master, tolerate, or reduce external and internal demands and conflicts. [1]
Coping strategies: An action, series of actions, or a thought process used in meeting a stressful or unpleasant situation or in modifying one’s reaction to such a situation. [2]
Crisis: The inability to cope or adapt to a stressor.
Defense mechanisms: Unconscious reaction patterns used by individuals to protect themselves from anxiety that arises from stress and conflict. [3]
Emotion-focused coping: Adaptive coping strategies such as practicing mindfulness, meditation, and yoga; using humor and jokes; seeking spiritual or religious pursuits; engaging in physical activity or breathing exercises; and seeking social support.
Maladaptive coping responses: Ineffective responses to stressors such as avoidance of the stressful condition, withdrawal from a stressful environment, disengagement from stressful relationships, and misuse of drugs and/or alcohol.
Problem-focused coping: Adaptive coping strategies that typically focus on seeking treatment such as counseling or cognitive behavioral therapy.
Stress response: The body’s physiological response to a real or perceived stressor. For example, the respiratory, cardiovascular, and musculoskeletal systems are activated to breathe rapidly, stimulate the heart to pump more blood, dilate the blood vessels, and increase blood pressure to deliver more oxygenated blood to the muscles.
Stressors: Any internal or external event, force, or condition that results in physical or emotional stress.
- Amnie, A. G. (2018). Emerging themes in coping with lifetime stress and implication for stress management education. SAGE Open Medicine, 6. https://doi.org/10.1177%2F2050312118782545 ↵
- American Psychological Association. (n.d.). Stressor. APA Dictionary of Psychology . https://dictionary.apa.org ↵
- American Psychological Association. (n.d.). Stressor. APA Dictionary of Psychology . https://dictionary.apa.org ↵


6.6: Summary
6.1 Problem Solving to Find Entrepreneurial Solutions
Problem solving involves more than making decisions. Problem solving is a necessary component of entrepreneurial genesis, used to manage your business and helpful in addressing everyday personal situations. Entrepreneurs must know their personal strengths and capitalize on applicable problem-solving methods to create innovative products. Moving a startup ahead of the competition requires the entrepreneur to use all problem-solving sources and skills in the entrepreneur’s tool box. Problem-solving models can be adaptive or innovative, the latter being more common among entrepreneurs. Problem-solving skills include critical thinking, communication, decisiveness, resourcefulness, business and industry awareness, and an ability to analyze data. There are various types of problem solvers, including self-regulating, theorist, and petitioner problem solvers.
6.2 Creative Problem-Solving Process
The creative problem-solving process is a logical process. The steps to the creative problem-solving process are clarify, ideate, develop, implement, and evaluate. Each step is an aid to creating a solution. The steps are repeated cyclically until the entrepreneur develops an innovative solution. When entrepreneurs experience creativity block, tools to alleviate the block are available. These tools include crowdsourcing, brainstorming, and storyboarding. Each of these tools assist the entrepreneur in innovative thinking.
6.3 Design Thinking
Design thinking in business and entrepreneurship was made prevalent by David Kelley, founder of Stanford University’s Design School and cofounder of design company IDEO. Design thinking, which espouses an HCD approach, can be applied beyond product and graphic design to include the design of social policy, business strategy, services, and digital interactions. The five stages as espoused in Stanford’s design thinking model are empathizing, defining, ideating, prototyping, and testing. There are numerous design thinking tools that help develop and carry out these processes from various organizations and companies, ranging from IDEO to Google.
6.4 Lean Processes
Lean process is a systematic process for maximizing continuous improvement through minimizing surplus or unused material in the production of a current process. With origins in manufacturing, the lean process can be applied to internal organizational processes as well as external product development. Lean process uses observation, assessment and evaluation, and whiteboarding techniques to solve problems.


2.4.11: Derivability and the Quantifiers
If \(c\) is a constant not occurring in \(\Gamma\) or \(A(x)\) and \(\Gamma \Proves A(c)\) , then \(\Gamma \Proves \lforall{x}{A(x)}\) .
Proof. Let \(\pi_0\) be an \(\Log{LK}\) -derivation of \(\Gamma_0 \Sequent A(c)\) for some finite \(\Gamma_0 \subseteq \Gamma\) . By adding a \(\RightR{\lforall{}{}}\) inference, we obtain a proof of \(\Gamma_0 \Sequent \lforall{x}{A(x)}\) , since \(c\) does not occur in \(\Gamma\) or \(A(x)\) and thus the eigenvariable condition is satisfied. ◻
- \(A(t) \Proves \lexists{x}{A(x)}\) .
- \(\lforall{x}{A(x)} \Proves A(t)\) .
Proof.
-
The sequent
\(A(t) \Sequent \lexists{x}{A(x)}\)
is derivable:
-
The sequent
\(\lforall{x}{A(x)} \Sequent A(t)\)
is derivable:
◻


2.4: Cultural and Social Determinants Related to Medication Administration
-
- Last updated
- Save as PDF
- Ernstmeyer & Christman (Eds.)
- Chippewa Valley Technical College via OpenRN
Critical Thinking Activity
A nurse is providing patient education to a mother regarding a liquid antibiotic prescribed for her child to take at home. The prescription states amoxicillin 250 mg 1 teaspoon (5 ml) every 8 hours for 7 days. After talking with the mother, the nurse realizes the family does not have measuring spoons in their home.
In additional to the legal and ethical considerations affecting the safe administration of medication, there are also cultural and social influences that the nurse must consider. The United States has become increasingly diverse in the last century. According to the 2010 U.S. Census, approximately 36 percent of the population belongs to a racial or ethnic minority group. Though health indicators such as life expectancy and infant mortality have improved for most Americans, some minorities experience a disproportionate burden of preventable disease, death, and disability compared with non-minorities. [1]
The American Nurses Association Scope and Standards of Practice states that the need for health care is universal and transcends differences with respect to the culture; values; and preferences of the individual, family, group, community, and population. Diversity characterizes today’s healthcare environment, and nursing is responsive to the changing needs of society. To effectively promote meaningful patient outcomes that maximize quality of life across the lifespan, the ANA states that nurses must embrace diversity and engage in culturally congruent practice. Culturally congruent practice is the application of evidence-based nursing that is in agreement with the preferred cultural values, beliefs, worldview, and practices of the healthcare consumer and other stakeholders. Cultural competence represents the process by which nurses demonstrate culturally congruent practice. [2]
In addition to cultural beliefs, conditions in the places where people live, learn, work, and play affect a wide range of health risks and outcomes. These conditions are known as social determinants of health (SDOH). Differences in health are striking in communities with poor SDOH such as unstable housing, low income, unsafe neighborhoods, or substandard education. By applying what we know about SDOH, nurses can not only improve an individual’s health, but also improve health equity for communities and the population as a whole. Healthy People is a government agency that provides science-based, ten-year national objectives for improving the health of all Americans. Healthy People 2020 highlights the importance of addressing SDOH with a goal to “create social and physical environments that promote good health for all” as one of the four overarching goals for the decade. [3] , [4]
The U.S. Department of Health and Human Services has also set national standards for Culturally and Linguistically Appropriate Services (CLAS) in health and healthcare. The national CLAS standards are intended to advance health equity, improve quality, and help eliminate health care disparities by “providing effective, equitable, understandable, and respectful quality care and services that are responsive to diverse cultural health beliefs and practices, preferred languages, health literacy, and other communication needs.” [5]
The U.S. Department of Health and Human Services (HHS) defines health literacy as “the degree to which individuals have the capacity to obtain, process, and understand basic health information needed to make appropriate health decisions. Adequate health literacy may include being able to read and comprehend essential health-related materials such as information on a prescription bottle. A nurse that values health literacy makes it a priority to implement systems and interventions such as visual aids and counseling that increase understanding and thereby advance patient safety. [6]
Examples of Culturally Congruent Practice Related to Medication Therapy
There are several instances when a nurse must assess and accommodate a patient’s culture or social determinants of health when administering or teaching about medications. One example was provided above when a nurse should assist a patient to read a prescription bottle and its instructions to advocate for patient safety.
Another example of culturally congruent practice is when a nurse must consider cultural or religious beliefs, such as fasting, when administering medications. For example, a Muslim patient may participate in the Ramadan, which requires 12-hour fasting. A nurse can advocate for the patient and assist in altering the scheduling of medication to accommodate the patient’s belief and avoid the risk of treatment failure.
Drug Intake During Ramadan [7]
A third example of culturally congruent practice is considering when a patient’s ethnic background may affect their ability to respond to medications. For example, African Americans often require combination therapy to treat hypertension, whereas Asian and Hispanic patients often respond better to lower doses of antidepressants.
You can read more about these cultural accommodations at the following article links:
Treatment of Hypertension Among African Americans: The Jackson Heart Study
Prescribing Medication for Asians with Mental Disorders [8] , [9]
The US Department of Health and Human Services has created a free module for nurses to learn more about cultural competency.
Culturally Competent Nursing Care: A Cornerstone of Caring.
- Centers for Disease Control and Prevention. (2018, July 17). Health equity. https://www.cdc.gov/minorityhealth/index.html ↵
- American Nurses Association. (2015). Nursing : Scope and Standards of Practice (3rd edition). Available for all Chippewa Valley Technical College students and employees through OneSearch. ↵
- Social Determinants of Health: Know What Affects Health by Centers for Disease Control and Prevention is available in the public domain ↵
- Social Determinants of Health by Healthypeople.gov is available in the public domain ↵
- U.S. Department of Health and Human Services, Office of Minority Health. (n.d.). National standards for culturally and linguistically appropriate services (CLAS) in health and health care. https://thinkculturalhealth.hhs.gov/assets/pdfs/EnhancedNationalCLASStandards.pdf ↵
- Health Literacy by Healthypeople.gov is available in the public domain ↵
- Aadil, N., Houti, I. E., and Moussamih, S. (2004). Drug intake during Ramadan. BMJ (Clinical research ed.), 329 , 778–782. doi.org/10.1136/bmj.329.7469.778↵
- Harman, J., Walker, E. R., Charbonneau, V., Akylbekova, E. L., Nelson, C., and Wyatt, S. B. (2013). Treatment of hypertension among African Americans: the Jackson heart study. Journal of Clinical Hypertension, 15 (6), 367–374. https://www.ncbi.nlm.nih.gov/pubmed/23730984 ↵
- Chen, J. P., Barron, C., Lin, K. M., & Chung, H. (2002). Prescribing medication for Asians with mental disorders. The Western Journal of Medicine, 176 (4), 271–275. ↵


5.4: LU Decomposition
A variant of the Gaussian elimination algorithm can be used to compute the LU decomposition of a matrix. This procedure was invented by Alan Turing , the British mathematician considered the "father of computer science". The LU decomposition of a square matrix \(\mathbf{A}\) consists of a lower-triangular matrix \(\mathbf{L}\) and an upper-triangular matrix \(\mathbf{U}\), such that
\[\mathbf{A} = \mathbf{L}\, \mathbf{U}.\]
In certain special circumstances, LU decompositions provide a very efficient method for solving linear equations. Suppose that we have to solve a set of linear equations \(\mathbf{A} \vec{x} = \vec{b}\) many times, using the same \(\mathbf{A}\) but an indefinite number of \(\vec{b}\)'s which might not be known in advance. For example, the \(\vec{b}\)'s might represent an endless series of measurement outcomes, with \(\mathbf{A}\) representing some fixed experimental configuration. We would like to efficiently calculate \(\vec{x}\) for each \(\vec{b}\) that arrives. If this is done with Gaussian elimination, each calculation would take \(O(N^{3})\) time.
However, if we can perform an LU decomposition ahead of time , then the calculations can be performed much more quickly. The linear equations are
\[\mathbf{L}\, \mathbf{U} \vec{x} = \vec{b}.\]
This can be broken up into two separate equations:
\[\mathbf{L}\, \vec{y} = \vec{b}, \quad \mathrm{and}\;\;\; \mathbf{U} \vec{x} = \vec{y}.\]
Because \(\mathbf{L}\) is lower-triangular, we can solve the first equation by forward-substitution (similar to back-substitution, except that it goes from the first row to last) to find \(\vec{y}\). Then we can solve the second equation by back-substitution, to find \(\vec{x}\). The whole process takes \(O(N^{2})\) time, which is a tremendous improvement over performing a wholesale Gaussian elimination.
However, finding the LU decomposition takes \(O(N^{3})\) time (we won't go into details here, but it's basically a variant of the row reduction phase of the Gaussian elimination algorithm). Therefore, if we are interested in solving the linear equations only once, or a handful of times, the LU decomposition method does not improve performance. It's useful in situations where the LU decomposition is performed ahead of time. You can think of the LU decomposition as a way of re-arranging the Gaussian elimination algorithm, so that we don't need to know \(\vec{b}\) during in the first, expensive \(O(N^{3})\) phase.
In Python, you can perform the LU decomposition using the
scipy.linalg.lu
function. The forward-substitution and back-substitution steps can be performed using
scipy.linalg.solve_triangular
.


Skip to main content
Key Terms
-
addition method
-
an algebraic technique used to solve systems of linear equations in which the equations are added in a way that eliminates one variable, allowing the resulting equation to be solved for the remaining variable; substitution is then used to solve for the first variable
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augmented matrix
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a coefficient matrix adjoined with the constant column separated by a vertical line within the matrix brackets
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break-even point
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the point at which a cost function intersects a revenue function; where profit is zero
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coefficient matrix
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a matrix that contains only the coefficients from a system of equations
-
column
-
a set of numbers aligned vertically in a matrix
-
consistent system
-
a system for which there is a single solution to all equations in the system and it is an independent system, or if there are an infinite number of solutions and it is a dependent system
-
cost function
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the function used to calculate the costs of doing business; it usually has two parts, fixed costs and variable costs
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Cramer’s Rule
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a method for solving systems of equations that have the same number of equations as variables using determinants
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dependent system
-
a system of linear equations in which the two equations represent the same line; there are an infinite number of solutions to a dependent system
-
determinant
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a number calculated using the entries of a square matrix that determines such information as whether there is a solution to a system of equations
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entry
-
an element, coefficient, or constant in a matrix
-
feasible region
-
the solution to a system of nonlinear inequalities that is the region of the graph where the shaded regions of each inequality intersect
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Gaussian elimination
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using elementary row operations to obtain a matrix in row-echelon form
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identity matrix
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a square matrix containing ones down the main diagonal and zeros everywhere else; it acts as a 1 in matrix algebra
-
inconsistent system
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a system of linear equations with no common solution because they represent parallel lines, which have no point or line in common
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independent system
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a system of linear equations with exactly one solution pair
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main diagonal
-
entries from the upper left corner diagonally to the lower right corner of a square matrix
-
matrix
-
a rectangular array of numbers
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multiplicative inverse of a matrix
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a matrix that, when multiplied by the original, equals the identity matrix
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nonlinear inequality
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an inequality containing a nonlinear expression
-
partial fraction decomposition
-
the process of returning a simplified rational expression to its original form, a sum or difference of simpler rational expressions
-
partial fractions
-
the individual fractions that make up the sum or difference of a rational expression before combining them into a simplified rational expression
-
profit function
-
the profit function is written as
revenue minus cost
-
revenue function
-
the function that is used to calculate revenue, simply written as
where
quantity and
price
-
row
-
a set of numbers aligned horizontally in a matrix
-
row operations
-
adding one row to another row, multiplying a row by a constant, interchanging rows, and so on, with the goal of achieving row-echelon form
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row-echelon form
-
after performing row operations, the matrix form that contains ones down the main diagonal and zeros at every space below the diagonal
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row-equivalent
-
two matrices
and
are row-equivalent if one can be obtained from the other by performing basic row operations
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scalar multiple
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an entry of a matrix that has been multiplied by a scalar
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solution set
-
the set of all ordered pairs or triples that satisfy all equations in a system of equations
-
substitution method
-
an algebraic technique used to solve systems of linear equations in which one of the two equations is solved for one variable and then substituted into the second equation to solve for the second variable
-
system of linear equations
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a set of two or more equations in two or more variables that must be considered simultaneously.
-
system of nonlinear equations
-
a system of equations containing at least one equation that is of degree larger than one
-
system of nonlinear inequalities
-
a system of two or more inequalities in two or more variables containing at least one inequality that is not linear


9.12: SmartArt
Learning Outcomes
- Create and insert SmartArt.
SmartArt is a dynamic type of image that you will often see in PowerPoint slides. SmartArt can be used to group lists of information together, through bullet lists for example, or to show a process, through cycles. Fortunately, you do not need to be a graphic designer to create and insert simple and effective SmartArt into a PowerPoint presentation.
Before you actually insert SmartArt, you should determine what you are attempting to convey and the best way to convey it. One helpful item here is the descriptions provided for each basic SmartArt graphic shape. You can access these descriptions by selecting the Insert a SmartArt Graphic option on a new slide. When you do, you will see this window:
The graphic styles displayed immediately under All are the commonly used ones, but you can navigate to specific styles using the menu on the left. For this walkthrough, we will create a basic cycle SmartArt graphic. This type of graphic is useful when describing a process, such as what happens when a customer returns a defective item. This example will be used to describe how to create a SmartArt graphic.
Once you click OK, the graphic is automatically sized into your slide, just like inserting any image. Remember: at the end of the day, a SmartArt graphic is just an image. Therefore, you add them to slides using the same steps shown on the previous page. You have to insert a SmartArt graphic before you can actually create the graphic.
The graphic inserts into the slide with default options, but those are very easy to change, as we will soon see
Using the text box on the left, type in what should be displayed in each portion of the graphic. To move between portions of the graphic, in this case the circles, click on the next bullet in the text box or on the next shape in the graphic. Below, all text has been updated and a title has been added to the slide.
You can edit the text at any time by clicking on the “Type your text here” box or the circle you wish to edit. If you have left the slide or presentation and come back to edit it later, you will need to click on some part of the SmartArt graphic to bring the “Type your text here” box back onto the screen.
If you want to change the color scheme, layout, number of shapes in the graphic, or any other option, you can do so using the Design tab and the options available in that ribbon. Note this Design tab is only available after you have clicked on the SmartArt graphic. This is not the standard Design tab that is always available in PowerPoint.
Once you have created your SmartArt graphic, you can use the Convert to Shapes option to make your SmartArt graphic a static image. Once you do this, you can still edit the text inside the shapes, but you cannot change other options such as color, layout, or number of shapes.
Contributors and Attributions
- SmartArt. Authored by : Shelli Carter. Provided by : Lumen Learning. License : CC BY: Attribution


16.7: Activities
- Draw two different connected graphs with five vertices each in which every edge is a bridge.
- How many edges are in each of the examples that you drew in Task a?
- Would it be possible to add an edge to either of the examples that you drew in Task a without creating a cycle?
- Draw two different simple graphs with \(5\) vertices in which every pair of vertices has a single path between them.
- How many edges are in each of the examples that you drew in Task a?
- Would it be possible to add an edge to either of the examples that you drew in Task a without creating a cycle?
Suppose that \(G\) is a connected graph that consists entirely of a proper cycle. (See Figure \(\PageIndex{1}\).)
Let \(G'\) represent the subgraph of \(G\) that results by removing a single edge. Argue that \(G'\) remains connected.
Suppose that \(H\) is a connected graph that contains a proper cycle. Let \(H'\) represent the subgraph of \(H\) that results by removing a single edge from \(H\text{,}\) where the edge removed is part of the proper cycle that \(H\)contains. Argue that \(H'\) remains connected.
Notes.
- Your argument here needs to be (slightly) different from your argument in Activity 16.7.3.
- Make sure you are using the technical definition of connected graph in your argument. What are you assuming about \(H\text{,}\) and what do you need to verify about \(H'\text{?}\)


11.E: The Giant Planets (Exercises)
For Further Exploration
Articles
Jupiter
Aguirre, Edwin. “Hubble Zooms in on Jupiter’s New Red Spot.” Sky & Telescope (August 2006): 26.
Beatty, J. “Into the Giant.” Sky & Telescope (April 1996): 20. On the Galileo probe.
Beebe, R. “Queen of the Giant Storms.” Sky & Telescope (October 1990): 359. Excellent review of the Red Spot.
Johnson, T. “The Galileo Mission to Jupiter and Its Moons.” Scientific American (February 2000): 40. Results about Jupiter, Io, Ganymede, and Callisto.
Simon, A. “The Not-So-Great Red Spot.” Sky & Telescope (March 2016): 18. On how the huge storm on Jupiter is evolving with time.
Smith, B. “Voyage of the Century.” National Geographic (August 1990): 48. Beautiful summary of the Voyager mission to all four outer planets.
Stern, S. “Jupiter Up Close and Personal.” Astronomy (August 2007): 28. On the New Horizons mission flyby in February 2007.
Saturn
Gore, R. “The Riddle of the Rings.” National Geographic (July 1981): 3. Colorful report on the Voyager mission.
McEwen, A. “Cassini Unveils Saturn.” Astronomy (July 2006): 30. A report on the first two years of discoveries in the Saturn system.
Spilker, L. “Saturn Revolution.” Astronomy (October 2008): 34. On results from the Cassini mission.
Talcott, R. “Saturn’s Sweet Surprises.” Astronomy (June 2007): 52. On Cassini mission results.
Uranus and Neptune
Cowling, T. “Big Blue: The Twin Worlds of Uranus and Neptune.” Astronomy (October 1990): 42. Nice, long review of the two planets.
Gore, R. “Neptune: Voyager’s Last Picture Show.” National Geographic (August 1990): 35.
Lunine, J. “Neptune at 150.” Sky & Telescope (September 1996): 38. Nice review.
Websites
Jupiter
NASA Solar System Exploration: http://Solarsystem.nasa.gov/planets/jupiter
Nine Planets Site: http://nineplanets.org/jupiter.html
Planetary Sciences Site: http://nssdc.gsfc.nasa.gov/planetary...piterpage.html
Saturn
NASA Solar System Exploration: http://Solarsystem.nasa.gov/planets/saturn
Nine Planets Site: http://nineplanets.org/saturn.html
Planetary Sciences Site: http://nssdc.gsfc.nasa.gov/planetary...aturnpage.html
Uranus
NASA Solar System Exploration: http://Solarsystem.nasa.gov/planets/uranus
Nine Planets Site: http://nineplanets.org/uranus.html
Planetary Sciences Site: http://nssdc.gsfc.nasa.gov/planetary...ranuspage.html
Neptune
NASA Solar System Exploration: http://Solarsystem.nasa.gov/planets/neptune
Nine Planets Site: http://nineplanets.org/neptune.html
Planetary Sciences Site: http://nssdc.gsfc.nasa.gov/planetary...ptunepage.html
Missions
Cassini Mission Site at the Jet Propulsion Lab: http://saturn.jpl.nasa.gov/index.cfm
Cassini-Huygens Mission Site at European Space Agency: http://sci.esa.int/cassini-huygens/
NASA Galileo Mission Site: http://Solarsystem.nasa.gov/galileo/
NASA’s Juno Mission to Jupiter: http://www.nasa.gov/mission_pages/ju...ain/index.html
Voyager Mission Site at the Jet Propulsion Lab: http://voyager.jpl.nasa.gov/
Videos
Cassini: 15 Years of Exploration: https://www.youtube.com/watch?v=2z8fzz_MBAw . Quick visual summary of mission highlights (2:29).
In the Land of Enchantment: The Epic Story of the Cassini Mission to Saturn: https://www.youtube.com/watch?v=Vx135n8VFxY . An inspiring illustrated lecture by Cassini Mission Imagining Lead Scientist Carolyn Porco (1:37:52).
Jupiter: The Largest Planet: http://www.youtube.com/watch?v=s56pxa9lpvo . Produced by NASA’s Goddard Space Flight Center and Science on a Sphere (7:29).
Collaborative Group Activities
- A new member of Congress has asked your group to investigate why the Galileo probe launched into the Jupiter atmosphere in 1995 survived only 57 minutes and whether this was an example of a terrible scandal. Make a list of all the reasons the probe did not last longer, and why it was not made more durable. (Remember that the probe had to hitch a ride to Jupiter!)
- Select one of the jovian planets and organize your group to write a script for an evening news weather report for the planet you chose. Be sure you specify roughly how high in the atmosphere the region lies for which you are giving the report.
- What does your group think should be the next step to learn more about the giant planets? Put cost considerations aside for a moment: What kind of mission would you recommend to NASA to learn more about these giant worlds? Which world or worlds should get the highest priority and why?
- Suppose that an extremely dedicated (and slightly crazy) astronomer volunteers to become a human probe into Jupiter (and somehow manages to survive the trip through Jupiter’s magnetosphere alive). As she enters the upper atmosphere of Jupiter, would she fall faster or slower than she would fall doing the same suicidal jump into the atmosphere of solid Earth? Groups that have some algebra background could even calculate the force she would feel compared to the force on Earth. (Bonus question: If she were in a capsule, falling into Jupiter feet first, and the floor of the capsule had a scale, what would the scale show as her weight compared to her weight on Earth?)
- Would you or anyone in your group volunteer for a one-way, life-long mission to a space station orbiting any of the gas giants without ever being able to return to Earth? What are the challenges of such a mission? Should we leave all exploration of the outer solar system to unmanned space probes?
Review Questions
- What are the main challenges involved in sending probes to the giant planets?
- Why is it difficult to drop a probe like Galileo? How did engineers solve this problem?
- Explain why visual observation of the gas giants is not sufficient to determine their rotation periods, and what evidence was used to deduce the correct periods.
- What are the seasons like on Jupiter?
- What is the consequence of Uranus’ spin axis being 98° away from perpendicular to its orbital plane?
- Describe the seasons on the planet Uranus.
- At the pressures in Jupiter’s interior, describe the physical state of the hydrogen found there.
- Which of the gas giants has the largest icy/rocky core compared to its overall size?
- In the context of the giant planets and the conditions in their interiors, what is meant by “rock” and “ice”?
- What is the primary source of Jupiter’s internal heat?
- Describe the interior heat source of Saturn.
- Which planet has the strongest magnetic field, and hence the largest magnetosphere? What is its source?
- What are the visible clouds on the four giant planets composed of, and why are they different from each other?
- Compare the atmospheric circulation (weather) of the four giant planets.
- What are the main atmospheric heat sources of each of the giant planets?
- Why do the upper levels of Neptune’s atmosphere appear blue?
- How do storms on Jupiter differ from storm systems on Earth?
Thought Questions
- Describe the differences in the chemical makeup of the inner and outer parts of the solar system. What is the relationship between what the planets are made of and the temperature where they formed?

- Jupiter is denser than water, yet composed for the most part of two light gases, hydrogen and helium. What makes Jupiter as dense as it is?
- Would you expect to find free oxygen gas in the atmospheres of the giant planets? Why or why not?
- Why would a tourist brochure (of the future) describing the most dramatic natural sights of the giant planets have to be revised more often than one for the terrestrial planets?
- The water clouds believed to be present on Jupiter and Saturn exist at temperatures and pressures similar to those in the clouds of the terrestrial atmosphere. What would it be like to visit such a location on Jupiter or Saturn? In what ways would the environment differ from that in the clouds of Earth?
- Describe the different processes that lead to substantial internal heat sources for Jupiter and Saturn. Since these two objects generate much of their energy internally, should they be called stars instead of planets? Justify your answer.
- Research the Galileo mission. What technical problems occurred between the mission launch and the arrival of the craft in Jupiter’s system, and how did the mission engineers deal with them? (Good sources of information include Astronomy and Sky & Telescope articles, plus the mission website.)
Figuring for Yourself
- How many times more pressure exists in the interior of Jupiter compared to that of Earth?
- Calculate the wind speed at the edge of Neptune’s Great Dark Spot, which was 10,000 km in diameter and rotated in 17 d.
- Calculate how many Earths would fit into the volumes of Saturn, Uranus, and Neptune.
- As the Voyager spacecraft penetrated into the outer solar system, the illumination from the Sun declined. Relative to the situation at Earth, how bright is the sunlight at each of the jovian planets?
- The ions in the inner parts of Jupiter’s magnetosphere rotate with the same period as Jupiter. Calculate how fast they are moving at the orbit of Jupiter’s moon Io (see Appendix G). Will these ions strike Io from behind or in front as it moves about Jupiter?


As you develop your identity as an online learner, you will want to consider the role of information management in your learning process. Strong independent learners actively read, evaluate, and use information for current course tasks, but more importantly, to develop a resource file of information that will support professional growth.
Many online learners feel overwhelmed at the volume of reading and the wealth of online resources available to them. Managing information well requires you to develop skills in identifying the purpose for your reading (What do you need to learn from this reading? Why is it important to you personally and professionally?), and the strategy that will help you achieve your purpose (skimming, reading key portions, a close reading). In the
Strategic Reading
module of this workshop, you will discover additional ways to manage the reading process.
Early in your learning journey, you will want to select a system for managing information. As you will frequently work with electronic texts and articles, selecting a system that allows you to store, search, and retrieve readings and notes from current and past courses. Online note systems, such as OneNote or Evernote, are highly effective for this purpose.
Benefits of Using an Online Notebook
Online notebook platforms allow you to do the following:
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Create individual notebooks for courses or assignments, creating additional sections or pages for weekly module topics
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Create flexible notes that include text, images, audio, and video files
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Store PDFs and other course documents for your own records (note: you will eventually lose access to Moodle pages when courses are complete)
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Clip and store relevant information from the web
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Search stored content to quickly find relevant information, making connections between courses and your previous learning
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Sync notes across all of your devices
Choose a Notebook
Two fully-featured and common software platforms are Onenote and Evernote
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Advantages
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Disadvantages
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OneNote
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-Included in Office 365 subscriptions (free to KPU students)
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-Mac version is less fully featured
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Evernote
*Used under license from Evernote Corporation
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-Simple interface is easy to learn and use
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-Basic version is free, but additional features require an annual subscription
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To evaluate which platform best serves your needs, you may wish to investigate by trying out each on your preferred devices. You may also wish to explore the following linked video tutorials for further information, and to begin developing your organizational system.
OneNote:
Evernote:
Comparison of Notebook Apps
After investigating and installing your preferred digital notebook, create a notebook for each of your semester courses. Save your course presentation as a file in each of the notebooks.


12.2: Concerto
Introduction
Today the term concerto usually refers to a musical work in which one solo instrument is accompanied by an orchestra. The concerto first arose in the baroque with the concerto grosso (Italian for big concert(o )), which contrasted a small group of instruments with the rest of the orchestra. While the concerto grosso is confined to the baroque period, the solo concerto has continued as a vital musical force to this day.
The Concerto Grosso
In the late sixteenth century there was often no clear distinction made between a concerto and a sinfonia. Both of these terms were even used throughout the seventeenth century, in Italy, to describe vocal music with instrumental accompaniment; Giovanni Gabrieli published motets using either of these terms indiscriminately.
Starting at about 1675, composers started to write works for divided orchestra, often called concerto grosso . The smaller division, which was effectively a group of soloists, was referred to in these works as the concertino and the accompanying instruments were called the ripieno , while tutti was used to indicate the two groups playing simultaneously.
The concerto grosso is a form of baroque music in which the musical material is passed between a small group of soloists (the concertino ) and full orchestra (the ripieno or concerto grosso ). This is in contrast to the solo concerto (discussed below), which features a single solo instrument with the melody line, accompanied by the orchestra.
The form developed in the late seventeenth century, although the name was not used at first. Alessandro Stradella seems to have written the first music in which two groups of different sizes are combined in the characteristic way. The name was first used by Giovanni Lorenzo Gregori in a set of ten compositions published in Lucca in 1698.
The first major composer to use the term concerto grosso was Arcangelo Corelli. After Corelli’s death, a collection of twelve of his concertos grossi was published; not long after, composers such as Francesco Geminiani, Pietro Locatelli, and Giuseppe Torelli wrote concertos in the style of Corelli. He also had a strong influence on Antonio Vivaldi.
Two distinct forms of the concerto grosso exist: the concerto da chiesa (church concert) and the concerto da camera (chamber concert). The concerto da chiesa alternated slow and fast movements; the concerto da camera had the character of a suite, being introduced by a prelude and incorporating popular dance forms. These distinctions blurred over time.
Corelli’s concertino group was invariably two violins and a cello, with a string section as ripieno group. Both were accompanied by a basso continuo with some combination of harpsichord, organ, lute or theorbo. Handel wrote several collections of concertos grossi , and several of the Brandenburg Concertos by Bach also loosely follow the concerto grosso form.
The concerto grosso form was superseded by the solo concerto and the sinfonia concertante in the late eighteenth century, and new examples of the form did not appear for more than a century. In the twentieth century, the concerto grosso has been used by composers such as Igor Stravinsky, Ernest Bloch, Ralph Vaughan Williams, Bohuslav Martinů, Malcolm Williamson, Henry Cowell,Alfred Schnittke, William Bolcom, Heitor Villa-Lobos, Andrei Eshpai, Eino Tamberg, Krzysztof Penderecki, Jean Françaix and Philip Glass. While Edward Elgar may not be considered a modern composer, his romantic Introduction and Allegro strongly resembled the instrumentation setup of a concerto grosso .
Read about and listen to the Concerto Grosso in D by G. F. Handel here .
The Brandenburg Concertos , 1721, were presented to the Margrave of Brandenburg as part of J. S. Bach’s employment application. You can hear performances of Bach’s Concertos No. 2 and No. 5 below:
The Solo Concerto
A solo concerto is a concerto in which a single soloist is accompanied by an orchestra. It is the most common type of concerto, and it originated during the baroque period (c. 1600–1750) as an alternative to the traditional concertino (solo group of instruments) in a concerto grosso .
A typical concerto has the following structure: 1. fast movement, 2. slow movement, 3. fast movement. There are many examples of concertos that do not follow this arrangement, however.
The earliest known solo concertos are nos. 6 and 12 of Giuseppe Torelli’s Op. 6 of 1698. These works employ both a three-movement cycle and clear (if diminutive) ritornello form like that of the ripieno concerto, except that sections for the soloist and continuo separate the orchestral ritornellos . Active in Bologna, Torelli would have known of the operatic arias and the numerous sonatas and sinfonias for trumpet and strings produced in Bologna since the 1660s. He himself composed more than a dozen such works for trumpet, two dated in the early 1690s. Other early violin concertos are the four in Tomaso Albinoni’s Op. 2 (1700) and the six in Torelli’s important Op. 8 (1709 – the other six works in this set are double concertos for two violins).
The most influential and prolific composer of concertos during the baroque period was the Venetian Antonio Vivaldi (1678–1741). In addition to his nearly 60 extant ripieno concertos , Vivaldi composed approximately 425 concertos for one or more soloists, including about 350 solo concertos (two-thirds for solo violin) and 45 double concertos (over half for two violins). Vivaldi’s concertos firmly establish the three-movement form as the norm. The virtuosity of the solo sections increases markedly, especially in the later works, and concurrently the texture becomes more homophonic.
Concertos for instruments other than violin began to appear early in the 18th century, including the oboe concertos of George Frideric Handel and the numerous concertos for flute, oboe, bassoon, cello, and other instruments by Vivaldi. The earliest organ concertos can probably be credited to Handel (sixteen concertos, c. 1735–51), the earliest harpsichord concertos to Johann Sebastian Bach (fourteen concertos for one to four harpsichords, c. 1735–40). In the latter case, all but probably one of the concertos are arrangements of existing works, though Bach had already approached the idea of a harpsichord concerto before 1721 in the Brandenburg Concerto No. 5 .
You can hear J. S. Bach’s Violin Concerto in A minor below:
Listen to the Keyboard Concerto in F Minor by J. S. Bach here .
Vivaldi’s Four Seasons (1723) are comprised of four violin concertos, each of which is accompanied by a sonnet that was probably written by Vivaldi. The Four Seasons is an example of program music—music that attempts to describe extra-musical phenomena (in this case the four seasons) in musical terms.
Listen to Vivaldi’s Four Seasons here .
Contributors and Attributions
- Revision and adaptation. Provided by : Lumen Learning. License : CC BY-SA: Attribution-ShareAlike
- the stolen violin. Authored by : Luz Adriana Villa. Located at : https://www.flickr.com/photos/luchilu/460465940/ . License : CC BY: Attribution
- Concerto Grosso. Provided by : Wikipedia. Located at : https://en.Wikipedia.org/wiki/Concerto_grosso . License : CC BY-SA: Attribution-ShareAlike
- Solo Concerto. Provided by : Wikipedia. Located at : https://en.Wikipedia.org/wiki/Solo_concerto . License : CC BY-SA: Attribution-ShareAlike
- Brandenburg Concerto No. 2 in F major, BWV 1047. Provided by : EuroArtsChannel. Located at : https://youtu.be/aDB5Bi18iW8 . License : All Rights Reserved . License Terms : Standard YouTube license
- Bach: Brandenburg Concerto No. 5 in D major, BWV 1050. Provided by : EuroArtsChannel. Located at : https://youtu.be/rnAcRm7IL74 . License : All Rights Reserved . License Terms : Standard YouTube license
- Bach A Minor violin concerto, BWV 1041. Provided by : TheGreatPerformers. Located at : https://youtu.be/lJ-xJ1ChNh8 . License : All Rights Reserved . License Terms : Standard YouTube license


7.2: Multiple Bonds
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- Last updated
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- Scott Van Bramer
- Widener University
Learning Objectives
- Describe multiple covalent bonding in terms of atomic orbital overlap
- Relate the concept of resonance to π-bonding and electron delocalization
The hybrid orbital model accounts for the geometry of molecules with single covalent bonds. It also describes how double and triple bonds form. Molecules with dobule and triple bonds use both σ and π bonds. This section describes how the hybrid orbital model works to visualize the creation of multiple bonds using σ and π bonds.
Double Bonds
The Lewis structure of ethene, C 2 H 4 , shows each carbon atom is connected to the other carbon atom and to two hydrogen atoms. As a result each carbon atom has trigonal planar geometry - according to VSEPR - and is sp 2 hybridized. Figure \(\PageIndex{1}\) shows the energy diagram for the atomic orbitals and the hybrid orbitals. The sp 2 hybrid orbitals overlap to make σ bonds to the hydrogen atoms and between the carbon atoms.
The π bond in the C=C double bond is formed by overlap of the unused 2 p orbital, only two of the three p orbitals are used for hybridization so one is left over. This unhybridized p orbital is shown with the red and blue lobes in Figure \(\PageIndex{2}\). This unhybridized 2 p orbital is perpendicular to the plane of the sp 2 hybrid orbitals. This lets the unhybridized 2 p orbitals on the carbon atoms overlap side-by-side, above and below the internuclear axis, and form a π bond .
For the unhybridized 2 p orbitals in ethene to overlap and form a π bond, the four hydrogen atoms and the two carbon atoms all must be in the same plane so that the ethene molecule is flat. If the molecule is twisted around the C=C bond the p orbitals are not overlapping and the π bond can not form. The planar configuration for the ethene molecule occurs because it is the most stable bonding arrangement. This demonstrates a significant difference between σ bonds, which rotate or spin easily, and π bonds, which do not allow rotation. Rotation around the internuclear axis does not change the extent to which the σ bonding orbitals overlap because the bonding electron density is symmetric about the axis. Rotation about the internuclear axis is much more difficult for multiple bonds because it would change the overlap of the π bonding orbitals and require breaking the π bond.
Triple Bonds
In molecules with sp hybrid orbitals there are two unhybridized p orbitals, shown in Figure \(\PageIndex{3}\) so they are capable of forming two π bonds. Figure \(\PageIndex{4}\) shows the bonding arrangement for acetylene, H−C≡C−H, a linear molecule. The sp hybrid orbitals of the two carbon atoms overlap end to end to form a σ bond between the two carbon atoms. The remaining sp orbitals form σ bonds with hydrogen atoms. This leaves two unhybridized p orbitals on each carbon atom that can overlap to form two π bonds. The two carbon atoms of acetylene are bound by one σ bond and two π bonds, giving a triple bond.
Resonance Structures
Hybridization involves only σ bonds, lone pairs of electrons, and single unpaired electrons (radicals). Structures that account for these features describe the correct hybridization of the atoms. However, many structures also include resonance forms. Remember that resonance forms occur when various arrangements of π bonds are possible without changing the three dimensional structure of the molecule. The orientation of the atoms stays the same, so the hybridization is the same for each resonance structure. The difference between resonances structures is the arrangement of π bonds between the unhybridized p orbitals. Resonance does not influence the assignment of hybridization.
For example, benzene has two resonance forms (Figure \(\PageIndex{5}\)). Either of these forms show each carbon atom is bonded to three other atoms with no lone pairs, so the hybridization is sp 2 . The electrons in the unhybridized p orbitals form π bonds but there are two possible configurations. The difference between these two structures is only dependent on which p orbitals are overlapping. Neither resonance structure completely describes the electrons in the π bonds. They are not located in one position or the other, but are in both configurations at the same time.
Example \(\PageIndex{1}\): Assignment of Hybridization Involving Resonance
One component of acid rain is produced by the reaction of sulfur dioxide with atmospheric water vapor to form sulfuric acid. Sulfur dioxide, \(\ce{SO2}\), is a major component of volcanic gases and a product of the combustion of sulfur-containing coal. What is the hybridization of the \(S\) atom in \(\ce{SO2}\)?
Solution
The resonance structures of \(\ce{SO2}\) are
The sulfur atom is surrounded by two bonds and one lone pair of electrons in either resonance structure. Therefore, the electron-pair geometry is trigonal planar, and the hybridization of the sulfur atom is sp 2 .
Exercise \(\PageIndex{1}\)
Another acid in acid rain is nitric acid, HNO 3 , which is produced by the reaction of nitrogen dioxide, NO 2 , with atmospheric water vapor. What is the hybridization of the nitrogen atom in NO 2 ? (Note: the lone electron on nitrogen occupies a hybridized orbital just as a lone pair would.)
- Answer
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sp 2
Summary
Multiple bonds consist of a σ bond located along the axis between two atoms and one or two π bonds. The σ bonds are usually formed by the overlap of hybridized atomic orbitals, while the π bonds are formed by the side-by-side overlap of unhybridized orbitals. Resonance occurs when there are multiple unhybridized orbitals with the appropriate alignment to overlap, so the placement of π bonds can vary.


13.1: Physical Geography
The definition of Southern California is geographically complex and has been shaped by both natural and political forces. The region is generally considered to encompass the area south of the 35°45' latitude, but its northern boundary is not a straight line. Instead, it follows the northern boundaries of San Luis Obispo, Kern, and San Bernardino counties, or alternatively, Point Conception and the Tehachapi Mountains.
Following the acquisition of California by the United States, pro-slavery politicians attempted to divide the state at 36°30', the line of the Missouri Compromise. This would have created a separate slave state in the southern half of California. However, the Compromise of 1850 admitted California to the Union as a free state, preventing the division of the state. Despite the abolition of slavery, tensions between Northern and Southern California persisted. In the 1850s, Californians (dissatisfied with inequitable taxes and land laws) and pro-slavery Southerners in the lightly populated "cow counties" of southern California attempted three times to achieve a separate statehood or territorial status separate from Northern California. The last attempt, the Pico Act of 1859, was passed by the California State Legislature and approved by nearly 75 percent of voters. However, the secession crisis following the election of Abraham Lincoln in 1860 and the subsequent American Civil War led to the proposal never coming to a vote.
The complex history of Southern California's definition reflects the region's unique geographical and cultural identity. The region has been shaped by a diversity of influences, including its mountains, dry climate, its proximity to Mexico, and its role as the center of the American film industry.
Climate
Despite the popular image of California as a place of sunshine and perfect weather, the local climate can be very diverse, with some areas experiencing more extreme conditions. However, the weather in the region is usually mild, especially in the winter, and dry, with rainfall ranging from moderate in the coastal regions to almost none in the desert.
Around the coastal areas, the weather does not vary as dramatically as it does inland. Climate is affected by factors such as latitude, topography, and proximity to water masses - primarily the cold currents along the coast of the Pacific Ocean, and southern California's mountain ranges. The Transverse Ranges and the Peninsular Ranges are key players in the region's climate.
Essentially, the mountain ranges separate southern California into two distinct climatic regions: The heavy-populated coastal area west of these mountains is the one most associated with the term "southern California" and is characterized by pleasant weather all-year round, without frequent heat spells in the summer and without low temperatures in winter. By comparison, the area east of the ranges, between the mountains and the borders with Nevada and Arizona, is dominated by the Sonoran Desert and the Mojave Desert and tends to be more arid and register more extreme temperatures in both summer and winter.
Low Clouds, "May Gray" & "June Gloom"
Low clouds and fog are common weather phenomena in Southern California. This is due to the region's topography and proximity to the Pacific Ocean. Coastal fogs are often created by the interaction of seasonal inversion layers and the coastal marine layer. These fogs can reach as far inland as 20 miles, butting up against inland mountains or coastal mountain ranges. Coastal fogs can vary in density, from light "ground fogs" to dense "Tule fog." Tule fog is most common in the winter and spring when cold air from the mountains interacts with warmer ocean air masses.
In recent decades, the prevalence of low clouds and fog on the California coast has decreased. This is due to a combination of urban heat and climate change. Scientists have found that stratus cloud cover has decreased between 25% and 50% since the 1970s.
In contrast with the sunny summer, late spring in southern California is often overcast, due to the marine onshore air. This period, known to the locals as "May Gray" and "June Gloom", dims the coastal skies of sunny southern California. During this time, the coastal clouds may remain all day, but often give way to some hazy afternoon sunshine. The number of gloomy days during this period vary from year to year. Years with warmer ocean temperatures, influenced by the broader El Niño weather pattern, may result in fewer gray days in June, whereas the cooler ocean temperatures associated with a La Niña pattern, usually foretell more gray days in the season.
June Gloom is caused by the interaction of the California Current and the marine layer. The California Current is a cold ocean current that flows southward along the coast of California. The marine layer is a layer of cool, moist air that sits on top of the ocean. When the marine layer spreads over the California Current, it cools down and condenses, forming low-altitude stratus clouds. These clouds then move inland, bringing overcast skies and cool temperatures to the coastal regions of California.
Wildfires
Because of the hot, dry, and windy nature of southern California, wildfires are common. While most of them only affect small areas, wildfire can quickly get out of control and spread across large areas of woodland, particularly when fanned by the Santa Ana winds. Hot and extremely dry, they are also known as "Devil winds", and move towards the coastal region from the continental interior of the American West, where high pressure systems over the southwestern deserts increase in temperature.
Because natural wildfires are more likely to appear towards the end of long, dry summers, they have become a more serious problem in recent years because of the changing climate, overpopulation and decreased controlled fires, which makes wildfires increasingly larger and more frequent. Climate change has also widened the wildfire "season" from a few summer months to virtually the entire year.