Other
Another separable differential equation example.
Watch the next lesson: https://www.khanacademy.org/math/differential-equations/first-order-differential-equations/modeling-with-differential-equations/v/particular-solution-given-initial-conditions-for-population?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-2?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.
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Calculating the foci (or focuses) of an Ellipse.
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra2/conics_precalc/ellipses-precalc/e/ellipse_intuition?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Watch the next lesson: https://www.khanacademy.org/math/algebra2/conics_precalc/ellipses-precalc/v/ellipse-focus-intuition-exercise?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/conics_precalc/ellipses-precalc/v/conic-sections-intro-to-ellipses?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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Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/hu....manities/us-governme
Thomas Hobbes's Leviathan and the idea of a social contract.
View more lessons or practice this subject at https://www.khanacademy.org/humanities/ap-us-government-and-politics/foundations-of-american-democracy/ideals-of-democracy/v/thomas-hobbes-and-social-contract?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!
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Find two numbers whose products is -16 and the sum of whose squares is a minimum.
Practice this yourself on Khan Academy right now: https://www.khanacademy.org/e/optimization?utm_source=YTdescription&utm_medium=YTdescription&utm_campaign=YTdescription
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ec....onomics-finance-doma
Relationship between the GDP deflator, nominal GDP and real GDP
Watch the next lesson: https://www.khanacademy.org/economics-finance-domain/macroeconomics/gdp-topic/real-nominal-gdp-tutorial/v/example-calculating-real-gdp-with-a-deflator?utm_source=YT&utm_medium=Desc&utm_campaign=macroeconomics
Missed the previous lesson? https://www.khanacademy.org/economics-finance-domain/macroeconomics/gdp-topic/real-nominal-gdp-tutorial/v/real-gdp-and-nominal-gdp?utm_source=YT&utm_medium=Desc&utm_campaign=macroeconomics
Macroeconomics on Khan Academy: Topics covered in a traditional college level introductory macroeconomics 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.
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Using a home purchase to illustrate assets, liabilities and owner's equity. Created by Sal Khan.
Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/housing/home-equity-tutorial/v/more-on-balance-sheets-and-equity?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets
Finance and capital markets on Khan Academy: This old and badly drawn tutorial covers a topic essential to anyone planning to not live in the woods -- your personal balance sheet. Since homes are usually the biggest part of these personal balance sheets, we cover that too.
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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Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/ap-calculus-bc/bc
Using the recursive formula of a sequence to find its fifth term. Created by Sal Khan.
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/ap-calculus-bc/bc-series/bc-inf-sequences/e/convergence-and-divergence-of-sequences?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC
Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-bc/bc-series/bc-inf-sequences/v/identifying-sequence-convergence-divergence?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC
Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-bc/bc-series/bc-inf-sequences/v/term-of-recursive-sequence?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-
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We're thinking about the probability of rolling doubles on a pair of dice. Let's create a grid of all possible outcomes.
Watch the next lesson: https://www.khanacademy.org/math/precalculus/prob_comb/independent_events_precalc/v/lebron-asks-about-the-chances-of-making-10-free-throws?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus
Missed the previous lesson?
https://www.khanacademy.org/math/precalculus/prob_comb/independent_events_precalc/v/getting-at-least-one-heads?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.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Precalculus channel:
https://www.youtube.com/channe....l/UCBeHztHRWuVvnlwm2
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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/calculus-all-old/
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/differential-calculus/taking-derivatives/derivative_intro/e/tangent-slope-is-limiting-value-of-secant-slope?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus
Watch the next lesson: https://www.khanacademy.org/math/differential-calculus/taking-derivatives/derivative_intro/v/tangent-slope-as-limiting-value-of-secant-slope-example-2?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus
Missed the previous lesson?
https://www.khanacademy.org/math/differential-calculus/taking-derivatives/derivative_intro/v/calculus-derivatives-1-new-hd-version?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/ma....th/algebra/x2f8bb115
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra2/systems_eq_ineq/systems_tutorial_precalc/e/systems_of_equations_with_substitution?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Watch the next lesson: https://www.khanacademy.org/math/algebra2/systems_eq_ineq/systems_tutorial_precalc/v/inconsistent-systems-of-equations?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/systems_eq_ineq/systems_tutorial_precalc/v/solving-systems-with-substitution?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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Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/vectors/e/scaling_vectors?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/vectors/v/multiplying-vector-by-scalar?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/vectors/v/real-coordinate-spaces?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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Finding the solid of revolution (constructed by revolving around the x-axis) using the disc method. Created by Sal Khan.
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-definite-integrals/ab-disk-method/e/the-disk-method?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-definite-integrals/ab-disk-method/v/generalizing-disc-method-around-x-axis?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-definite-integrals/ab-horizontal-area/v/area-between-two-functions-of-y?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
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/sc....ience/ap-biology/cel
Mitosis is how cells divide! Learn what happens in all the phases of mitosis: prophase, metaphase, anaphase, and telophase.
Watch the next lesson: https://www.khanacademy.org/test-prep/mcat/cells/cellular-division/v/comparing-mitosis-and-meiosis?utm_source=YT&utm_medium=Desc&utm_campaign=mcat
Missed the previous lesson? https://www.khanacademy.org/test-prep/mcat/cells/cellular-division/v/interphase?utm_source=YT&utm_medium=Desc&utm_campaign=mcat
MCAT on Khan Academy: Go ahead and practice some passage-based questions!
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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Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ec....onomics-finance-doma
Thinking about different markets that are in-between monopolies and perfect competition
Watch the next lesson: https://www.khanacademy.org/economics-finance-domain/microeconomics/perfect-competition-topic/monopolistic-competition-oligop/v/monopolistic-competition-and-economic-profit?utm_source=YT&utm_medium=Desc&utm_campaign=microeconomics
Missed the previous lesson? https://www.khanacademy.org/economics-finance-domain/microeconomics/perfect-competition-topic/monopolies-tutorial/v/review-of-revenue-and-cost-graphs-for-a-monopoly-1?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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Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/probability/random-variables-topic/random_variables_prob_dist/e/constructing-probability-distributions?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics
Watch the next lesson: https://www.khanacademy.org/math/probability/random-variables-topic/random_variables_prob_dist/v/probability-density-functions?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics
Missed the previous lesson?
https://www.khanacademy.org/math/probability/random-variables-topic/random_variables_prob_dist/v/discrete-and-continuous-random-variables?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics
Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predictions, testing, and analyzing. Our lives are full of probabilities! Statistics is related to probability because much of the data we use when determining probable outcomes comes from our understanding of statistics. In these tutorials, we will cover a range of topics, some which include: independent events, dependent probability, combinatorics, hypothesis testing, descriptive statistics, random variables, probability distributions, regression, and inferential statistics. So buckle up and hop on for a wild ride. We bet you're going to be challenged AND love it!
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 Probability and Statistics channel:
https://www.youtube.com/channe....l/UCRXuOXLW3LcQLWvxb
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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/differential-equa
Introduction to first order homogenous equations.
Watch the next lesson: https://www.khanacademy.org/math/differential-equations/first-order-differential-equations/homogeneous-equations/v/first-order-homogenous-equations-2?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialEquations
Missed the previous lesson?
https://www.khanacademy.org/math/differential-equations/first-order-differential-equations/exact-equations/v/integrating-factors-2?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/ap-calculus-ab/ab
Who knows, you may end up running a shoe factory one day. So it might not be a bad idea to know how to maximize profits. Created by Sal Khan.
Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-derivatives/ab-optimization/v/minimizing-the-cost-of-a-storage-container?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-optimization/v/optimizing-box-volume-analytically?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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The area under a curve is commonly approximated using rectangles (e.g. left, right, and midpoint Riemann sums), but it can also be approximated by trapezoids. Trapezoidal sums actually give a better approximation than rectangular sums. Created by Sal Khan.
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/ap-calculus-ab/ab-accumulation-riemann-sums/ab-def-integral/e/evaluating-a-definite-integral-from-a-graph?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-accumulation-riemann-sums/ab-summation-notation/v/sigma-notation-sum?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-accumulation-riemann-sums/ab-midpoint-trapezoid/v/midpoint-sums?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/functions_and_graphs/piecewise-functions-tutorial/e/graphs-of-absolute-value-functions?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/absolute-value-graphing-exercise-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/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
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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
This example of combining like terms in an expression gets a little hairy. Listen closely.
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra/introduction-to-algebra/manipulating-expressions/e/combining_like_terms_1?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Watch the next lesson: https://www.khanacademy.org/math/algebra/introduction-to-algebra/manipulating-expressions/v/combining-like-terms-and-the-distributive-property?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Missed the previous lesson?
https://www.khanacademy.org/math/algebra/introduction-to-algebra/manipulating-expressions/v/combining-like-terms-2?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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