Definition and intuition for type 3 regions Watch the next lesson: https://www.khanacademy.org/math/multivariable-calculus/divergence_theorem_topic/divergence_theorem_proof/v/divergence-theorem-proof-part-1?utm_source=YT&utm_medium=Desc&utm_campaign=MultivariableCalculus Missed the previous lesson? https://www.khanacademy.org/math/multivariable-calculus/divergence_theorem_topic/region_types_3d/v/type-ii-regions-in-three-dimensions?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. ... https://www.youtube.com/watch?v=bxGnbVOtRYo Note: All Khan Academy content is available for free at (www.khanacademy.org)

More on complementary and supplementary angles. Introduction to opposite angles. Watch the next lesson: https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/old_angles/v/angles-part-3?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry Missed the previous lesson? https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/old_angles/v/introduction-to-angles-old?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. ... https://www.youtube.com/watch?v=zrqzG6xKa1A Note: All Khan Academy content is available for free at (www.khanacademy.org)

How bubbles destroy wealth. Created by Sal Khan. Watch the next lesson: https://www.khanacademy.org/economics-finance-domain/core-finance/investment-vehicles-tutorial/investment-consumption/v/back-of-envelope-office-space-conundrum?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/investment-consumption/v/wealth-destruction-1?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets Finance and capital markets on Khan Academy: When are you using capital to create more things (investment) vs. for consumption (we all need to consume a bit to be happy). When you do invest, how do you compare risk to return? Can capital include human abilities? This tutorial hodge-podge covers it all. 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. ... https://www.youtube.com/watch?v=eRImmzuExyg Note: All Khan Academy content is available for free at (www.khanacademy.org)

A deep dive into Article VII, which established the conditions for the ratification of the US Constitution. In this video, Kim discusses Article VII with scholars Mark Graber and Michael Rappaport. To read more about Article VII, visit the National Constitution Center’s Interactive Constitution. On this site, leading scholars interact and explore the Constitution and its history. For each provision of the Constitution, experts from different political perspectives coauthor interpretive explanations when they agree and write separately when their opinions diverge. View more lessons or practice this subject at https://www.khanacademy.org/humanities/ap-us-government-and-politics/foundations-of-american-democracy/ratification-of-the-us-constitution/v/article-vii-of-the-constitution?utm_source=youtube&utm_medium=desc&utm_campaign=usgovernmentandcivics Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help! Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc ... https://www.youtube.com/watch?v=_VuMqbtphr0 Note: All Khan Academy content is available for free at (www.khanacademy.org)