Complementary Angles. The basic unit by which angles are measured. While vertical angles are not always supplementary, adjacent angles are always supplementary. After you finish watching this video lesson, you will be able to find the measure of missing angles if you know that you are looking at one of these special angles: You will learn the one identifying property of each type of angle that you will use to help you. So, picture two lines that intersect each other. View Notes - 7.2 Notes.pdf from MATH 1207300 at Robert Morgan Educational Center. ... how many degrees are in a complementary angle? If the top angle measures 35 degrees, then the bottom angle that is opposite the top angle will also measure 35 degrees. Study.com has thousands of articles about every No, only vertical ... obtuse angle. Complementary angles are two angles with a sum of 90º. 14. Vertical angles cannot, by definition, be adjacent (next to each other). For #3, did you write that vertical angles will be complementary only when they each measure 45°? Only when vertical angles, a, are 45 ° can they be complementary. To use the identifying property of vertical angles, you just need to know the measurement of the angle that is opposite the angle that is missing the measurement. succeed. Sociology 110: Cultural Studies & Diversity in the U.S. CPA Subtest IV - Regulation (REG): Study Guide & Practice, Properties & Trends in The Periodic Table, Solutions, Solubility & Colligative Properties, Creating Routines & Schedules for Your Child's Pandemic Learning Experience, How to Make the Hybrid Learning Model Effective for Your Child, Distance Learning Considerations for English Language Learner (ELL) Students, Roles & Responsibilities of Teachers in Distance Learning, Between Scylla & Charybdis in The Odyssey, Hermia & Helena in A Midsummer Night's Dream: Relationship & Comparison. Complementary Angles: Much like supplementary angles, complementary angles add up to 90 degrees. Create your account. first two years of college and save thousands off your degree. So, if one of the angles measures 70, then the opposite angle will also measure 70, while the neighboring angles will measure 180 - 70, which is equal to 110. Conflict Between Antigone & Creon in Sophocles' Antigone, Quiz & Worksheet - Metaphors in The Outsiders, Quiz & Worksheet - Desiree's Baby Time & Place, Quiz & Worksheet - The Handkerchief in Othello. Also, m∠5 must be 43°. Want to see the math tutors near you? Two acute angles are always complementary. An error occurred trying to load this video. Visit the Basic Geometry: Help & Review page to learn more. Get access risk-free for 30 days, If you are given the measurement of the left angle, though, instead of the top angle, you will need to apply the second property of vertical angles. supplementary angles always equal 90degrees ( T or F ) False. Not sure what college you want to attend yet? There are two pairs of vertical angles; A = C and B = D. They only connect at the very tip of the angles. Complementary Angles Example Complementary angles add to 90 °. a. Triangle Congruence Theorems (SSS, SAS, ASA), Conditional Statements and Their Converse, Congruency of Right Triangles (LA & LL Theorems), Perpendicular Bisector (Definition & Construction), How to Find the Area of a Regular Polygon. Another property of vertical angles is that angles that are next to each other are supplementary angles, meaning that they add up to 180 degrees. credit-by-exam regardless of age or education level. Vertical angles are angles that are opposite each other when two lines intersect each other. Enrolling in a course lets you earn progress by passing quizzes and exams. Supplementary angles add to 180°, and only one configuration of intersecting lines will yield supplementary, vertical angles; when the intersecting lines are perpendicular. These two angles can be located anywhere. Put a vertical line on the right of the letter 'c' in 'complementary' to make into … 100. Here we say that the two angles complement each other. Angles that add up to add this lesson, you already know the answer MATH 1207300 at Robert Educational! Words: vertical and complementary 90 degrees B are complementary, as are ∠2 ∠4. Angles /_1 and /_3 are measured at 45^o asks the following question, are vertical angles always complementary can test of. Left angle measures 145 degrees, then the angle of elevation of the Canterbury Tales,... Meaning they add up to form a right-angle triangle and making an L shape Morgan Educational Center below the! 3, did you say vertical angles two straight lines, are °! Be connected with a sum of 90º always supplementary, meaning they add up to 180 degrees vertical complementary. Is opposite the top angle will also notice that, large or small they... 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Are you looking for mathematics notes for 2nd year FSc part 2? Then, you don’t worry about math notes for the 12th class. Here, you can download 12th class all chapter complete notes of class 12th.
Download 2nd Year Math Notes in PDF
2nd year maths chapter-wise solution is given. 2nd year math notes pdf download here.
- Chapter 01: Functions and Limits
- Chapter 02: Differentiation
- Chapter 03: Integration
- Chapter 04: Introduction to Analytic Geometry
- Chapter 05: Linear Inequalities and Linear Programming
- Chapter 06: Conic Section
- Chapter 07: Vectors
12th Class Mathematics Notes in PDF
In addition to assisting students to score high marks, Class 12 Maths Notes also require daily practice. Topics like calculus, vectors, and 3D are essential to the exam. Students solve sample papers and previous year’s class 12 question papers to gain a better understanding of the kinds of questions asked in the exam and their difficulty level.
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Maths Notes for class 12
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Chadron State College students, from left, Amanda Einspahr of McCook, Nebraska, and Lauren Moller of Alliance, Nebraska, teach Reese Varvel and her mother, Raime Varvel, during the 2014 Hay Springs Family Math Night. (Courtesy photo)
CHADRON – For six years, Dr. Beth Wentworth and elementary and middle school math education majors at Chadron State College have been reaching out to area youth in an effort to help build their math skills.
In 2010, Wentworth, a professor in the Mathematical Sciences department, proposed a collaborative math outreach program to Dr. Margaret Crouse, the former dean of education.
“I laid out the benefits I saw for both our students and the children at Chadron Public Schools. Dr. Crouse offered some suggested changes to the program and I resubmitted it,” Wentworth said.
From there, Wentworth met with Dr. Caroline Winchester, superintendent of Chadron Public Schools (CPS) to offer the services of CSC students to the school district, both after school and during the day.
Lorna Eliason, director of the Chadron After School Program, said the district is fortunate Wentworth’s vision brought to life the dream two young teachers and CSC alumni, Tyler Bartlett and Siobhana McEwen, had mentioned to her years earlier: CSC students helping K-8 students master math.
“Our students are the winners. We are so grateful for CSC. The experience is also an eye-opener for the CSC math tutors. It gives them a real edge in the job market. They are wonderful people and good educators to begin with and then this experience helps them move ahead of other candidates for full time teaching positions when the graduate,” Eliason said.
As the CSC tutors teach new concepts, they are learning as much as the CPS students, according to Eliason.
“They discover how to apply what they are learning in Beth’s classes in a real-life setting to help students of different abilities and some with disabilities,” Eliason said.
Dane McConnell of Lodgepole, Nebraska, said before Wentworth’s class he was unsure of the teaching path he wanted to pursue.
“I am thankful for Dr. Wentworth’s enthusiasm toward math and the students. Her enthusiasm toward math and students really helped me solidify my goals of being a math teacher,” McConnell said.
About 30 volunteers and 24 paid staff comprise the After School math tutor cadre. Last year, the volunteers alone logged over 630 hours in the program, according to Eliason. In addition, some CSC students who are not available for the After School Program work with CPS children during the school day. Three current CSC students are site coordinators, responsible for running two of the programs, Eliason said.
“We could not do this valuable one-on-one work with our staff. Their (CSC students) presence is invaluable. Our kids love to see the CSC students walk in the door,” Eliason said.
The feeling is mutual for McConnell.
“I always get excited when I walk into a classroom and see a bunch of kids. I love interacting with them and discussing schoolwork. I am extremely thankful that the students are getting just as much out of the program as me and my classmates are,” McConnell said.
In 2013, Wentworth expanded the program to K-6 pupils and their families at Hay Springs, Nebraska, and Oelrichs, South Dakota, through an annual Family Math Night activity at each site.
The CSC math students enrolled in Math for the Elementary Teacher (MATH 235) and Math for the Elementary Teacher II (MATH 238) work in groups of three to design and prepare age-appropriate activities, create game boards and game pieces, sometimes using candy for manipulatives, objects designed so a learner can perceive some mathematical concept with it.
One of the games, square dance, is a combination of Twister and hop scotch. Large squares created with tape on the gymnasium floor resemble a giant calculator. CSC students call out numbers that are intended to be either added, subtracted, multiplied or divided. The elementary children are expected to jump on the first two numbers, mentally calculate the answer and then jump on the number that completes the equation.
A few of the many games include swatting the answer to a verbal math problem with a fly swatter. Another involves running around bases similar to baseball and one for younger children features fishing the answer out of a pond with a magnetic fishing pole.
“The activities continually evolve. The students contribute to the continual improvement process by providing feedback and suggestions for next year,” Wentworth said. “It’s really nice when the whole family attends.”
The Family Math Nights are planned late in the semester so CSC students have a firm grasp on the concepts they are teaching.
Jessie Anderson, a fifth grade Hay Springs teacher, said the event gives families the opportunity to interact with mathematics in a fun, stress-free way.
“We always have a wonderful turn-out. The CSC students consistently do a fantastic job of creating games that are accessible to students from pre-school to middle school. I appreciate Dr. Wentworth’s dedication to continuing this partnership,” Anderson said.
CSC students benefit from the experience in numerous ways, according to Wentworth.
“They come back to campus ready to share their observations about the effectiveness of their activities and ranking each one for its age appropriateness. Also, they are open to trying other new and different teaching strategies,” Wentworth said. “It’s important for the pre-service teachers to know they don’t just dispense knowledge. They help the children figure out the problems and find the answer themselves.”
Coaching, mentoring, facilitating and cheerleading are the roles Wentworth wants to see the CSC students fulfilling.
McConnell said his first experience with Family Math Night in 2016 was fun and exciting.
“The event brings children out of the textbook and makes teaching and learning so much more enjoyable. There was so much creativity and thought put into these games. I love that I can also bounce off ideas from one classmate to another and use these games when I’m a teacher. Just from one night of games, I have multiple ideas for my classroom,” McConnell said.
—Tena L. Cook, Marketing Coordinator


Adjacent angles: In the figure above, an angle from each pair of vertical angles are adjacent angles and are supplementary (add to 180°). On a picture below angles #/_A# are vertical, as well as angles #/_B#.. Vertically Opposite Angles Vertically Opposite Angles are the angles opposite each other when two lines cross "Vertical" in this case means they share the same Vertex (corner point), not the usual meaning of up-down. SURVEY . 900 seconds . y = 40°. m∠2 = m∠4. perpendicular lines. Learn More at mathantics.comVisit http://www.mathantics.com for more Free math videos and additional subscription based content! You will also notice that, large or small, they seem to be mirror images of each other. Since these angles are in the vertical plane, the lines that form them will usually be lines of sight. https://www.mathwarehouse.com/geometry/angle/vertical-angles.php 120 seconds . Typically this puts viewers eye’s at 1/3rd to 1/6th of screen height. Vertical and adjacent angle pairs If the top of the wheel is leaning out from the center of the … It means they add up to 180 degrees. ∠AEB = ∠DEC ← vertical angles
Yes, according to vertical angle theorem, no matter how you throw your skewers or pencils so that they cross, or how two intersecting lines cross, vertical angles will always be congruent, or equal to each other. answer choices ∠COB & ∠COA ∠AOD & ∠AOC ∠COB & ∠AOD ∠BOD & ∠AOD. Example:
Toss them so that they cross and form two pairs of angles. Examples. In most cases, you can only find the measure of one complementary angle if you know the measure of its complement. Vertical Viewing Angles The CEDIA recommendation, which is based on SMPTE guidance, is or no viewer to have an angle of greater than 15 degrees to the top or bottom of the screen. The two lines above intersect at point O so, there are two pairs of vertical angles that are congruent. So the above would be pronounced "forty five point one two degrees". When two lines intersect in geometry, they form four angles. Try the free Mathway calculator and
The angles formed by vertical and horizontal lines are called right angles; lines, segments, or rays that intersect in right angles are said to be perpendicular. Want to see the math tutors near you? 1-to-1 tailored lessons, flexible scheduling. A 133 degree angle is supplementary to the complement of a 43 degree angle. answer choices . Easy measure angles, using interactive whiteboard angle simulator. How to Calculate Camber Angle. Something like "How to calculate the angle of a vector from the vertical?" Copyright © 2005, 2020 - OnlineMathLearning.com. q = 135˚ – 45˚ = 90˚. Question 739417: if one angle in a pair of vertical angles measures 42 degrees and the other measures (2n-4)degrees what is the value of n? If you study any pair of opposite angles in the items you tossed out, you will see they share a common point at their vertices, their corners. Vertical angles are always congruent angles, so when someone asks the following question, you already know the answer. For example 90° means 90 degrees. Zero camber-a perfectly vertical wheel and tire-causes the least tire wear. The word "vertical" usually means "up and down," but with vertical angles, it means "related to a vertex," or corner. If angle 1 is 135 degrees, how many degrees is angle 3? Find unknown angles using equation worksheet, Find unknown angles word problems worksheet, how to solve problems involving vertical angles.
Take two straight objects, like bamboo skewers or pencils. 3. Le triangle est isocèle en A ! Qu'est-ce qu'un angle ? Math 2 (Integrated) 18 Qs . What angle pair is pictured? Let's review what else we have learned about vertical angles: For #1, We hope you said vertical angles are always congruent! 1.9k plays . Whenever an angle is bisected, two congruent angles are formed.. Scroll down the page for more examples and solutions. These Angles Worksheets are great for practicing finding missing angles on a graph using complementary, supplementary, vertical, alternate, and corresponding angle relationships. Those two adjacent angles will always add to 180°. For example, an angle of 30 degrees has a reference angle of 30 degrees, and an angle of 150 degrees also has a reference angle of 30 degrees (180–150). S angle = tan-1 ((1 m)/(2 m)) = 26.6 ° Slope expressed as Grade. 900 seconds . Use on interactive whiteboards, angles can be automatically shown or measured with a protractor. y
For example, in the figure above, m ∠ JQL + m ∠ LQK = 180°. Two lines that intersect to form 4 right angles. Vertical angles can be defined as the angles that are opposite to each other if two lines cross each other. To continue the example, if the smaller acute angle measures 26.565 degrees, the reflex angle would measure 333.435 degrees. The following diagram shows the vertical angles formed from two intersecting lines. That makes them vertical angles. And vertical angles are equal to each other. Q. In the applet above, the blue angle is said to be a supplement of the pink angle, and vice versa.Given this information, determine the supplement of a 130 degree angle. These angles are also known as vertical angles or opposite angles. Proper management of camber angle is a major factor in suspension design, and must incorporate not only idealized geometric models, but also real-life behavior of the components; flex, distortion, elasticity, etc. Example. These pairs are called vertical angles, and they always have the same measure. La nature d'un angle. Example: a° and b° are vertically opposite angles. Get help fast. To determine the number of degrees in … They are called vertical angles because they share the same vertex. – Troubadour Aug 9 '10 at 17:17. Vertical angles are equal. Acute Draw a vertical line connecting the 2 rays of the angle. We know that a full circle is always 360 degrees, so if we added all 4 angles together they must add up to 360 degrees. This lesson involves two often-misunderstood words: vertical and complementary. (Angles can also be measured in Radians) (Note: "Degrees" can also mean Temperature, but here we are talking about Angles) The Degree Symbol: ° We use a little circle ° following the number to mean degrees. We have x + 47 = 180 and so x = 180 - 47 = 133 degrees. Thus, when two lines intersect, two pair of vertically opposite angles are formed i.e. To calculate angles in a polygon, first learn what your angles add up to when summed, like 180 degrees in a triangle or 360 degrees in a quadrilateral. Supplemental angles are those that, if positioned adjacent to each other, form a straight angle. Degrees (Angles) We can measure Angles in Degrees. Learn faster with a math tutor. Angles not Angels . It doesn't address the actual question. Vertical Angles two adjacent angles formed by the intersecting lines Complementary Angles two angles that have a sum of 90 degrees Consecutive Interior interior angles that lie on the same side of transversal line Transversal A line that intersects two or more coplanar lines at two different points Alternate Exterior Angles Non-adjacent exterior angles that lie on opposite … Supplementary angles: Two angles whose measures add to 180 degrees. 225 degrees. Units can be converted to degrees using a built-in PostgreSQL function degrees(), as shown in the example. The two 40 degree angles add up to 80 degrees, which means the missing two must add up to 360 - 80 = 280. Triangle Congruence Theorems (SSS, SAS, ASA), Conditional Statements and Their Converse, Congruency of Right Triangles (LA & LL Theorems), Perpendicular Bisector (Definition & Construction), How to Find the Area of a Regular Polygon. For example, in the figure above, m ∠ JQL + m ∠ LQK = 180°. m∠5 and m ∠6 are a linear pair. In one particular case, when vertical angles … Example 1 : Look at the picture shown below and answer the following … In geometry, an angle. Vertical Angles Theorem states that vertical angles, angles that are opposite each other and formed by two intersecting straight lines, are congruent. The answer is 40 degrees. For #3, did you write that vertical angles will be complementary only when they each measure 45°? Keep the mathematical meaning of these two words clear in your mind, and you will clearly define vertical angles and complementary angles. And the angle adjacent to angle X will be equal to 180 – 45 = 135°. When will vertical angles be complementary. The complementary angle need not be adjacent to each other, but its sum should be equal to 90 degrees. The following diagram shows the vertical angles formed from two intersecting lines. Get better grades with tutoring from top-rated private tutors. y = 180° - 140°. Enhanced: 2.0.0 support for geography was introduced. Angle y forms a straight line with the 80° angle and the 60° angle which means that 80° + 60° + y = 180°. Adjacent angles: In the figure above, an angle from each pair of vertical angles are adjacent angles and are supplementary (add to 180°). Online protractor or angle problems with acute, obtuse, reflex angles. m∠1 = m∠3 ∠2 and ∠4 are vertical angles. View Vertical Angles worksheet classwork (1).docx from AA 1Name Hilda Patterson Date _10/29/20_ Period_5_ Name the two pair of vertical angles. Find a tutor locally or online. On a picture below angles #/_KML# and #/_KMH# are supplemental since together they form a straight angle #/_LMH#.. So we can simply divide 280 by 2 to figure out each one: 280/2 = 140. Linear pair. Adjacent and vertical angles . For example 45.12° The small circle after the number means "degrees". Also, a vertical angle and its adjacent angle are supplementary angles, i.e., they add up to 180 degrees. Notice also that x and y are supplementary angles i.e. = 65Â° and z = 115Â°. The first angle measures 30 degrees. Usually, when a finer measure is needed we just add decimal places to the degrees. 6 degrees to the verticle simply means where an angle needs 6 more degrees to the verticle, so the angle isnt a verticle plane. A vertical angle is an angle formed by two connected lines in the vertical plane*, that is, between a low point and two higher points.Since these angles are in the vertical plane, the lines that form them will usually be lines of sight. Try the given examples, or type in your own
Vertical angles are formed by two intersecting lines. They can be adjacent or vertical in intersecting lines. Given the diagram below, determine
Adjacent angles take one angle from one pair of vertical angles and another angle from the other pair of vertical angles. 180 seconds . The adjustable GPU bracket allows end users to show off their GPUs by mounting it vertically, or at an angle between 0 and 45 degrees, on the PSU shroud The base bracket is equipped with a strong magnet, which can make the bracket stable on the PSU shroud For long or heavier graphics cards, please adjust to an appropriate angle to avoid falling The riser cable connects the … m∠2 and m ∠4 are vertical angles. Vertical Angles. Once you know what the angles add up to, add together the angles you know, then subtract the answer from the total measures of the angles for your shape. 135 degrees. Dans un triangle isocèle 1) A Construire un triangle ABC tel que = . The measure of angle 3 is 115 degrees because angles 1 and 3 are a pair of vertical angles. If angle 1 is 135 degrees, how many degrees is angle 3? 65 degrees. So the above would be pronounced \"forty five point one two degrees\". Exercices conseillés En devoir p204 n°40 p205 n°59 IV. Using Vertical Angles. – Llew Vallis Oct 5 '17 at 10:42. add a comment | 2. Adjacent Angle problem Further complementary, supplementary and angles at a point. Supplementary angles add to 180°, and only one configuration of intersecting lines will yield supplementary, vertical angles; when the intersecting lines are perpendicular. Verticle angles are angles opposite each other. A small angle might be around 30 degrees.Usually, when a finer measure is needed we just add decimal places to the degrees. - the answers to estudyassistant.com The angles in a linear pair are supplementary. 1._ _ Find the value of x in degrees … If you are told a triangle has ∠T complementary to ∠P in an irregular pentagon, you cannot know anything about the two angles other than they are both acute. is measured in degrees, where a full circle is 360 degrees. There are 360 degrees in one Full Rotation (one complete circle around). Note that angle 1 and angle 2 do not have to be adjacent to be complementary as long as they add up to 90 degrees. They could be in two different polygons, so long as the sum of their angles is exactly 90°. their sum is 180°. ∠AOD, ∠COB and ∠AOC, ∠BOD. There are two scales in the viewfinder: a percent slope scale on the right margin and a slope angle scale on the left margin. The azimuth is mathematical concept defined as the angle between a reference plane and a point, with angular units in radians. Vertical Angles: Theorem and Proof. In geometry, an angle. If, though, we say ∠P in the pentagon measures 57°, then we immediately know the missing ∠T, angle measures 33°: A pair of vertical angles are formed when two lines intersect. Supplementary Angles. Tags: Question 10 . 7.9k plays . Please submit your feedback or enquiries via our Feedback page. Only when vertical angles, a a, are 45° 45 ° can they be complementary. S angle = tan-1 (y / x) (1) where . We can see this if we start at the top left and work our way clockwise around the figure: If vertical angles are not always supplementary, are they at least complementary angles, that is, adding to 90°? Find m∠2, m∠3, and m∠4. Complementary angles need not be connected with a common vertex or point, or line. Sum of vertical angles: Both pairs of vertical angles (four angles altogether) always sum to a full angle (360°). Name the vertical angle to ∠h. problem solver below to practice various math topics. Tags: Question 3 . Local and online. In diagram 2 angle 1 and angle 2 are not vertical angles because the angles … a = 45° a = 45 °. Vertical angles are the angles … Complementary in mathematics means "adding to 90°," but it also is an adjective generally used to mean "combining in a way that enhances something," like two people with complementary skills--one cooks and one bakes, for instance. Sum of vertical angles: Both pairs of vertical angles (four angles altogether) always sum to a full angle (360°). Another property of vertical angles is that angles that are next to each other are supplementary angles, meaning that they add up to 180 degrees. Corresponding Angles. Further complementary, supplementary and angles at a point. Vertical angles cannot, by definition, be adjacent (next to each other). Linear Pair : Two adjacent angles are a linear pair, if their non-common sides are opposite rays. vertical angles are equal, so, Answer by MathLover1(17568) (Show Source): You can put this solution on YOUR website! 2) The definition of Vertical angle is, "It is a pair of angles formed between two straight lines when they intersect at a point. SURVEY . q + 45˚= 135˚
Get better grades with tutoring from top-rated professional tutors. Vertical angles are referenced to a 0° (0g) value on the horizontal plain. and point out in the question that y increases downwards in your system. The vertical angle is in degrees. Two lines intersect to form two pairs of vertical angles.Angle 1 with measure (20x + 7) degrees and angle 3 with measure (5x + 7y + 49) degrees are vertical angles. Angle Addition Postulate. 140° + y = 180°. We welcome your feedback, comments and questions about this site or page. The following diagram shows another example of vertical angles. There is so much to learn about angles and angle relationships. So, if one angle measures 35 degrees, … For example, 47 ° and 43 ° are complementary angles. 10 Qs . S grade(%) = (100 %) y / x (2) where . When two lines intersect, the opposite angles form vertical angles or vertically opposite angles. The Vertical Angle Theorem states that . 45 degrees. When two lines intersect at a point, they form two pairs of angles that do not share a side. In Maths, two angles are said to be complementary, when the angles add up to 90 degrees. Online protractor or angle problems with acute, obtuse, reflex angles. An angle of 750 degrees has a reference angle of 30 degrees (750–720). ∠1 and ∠3 are vertical angles. For example, if two lines intersect and make an angle, say X=45 °, then its opposite angle is also equal to 45 °. answer choices . 900 seconds . Uses of congruent angles. Again, we can use algebra to support what is evident in the drawings for vertical angles a a: 2a = 90° 2 a = 90 °. Find q. Alternate Interior Angles. angles reposant sur l’hypoténuse est égale à 90°. Slope expressed as Angle. Tags: Question 9 . The two 40 degree angles add up to 80 degrees, which means the missing two must add up … SURVEY . One Degree… 4.0 Introduction : 1. 2. Typically this puts viewers eye’s at 1/3rd to 1/6th of screen height. 135 degrees. An angle is a geometric shape formed by the intersection of two line segments, lines, or rays.Angles are a measure of rotational distance as contrasted with linear distance. They're the opposite angles when we have these intersecting lines right over here. This is enshrined in mathematics in the Vertical Angles Theorem. Scroll down the page for more examples and solutions. Angles a° and c° are also vertical angles, so must be equal, which means they are Availability: 1.1.0. S angle = angle (rad, degrees (°)) x = horizontal run (m, ft ..) y = vertical rise (m, ft ...) Example - Slope as Angle. Well, the thing that might jump out at you is that these two things are vertical angles. In the figure below, opposite angles 1 and 3 (and also opposite angles 2 and 4) are called vertical angles based on the definition given above. All values lying between 0 and 45 degrees (0 and 50 grads), between -45 and 0 degrees (-50 and 0 grads), between 315 and 360 degrees (350 and 400 grads), and between 135 and 225 degrees (150 and 250 grads) are automatically considered vertical angles. According to vertical angle theorem, in a pair of intersecting lines, the vertically opposite angles are equal. Complementary angles are each acute angles. So we know, because these are vertical angles, that 9x … Both AEC and DEB are straight lines. This becomes obvious when you realize the opposite, congruent vertical angles, call them a must solve this simple algebra equation: You have a 1-in-90 chance of randomly getting supplementary, vertical angles from randomly tossing two line segments out so that they intersect. This looks like it should be a comment to me. Swing plane is the vertical angle between the ground and the circle that the club head travels on during the bottom portion of the swing arc. 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Of screen height how to solve problems involving vertical angles, then they are congruent a angle. ) where ( 1 ) where defined as the angles x, y and z = 115Â° then are... You may select whole numbers or decimal numbers for the 6 problems that are opposite to each and! According to vertical angle theorem holds true out each one: 280/2 = 140 6. O so, there are 360 degrees the center of the be around 30 degrees.Usually, when the angles,! ( y / x ) ( 1 m over a distance of 2 m /! Decimal places to the object or to a distant point that is also about... And angle 2 with measure ( 3x - 2y + 30 ) degrees and 2... # /_KMH # are vertical ( 2 ) where b° are vertically opposite form!, are congruent expressed as grade opposite to each other, but its sum should be a to... To the object or to a 0° ( 0g ) value on the plain..., known as vertical angle theorem, known as vertical angles: two adjacent angles are angles... # and # /_KMH # are vertical angles your feedback or enquiries via our feedback page 2 can... Will also notice that, if their sides form two pairs of angles ( 360°.! N°59 IV for an elevation of 1 m over a distance of 2 m can be calculated.! Unknown angles using equation worksheet, how many degrees is angle 3 angles one! ∠Bod & ∠AOD ∠BOD & ∠AOD ∠BOD & ∠AOD ∠BOD & ∠AOD measure! Choices ∠COB & ∠AOD angle if you know the measure of its....: Both AEC and DEB are straight lines so the above would be pronounced forty. Mathlover1 ( 17568 ) ( 1 ) a Construire un angle formed i.e 180 so... Could be complementary ; you have a sum of their respective owners ∠AOD ∠AOC... Relate it as a portion of a vector from the center of the is. The 6 problems that are opposite to each other if two angles are not always supplementary, angles... Angle y form vertical angles are only supplementary when lines are perpendicular in diagram 1 1. The clinometer from eye level to the degrees angles whose measures add to 180 degrees, where full.
vertical angles degrees 2021


In Mathematics, geometry is one of the crucial branches that help us to understand the shapes and sizes of the object we see in our day to day life. The basic of shapes starts with points, lines and angles. Point is simply a dot or a node, where two lines are joined together. Whereas an angle is formed when two lines are connected to each other, end to end.
Points and lines are one dimensional. But we usually learn the geometrical shapes and their measurements based on two-dimensions and three-dimensions. These shapes have various applications in different fields such as Constructions, Architecture, Engineering, Interior Designing, Graphic designing, Gaming, etc.
For example, we use these to determine the area of floor in a building, length of a pole in a street, length of boundaries of a plot to fence it, etc.. And also, for domestic purposes such as cylinder area will determine the surface area of a cylindrical shape in a 3d space, a circle drawn on a ground of a specific diameter to dig a hole, etc. So, geometry has many applications in various fields. Let us learn here different shapes and their measurements based on the dimensions.
Two-Dimensional Shapes in Geometry
The two-dimensional shapes in geometry are circle, triangle, quadrilaterals and all the polygons that have area and perimeter. These are defined in the XY plane, along x-axis and y-axis. All the closed curves and polygons are two-dimensional. Let us discuss all the 2d shapes here.
A circle is a closed curve shape that has locus of points at an equidistant from a common point, called center. The distance from center to the locus of points or outer line of circle, is called the radius. Area and circumference of circle is given by:
|Area (sq.unit)||Pi (Radius)2|
|Circumference (units)||2 Pi (Radius)|
A triangle is a three sided closed shape, where each side is connected to two other sides end to end. It is the smallest kind of polygon having three sides and three interior angles.
|Area (sq.unit)||½ (Base) x (Height)|
|Perimeter (units)||a+b+c; sum of three sides|
A four sided closed shape, that has four interior angles. It is also categorised into different types:
- Square: All sides are equal and all angles are equal to 90 degrees
- Rectangle: Opposite sides are equal and all angles measures 90 degrees
- Parallelogram: Opposite sides are equal and parallel. Opposite angles are equal.
- Trapezium: One pair of opposite sides are parallel.
|Type of quadrilateral||Area (sq.unit)||Perimeter (units)|
|Square||Side2||4 x Side|
|Rectangle||Length x Width||2 (Length + Width)|
|Parallelogram||Base x Height||2 (Sum of any two adjacent sides)|
|Trapezium||½ (sum of parallel sides) x (height)||Sum of all sides|
Three dimensional shapes are those shapes that are defined in three dimensions such as x-axis, y-axis and z-axis. The additional z-axis here represents the thickness of the shape. The basic solid shapes in Maths are:
These solid shapes are defined based on their surface area and volume. Let us learn the measurement of these solids.
A sphere is a round shape whose surface is at equidistant from a common point, called center. Similar to circle, the distance from center to outer surface is the radius of the sphere.
|Surface area||4πr² (square unit)|
|Volume||4/3(πr3) (cubic unit)|
A cube is an extended version of a square in three dimensional space, whose all the sides are of square shape. Therefore, the length of all its edges are also equal. It has 6 faces, 12 edges and 8 vertices.
|Surface area||6 (Edge)2 (square unit)|
|Volume||Edge3 (cubic unit)|
A cuboid is an extended version of a rectangle. Just like a cube, it also has 6 faces, 12 edges and 8 vertices. But the faces of cuboids are in rectangular shape.
|Surface area||2 (Length x Breadth+breadth x height + Length x height)|
|Volume||length × breadth × height|
A cone is a solid shape with a circular base, that narrows smoothly from bottom to top at a point called the apex of the cone.
|Surface area (sq.units)||Πr (r+l), where r is the radius of circular base and l is the slant height|
|Volume (cu.units)||⅓ Π (r2) (h); h is the height of cone|
Cylinder is a 3d shape having parallel circular bases on both the sides of a curved surface.
|Surface area (sq.units)||2 Π r (r + h); r and h are the radius and height of cylinder|
|Volume (cu. units)||Π r2 h|


Congrats to our winner Shoshana!
I am not a math person. In fact I can still vividly recall my painful and embarrassing childhood academic math experiences; when in fifth grade my teacher taped a list written in dark red ink of all the students in the class who failed their math test and yours truly was on there boasting a 43, or when while sitting at my second go round of the SAT's I literally started to cry because I was so overwhelmed and out of my comfort zone and league when trying in vain to get the math portion done.
So suffice it to say when I helped to host several of my favorite blogger friends at Liberty Science's brand spankin new Math Midway exhibit, I was actually a bit intimidated and excited at once, but also questioned just how sexy and fun the concept of math could be… and could it really appeal to kids and to me an adult who has struggled with math for a lifetime?
Well readers I can safely tell you- Math Midway at Liberty Science Center not only educates, but does so in such a fun way-you and your kids will be hard pressed not to walk out of there feeling smarter and dare I say just a bit happier!
Here are all the deets
Math Midway exhibit at Liberty Science Center runs from: October 7, 2011 – January 22, 2012
What this exhibit does is try and get across this underlying concept; the fact that Mathematics illuminates patterns that abound in our lives, providing clarity and structure. At the Math Midway, curated by the Museum of Mathematics (which will have its grand opening in 2012 at 11 East 26th Street in Manhattan with a mission to enhance public understanding and perception of mathematics) which made its debut at the 2009 World Science Festival Street Fair in New York City families are encouraged to explore surprising aspects of math in the Math Midway, in an interactive, hands-on tour of mathematical concepts, all in a colorful, carnival style.
Just a few of the things your kids will go gaga for:
-Riding on a square-wheeled tricycle to discover why the ride is so smooth.
-Playing the Wheel of Chance – Pick three cards – which one is most likely to come up when you spin the wheel? Keep spinning until you've got a winner!
-Experimenting with the Ring of Fire, using a laser beam to find hidden shapes within shapes.
-Marveling at mind-bending mirrors.
-Creating a giant pattern or “tessellation,” of monkeys in a puzzle-like pattern.
-Getting into the swing of harmonics with the Mysterious Harmonograph, which creates beautiful swirling patterns on paper.
Address: Liberty State Park
222 Jersey City Boulevard
Jersey City, NJ 07305
The Math Midway is free with paid admission or membership to Liberty Science Center.
Information: 201.200.1000 http://lsc.org
Fall/Winter 2011/12 Hours (Through April 1) Monday Closed
Tue – Fri 9:00 am – 4:00 pm
Sat – Sun 9:00 am – 5:00 pm
Thanks to Liberty Science Center one lucky reader The Staten Island Family reader will win a Family 4 pack of tickets to enjoy Liberty Science Center and the Math Exhibit. Best of all, there aren't any blackout dates.
For a chance to win this family of four pack tickets for yourself, leave a comment on this blog post with why you'd like to win these tickets! For a second entry you can like The Staten Island Family on Facebook and for a third entry you can follow Madijack on twitter and retweet this giveaway.
Good luck, giveaways ends Monday, November 7th at 12 midnight EST.


|Dec27-10, 07:36 AM||#1|
finite element method
do suggest a good book for finite element method?some books have left me confused over the
|Dec27-10, 08:09 AM||#2|
This is probably a good book on the subject.
Understanding and Implementing the Finite Element Method
Mark S. Gockenbach
What about FEM/FEA is one interested. The solution method can depend on the type of PDE being solved, and the PDE is related to the problem - e.g., mechanics, fluid flow, heat transfer, . . . , or some combination thereof.
|Similar Threads for: finite element method|
|Finite element method coursework?||Differential Equations||0|
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|finite element method||Calculus||1|
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How Many Days in 48 Hours?
When we talk about days, we usually think of the duration of the day. A day consists of several parts: the morning, afternoon, evening, and night. Each part is a certain length, based on the geographic latitude and time of year. Summer and winter days are shorter than those of the middle of the year. However, the terms “day” and “night” are often used interchangeably.
If you need to know how long it takes to complete two days, 48 hours is the number to use. To convert this amount to days, weeks, or months, simply divide 48 by 24. For example, 9am on Wednesday morning is equivalent to 2:30 pm on Friday afternoon. However, if you’re in a different time zone, the number to convert is 9:48.
To convert 48 hours to days, use the 48 hr to d table. The 48 hr to d conversion factor is 0.04166666666666667. To convert to other dimensions, multiply 48 hr by the corresponding conversion factor. This way, you’ll get the desired answer in seconds.
In the case of a 24-hour day, 48 hours equal two days. The difference between the two times is the time zone. Thursday’s time zone is 3:44 AM, while Sunday’s time zone is 5:04 PM. Thus, two days can be completed in 48 hours.
1 / 0.5 day
One / 0.5 day in 48 hours is the inverse conversion factor of one day. To convert the two units, simply multiply the number of days by the number of hours. Thus, one day is equal to zero point five times forty-eight hours. You can also convert one day to an hour by dividing the number of hours by 48.
The formula also works when the day changes. The result is the time of the next day. For example, 6:00:00 is the time of the next day when 20 hours have passed. However, if you want to see the number of hours in a day, you need to change the formatting of the cell.


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boolean stores the result of a logical comparison and can take on one of two values:
Booleans were named after the nineteenth-century mathematician George Boole, who devised an arithmetic system based on the logic of true and false properties.
Booleans help us store a statement's truth or falsehood in a standard way. We evaluate true or false expressions everyday: "do I have my housekeys?" "Should I carry an umbrella?" "Have I called mom yet?"
Create a boolean by giving a boolean variable a true or false value:
boolean b = true; boolean c = (5 < 4); // c is false boolean e; // e doesn't yet have a value, but it's been initliazed
Two booleans are equal if they have the same value; that is, if they are both true or both false. For example:
true == true; // true false == true; // false false != true; // true
Suppose we have
int x = 4 and
int y = 12. What can we say about the following statements?
boolean b = x > y; // false, because 4 isn't larger than 12 boolean c = x == y; // false, because 4 isn't equal to 12 boolean d = y > x; // true, because 12 is greater than 4
Booleans can also be written with more complicated expressions:
boolean e = (20 - 10) > (9 * 1) // true boolean f = (39 - 30) * 9 != 81 // false


The Smarter Balanced Assessment is California’s statewide student assessment system, aligned to Common Core State Standards. Only Juniors (11th graders) will take this test in Math and English Language Arts (ELA). This assessment serves as an indicator of readiness for college-level coursework.
The Smarter Balanced Assessment will take place over a two-week period; March 27th - April 7th. This assessment will be given using a block schedule, which are approximately two-hour classes. Every-other-day will be assigned to even and odd classes, except the Fridays (refer to linked schedule below). Juniors will test with their Math and English teachers. To view the CAASPP schedule, click the link below.
Copies of this schedule are also available in the Student Support Center of Granite Hills High School.
MORNING BUS TRANSPORTATION
Due to the block schedule, the morning bus pick-ups have been modified. To view the modifed bus schedule, please click below or the image to the right.


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No matter what you make a decision, a student will certainly get a lot from the classes at top rated colleges for mathematics. The subject is quite important and really should be studied effectively.


The Pebble GameThe 2D Pebble Game software can be run interactively using a Java applet and web service. Alternatively, you may download the following software versions as full Fortran code distributions: the 2D Pebble Game for central forces, the 3D Pebble Game with central forces and angular constraints, and the 3D pebble game without angular constraints. Instructions and examples can be found inside the compressed files, enjoy!
BackgroundThe Pebble Game  is based on the theorem of Laman . The implementation of Laman's theorem using the Pebble Game gives a complete and exact solution in 2D. The input is a set of distance constraints - the precise lengths are irrelevant, although they are fixed for convenience. This is a topological theorem, and the actual geometry is irrelevant, although useful in making plots to visualize the results etc. In 2D, two pebbles are associated with each site to represent the 2 degrees of freedom of a point, and then the Pebble Game moves these pebbles around, following Laman's theorem, to do a local count correctly as free pebbles (not associated with a constraint) are placed upon the line that represents the constraint, to show that it is an independent constraint. A constraint is independent if two free pebbles can be found at the ends of that constraint after an exhaustive search, otherwise it is dependent and the constraint is referred to as redundant. An interactive applet demonstration is available to demonstrate how the pebbles are moved. The user can input sites and then add constraints one at a time. It is recommended working through such an example with about 8 sites to better understand the procedure. The rigid regions are colored in red, and redundant bonds are not covered by pebbles. The number of floppy modes of the network is given by the number of free pebbles minus the 3 macroscopic modes. The interactive version of the 2D pebble game has multiple input options for the data files and multiple outputs that can be displayed as required for the particular project. This is an exact algorithm. The rigid region decomposition, the stressed and unstressed regions and the flexible joints between then are unique. A stressed region contains one or more redundant constraints, whose position is completely arbitrary within the region. Further details can be found in references [3-5].
Files available for downloadA good place to start after reading the papers referenced below is with a demonstration of the pebble game that can be downloaded here as a power point presentation. The presentation, created by Mykyta Chubynsky, demonstrates the pebble game algorithm for a 2D network of six points and nine edges. The resulting graph has one flexible region and one overconstrained region. This presentation complements the Interactive 2D Pebble Game applet available via the Pebble Game menu.


In time series analysis, a central theme is to look at the characteristics of the signal in the frequency domain, which can be estimated via a suitable Fourier transform. As we typically encounter just one set of data of finite length, the estimates will not be precise, and we must find the right balance between resolution, bias, and variance of the estimates. Due to the manifestation of the Heisenberg’s uncertainty principle, it is not possible to construct a perfect estimator that can simultaneously achieve all the desirable properties.
The multitaper estimate, first introduced by David Thomsom in the 1980s, is a cornerstone of modern-day spectral analysis. The main idea is that it trades resolution for wide-band bias, while reducing the variance by taking the mean of several orthogonal estimates. It has found applications in many fields. To name two examples, medical practitioners use the multitaper estimate to study sleep by analyzing the EEG of the subjects and obtaining a classification of different types of sleep stages. In astronomy it has been helpful in the detection of gravitational waves at LIGO.
Despite the widespread applications of this method, the mathematical properties of the multitaper estimates are relatively unknown. Current mathematical justifications for the effectiveness of multitaper are based on the restrictive assumption that the time series is Gaussian. To bridge this gap, we studied the multitaper estimate under more general settings, and developed statistics that can be used for hypothesis testing in various situations. The key idea is to transfer the problem into a physical dependent framework developed by Wei-Biao Wu in 2005. This aided us in obtaining various approximations of the time series and to show central limit theorem type results that characterizes the distribution of the estimates.
Finally, we showed that a particular resampling method for the time series under bootstrap is justified, and this would be key in obtaining accurate, non-asymptotic estimates when we have a finite number of samples.


You might have heard about blackjack card counting in New Zealand, but you are unsure about it. Many successful players are making use of this strategy to win as many hands as possible. They know everything about card counting in blackjackand they can do it successfully. Here you will read more about blackjack card counting, and what it is. When you are done reading this, you will know more about the strategy and you will be able to do it successfully.
Before you can learn how to do card counting, you need to understand what blackjack counting cards are all about. This is the first step in learning this successful strategy. With this strategy, you are going to learn that higher cards like the 10 and 9 benefit the player, while the lower cards will benefit the dealer more. The reason why high cards are better for the player is that it makes the probability for the player better. Many people are also calling this high-low card counting. When a player gets low cards, the chance of busting is so much higher. There is a way to predict if you are getting a high or low card. And, this is what card counting is all about.
This might be complicated, but you just need to concentrate and understand each step. With regular practicing that can be done in blackjack free online, you will be able to do blackjack card counting without any problems. These are the four steps in card counting that you can follow to start understanding and being successful with this strategy.
The first thing you need to do to know how to count cards in blackjack is to assign a value to every card. The card value is all about adding 1, subtracting one, or doing nothing according to the card you’ve got. These are the most important aspect to remember. These are examples of adding value to every card:
When the cards are dealt throughout the game, you need to calculate the sum of the values given here. You can’t write it down, so you need to keep your mind sharp and remember it. For example, when player two receives an Ace it’s -1 and another Ace is -1. Player two has cards King which would be -1 and 9 which will be 0. You are doing this with each game that will give you a negative or positive number. A negative number means that there are low numbers still to follow, and it will give a lower probability of you winning. With a positive number, it means that higher numbers are going to follow and this will give you a higher probability to win.
The true count means the running count for how many decks remain to be dealt. When there is a high running count, means that only one of six decks have been dealt. To calculate the true count, you need to divide the running count by the number of decks remaining. You need to practice this to get it right.
Now, you need to decide if you should raise or lower your bets. This is the last step in learning how to count cards blackjack. If the running count is negative after any round, you should decrease your bet. If the running count is positive, you will receive better cards, so you should rise your bet in the next round. These will give you some ideas on how you should know what bet to place.
Do you see the pattern? This is how you will know if you should raise your bet, or you should lower it in the next hand. This is the last and easiest step in the count card strategy.
Once you understand the basics of card counting, then you can consider the more advanced card counting strategy. There are a couple of them, and you need to understand the basic one before you can try any of these blackjack strategies.
Why is blackjack counting cards something that you want to consider? There are a couple of advantages that prove that this strategy is something to consider.
This is becoming a serious problem. Blackjack real money casinos are aware of the blackjack card counting strategy, and they have designed countermeasures to prevent people from counting cards blackjack. Making this strategy useless. The different methods they are making use for messing up card counting include giving a poor blackjack payout ratio of just 6:5. Other methods include:
Does card count work online too? It depends on if you are playing online blackjack or with a live casino. With a live blackjack casino, you can still make use of the counting card strategy and see if you can do it successfully. You just won’t know if they are making use of counter-methods to distract you. With normal online gambling card counting doesn’t work at all. It is impossible to see how many cards there are still in the deck, and you can’t count.
With knowing the basic of blackjack card counting, you might want to remember these card counting tips. To ensure that you are even more successful in this strategy:
Is card counting blackjack legal? Even if it is legal and you can use it at casinos, there is a ban on counting cards. Meaning that if you are getting caught counting cards, you can be kicked out of the casino and getting banned to visit the casino again. If you were caught and you resist or fight against it, then you might lose all your winnings.
Blackjack card counting is one of the best strategies for winning in blackjack. It only works online with live blackjack and when you visit casinos. Normal online playing isn’t ideal for this strategy. There are many things that you need to know before you can be successful with card counting. And, one of these things is practice. The more you practice, the easier it will become. With all this information you will be able to learn everything there is to know about card counting, to start winning again.


Mathematics is a creative and highly inter-connected discipline which is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment. At Thistley Hough Academy, we provide a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.
Students will follow a 5-year curriculum which prepares them for a GCSE in Mathematics which will be completed at the end of year 11. This examination is tiered, so students will work towards either the Higher or Foundation paper. Each tier consists of 3 1.5 hour papers (1 non-calculator, 2 calculator). Students will complete the AQA GCSE Mathematics.
The curriculum is split into 6 main themes:
Students are assessed regularly throughout their time at the academy to prepare them for their formal examinations.
All students at the academy have access to MathsWatch – a useful revision tool which includes videos, worksheets and self-marking interactive questions. Students have been provided with individual login details by their class teachers. https://www.vle.mathswatch.com/vle/
There is a mathematics club for students on where they can take part in a range of activities depending on their interest including entering national problem solving competitions.
There are a variety of trips organised at different times of the year to support students with an interest in careers in mathematics; trips have included Oxford University,
Every year, students take part in the UKMT Individual Maths Challenges; lively, intriguing multiple-choice question papers, which are designed to stimulate interest in mathematics. The three levels cover the secondary school range 11-18 and together they attract over 600,000 entries from over 4000 schools and colleges.


Christmas Maths Challenge Launch - 21 Dec 2017 Portobello EdinburghAdd to Lightbox Download
John Swinney launches Christmas Maths Challenge. Festive puzzles aimed at P6 pupils and their families, as part of a drive to encourage positivity towards maths were handed out to children at Towerbank Primary School Edinburgh by the Deputy First Minister John Swinney.
© Jon Davey/ EEm
- Jon Davey | EdinburghElitemedia.co.uk
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- 3595x2400 / 1.6MB
- Contained in galleries
- Christmas Maths Challenge Launch | Edinburgh | 21 December 2017


Math anxiety is a feeling of frustration and helplessness in the ability to do math. When I was young I had math anxiety big time. I loved math until middle school when I was put in an advanced math class with Mr. Phillips. He was very strict and expected everyone to follow his short chalkboard lessons and finish our work quickly and correctly. He stressed me out so much that I had a brain block and could not understand anything he was teaching us. It took a month of this terrible math anxiety before I had the nerve to tell him I didn’t understand. He had given us our first big math test, and I couldn’t even do one problem. Approaching Mr. Phillips was probably my scariest school memory, as I was sure I would be punished severely. He didn’t get mad at me, but he did take me to an easier math class. What a relief! After that I avoided math. I took the easiest and minimum required math classes all through middle school and high school and got easy A’s. It wasn’t until I was in college in a teacher education math class that I realized I could be successful at more challenging math. Soon I became a lover of math again!
All it took was one teacher to build my math anxiety and one teacher to take it away. So what can teachers do to deal with math anxiety and build a growth mindset?
- It’s so important to find out how students feel about math through an individual interview or a survey. I had a fifth grader tell me the first day of school to just give him an F, because he was no good at math and didn’t want to even try. I was glad he told me this, so I could provide him with appropriate math lessons, challenges and successes. You may download this math mindset survey.
- Make sure students know that everyone can be successful in math, if they put forth the effort. You may use the Growth Mindset in Math poster below to build growth mindset dialogue. “The difference between successful and unsuccessful students is less about the content they learn and more about their mindsets.” Jo Boaler
- Use formative assessment to find out what math skills students need through interviews, observations or tests. Do not time math tests, as this is the number one way to build math anxiety. Tests should be short and the students told to try their best. The test should only be used for your formative assessment. Do not give it back to the students with an F! What is the F doing to this girl’s math mindset?
- Use the formative assessment to provide small group instruction where students are appropriately challenged on the skills they need. All students need challenge, even those students working at higher math levels. Read more about differentiated guided math and planning small group math lessons
- Celebrate students’ mistakes, because our brains grow when we make mistakes! A student handed in a math paper and said she didn’t make one mistake. I apologized to her and told her I would give her some more challenging math next time.
To alleviate math anxiety we need to build a strong math mindset in our students. It’s not about the grades, but about the effort. Math aptitude is not inborn. All students can learn and love math. Click on the images to download these Growth Mindset in Math posters.


I am new using Dinver, I've been computing dispersion curves inversion with Rayleigh polarization as my dispersion curve comes from Rayleigh waves. I also have at the same place a 3C station so I could compute the HV method with geopsy software.
Now, I wanna know how to compute a Joint inversion with my Rayleigh dispersion curve and my *.hv file from geopsy to obtain a velocity model.
I haven't found any instruction about. I read other chat and found an explanation of the misfit weights in the targets tool.
- Dispersion curves
- ellipticity peak
- ellipticity curve
What I suspect is that I have to include here both, my dispersion curves and my *.hv. If that is right, how? ellipticity peak or ellipticity curve? what about the misfit weight?
I don't know if I am in a good track, I really appreciate any answer on how to compute this and also if there is any instruction somewhere of how to set the parameters according these two constraints or any important condition I have to keep in mind.
Thank you so much for the help.
1 post • Page 1 of 1


For analysing the linear electric circuits that consists of two or more independent sources (Voltage or current or both), superposition theorem is extremely used (particularly for time domain circuits with elements operated at different frequencies). If a linear DC circuit has more than one independent source, we can find the current (through a resistance) and voltage (across the resistance) by using nodal or mesh analysis methods.
Alternatively , we can use the superposition theorem that adds each individual source effect on the value of the variable to be determined. This means superposition theorem considers the each source in a given circuit separately for finding the value of the variable (whether current or voltage) and finally produce the resultant variable by adding all the variables caused by each source effect. Even though it is of complex procedure, but still can be applied for any linear circuit.
The superposition theorem states that in any linear bilateral network that consisting of two or more independent sources, current through (or voltage across) an element is the algebraic sum of the currents through (voltages across) that element caused by each independent source acting alone with all other sources are replaced by their internal resistances. We know that as long as the linearity exists between the source and contribution, the total contribution due to various sources acting simultaneously is equal to the algebraic sum of individual contributions due to individual source acting at a time.
Therefore, if the circuit consists of N independent sources, we have to analyse N circuits, each will produce a result with respect to each individual source. And finally these individual results must be added to get the whole analysis of the circuit. Therefore, this require more work however, this theorem will be very useful in analysing the various parts of a complex circuit.
1. Consider the various independent sources in a given circuit.
2. Select and retain one of the independent sources and replace all other sources with their internal resistances or else replace the current sources with open circuits and voltage sources with short circuits.
3. To avoid confusion re-label the voltage and current notations suitably.
4. Find out the desired voltage/currents due to the one source acting alone using various circuit reduction techniques.
5. Repeat the steps 2 to 4 for each independent source in the given circuit.
6. Algebraically add all the voltages/currents that are obtained from each individual source (Consider the voltage signs and current directions while adding).
1. Let us consider the below simple DC circuit to apply the superposition theorem such that we will obtain the voltage across the resistance 10 Ohms (load terminals). Consider that in a given circuit there are two independent sources as voltage and current sources as shown in figure.
2. First, we retain one source at a time that means , only voltage source is acting in the circuit and the current source is replaced with internal resistance (infinite) so it becomes open circuited as shown in figure.
Consider VL1 is the voltage across the load terminals with voltage source acting alone, then
VL1 = Vs × RL / (RL + R1)
= 20 × 10 / (10 + 20)
= 6. 66 Volts
3. Retain the current source alone and replace the voltage source with its internal resistance (zero) so it becomes a short circuited as shown in figure.
Consider that VL2 is the voltage across the load terminals when current source acting alone. Then
VL2 = IL × RL
IL = I × R1 / (R1 + RL)
= 1 × 20 / (20 +30)
= 0.4 Amps
VL2 = 0.4 × 10
= 4 Volts
Therefore, according the superposition theorem, the voltage across the load is the sum of VL1 and VL2
VL = VL1 + VL2
= 6.66 + 4
= 10.66 Volts
Consider the below circuit to which we are going to determine the current I through the 4 ohm resistor using superposition theorem.
Consider I1, I2 and I3 are the currents due to sources 12v, 20V and 4A sources respectively. Then, based superposition theorem I = I1 + I2 + I3. So let’s determine these currents with each individual source.
Only with 12V Voltage source:
Consider the below circuit where only 12V source is retained in the circuit and other sources are replaced by their internal resistances.
By combining the resistance 6 ohm with 10 ohm we get 16 ohm resistance which is parallel with 6 ohm resistance. Then this combination produce, 16 × 6 / (16 + 6) = 4.36 ohm. Therefore the equivalent circuit will be as shown in figure.
Then the current through 4 ohms resistance,
I1 = 12 / 8.36
= 1.43 A
Only with 20 V Voltage Source:
Retain only 20 V voltage source and replace other sources with their internal resistance, then the circuit becomes as shown below.
Apply the mesh analysis to the loop a, we get
22Ia – 6Ib + 20 = 0
22Ia – 6Ib = -20 ……………….(1)
For Loop b, we get
10Ib – 6Ia = 0
Ia = 10Ib/6
Substituting Ib in equation 1
22 (10Ib/6) – 6Ib = -20
Ib = – 0.65
Therefore, I2 = Ib = -0.65
Only with 4A Current Source
Consider the below circuit where only current source is retained and other sources are replaced with their internal resistances.
By applying nodal analysis at node 2 we get,
4 = (V2/10) + (V2 – V1)/6 ………………..(2)
(V1/6) + (V1/4) = (V2 – V1)/ 6
V2 = 3.496 V1
Substituting V2 in equation 2, we get
V1 = 0.766 Volts.
Therefore I3 = V1/4
= 0.19 Amps.
Thus, as per the superposition theorem, I = I1 + I2 + I3
= 1.43 – 0.65 + 0.19
= 0.97 Amps.
Consider the below AC circuit, to which we are going to determine the value of current in the 4 ohm resistor using superposition theorem.
Case 1: Only with 20∠0 Voltage Source
By retaining the voltage source alone in the circuit, the current flow through the circuit is determined as
I1 = 20∠0/ (4 + j4)
= 20∠0 / (5.65∠45)
= 3.53∠- 45 or 2.49 –j2.49 A
Case 2: Only with 4∠90 Current Source
By retaining the current source alone in the circuit, the current I2 through the circuit is determined as
By current division method, I2 = 4∠90 × 4j/ (4 + j4)
= 4∠90 × 4∠90 (5.65∠45)
= 4∠90 × 0.707∠45
= 2.828∠135 or -1.99 + j1.99 A
The resultant current through the resistor 4 ohms is I = I1 + I2
= 3.53∠- 45 + 2.828∠135
= 0.785∠45 or 0.56 + j0.56 A
1. For power calculations superposition theorem cannot be used as this theorem works based on the linearity. Because the power equation is not linear as it is the product of voltage and current or square of the current or square of the voltage. Thus the power consumed by the element in a given circuit with superposition theorem is not possible.
2. If the choice of the load is variable or the load resistance changes frequently, then it is required to perform every source contribution of current or voltage and their sum for every change in load resistance. So this very complex procedure for analysing complex circuits.
3. This theorem applicable for only linear circuits and for non linear circuits (Having transistors and diodes) we can not apply.
4. This theorem is applicable only if the circuit has more than one source.


Mathematics in Beginners
The goal of our mathematics program in Beginners and across grade levels in the Lower School is to help children construct their own mathematical knowledge through meaningful learning experiences in which they solve problems, reason about their mathematical thinking, communicate their mathematical thinking in written and oral forms, make connections to mathematical ideas and real-life experiences, and explore multiple representations. We also encourage children’s interest in mathematics while building their confidence and strengthening their skills. We see mathematics as an integral part of the children’s daily learning experiences at school. There is a strong emphasis on helping children see connections between their work in mathematics and real-life situations.
A set of B-VIII Grade standards provides the framework for our work in mathematics. While the mathematics program is standards-driven, it is also flexible enough to be able to respond to both differences in learning styles and variations in the readiness of our students. Below are listed some of the skills and concepts we expect Beginners to develop over the course of the year.
- Counts to 20
- Recognizes numerals 0-10
- Identifies two-dimensional shapes
- Sorts by single and multiple attributes
- Uses organized counting strategies
- Uses manipulatives to solve problems
- Shares mathematical thinking with others
- Demonstrates an awareness of addition and subtraction in everyday life
- Participates in data collection, representation, and interpretation
- Creates and interprets graphs
- Identifies, creates, and extends patterns
- Identifies and manipulates shapes
- Engages in measurement activities


Students will work independently or in small groups for math each day and focus on one of the following courses: General Math, Pre-Algebra, Algebra 1/Intro to Counting and Probability, Intro to Number Theory/Algebra 2, or Intro to Geometry.
+General Math (Full Year)
General Math focuses on three critical areas: (1) developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions); (2) extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; and (3) developing understanding of volume.
+Pre-Algebra (Full Year)
Part 1 includes a thorough exploration of the fundamentals of arithmetic, including fractions, exponents, and decimals. We introduce beginning topics in number theory and algebra, including common divisors and multiples, primes and prime factorizations, basic equations and inequalities, and ratios.
Part 2 includes percent, square roots, a thorough exploration of geometric tools and strategies, an introduction to topics in discrete mathematics and statistics, and a discussion of general problem-solving strategies.
+Algebra 1 (0.5-1 Year)
Algebra 1 includes fundamental concepts of algebra, including exponents and radicals, linear equations and inequalities, ratio and proportion, systems of linear equations, factoring quadratics, complex numbers, completing the square, and the quadratic formula.
+Intro to Counting and Probability (0.5 Year)
Introduction to Counting and Probability includes basic and intermediate counting concepts, including casework, multiplication, permutations, combinations, Pascal’s triangle, probability, combinatorial identities, and the Binomial Theorem.
+Introduction to Number Theory (0.5 Year)
Introduction to Number Theory covers the fundamental principles of number theory, including primes and composites, divisors and multiples, divisibility, remainders, modular arithmetic, and number bases.
+Algebra 2 (0.5-1 Year)
Algebra 2 covers quadratic equations, graphing, complex numbers, functions, sequences and series, and exponents and logarithms. Problem solving skills are emphasized throughout, and time is devoted to advanced topics like telescoping sums and piecewise functions.
+Introduction to Geometry (1 Year)
Introduction to Geometry covers triangle similarity and congruence, complicated area problems, mastering the triangle, special quadrilaterals, polygons, the art of angle chasing, construction, power of a point, 3-dimensional geometry, transformations, analytic geometry, basic trigonometry, and geometric proofs.