Training: Describing Images Description-Enhanced Assessments for Students with
Training: Describing Images Description-Enhanced Assessments for Students with Visual and Print Disabilities Bryan Gould WGBH National Center for Accessible Media DESCRIPTION-ENHANCED ASSESSMENTS FOR STUDENTS WITH VISUAL AND PRINT DISABILITIES
Overview: The Utah, Colorado, and Kansas state education agencies are working together to examine the use of description as an accommodation for students with visual and print disabilities in order to provide access to visual and complex images within state assessments. DESCRIPTION-ENHANCED ASSESSMENTS FOR STUDENTS
WITH VISUAL AND PRINT DISABILITIES Image Description has the potential to: 1. control standardized test administration 2. increase independent access to visual content 3. reduce costs in test construction DESCRIPTION-ENHANCED ASSESSMENTS FOR STUDENTS WITH VISUAL AND PRINT DISABILITIES
The Problem: Image description is not an approved accommodation for use in any state assessments in any state. DESCRIPTION-ENHANCED ASSESSMENTS FOR STUDENTS WITH VISUAL AND PRINT DISABILITIES The Solution: Train teachers in research-based descriptive practices
Test descriptions using retired test items from the Utah Performance Assessment System Conduct two rounds of assessment with 450 students to measure comprehension and evaluate efficiency, clarity, and comprehension Produce guidelines for best practices in description of test items for national dissemination Results will provide DATA that will show whether image description can be considered a viable accommodation
DESCRIPTION-ENHANCED ASSESSMENTS FOR STUDENTS WITH VISUAL AND PRINT DISABILITIES Project partners:
Utah, Colorado, and Kansas state education agencies WGBH National Center for Accessible Media The National Center on Severe and Sensory Disabilities Panel of national advisors WE NEED YOUR HELP! Please Contact Kay or Silvia at The National Center on Severe and Sensory Disabilities at the University of Northern Colorado.
Narration: On this farm, cows enjoy their favorite foods. Description: A cow chews on a mouthful of straw. Narration: Now, lets see how a cows digestive system works. NCAM (est. 1993) Research and Development
supports national policy decisions develops technical solutions conducts research promotes advocacy via outreach Recorded Audio HTML How to Write Descriptions
Detailed knowledge of the subject matter Good writing skills and an excellent command of the vocabulary associated with the subject Adequate access to reference and support materials to ensure that the descriptions are as clear and accurate as possible Descriptions should be reviewed for accuracy by someone other than the original writer Consider Context: Why is the image there?
Who is the intended audience? If there is no description what will the viewer miss? Description carries both an obligation and a responsibility to present information factually, without opinion or prejudice, in a manner that facilitates understanding. - Kay Ferrell What the describer selects for description, the manner it is described in, and how it is
positioned in the modified text is final. - Phil Piety Describing for Children Learning and Experience Describing for Children Description for children is fundamentally different than description for adults. With adults, one can assume a certain level
of exposure, whether it originates in literature or in other cultural experiences. The same cannot be said for children with vision loss, whose experiences are limited by the visual impairment and time itself. Information Gathering Children with visual impairment generally gather information ways that are different than sighted children:
Inconsistent (things do not always make noise or produce an odor) Fragmented (comes in bits and pieces) Passive (not under the childs control) Learning Principles Children with visual impairment generally share the following learning principles: Parts to Wholes Deliberate vs. Incidental
Limited Opportunities for Imitation and Practice Parts to Wholes A blind child can only touch an area as large as his or her hand at any one point in time, and then must put together those multiple tactile experiences to get a sense of the whole object.
Its a bit like putting together a puzzle without knowing what the end product looks like. Deliberate vs. Incidental Children with visual impairment usually will not benefit from incidental learning. Home Plate QuickTime and a
decompressor are needed to see this picture. Imitation and Practice Children often learn skills by watching others perform them, trying it themselves, and practicing the behavior repeatedly until they obtain the desired result. Description as Education
These different learning styles and ways of gathering information, affect how children with vision loss form concepts and categorize those concepts for later use. Description as Education It is particularly important that description provides the bridge between what the child experiences incidentally, and what the typical child experiences with vision.
Description as Education For example, descriptions can make concepts easier to learn by presenting them deductively, from the general to the specific. In effect, the describer provides the structure that serves as an organizer for learning. Description as Education
Think about description from the point of view of the child with vision loss. What seems obvious to a sighted child may be totally obscured to a child with vision loss. Describing for Younger Children Young children generally have short attention spans and may find it difficult to listen to and absorb large amounts of verbal information (RNIB, 2006).
Describing for Younger Children Short sentences Vocabulary that is age appropriate
Keep it focused on action and emotion Few details Emphasize the tactile A tennis ball is the size of an apple and covered with fuzz. The machine is as big as a refrigerator. Word Choice
Slacks Trousers Capris Jeans Cargos Sweats Corduroys Khakis Describing for Older Children &
Adults Two people with the exact same visual diagnosis, age, and vision loss may have entirely different experiences in terms of concept development: one cannot be sure that everyone has had the same experience. Describing for Older Children & Adults Description writers have no control over who
is listening to the description, and they need to prepare for multiple levels of understanding. Describing for Older Children & Adults Assume more experience with visual elements, however, the audience is still varied Longer sentences Focus on tactile, color, placement of objects
Add social concerns Add more parts to wholes Keep it focused Vocabulary that is age appropriate Details Help "A boy holds a fish in one hand and a bucket of fish in the other. An approximation can add useful detail. Great Day of Fishing: "A boy holds a fish in one
hand and a bucket of about twelve fish in the other. Not a Great Day: "A boy holds a fish in one hand and a bucket of 3 or 4 fish in the other." Cutting to the Chase Old vs A man about 80 years old, with a bent spine and white hair Helpful: An old man walks barefoot on a dirt road, straining to carry a heavy load of hay.
Ok: "An old man and old woman smile as they stand in front of a garden. Even Better: "Grandpa and Grandma smile as they stand in front of a garden. (if Grandpa & Grandma have already been introduced) How to Write Descriptions Detailed knowledge of the subject matter Good writing skills and an excellent command of the vocabulary associated with the subject
Adequate access to reference and support materials to ensure that the descriptions are as clear and accurate as possible Descriptions should be reviewed for accuracy by someone other than the original writer Consider Context: Why is the image there? Who is the intended audience? If there is no description what will the viewer miss?
Easy Medium Difficult Easy images include anything that can easily be described within a minute or two by a trained describer. Medium images take more effort and usually require more description than a sentence or two. Difficult images require the describer to stop to consider how to best describe this image and often require the describer to create a data table or nested list. Easy
QuickTime and a decompressor are needed to see this picture. QuickTime and a decompressor are needed to see this picture. Medium & Difficult
1. Any graphic/diagram that may have begun as a data table. These include line graphs, pie charts, bar charts, scatter plots, and data tables themselves 2. Diagrams that integrate data within the image. These includes maps, Venn diagrams and complex diagrams like the carbon cycle 3. Flow charts, concept/idea webs and choice trees 4. Complex math equations and geometry STEM Description Guidelines
Four years of NSF-funded research produced guidelines for making STEM images accessible. STEM = Science, Technology, Engineering and Math STEM Description Guidelines Discovered significant differences between descriptions provided and what blind/VI readers required and desired.
New description methods were developed, tested and shown to be more effective and efficient that previous description methods. Training in new description methods given to over 70 organizations: K-12 teachers and professionals, colleges and universities, text book publishers, assistive technology companies Alternative Media Producers: Bookshare, RFB&D, American Printing House for the Blind, American Foundation for the Blind Hundreds of publications, books, websites, etc., now employ these guidelines for image description.
Brevity The most frequent recommendation from respondents was for more brevity in description. It takes people with visual impairments more time to read books and articles than people without visual impairments and the process should not be further slowed down by unnecessarily long image descriptions.
Brevity PREVIOUS Descriptive Practice: The figure is a Venn diagram and shows 2 intersecting circles inside a large rectangle. The circles do not touch the rectangle. The circle on the left is labeled Africa and the number 93 is under Africa and above the circle. The circle on the right is labeled Asia and the number 155 is under Asia
and above the circle. The intersection of the 2 circles is shaded and has the number 70 in the shaded region. PREFERRED Descriptive Practice: The Venn diagram shows 2 intersecting circles, one labeled Africa 93 and the other labeled Asia 155. The area of intersection is labeled 70
Data Description should focus on the data and not extraneous visual elements. Elaborately illustrated diagrams often contain key data that can be made accessible by presenting the data separate from description of the overall image. PREVIOUS: Description emphasizes visual Carbon Cycle
In a diagram titled "Carbon Cycle," numbers and arrows illustrate the movement of carbon through Earth's atmosphere, land, ocean, and interior. Black numbers indicate amounts of stored carbon. Purple numbers and arrows indicate annual fluctuations of carbon. Amounts are measured in GtC - giga tons of carbon. Colorful pictures depict a sunny landscape with elements of the carbon cycle. Four long arrows encircle the landscape, representing the cycling of carbon. Carbon is stored in many places: 750 GtC in the atmosphere; 610 GtC in vegetation; 4,000 GtC in fossil fuels and cement production; 1,580 GtC in soils; 3 GtC underwater in marine biota; less than 700 GtC in dissolved organic carbon underwater; 150 GtC in soil sediments beneath the water; 38,100 GtC in the deep ocean; and 1,020 in the surface ocean. On land, many factors cause annual fluctuations of carbon in the atmosphere. An arrow points away from a factory's smoky chimneys, illustrating how fossil fuels and cement production release 5.5 GtC into the atmosphere. On the other side of a river, an arrow points to a grove of pine trees, illustrating the trees absorption of 0.5 GtC from the atmosphere.
Across the hilly landscape, cows graze near a tractor plowing a field. Nearby, arrows point to and from another grove of trees: one arrow rises from the trees and another points to it, illustrating an exchange of carbon: 121.3 GtC is absorbed by the trees and 60 GtC is released into the atmosphere. A fire burns beside several fallen trees, depicting deforestation. An arrow rises from the fire, showing how deforestation releases 1.6 GtC into the atmosphere. Another arrow points away from a layer of brown soil beneath the trees, illustrating how soils release 1,580 GtC into the atmosphere. In the ocean, depicted as a deep blue pool, many factors cause annual fluctuations of carbon. One arrow rises from the surface ocean and another points to it, illustrating an exchange of carbon: the atmosphere absorbs 90 GtC from the surface ocean and releases back 92 GtC. Another pair of arrows shows how the surface ocean exchanges carbon with marine biota: marine biota absorb 50 GtC from the surface ocean and release back 40 GtC. In addition, the surface ocean exchanges carbon with the deep ocean: the deep ocean absorbs 91.6 GtC and releases back 100 GtC. Other annual fluctuations occur
without exchanges: an arrow points from marine biota to dissolved organic carbon in the ocean, illustrating a release of 6 GtC. The direction of another arrow shows how dissolved organic carbon releases 6 GtC to the deep ocean. An arrow points from the deep ocean to the layer of brown sediments beneath it, illustrating how the deep ocean releases 0.2 GtC to the sediments. PREFERRED: Description emphasizes data The diagram is titled "Carbon Cycle." Colorful pictures depict farms, forests, rivers, oceans and industry. Four arrows encircle the diagram, representing the cycling of carbon. Smaller arrows illustrate Storage of Carbon and Fluxes in Carbon through Earth's atmosphere, oceans and land. Amounts are measured in G t C - gigatons of carbon.
Carbon Storage and Annual Fluxes in Carbon are depicted in the following tables. Storage Area GtC Flux GtC Atmosphere
750 Atmosphere to Vegetation 121.3 Vegetation 610
Vegetation to Atmosphere 60 Fossil Fuels and Cement Production 4,000
Soils to Atmosphere 60 Forest Fires to Atmosphere 1.6 Soils
1,580 .5 Surface Ocean 1,020 Atmosphere to Evergreen Forest
Deep Ocean 38,100 5.5 Marine Biota 3
Fossil Fuels and Cement Production to Atmosphere Underwater Dissolved Organic Carbon less than 700 Surface Ocean to
Atmosphere 90 Ocean Sediments 150 Atmosphere to Surface Ocean
92 Surface Ocean to Marine Biota 50 Marine Biota to Surface Ocean
40 Clarity If the reader needs to listen to a description several times because it is poorly written or is presented in a confusing manner, then it is not accessible. Clarity
Drill-Down Organization Drill-Down = brief summary followed by extended description and/or specific data. Drill-Down organization allows the reader to either continue reading for more information or stop when they have read all they want. Drill-Down
The figure is a pie chart. Title: Figure 5-2. Distribution of injury deaths by intent: United States, 2003-2004.
Unintentional 67% Suicide 19% Homicide 11% Undetermined 3% Legal intervention or operations of war less than 1% Tables Tables, charts and graphs should be presented as tables, not as narrative
description. Proper coding (captions, table headers, and table data) provide better access to tables than narrative description. Brief summaries or overviews of the charts should be presented before the tables. Tables Processes
Processes that are presented visually can be converted into nested lists with good results. Flow Charts Diagrams
Illustrated Chemical Reactions And More! PREVIOUS The figure is a flowchart. Three lines used in the chart represent various transitions. Solid black lines represent Expected transitions, dotted grey lines represent Nonproblematic unexpected transitions, and dashed black lines represent Problematic unexpected transitions. This description will describe the linear flow of the chart without describing its layout. Forming the goal: Forming the goal has one Expected transition to Forming the intention. Forming the intention has one expected transition to Specifying the action.
Specifying the action has one expected transition to Executing the action. Executing the action one Expected transition to Perceiving the system state. Executing the action also has two Nonproblematic unexpected transitions back to itself and back to Specifying the action. Perceiving the system state has one Expected transition to Interpreting the system state. Perceiving the system state also has two Problematic unexpected transitions back to itself and back to Executing the action; there is also one Expected transition to Interpreting the system state Interpreting the system state has one Expected transition to Evaluating the outcome. Interpreting the system state also has one Problematic unexpected transition back to itself and two Nonproblematic unexpected transitions back to Executing the action and Specifying the action. Evaluating the outcome has two Expected transitions. If the intention is maintained, but a new action is
required, the Expected transition leads back to Specifying the action. If a new intention is warranted, the Expected transition leads back to Forming the intention. PREFFERED The figure is a flow chart with 7 stages of action. 3 types of lines represent different transitions between the stages of action. The lines are labeled: Expected transitions, Non-problematic unexpected transitions, and Problematic unexpected transitions. Here the flow chart is described as a nested list in which possible transitions are listed beneath each stage of action. 1. Forming the goal * Expected transition to Forming the intention 2. Forming the intention
* Expected transition to Specifying the action 3. Specifying the action * Expected transition to Executing the action 4. Executing the action * Expected transition to Perceiving the system state * Non-problematic unexpected transition to Executing the action * Non-problematic unexpected transition to Specifying the action 5. Perceiving the system state * Expected transition to Interpreting the system state * Problematic unexpected transitions to Perceiving the system state
* Problematic unexpected transitions to Executing the action 6. Interpreting the system state * Expected transition to Evaluating the outcome * Problematic unexpected transition to Interpreting the system state * Non-problematic unexpected transitions to Executing the action * Non-problematic unexpected transitions Specifying the action 7. Evaluating the outcome * If intention is maintained, and a new action is required then Expected transition to Specifying the action * If a new intention is warranted then Expected transition to Forming the intention
Mathematics Math equations should be marked up with MathML and rendered in a way that is preferable to the individual reader. z equals 2 a plus b squared over c 2 2
b a + b ( ) z=2a+ z=2 c
a + b ( ) z=2 c z equals 2 times the fraction open parenthesis a plus b close parenthesis superscript 2 over c
or z equals 2 frac open parens a plus b close parens squared over c or z equals 2 a plus b squared over c Math Resources Design Science Math Type and Math Player
http://www.dessci.com/en/ gh Braille, Tactile Graphics, DTBs, NIMAS http://gh-accessibility.com/ Infty Reader Resource List for Accessing Math and Science www.inftyreader.org Narrative Description
Many STEM images are best described by linear, narrative description or traditional description. Follow the guidelines! Brevity Drill-Down Organization
Clarity Emphasis on Data Narrative Description The fish embryo is long, narrow and straight. Its head is small, round, and contains gill arches. A large flap extends to the left, from just below the head to the middle of the embryo. A segmented bony structure
runs the length of the embryo on the right. The reptile embryo is much longer and fatter than the fish embryo, but is curled into a fetal position. Its head is bent forward and is twice as large as that of the fish embryo. The reptile embryo has twice as many gill arches as the fish embryo, but the flap on the left side is only half as long. A segmented bony
structure runs the length of the embryo on the right. The bird embryo is curved more than the fish embryo, but is not as long or as curved as the reptile embryo. The head of the bird embryo is almost as large as that of the reptile embryo, but has fewer gill arches. A flap the same size as that of the reptile embryo extends to the left. A segmented bony
structure runs the length of the embryo on the right. Arrows point to the gill arches of all three embryos. Navigation Control Description presented as text is generally preferred over recorded audio because text readers provide superior navigation control. Properly marked up HTML, especially lists and tables, provides speedy and independent access to data that is unavailable through
traditional linear, narrative description. Four Words to Remember Brevity Data Clarity Control Guidelines for Describing STEM Images
http://ncam.wgbh.org/experience_learn/educational_media/stemdx Your Turn QuickTime and a decompressor are needed to see this picture. The Breathing Process
Diagram of the breathing process. Inhalation A muscle at the base the lungs, called the diaphragm, moves downward. Inside the lungs, pressure decreases and air rushes in. Ribs move upward and outward. Volume of the chest cavity increases. Air flows into the nose and mouth. Exhalation
Diaphragm moves upward. Inside the lungs, pressure increases and air moves out. Ribs move downward and inward. Volume of chest cavity decreases. Air flows out through the nose and mouth. A diagram titled: The Promise of Stem Cell Research. A petri dish is labeled, Cultured Pluripotent Stem Cells. Arrows connect the dish of Stem Cells to the following items:
Identify drug targets and test potential therapeutics Toxicity Testing Tissues/Cells for Transplantation Bone marrow for leukemia & chemotherapy Nerve cells for Parkinsons & Alzhiemer's disease Heart muscle cells for heart disease Pancreatic islet cells for diabetes ? (left blank) Study cell differentiation Understanding prevention and treatment of birth
defects An illustration labeled, "Geological unconformities." The illustration shows a cross-section of a grassy hill, with five horizontal layers. The layers alternate between layers of rock and layers of soil. In one area, a U-shaped section of mixed rocks and soil cuts down from the surface through four layers. This section is labeled "mixed strata." The hill slopes down to trees and water. The steep slope is
not grassy and the layers are visible. This is labeled "exposed buried strata." On the other side of the water is a smaller hill with three horizontal layers that match the first three layers of the first hill. An illustration shows a cross-section of the human heart. The heart is made up of four chambers, two smaller ones on top (the left and right atrium) and two larger ones below (the left and right ventricle.) A series of arteries and veins carry blood to and from the chambers. Valves separate some of the
chambers and blood vessels. The diagram includes the following labels. right atrium: small upper chamber superior vena cava: carries blood from above into the right atrium inferior vena cava: carries blood from below into the right atrium right pulmonary veins: small blood vessels connected to the right atrium right ventricle: large lower chamber tricuspid valve: separates the right atrium and right ventricle pulmonary artery: carries blood from the right ventricle to the lungs pulmonary valve: separates the right ventricle and pulmonary artery left atrium: small upper chamber
left pulmonary veins: small blood vessels connected to the left atrium left ventricle: large lower chamber mitral valve: separates the left atrium and left ventricle aorta: carries blood from the left ventricle to the rest of the body aortic valve: separates the left ventricle and the aorta My Turn QuickTime and a decompressor
are needed to see this picture. Image Description within Assessments Use this information to answer the question. Each funnel has a soil sample that water was poured into and trapped by the cup below. Funnel 1 contains sand and the water in the cup measures 100ml Funnel 2 contains silt and the water in the cup measures 60ml Funnel 3 contains clay and the water in the cup measures 20ml
In this experiment, the same amount of water was poured into each funnel onto the soil. Which soil slowed the water down the most? A. silt B. sand C. clay Draft 1 A drawing shows three funnels each positioned over a different cup. Each funnel contains a soil sample and each
cup contains a volume of water. Funnel 1 contains sand and the cup measures 100ml Funnel 2 contains silt and the cup measures 60ml Funnel 3 contains clay and the cup measures 20ml Draft 2 A drawing shows 3 funnels each positioned over a different cup. Funnel 1 contains sand, the cup measures 100ml Funnel 2 contains silt, the cup measures 60ml
Funnel 3 contains clay, the cup measures 20ml Description: A rectangular prism: 4 ft long, 4 ft wide and 8 ft tall. Two pie charts show the Number of Cats and Dogs Owned. Percentage of cats owned per U.S. cat-owning households. One cat: 48.0% Two cats: 27.9%
Three cats: 10.7% Four or more cats: 13.4% Percentage of dogs owned per U.S. dog-owning households. One dog: 62.2% Two dogs: 24.5% Three dogs: 7.0% Four or more dogs: 6.3% Your Turn
QuickTime and a decompressor are needed to see this picture. Answer Choice A Tree Diagram B Tea Pie Cake
Coffee Pie Cake Answer Choice B Tree Diagram C Tea Pie Cake Coffee
Pie Cake Soda Pie Cake The model of the water cycle is a diagram with labels A, B, C and D. A cloud is labeled A. Arrows point from the cloud down to land.
The land is labeled B. The land slopes down to water. The water is labeled C. An arrow points from the water up to the sky. The sky is labeled D. The model of the water cycle is a diagram with labels A, B, C and D. A cloud is labeled A. Arrows point from the cloud down to land. The land is labeled B.
The land slopes down to water. The water is labeled C. An arrow points from the water up to the sky. The sky is labeled D. The labels are repeated here: A is the cloud B is the land below the cloud C is the water D is the air above the water A Time Line 1550 to 1620
1558 Elizabeth becomes Queen of England 1564 William Shakespeare is born in Stratford-on-Avon 1568 William Shakespeare's father becomes bailiff of Stratford 1582 William Shakespeare marries Anne Hathaway 1588 The Spanish Armada is destroyed 1592 Plague closes London's Theatres 1599 The Globe Theatre is built 1606 Shakespeare writes Macbeth 1612 Shakespeare writes The Tempest 1616 Shakespeare dies
A chart titled Evaporation of Water shows changes in water as temperature increases over time. The data is represented in the following table. Time Temperature State of water
0 - 10 -20C - 0C Solid 10 - 20 0C, no change
Melting 20 - 30 0C - 100C Liquid 30 - 40
100C, no change Boiling 40 - 50 100C - 120C Gas A chart titled Evaporation of Water shows changes in water as temperature increases over time.
0 minutes to 10 minutes. Temperature increases from -20C to 0C. Water is solid. 10 min to 20 min. Temperature holds at 0C. Water is melting. 20 min to 30 min. Temperature increases from 0C to 100C. Water is liquid. 30 min to 40 min. Temperature holds at 100C. Water is boiling. 40 min to 50 min. Temperature increases from 100C to 120. Water is gas.
Contact Information If you would like more information about being a TEACHER PARTICIPANT in the project, contact the National Center on Severe and Sensory Disabilities at the University of Northern Colorado. [email protected][email protected] Contact Information
Bryan Gould WGBH National Center for Accessible Media [email protected] The Describers Role The describer is a gatekeeper of information. It is a role that is both powerful and difficult. The describer must balance all of the visual and linguistic factors, must select which information is to be presented and
how it will be presented within the [time] constraints. - Phil Piety Agenda: 15 - Survey participants about current image description training and practices 10 - Introduction to WGBH and NCAM 30 - Description fundamentals 30 - Guidelines for Describing STEM Images
15 - Group Exercise - describe several images 15 - Break 20 - Guidelines for describing images for K-12 15 - Group Exercise - describe several images from K-12 assessments 15 - Survey evaluation
140 Ran out of parts (Thrust Washers, Check Balls, Retainers) Snap Ring jammed in tooling head (bent) - right side. PCV drive failure. Failed to engage bolt at 9:00 position (tally all that apply) Manifold screw rundown failure. Spring jammed...
What is Evolution? evolution - change over time organic evolution - change in living populations over time microevolution - genetic changes within a species over time macroevolution - generation of new species from a common ancestral lineage over time Common...
Prolog Meta-programmes les prédicats findall, bagof et setof (partie de SWI Prolog et beaucoup d'autres) généralisent le prédicat toutes_solutions Prolog pour les Systèmes Experts Tout ceci donne de bons outils pour programmer un système expert. On verra un petit exemple...
BT Group . BT TV and content (BT Sport) Fibre rollout. Invested +£3bn, trailing Ultrafast, up to 500Mbps ... Evolved to meet changing environment (recent updates include; Fraud, Termination of Service, anti bribery and corruption, data protection). ... Cost to...
Derivative of ?? ??? ??=??????. In other words, keep the exponent the same and multiply by the derivative of the exponent. This is a process called differentiation by substitution. (though it may not be necessary for all problems) Remember: ?...
Now Point A is where the original vector starts (and ends at Point B) the negative vector starts at point B and ends at A A B (D) Vector Addition - Geometric Perspective We can visualize the addition of vectors...
Electrical (Fire): Use of electrical power that results in electrical overheating or arcing to the point of combustion or ignition of flammables, or electrical component damage Common Hazards and Descriptions Electrical (Static/ESD): The moving or rubbing of wool, nylon, other...
Ready to download the document? Go ahead and hit continue!