Other
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/algebra/x2f8bb115
Multiple arguments for what we could get when we divide zero by zero. We will later see that this can be considered indeterminate
Watch the next lesson: https://www.khanacademy.org/math/algebra2/functions_and_graphs/undefined_indeterminate/v/undefined-and-indeterminate?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/functions_and_graphs/undefined_indeterminate/v/why-dividing-by-zero-is-undefined?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra II channel:
https://www.youtube.com/channe....l/UCsCA3_VozRtgUT7wW
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Worked example that thinks about the relationship between an arc length and the angle that is subtended by the arc.
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/radians_tutorial/e/cc-radians-and-arc-length?utm_source=YT&utm_medium=Desc&utm_campaign=Trigonometry
Watch the next lesson: https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/radians_tutorial/v/we-converting-degrees-to-radians?utm_source=YT&utm_medium=Desc&utm_campaign=Trigonometry
Missed the previous lesson?
https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/radians_tutorial/v/ratio-between-cocentric-arcs?utm_source=YT&utm_medium=Desc&utm_campaign=Trigonometry
Trigonometry on Khan Academy: Big, fancy word, right? Don't be fooled. Looking at the prefix, tri-, you could probably assume that trigonometry ("trig" as it's sometimes called) has something to do with triangles. You would be right! Trig is the study of the properties of triangles. Why is it important? It's used in measuring precise distances, particularly in industries like satellite systems and sciences like astronomy. It's not only space, however. Trig is present in architecture and music, too. Now you may wonder...how is knowing the measurement and properties of triangles relevant to music?? THAT is a great question. Maybe you'll learn the answer from us in these tutorials!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Trigonometry channel:
https://www.youtube.com/channe....l/UCYQSs1lFJZKpyqNQQ
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Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/old-ap-calculus-a
Given the graph of a function, Sal sketches the graph of its derivative. Created by Sal Khan.
Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-derivatives-analyze-functions/ab-connecting-func-and-derivatives/v/intuitively-drawing-the-anitderivative-of-a-function?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-derivatives-analyze-functions/ab-inflection-points/v/mistakes-when-finding-inflection-points-not-checking-candidates?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.
About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channe....l/UCyoj0ZF4uw8VTFbml
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Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra2/polynomial_and_rational/binomial_theorem/e/binomial-theorem?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Watch the next lesson: https://www.khanacademy.org/math/algebra2/polynomial_and_rational/binomial_theorem/v/pascals-triangle-binomial-theorem?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/polynomial_and_rational/polynomial-end-behavior/v/polynomial-end-behavior-exercise-example?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra II channel:
https://www.youtube.com/channe....l/UCsCA3_VozRtgUT7wW
Subscribe to Khan Academy: https://www.youtube.com/subscr....iption_center?add_us
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/algebra/x2f8bb115
Factor 45x^2-125 as 5(3x+5)(3x-5).
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra2/polynomial_and_rational/quad_factoring/e/factoring_difference_of_squares_3?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Watch the next lesson: https://www.khanacademy.org/math/algebra2/polynomial_and_rational/quad_factoring/v/factoring-trinomials-by-grouping-5?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/polynomial_and_rational/quad_factoring/v/u09-l2-t1-we3-factoring-special-products-3?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra II channel:
https://www.youtube.com/channe....l/UCsCA3_VozRtgUT7wW
Subscribe to Khan Academy: https://www.youtube.com/subscr....iption_center?add_us
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/geometry/cc-geometry-circles/central-inscribed-circumscribed/e/central--inscribed--and-circumscribed-angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry
Watch the next lesson: https://www.khanacademy.org/math/geometry/cc-geometry-circles/central-inscribed-circumscribed/v/hypotenuse-of-right-triangle-inscribed-in-circle?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry
Missed the previous lesson?
https://www.khanacademy.org/math/geometry/cc-geometry-circles/central-inscribed-circumscribed/v/measure-of-circumscribed-angle?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry
Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channe....l/UCD3OtKxPRUFw8kzYl
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Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ec....onomics-finance-doma
Comparing Accrual and Cash Accounting. Created by Sal Khan.
Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/accounting-and-financial-stateme/financial-statements-tutorial/v/balance-sheet-and-income-statement-relationship?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets
Missed the previous lesson? Watch here: https://www.khanacademy.org/economics-finance-domain/core-finance/accounting-and-financial-stateme/cash-accrual-accounting/v/accrual-basis-of-accounting?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets
Finance and capital markets on Khan Academy: In exchange for being treated as a person-like-legal entity (and the limited liability this gives for its owners), most corporations pay taxes. This tutorial focuses on what corporations are, "double taxation" and a few ways that multinationals might try to get out of paying taxes.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channe....l/UCQ1Rt02HirUvBK2D2
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Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/differential-equations/first-order-differential-equations/separable-equations/e/separable-differential-equations?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialEquations
Watch the next lesson: https://www.khanacademy.org/math/differential-equations/first-order-differential-equations/separable-equations/v/separable-differential-equations?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialEquations
Missed the previous lesson?
https://www.khanacademy.org/math/differential-equations/first-order-differential-equations/separable-equations/v/separable-differential-equations-introduction?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialEquations
Differential Equations on Khan Academy: Differential equations, separable equations, exact equations, integrating factors, homogeneous equations.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to KhanAcademy’s Differential Equations channel:: https://www.youtube.com/channe....l/UCxSQHGkaDv8UKXE0T
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Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/algebra/x2f8bb115
Jesse Roe and Sal talk about the difference between equations and functions
Watch the next lesson: https://www.khanacademy.org/math/algebra2/functions_and_graphs/function-introduction/v/relations-and-functions?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/functions_and_graphs/function-introduction/v/what-is-a-function?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra II channel:
https://www.youtube.com/channe....l/UCsCA3_VozRtgUT7wW
Subscribe to Khan Academy: https://www.youtube.com/subscr....iption_center?add_us
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/hu....manities/world-histo
Thinking about how the Industrial Revolution(s) and capitalism helped catalyze far-flung imperialism during the 1800s.
World History on Khan Academy: From prehistory to today, this course covers the human events that have shaped our planet.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to KhanAcademy: https://www.youtube.com/subscr....iption_center?add_us
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/algebra-home/alg-
Demonstrating why synthetic division gives you the same result as traditional algebraic long division
Watch the next lesson: https://www.khanacademy.org/math/algebra2/polynomial_and_rational/polynomial-remainder-theorem-tutorial/v/polynomial-remainder-theorem?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/polynomial_and_rational/synthetic-division/v/synthetic-division-example-2?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra II channel:
https://www.youtube.com/channe....l/UCsCA3_VozRtgUT7wW
Subscribe to Khan Academy: https://www.youtube.com/subscr....iption_center?add_us
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/algebra2/x2ec2f6f
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra/exponent-equations/fractional-exponents-tut/e/exponents_4?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Watch the next lesson: https://www.khanacademy.org/math/algebra/exponent-equations/fractional-exponents-tut/v/negative-fractional-exponent-examples-2?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Missed the previous lesson?
https://www.khanacademy.org/math/algebra/exponent-equations/fractional-exponents-tut/v/simplifying-with-exponent-properties?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra channel:
https://www.youtube.com/channe....l/UCYZrCV8PNENpJt36V
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Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/ap-calculus-ab/ab
You're on a ladder. The bottom of the ladder starts slipping away from the wall. Amidst your fright, you realize this would make a great related rates problem... Created by Sal Khan.
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-derivatives/ab-related-rates/e/related-rates-pythagorean-theorem?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-derivatives/ab-related-rates/v/related-rates-of-water-pouring-into-cone?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-derivatives/ab-related-rates/v/rate-of-change-of-distance-between-approaching-cars?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.
About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channe....l/UCyoj0ZF4uw8VTFbml
Subscribe to Khan Academy: https://www.youtube.com/subscr....iption_center?add_us
Creating scaling and reflection transformation matrices (which are diagonal)
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/lin_trans_examples/v/linear-transformation-examples-rotations-in-r2?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/linear_transformations/v/more-on-matrix-addition-and-scalar-multiplication?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channe....l/UCGYSKl6e3HM0PP7QR
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Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/linear-algebra/al
Projections onto subspaces
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthogonal_projections/v/linear-alg-visualizing-a-projection-onto-a-plane?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/alternate_bases/othogonal_complements/v/linear-alg-rowspace-solution-to-ax-b-example?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
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In this video, we think about what |a-b| really means, and we verify that |a-b| = |b-a| by looking at an example.
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-add-and-subtract/cc-7th-absolute-value/e/absolute-value-to-find-distance?utm_source=YT&utm_medium=Desc&utm_campaign=7thgrade
Watch the next lesson: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-add-and-subtract/cc-7th-absolute-value/v/interpreting-absolute-value-as-distance?utm_source=YT&utm_medium=Desc&utm_campaign=7thgrade
Missed the previous lesson?
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-add-and-subtract/cc-7th-add-sub-word-problems-w-negatives/v/interpreting-negative-number-statements?utm_source=YT&utm_medium=Desc&utm_campaign=7thgrade
Grade 7th on Khan Academy: 7th grade takes much of what you learned in 6th grade to an entirely new level. In particular, you'll now learn to do everything with negative numbers (we're talking everything--adding, subtracting, multiplying, dividing, fractions, decimals... everything!). You'll also take your algebraic skills to new heights by tackling two-step equations. 7th grade is also when you start thinking about probability (which is super important for realizing that casinos and lotteries are really just ways of taking money away from people who don't know probability) and dig deeper into the world of data and statistics. Onward! (Content was selected for this grade level based on a typical curriculum in the United States.)
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
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Given the graph of a function, can you identify the graph of its antiderivative? Created by Sal Khan.
Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-antiderivatives-ftc/ab-ftc-opt-vids/v/proof-of-fundamental-theorem-of-calculus?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-antiderivatives-ftc/ab-behavior-of-antiderivative/v/interpreting-behavior-of-antiderivative?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.
About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channe....l/UCyoj0ZF4uw8VTFbml
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