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
Learn how to use the Khan Academy number line widget.
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/cc-third-grade-math/cc-3rd-fractions-topic/cc-3rd-fractions-on-the-number-line/e/fractions_on_the_number_line_1?utm_source=YT&utm_medium=Desc&utm_campaign=3rdgrade
Watch the next lesson: https://www.khanacademy.org/math/cc-third-grade-math/cc-3rd-fractions-topic/cc-3rd-fractions-and-whole-numbers/v/different-ways-to-represent-1-as-a-fraction?utm_source=YT&utm_medium=Desc&utm_campaign=3rdgrade
Missed the previous lesson? https://www.khanacademy.org/math/cc-third-grade-math/cc-3rd-fractions-topic/cc-3rd-fractions-on-the-number-line/v/fractions-on-a-number-line?utm_source=YT&utm_medium=Desc&utm_campaign=3rdgrade
Grade 3rd on Khan Academy: We know you've been rocking through 2nd grade adding and subtracting all kinds of whole numbers (up to 2 digits, right?). That's awesome! In 3rd grade math we want you to start using bigger numbers and start multiplying and dividing, too. By the way, did you know that some numbers aren’t actually “whole?” They’re “partially whole.” We call them fractions! We want you to start playing around and having fun with those, too. There's also area, perimeter, and place value to be discovered. Whew. We have so much to do and can't wait to do it with you. Let's go!
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https://www.youtube.com/watch?v=xeoVPSBP9WI
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Nierria earns $75 for 4 hours of tutoring. How much does Nierria earn per hour of tutoring?
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https://www.youtube.com/watch?v=rpGGMSFO6Ks
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Lindsay finds the missing digit in an estimation problem by using a number line.
Practice this yourself on Khan Academy right now: https://www.khanacademy.org/math/cc-fourth-grade-math/cc-4th-place-value-rounding/cc-4th-rounding/e/rounding-whole-numbers-2
Watch the next lesson: https://www.khanacademy.org/math/cc-fourth-grade-math/cc-4th-decimals/cc-4th-decimals-intro/v/introduction-to-decimals
Missed the previous lesson? https://www.khanacademy.org/math/cc-fourth-grade-math/cc-4th-place-value-rounding/cc-4th-rounding/v/rounding-whole-numbers-3
4th grade math on Khan Academy: 4th grade is the time to start really fine-tuning your arithmetic skills. Not only will you be a multi-digit addition and subtraction rockstar, but you'll extend the multiplication and division that you started in 3rd grade to several digits. You'll also discover that you sometimes have something left over (called a "remainder") when you divide. In 3rd grade you learned what a fraction is. Now you'll start adding, subtracting, multiplying, and comparing them. You'll also see how they relate to decimals. On other fronts, you'll learn how to convert between different units (which is super important when comparing the size and speed of robot unicorns in different countries) and continue your journey thinking about various shapes in two dimensions. Some of the foundational concepts of geometry (like lines, rays and angles) also get introduced. As always, we'll round this out with a healthy dose of applied word problems and explorations of number patterns and properties (including the ideas of factors, multiples and prime numbers). The fun must not stop! (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=Hixy7TX-Nwo
Note: All Khan Academy content is available for free at (www.khanacademy.org)
When a tax is imposed on a market consumer and producer surplus are both reduced and that reduction becomes tax revenue. The incidence of a tax is the way in which a tax reduced consumer and producer surplus. In this video, learn how to identify areas representing tax incidence in a market graph.
AP(R) Microeconomics on Khan Academy: Microeconomics is the study of individual decisionmakers in an economy, such as people, households, and firms. Learn how markets work, how incentives drive decisionmaking, and how market structure influences market outcomes. We hit the traditional topics from an AP Microeconomics course, including basic economic concepts, markets, production and costs, profit maximization perfect competition, imperfectly competitive market structures, game theory, factor markets, and income inequality.
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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https://www.youtube.com/watch?v=1-8O5AHIb6s
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Another example applying Green's Theorem
Watch the next lesson: https://www.khanacademy.org/math/multivariable-calculus/line_integrals_topic/2d_divergence_theorem/v/constructing-a-unit-normal-vector-to-a-curve?utm_source=YT&utm_medium=Desc&utm_campaign=MultivariableCalculus
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https://www.khanacademy.org/math/multivariable-calculus/line_integrals_topic/greens_theorem/v/green-s-theorem-example-1?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=sSyPAAyL8nQ
Note: All Khan Academy content is available for free at (www.khanacademy.org)
163-166, pg. 174. Created by Sal Khan.
Watch the next lesson: https://www.khanacademy.org/test-prep/gmat/problem-solving/v/gmat-math-33?utm_source=YT&utm_medium=Desc&utm_campaign=GMAT
Missed the previous lesson? https://www.khanacademy.org/test-prep/gmat/problem-solving/v/gmat-math-31?utm_source=YT&utm_medium=Desc&utm_campaign=GMAT
GMAT on Khan Academy: Sal works through the 249 problem solving questions in chapter 5 of the the 11th edition of the official GMAC GMAT Review (ISBN Number: 0-9765709-0-4 published in 2005)
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=uG2VpBYd-Hk
Ordering numbers using place value
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https://www.youtube.com/watch?v=3phL9GRSY3g
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Another example of solving a system of linear equations by putting an augmented matrix into reduced row echelon form
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/matrices_elimination/v/matrices-reduced-row-echelon-form-3?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
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https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/matrices_elimination/v/matrices-reduced-row-echelon-form-1?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.
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https://www.youtube.com/watch?v=lP1DGtZ8Wys
Note: All Khan Academy content is available for free at (www.khanacademy.org)