Link to go to challenge: http://www.khanacademy.org/cs/puzzle-game-challenge/1418760249 ... https://www.youtube.com/watch?v=pnoShVR_XEc Note: All Khan Academy content is available for free at (www.khanacademy.org)

Use the Pythagorean theorem and proportional reasoning in context. View more lessons or practice this subject at https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-pyth-theorem . 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 ... https://www.youtube.com/watch?v=jVvpQAIrJ-o Note: All Khan Academy content is available for free at (www.khanacademy.org)

This is the more general form of a quadratic approximation for a scalar-valued multivariable function. It is analogous to a quadratic Taylor polynomial in the single-variable world. ... https://www.youtube.com/watch?v=ClFrIg0PpnM Note: All Khan Academy content is available for free at (www.khanacademy.org)

Showing that, unlike line integrals of scalar fields, line integrals over vector fields are path direction dependent Watch the next lesson: https://www.khanacademy.org/math/multivariable-calculus/line_integrals_topic/line_integrals_vectors/v/path-independence-for-line-integrals?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_vectors/v/scalar-field-line-integral-independent-of-path-direction?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. ... https://www.youtube.com/watch?v=fuSOY9r1R6w Note: All Khan Academy content is available for free at (www.khanacademy.org)