More free lessons at: http://www.khanacademy.org/video?v=nMrJ6nbOQhQ

Arrhenius, Bronsted Lowry, and Lewis Acids and Bases.
More free lessons at: http://www.khanacademy.org/video?v=vShCnTY1-T0

Watch the next lesson: https://www.khanacademy.org/math/algebra2/logarithms-tutorial/logarithm_basics/v/exponential-equation?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/logarithms-tutorial/logarithm_basics/v/exponential-to-logarithmic-form?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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Intuition behind the Divergence Theorem in three dimensions

Watch the next lesson: https://www.khanacademy.org/math/multivariable-calculus/divergence_theorem_topic/divergence_theorem/v/divergence-theorem-example-1?utm_source=YT&utm_medium=Desc&utm_campaign=MultivariableCalculus

Missed the previous lesson?
https://www.khanacademy.org/math/multivariable-calculus/surface-integrals/stokes_proof/v/stokes-theorem-proof-part-7?utm_source=YT&utm_medium=Desc&utm_campaign=MultivariableCalculus

Multivariable Calculus on Khan Academy: Think calculus. Then think algebra II and working with two variables in a single equation. Now generalize and combine these two mathematical concepts, and you begin to see some of what Multivariable calculus entails, only now include multi dimensional thinking. Typical concepts or operations may include: limits and continuity, partial differentiation, multiple integration, scalar functions, and fundamental theorem of calculus in multiple dimensions.

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 Multivariable Calculus channel:
https://www.youtube.com/channe....l/UCQQZDc22yCogOyx6D
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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

What is the minimum possible value of x^2+y^2 given that their product has to be fixed at xy = -16. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-derivatives/ab-optimization/v/optimizing-box-volume-graphically?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-balloon-height?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

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/coefficient-in-binomial-expansion?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/polynomial_and_rational/binomial_theorem/v/binomial-theorem?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/integral-calculus

Infinite both ways! Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-bc/bc-antiderivatives-ftc/bc-improper-integrals/v/divergent-improper-integral?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-bc/bc-antiderivatives-ftc/bc-improper-integrals/v/introduction-to-improper-integrals?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC

AP Calculus BC on Khan Academy: Learn AP Calculus BC - everything from AP Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP Test

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 Academy's AP Calculus BC channel: https://www.youtube.com/channe....l/UC5A2DBjjUVNz8axD-
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/ec....onomics-finance-doma

Comparing ETF's, open-end, and closed-end funds. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/investment-vehicles-tutorial/mutual-funds/v/ponzi-schemes?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here: https://www.khanacademy.org/economics-finance-domain/core-finance/investment-vehicles-tutorial/mutual-funds/v/closed-end-mutual-funds?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: If we're not in the mood to research and pick our own stocks, mutual funds and/or ETFs might be a good option. This tutorial explains what they are and how they are different.

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/algebra2/exponential_and_logarithmic_func/log_functions/e/graphs-of-exponentials-and-logarithms?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

Watch the next lesson: https://www.khanacademy.org/math/algebra2/exponential_and_logarithmic_func/log_functions/v/vi-and-sal-explore-how-we-think-about-scale?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/exponential_and_logarithmic_func/log_functions/v/matching-exponential-functions?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

Autoionization of water into hydronium and hydroxide ions

Watch the next lesson: https://www.khanacademy.org/science/biology/water-acids-and-bases/acids-bases-and-ph/v/arrhenius-definition-of-acids-and-bases?utm_source=YT&utm_medium=Desc&utm_campaign=biology

Missed the previous lesson? https://www.khanacademy.org/science/biology/water-acids-and-bases/water-as-a-solid-liquid-and-gas/v/liquid-water-denser-than-solid-water-ice?utm_source=YT&utm_medium=Desc&utm_campaign=biology

Biology on Khan Academy: Life is beautiful! From atoms to cells, from genes to proteins, from populations to ecosystems, biology is the study of the fascinating and intricate systems that make life possible. Dive in to learn more about the many branches of biology and why they are exciting and important. Covers topics seen in a high school or first-year college biology course.

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 Biology channel: https://www.youtube.com/channe....l/UC82qE46vcTn7lP4tK
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In this example, you are analyzing the rate of change of a balloon's altitude based on the angle you have to crane your neck to look at it. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-derivatives/ab-optimization/v/minimizing-sum-of-squares?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/speed-of-shadow-of-diving-bird?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

Using the squeeze theorem to prove that the limit as x approaches 0 of (sin x)/x =1

Watch the next lesson: https://www.khanacademy.org/math/differential-calculus/limits_topic/epsilon_delta/v/limit-intuition-review?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

Missed the previous lesson?
https://www.khanacademy.org/math/differential-calculus/limits_topic/squeeze_theorem/v/squeeze-theorem?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus

Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilon-delta definition of limits.

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 Calculus channel:
https://www.youtube.com/channe....l/UCNLzjGl1HBdZrHXo4
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Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/hu....manities/us-history/

Woodrow Wilson attempted to build a more peaceful world after the horrors of World War I. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/humanities/world-history/euro-hist/ww1-aftermath/v/paris-peace-conference-and-treaty-of-versailles?utm_source=YT&utm_medium=Desc&utm_campaign=worldhistory

Missed the previous lesson? https://www.khanacademy.org/humanities/world-history/euro-hist/ww1-aftermath/v/deaths-in-world-war-i?utm_source=YT&utm_medium=Desc&utm_campaign=worldhistory

World history on Khan Academy: From the earliest civilizations to the modern world, geography, religion, trade, and politics have bound peoples and nations together — and torn them apart. Take a journey through time and space and discover the fascinating history behind the complex world we inhabit today.

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 World History channel: https://www.youtube.com/channe....l/UC6KRvvmvkCchFMo2E
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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/arithmetic-home/a

Use an understanding of place-value to subtract.

Watch the next lesson: https://www.khanacademy.org/math/cc-third-grade-math/cc-3rd-add-sub-topic/cc-3rd-add-sub-missing-value/v/missing-number-for-addition-and-subtraction-within-1000?utm_source=YT&utm_medium=Desc&utm_campaign=3rdgrade

Missed the previous lesson? https://www.khanacademy.org/math/cc-third-grade-math/cc-3rd-add-sub-topic/cc-3rd-regrouping-3-dig/v/regrouping-from-0-when-subtracting-three-digit-numbers?utm_source=YT&utm_medium=Desc&utm_campaign=3rdgrade

Grade 3rd on Khan Academy: We know you've been rocking through 2nd grade adding and subtracting all kinds of whole numbers (up to 2 digits, right?). That's awesome! In 3rd grade math we want you to start using bigger numbers and start multiplying and dividing, too. By the way, did you know that some numbers aren’t actually “whole?” They’re “partially whole.” We call them fractions! We want you to start playing around and having fun with those, too. There's also area, perimeter, and place value to be discovered. Whew. We have so much to do and can't wait to do it with you. Let's go!

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 3rd grade channel:
https://www.youtube.com/channe....l/UCwRBaZv81l-p3Ch2x
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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

In this video, learn about calculating the price elasticity of demand using the midpoint method (also called the arc elasticity method).

Watch the next lesson: https://www.khanacademy.org/economics-finance-domain/microeconomics/elasticity-tutorial/price-elasticity-tutorial/v/more-on-elasticity-of-demand?utm_source=YT&utm_medium=Desc&utm_campaign=microeconomics

Missed the previous lesson? https://www.khanacademy.org/economics-finance-domain/microeconomics/supply-demand-equilibrium/oil-prices-tutorial/v/breakdown-of-gas-prices?utm_source=YT&utm_medium=Desc&utm_campaign=microeconomics

Microeconomics on Khan Academy: Topics covered in a traditional college level introductory microeconomics course

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 Microeconomics channel: https://www.youtube.com/channe....l/UC_6zQ54DjQJdLodws
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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-home/alg-

Sal gives many examples where he determines the domains of functions according to mathematical limitations.

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra/algebra-functions/determining-the-domain-of-a-function/e/domain-of-algebraic-functions?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

Watch the next lesson: https://www.khanacademy.org/math/algebra/algebra-functions/determining-the-domain-of-a-function/v/domain-of-a-modeling-function-example-1?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

Missed the previous lesson?
https://www.khanacademy.org/math/algebra/algebra-functions/determining-the-domain-of-a-function/v/domain-of-a-radical-function?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/algebra/x2f8bb115

Graphing piecewise function

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra2/functions_and_graphs/piecewise-functions-tutorial/e/piecewise-graphs-linear?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

Watch the next lesson: https://www.khanacademy.org/math/algebra2/functions_and_graphs/piecewise-functions-tutorial/v/matching-expressions-to-define-intervals-of-functions-example?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII

Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/functions_and_graphs/piecewise-functions-tutorial/v/piecewise-function-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

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/trigonometry/less-basic-trigonometry/trig-symmetry-periodicity/e/symmetry-and-periodicity-of-trig-functions?utm_source=YT&utm_medium=Desc&utm_campaign=Trigonometry

Watch the next lesson: https://www.khanacademy.org/math/trigonometry/less-basic-trigonometry/trig-symmetry-periodicity/v/tan-symmetries-unit-circle?utm_source=YT&utm_medium=Desc&utm_campaign=Trigonometry

Missed the previous lesson?
https://www.khanacademy.org/math/trigonometry/trig-function-graphs/long_live_tau/v/pi-is-still-wrong?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
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/linear-algebra/ve

Solving a system of linear equations by putting an augmented matrix into reduced row echelon form

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/matrices_elimination/v/matrices-reduced-row-echelon-form-2?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/dot_cross_products/v/distance-between-planes?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
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/ec....onomics-finance-doma

Raising money from an angel investor. Pre-money and post-money valuation. Created by Sal Khan.

Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/stock-and-bonds/venture-capital-and-capital-markets/v/getting-a-seed-round-from-a-vc?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Missed the previous lesson? Watch here: https://www.khanacademy.org/economics-finance-domain/core-finance/stock-and-bonds/valuation-and-investing/v/ebitda?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets

Finance and capital markets on Khan Academy: This is an old set of videos, but if you put up with Sal's messy handwriting (it has since improved) and spotty sound, there is a lot to be learned here. In particular, this tutorial walks through starting, financing and taking public a company (and even talks about what happens if it has trouble paying its debts).

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
Subscribe to Khan Academy: https://www.youtube.com/subscr....iption_center?add_us