Uncontrolled systems always evolve toward more stable states—that is, toward more uniform energy distribution (e.g., water flows downhill, objects hotter than their surrounding environment cool down).
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https://www.youtube.com/watch?v=FPPv1mkRpKw
Note: All Khan Academy content is available for free at (www.khanacademy.org)
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.
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https://www.youtube.com/watch?v=_kbd6troMgA
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Using a position vector valued function to describe a curve or path
Watch the next lesson: https://www.khanacademy.org/math/multivariable-calculus/line_integrals_topic/position_vector_functions/v/derivative-of-a-position-vector-valued-function?utm_source=YT&utm_medium=Desc&utm_campaign=MultivariableCalculus
Missed the previous lesson?
https://www.khanacademy.org/math/multivariable-calculus/line_integrals_topic/line_integrals/v/line-integral-example-2-part-2?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.
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https://www.youtube.com/watch?v=sBldw95xMD4
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Exploring the normal distribution
Watch the next lesson: https://www.khanacademy.org/math/probability/statistics-inferential/normal_distribution/v/normal-distribution-excel-exercise?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics
Missed the previous lesson?
https://www.khanacademy.org/math/probability/regression/regression-correlation/v/covariance-and-the-regression-line?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.
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https://www.youtube.com/watch?v=hgtMWR3TFnY
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Watch Sal work through a basic Structure in expressions problem.
Watch the next lesson: https://www.khanacademy.org/test-prep/new-sat/new-sat-math/new-sat-passport-advanced-mathematics/v/sat-math-p4-harder?utm_source=YT&utm_medium=Desc&utm_campaign=NewSAT
Missed the previous lesson?
https://www.khanacademy.org/test-prep/new-sat/new-sat-math/new-sat-passport-advanced-mathematics/v/sat-math-p8-harder?utm_source=YT&utm_medium=Desc&utm_campaign=NewSAT
New SAT (starting March 2016) on Khan Academy: Practice all of the skills you’ll need for the new SAT. We also have four official practice exams from College Board. The October 2015 PSAT is in the style of the new SAT.
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=b_dDoAbqp1M
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Solving systems by elimination 2
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-systems-topic/cc-8th-systems-elimination/e/systems_of_equations_with_elimination_0.5?utm_source=YT&utm_medium=Desc&utm_campaign=8thgrade
Watch the next lesson: https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-systems-topic/cc-8th-systems-elimination/v/addition-elimination-method-1?utm_source=YT&utm_medium=Desc&utm_campaign=8thgrade
Missed the previous lesson?
https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-systems-topic/cc-8th-systems-elimination/v/solving-systems-by-elimination?utm_source=YT&utm_medium=Desc&utm_campaign=8thgrade
8th grade on Khan Academy: 8th grade is all about tackling the meat of algebra and getting exposure to some of the foundational concepts in geometry. If you get this stuff (and you should because you're incredibly persistent), the rest of your life will be easy. Okay, maybe not your whole life, but at least your mathematical life. Seriously, if you really get the equations and functions stuff we cover here, most of high school will feel intuitive, even relaxing. (Content was selected for this grade level based on a typical curriculum in the United States.)
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https://www.youtube.com/watch?v=Y6JsEja15Vk
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Watch Sal work through a basic Key features of graphs problem.
Watch the next lesson: https://www.khanacademy.org/test-prep/new-sat/new-sat-math/new-sat-problem-solving-data-analysis/v/sat-math-q5-harder?utm_source=YT&utm_medium=Desc&utm_campaign=NewSAT
Missed the previous lesson?
https://www.khanacademy.org/test-prep/new-sat/new-sat-math/new-sat-problem-solving-data-analysis/v/sat-math-q4-harder?utm_source=YT&utm_medium=Desc&utm_campaign=NewSAT
New SAT (starting March 2016) on Khan Academy: Practice all of the skills you’ll need for the new SAT. We also have four official practice exams from College Board. The October 2015 PSAT is in the style of the new SAT.
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=w3NwqsQuWZE
Note: All Khan Academy content is available for free at (www.khanacademy.org)
What happens when the characteristic equations has complex roots?!
Watch the next lesson: https://www.khanacademy.org/math/differential-equations/second-order-differential-equations/complex-roots-characteristic-equation/v/complex-roots-of-the-characteristic-equations-2?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialEquations
Missed the previous lesson?
https://www.khanacademy.org/math/differential-equations/second-order-differential-equations/linear-homogeneous-2nd-order/v/2nd-order-linear-homogeneous-differential-equations-4?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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https://www.youtube.com/watch?v=6xEO4BeawzA
Note: All Khan Academy content is available for free at (www.khanacademy.org)