When graphing a real-world relationship, we need to pick labels and axis scales that are appropriate for the purpose of our model.
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https://www.youtube.com/watch?v=IoPQtvXkde0
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Taking the derivative when y is defined implicitly.
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https://www.youtube.com/watch?v=sL6MC-lKOrw
Note: All Khan Academy content is available for free at (www.khanacademy.org)
When an expression can be viewed as the difference of two perfect squares, i.e. a²-b², then we can factor it as (a+b)(a-b). For example, x²-25 can be factored as (x+5)(x-5). This method is based on the pattern (a+b)(a-b)=a²-b², which can be verified by expanding the parentheses in (a+b)(a-b).
Watch the next lesson: https://www.khanacademy.org/math/high-school-math/math2/math2-factorization/math2-diff-of-squares/v/factoring-to-produce-difference-of-squares?utm_source=YT&utm_medium=Desc&utm_campaign=highschoolmath
Missed the previous lesson? https://www.khanacademy.org/math/high-school-math/math2/math2-factorization/math2-factor-polynomials/v/factoring-trinomials-by-grouping-1?utm_source=YT&utm_medium=Desc&utm_campaign=highschoolmath
High School Math on Khan Academy: Did you realize that the word "algebra" comes from Arabic (just like "algorithm" and "al jazeera" and "Aladdin")? And what is so great about algebra anyway? This tutorial doesn't explore algebra so much as it introduces the history and ideas that underpin it.
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.
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https://www.youtube.com/watch?v=HLNSouzygw0
Note: All Khan Academy content is available for free at (www.khanacademy.org)
2010 IIT JEE Paper 1 Problem 54 Series Sum
Watch the next lesson: https://www.khanacademy.org/math/precalculus/seq_induction/deductive-and-inductive-reasoning/v/deductive-reasoning-1?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus
Missed the previous lesson?
https://www.khanacademy.org/math/precalculus/seq_induction/advanced-sequences-series/v/2003-aime-ii-problem-8?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus
Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!
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.
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https://www.youtube.com/watch?v=A6fbDssPeac
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Showing segment congruence equivalent to having same length
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https://www.youtube.com/watch?v=Ko12Tf-lulQ
Note: All Khan Academy content is available for free at (www.khanacademy.org)
AP Calculus lead, Ben Hedrick, talks about the design and tips for the AP Calculus exams.
Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-continuity/ab-limits-graphically/v/introduction-to-limits-hd?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-continuity/ab-about-the-course/v/khan-academy-in-the-classroom-bill-scott?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.
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https://www.youtube.com/watch?v=_3VKtPGbSzk
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Let’s explore the meaning and origin of the word “alienated”.
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!
https://www.khanacademy.org/ela/new-6th-grade-reading-and-vocabulary/x8ddea1200317e822:what-defines-us/x8ddea1200317e822:identifying-point-of-view/v/alienated-vocabulary-625b
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!
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https://www.youtube.com/watch?v=Y41Mj-fUN9U
Note: All Khan Academy content is available for free at (www.khanacademy.org)
How the banks are connected. What happens when one bank fails.
More free lessons at: http://www.khanacademy.org/video?v=gX9aKDeAOz4
https://www.youtube.com/watch?v=gX9aKDeAOz4
Example word problem with geometric series
https://www.youtube.com/watch?v=qE3z1HQfxV0
Note: All Khan Academy content is available for free at (www.khanacademy.org)