The solution of the general differential equation dy/dx=ky (for some k) is C_e__ (for some C). See how this is derived and used for finding a particular solution to a differential equation.
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-equations/ab-exp-models/e/exponential-model-equations?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-applying-def-integrals/v/area-under-rate-net-change?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-equations/ab-exp-models/v/particular-solution-given-initial-conditions-for-population?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.
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https://www.youtube.com/watch?v=pRuwcphjJeg
Note: All Khan Academy content is available for free at (www.khanacademy.org)
More free lessons at: http://www.khanacademy.org/video?v=naRUWPvsQbQ
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https://www.youtube.com/watch?v=naRUWPvsQbQ
Note: All Khan Academy content is available for free at (www.khanacademy.org)
A deep dive into the Fourth Amendment, which protects citizens from unreasonable searches and seizures. In this video, Kim discusses the Fourth Amendment with scholars Orin Kerr and Tracey Meares.
To read more about the Fourth Amendment, 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/civil-liberties-and-civil-rights/amendments-balancing-individual-freedom-with-public-order-and-safety/v/the-fourth-amendment?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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https://www.youtube.com/watch?v=J92qYl6m_MI
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Chris describes being a software engineer at Khan Academy.
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https://www.youtube.com/watch?v=ZK5xa3M9EHo
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Sum of Logarithms with Same Base
Watch the next lesson: https://www.khanacademy.org/math/algebra2/logarithms-tutorial/logarithm_properties/v/using-multiple-logarithm-properties-to-simplify?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/logarithms-tutorial/logarithm_properties/v/logarithm-of-a-power?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.
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https://www.youtube.com/watch?v=pkGrXzakRFs
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Another example of figuring out the sine, cosine, and tangent of an angle in a right triangle
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https://www.youtube.com/watch?v=QS4r_mqs-rY
Note: All Khan Academy content is available for free at (www.khanacademy.org)
2010 IIT JEE Paper 1 #38 Hairy Trig and Algebra (Part 2)
More free lessons at: http://www.khanacademy.org/video?v=6t9ogglXNIM
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https://www.youtube.com/watch?v=6t9ogglXNIM
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Galvanic (or voltaic) cells use a thermodynamically favored redox reaction to generate an electric current. Each half-reaction takes place in a separate compartment, or half-cell, containing an electrode. The electrode where oxidation occurs is the anode, and the electrode where reduction occurs is the cathode. Electrons flow through a wire connecting the two half-cells. To complete the circuit, a salt bridge is used, which allows ions to move between the half-cell solutions. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:applications-of-thermodynamics/x2eef969c74e0d802:galvanic-voltaic-and-electrolytic-cells/v/galvanic-voltaic-cells
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
Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc
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https://www.youtube.com/watch?v=inXgVjz1BDQ
Note: All Khan Academy content is available for free at (www.khanacademy.org)
David Hu explains his role as a software engineer at Khan Academy.
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https://www.youtube.com/watch?v=kCWDf4jRKS8
Note: All Khan Academy content is available for free at (www.khanacademy.org)