In this worked example, Sal finds the area of the image of a rectangle after a transformation defined by a given matrix. This is done by finding the area of the pre-image and multiplying by the matrix's determinant.
...
https://www.youtube.com/watch?v=aVuCoUxt3vc
Note: All Khan Academy content is available for free at (www.khanacademy.org)
The range is the difference between the largest and smallest numbers. The midrange is the average of the largest and smallest number. Practice with this problem.
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/probability/descriptive-statistics/box-and-whisker-plots/e/analyzing-data-with-box-plots?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics
Watch the next lesson: https://www.khanacademy.org/math/probability/descriptive-statistics/variance_std_deviation/v/range-variance-and-standard-deviation-as-measures-of-dispersion?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics
Missed the previous lesson?
https://www.khanacademy.org/math/probability/descriptive-statistics/box-and-whisker-plots/v/constructing-a-box-and-whisker-plot?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics
...
https://www.youtube.com/watch?v=7DtWXEPB_AI
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Learn how to evaluate an expression with variables using a technique called substitution (or "plugging in").
Watch the next lesson: https://www.khanacademy.org/math/algebra/introduction-to-algebra/variable-and-expressions/v/evaluate-a-formula-using-substitution?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Missed the previous lesson?
https://www.khanacademy.org/math/algebra/introduction-to-algebra/variable-and-expressions/v/why-aren-t-we-using-the-multiplication-sign?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.
...
https://www.youtube.com/watch?v=AJNDeVt9UOo
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Why we study differential calculus. Created by Sal Khan.
Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-derivative-intro/ab-derivative-intuition/v/derivative-as-a-concept?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-limits-opt-vids/v/proving-a-limit-using-epsilon-delta-definition?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.
...
https://www.youtube.com/watch?v=EKvHQc3QEow
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Sal finds the second derivative of y=6/x_. Second derivative is the derivative of the derivative of y.
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/ap-calculus-ab/ab-derivatives-advanced/ab-second-derivatives/e/second-derivatives?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-derivatives-advanced/ab-implicit-diff/v/implicit-differentiation-1?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-derivatives-advanced/ab-diff-mul-rules/v/applying-chain-rule-twice?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.
...
https://www.youtube.com/watch?v=WC5VYKI807Q
Note: All Khan Academy content is available for free at (www.khanacademy.org)
In this example, Sal takes two vectors given by magnitude and direction, and finds the magnitude and direction of their sum.
...
https://www.youtube.com/watch?v=yFPfO_eHJdY
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Learn to add 23 + 45 thinking about place value.
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/early-math/cc-early-math-add-sub-100/cc-early-math-add-subtract-100/e/addition_3?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath
Watch the next lesson: https://www.khanacademy.org/math/early-math/cc-early-math-add-sub-100/cc-early-math-add-subtract-100/v/addition-with-regrouping?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath
Missed the previous lesson?
https://www.khanacademy.org/math/early-math/cc-early-math-add-sub-100/cc-early-math-add-ones-tens/v/understanding-place-value-while-adding-tens?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath
Early Math on Khan Academy: Math begins with counting. It's the most important skill we learn in our early years and becomes the foundation for all other math concepts. Once we can count, we can add, subtract, and measure the world around us. Shortly thereafter, we can learn about place values, plots, graphs, time, money, and shapes. These early math skills are presented in this subject's tutorials in a straightforward, understandable, and (dare we say it) fun way!
...
https://www.youtube.com/watch?v=K5rmfHlHy20
Note: All Khan Academy content is available for free at (www.khanacademy.org)