Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/sc....ience/physics/work-a

Work needed to compress a spring is the same thing as the potential energy stored in the compressed spring. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/science/physics/work-and-energy/hookes-law/v/spring-potential-energy-example-mistake-in-math?utm_source=YT&utm_medium=Desc&utm_campaign=physics

Missed the previous lesson? https://www.khanacademy.org/science/physics/work-and-energy/hookes-law/v/intro-to-springs-and-hooke-s-law?utm_source=YT&utm_medium=Desc&utm_campaign=physics

Physics on Khan Academy: Physics is the study of the basic principles that govern the physical world around us. We'll start by looking at motion itself. Then, we'll learn about forces, momentum, energy, and other concepts in lots of different physical situations. To get the most out of physics, you'll need a solid understanding of algebra and a basic understanding of trigonometry.

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

Subscribe to Khan Academy’s Physics channel: https://www.youtube.com/channe....l/UC0oGarQW2lE5PxhGo
Subscribe to Khan Academy: https://www.youtube.com/subscr....iption_center?add_us

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/ap-calculus-ab/ab

With all the storage you might have to handle for your shoe factory, I bet you'd also like to be able to minize the cost of storage. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-derivatives/ab-optimization/v/expression-for-combined-area-of-triangle-and-square?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-optimization/v/optimizing-profit-at-a-shoe-factory?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.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channe....l/UCyoj0ZF4uw8VTFbml
Subscribe to Khan Academy: https://www.youtube.com/subscr....iption_center?add_us

Worked example that thinks about the relationship between an arc length and the angle that is subtended by the arc.

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/radians_tutorial/e/cc-radians-and-arc-length?utm_source=YT&utm_medium=Desc&utm_campaign=Trigonometry

Watch the next lesson: https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/radians_tutorial/v/we-converting-degrees-to-radians?utm_source=YT&utm_medium=Desc&utm_campaign=Trigonometry

Missed the previous lesson?
https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/radians_tutorial/v/ratio-between-cocentric-arcs?utm_source=YT&utm_medium=Desc&utm_campaign=Trigonometry

Trigonometry on Khan Academy: Big, fancy word, right? Don't be fooled. Looking at the prefix, tri-, you could probably assume that trigonometry ("trig" as it's sometimes called) has something to do with triangles. You would be right! Trig is the study of the properties of triangles. Why is it important? It's used in measuring precise distances, particularly in industries like satellite systems and sciences like astronomy. It's not only space, however. Trig is present in architecture and music, too. Now you may wonder...how is knowing the measurement and properties of triangles relevant to music?? THAT is a great question. Maybe you'll learn the answer from us in these tutorials!

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

Subscribe to Khan Academy’s Trigonometry channel:
https://www.youtube.com/channe....l/UCYQSs1lFJZKpyqNQQ
Subscribe to Khan Academy: https://www.youtube.com/subscr....iption_center?add_us

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/cc-sixth-grade-ma

It's nice to practice conversion problems, but how about applying our new knowledge of percentages to a real life problem like recycling? Hint: don't forget your long division!

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/percent-intro-pre-alg/e/finding_percents?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/percent-intro-pre-alg/v/identifying-percent-amount-and-base?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/percent-intro-pre-alg/v/finding-percentages-example?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!

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

Subscribe to KhanAcademy’s Pre-Algebra channel:: https://www.youtube.com/channe....l/UCIMlYkATtXOFswVoC
Subscribe to KhanAcademy: https://www.youtube.com/subscr....iption_center?add_us

This time, the cross section of our solid is given as the area between two curves.

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-definite-integrals/ab-vol-cross-sections/e/volumes-of-solids-of-known-cross-section?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-disk-method/v/disk-method-around-x-axis?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-definite-integrals/ab-vol-cross-sections/v/volume-solid-semicircle-cross-section?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.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channe....l/UCyoj0ZF4uw8VTFbml
Subscribe to Khan Academy: https://www.youtube.com/subscr....iption_center?add_us

Worked example where we walk through finding the major trig ratios

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/trigonometry/basic-trigonometry/reciprocal-trig-functions/e/reciprocal_trig_funcs?utm_source=YT&utm_medium=Desc&utm_campaign=Trigonometry

Watch the next lesson: https://www.khanacademy.org/math/trigonometry/basic-trigonometry/reciprocal-trig-functions/v/example-using-trig-to-solve-for-missing-information?utm_source=YT&utm_medium=Desc&utm_campaign=Trigonometry

Missed the previous lesson?
https://www.khanacademy.org/math/trigonometry/basic-trigonometry/trig-application-problems/v/figuring-out-coordinate-of-bended-figure-using-trig?utm_source=YT&utm_medium=Desc&utm_campaign=Trigonometry

Trigonometry on Khan Academy: Big, fancy word, right? Don't be fooled. Looking at the prefix, tri-, you could probably assume that trigonometry ("trig" as it's sometimes called) has something to do with triangles. You would be right! Trig is the study of the properties of triangles. Why is it important? It's used in measuring precise distances, particularly in industries like satellite systems and sciences like astronomy. It's not only space, however. Trig is present in architecture and music, too. Now you may wonder...how is knowing the measurement and properties of triangles relevant to music?? THAT is a great question. Maybe you'll learn the answer from us in these tutorials!

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

Subscribe to Khan Academy’s Trigonometry channel:
https://www.youtube.com/channe....l/UCYQSs1lFJZKpyqNQQ
Subscribe to Khan Academy: https://www.youtube.com/subscr....iption_center?add_us

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ec....onomics-finance-doma

How the equilibrium price or quantity might change due to changes in supply or demand
More free lessons at: http://www.khanacademy.org/video?v=NgPqyM3I_8o

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/algebra2/x2ec2f6f


Trigonometry on Khan Academy: Big, fancy word, right? Don't be fooled. Looking at the prefix, tri-, you could probably assume that trigonometry ("trig" as it's sometimes called) has something to do with triangles. You would be right! Trig is the study of the properties of triangles. Why is it important? It's used in measuring precise distances, particularly in industries like satellite systems and sciences like astronomy. It's not only space, however. Trig is present in architecture and music, too. Now you may wonder...how is knowing the measurement and properties of triangles relevant to music?? THAT is a great question. Maybe you'll learn the answer from us in these tutorials!

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

Subscribe to Khan Academy’s Trigonometry channel:
https://www.youtube.com/channe....l/UCYQSs1lFJZKpyqNQQ
Subscribe to Khan Academy: https://www.youtube.com/subscr....iption_center?add_us

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/cc-seventh-grade-

In this video, we think about what |a-b| really means, and we verify that |a-b| = |b-a| by looking at an example.

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-add-and-subtract/cc-7th-absolute-value/e/absolute-value-to-find-distance?utm_source=YT&utm_medium=Desc&utm_campaign=7thgrade

Watch the next lesson: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-add-and-subtract/cc-7th-absolute-value/v/interpreting-absolute-value-as-distance?utm_source=YT&utm_medium=Desc&utm_campaign=7thgrade

Missed the previous lesson?
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-add-and-subtract/cc-7th-add-sub-word-problems-w-negatives/v/interpreting-negative-number-statements?utm_source=YT&utm_medium=Desc&utm_campaign=7thgrade

Grade 7th on Khan Academy: 7th grade takes much of what you learned in 6th grade to an entirely new level. In particular, you'll now learn to do everything with negative numbers (we're talking everything--adding, subtracting, multiplying, dividing, fractions, decimals... everything!). You'll also take your algebraic skills to new heights by tackling two-step equations. 7th grade is also when you start thinking about probability (which is super important for realizing that casinos and lotteries are really just ways of taking money away from people who don't know probability) and dig deeper into the world of data and statistics. Onward! (Content was selected for this grade level based on a typical curriculum in the United States.)

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

Subscribe to Khan Academy à ªs 7th grade channel:
https://www.youtube.com/channe....l/UCzKsXcrLSLDG7VN1L
Subscribe to Khan Academy: https://www.youtube.com/subscr....iption_center?add_us

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/geometry/cc-geometry-circles/central-inscribed-circumscribed/e/central--inscribed--and-circumscribed-angles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/cc-geometry-circles/central-inscribed-circumscribed/v/hypotenuse-of-right-triangle-inscribed-in-circle?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/cc-geometry-circles/central-inscribed-circumscribed/v/measure-of-circumscribed-angle?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

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

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channe....l/UCD3OtKxPRUFw8kzYl
Subscribe to Khan Academy: https://www.youtube.com/subscr....iption_center?add_us

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/geometry/cc-geometry-circles/equation-of-a-circle/e/pythagorean-theorem-and-the-equation-of-a-circle?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Watch the next lesson: https://www.khanacademy.org/math/geometry/cc-geometry-circles/equation-of-a-circle/v/pythagorean-theorem-and-radii-of-circles?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/cc-geometry-circles/central-inscribed-circumscribed/v/hypotenuse-of-right-triangle-inscribed-in-circle?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

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

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channe....l/UCD3OtKxPRUFw8kzYl
Subscribe to Khan Academy: https://www.youtube.com/subscr....iption_center?add_us

Myelin sheaths, nodes of Ranvier, and saltatory conduction in neurons. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/science/health-and-medicine/human-anatomy-and-physiology/nervous-system-introduction/v/synapse-structure?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Missed the previous lesson? https://www.khanacademy.org/science/health-and-medicine/human-anatomy-and-physiology/nervous-system-introduction/v/electrotonic-action-potential?utm_source=YT&utm_medium=Desc&utm_campaign=healthandmedicine

Health & Medicine on Khan Academy: No organ quite symbolizes love like the heart. One reason may be that your heart helps you live, by moving ~5 liters (1.3 gallons) of blood through almost 100,000 kilometers (62,000 miles) of blood vessels every single minute! It has to do this all day, everyday, without ever taking a vacation! Now that is true love. Learn about how the heart works, how blood flows through the heart, where the blood goes after it leaves the heart, and what your heart is doing when it makes the sound “Lub Dub.”

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.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Health & Medicine channel: https://www.youtube.com/channe....l/UC1RAowgA3q8Gl7exS
Subscribe to Khan Academy: https://www.youtube.com/subscr....iption_center?add_us

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/algebra-home/alg-


Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!

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

Subscribe to KhanAcademy’s Pre-Algebra channel:: https://www.youtube.com/channe....l/UCIMlYkATtXOFswVoC
Subscribe to KhanAcademy: https://www.youtube.com/subscr....iption_center?add_us

What happens when you add zinc to a solution of copper sulfate? Identifying the half reactions to see what got oxidized and reduced.

Watch the next lesson: https://www.khanacademy.org/science/chemistry/oxidation-reduction/batter-galvanic-voltaic-cell/v/galvanic-cell-voltaic-cell?utm_source=YT&utm_medium=Desc&utm_campaign=chemistry

Missed the previous lesson? https://www.khanacademy.org/science/chemistry/oxidation-reduction/redox-oxidation-reduction/v/redox-titration?utm_source=YT&utm_medium=Desc&utm_campaign=chemistry

Chemistry on Khan Academy: Did you know that everything is made out of chemicals? Chemistry is the study of matter: its composition, properties, and reactivity. This material roughly covers a first-year high school or college course, and a good understanding of algebra is helpful.

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

Subscribe to Khan Academy’s Chemistry channel: https://www.youtube.com/channe....l/UCyEot66LrwWFEMONv
Subscribe to Khan Academy: https://www.youtube.com/subscr....iption_center?add_us

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/ap-calculus-ab/ab

Sal introduces the concept of concavity, what it means for a graph to be "concave up" or "concave down," and how this relates to the second derivative of a function. Created by Sal Khan.

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/ap-calculus-ab/ab-derivatives-analyze-functions/ab-concavity/e/recognizing_concavity?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-derivatives-analyze-functions/ab-concavity/v/recognizing-concavity-exercise?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-derivatives-analyze-functions/ab-find-abs-extrema/v/absolute-extrema-on-entire-domain?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.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channe....l/UCyoj0ZF4uw8VTFbml
Subscribe to Khan Academy: https://www.youtube.com/subscr....iption_center?add_us

Sal helps our favorite Sesame Street character understand how we elect the president of the United States. Check out more lessons about American civics on Khan Academy at http://www.khanacademy.org. And vote November 3 if you’re eligible!

View more lessons or practice this subject at https://www.khanacademy.org/humanities/us-government-and-civics/american-civics-parent/american-civics/v/sal-teaches-grover-about-the-electoral-college?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!

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

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/ap-calculus-ab/ab

Showing that the limit of sin(x)/x as x approaches 0 is equal to 1. If you find this fact confusing, you've reached the right place!

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-derivative-rules/ab-derivtive-rules-opt-vids/v/1-cosx-over-x-as-x-approaches-0?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-derivative-rules/ab-derivtive-rules-opt-vids/v/proof-d-dx-sqrt-x?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.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channe....l/UCyoj0ZF4uw8VTFbml
Subscribe to Khan Academy: https://www.youtube.com/subscr....iption_center?add_us

Learn how a zygote, the single cell produced by fertilization, divides by mitosis to produce all the tissues of the human body (including germ cells, which can undergo meiosis to make sperm and eggs). Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/test-prep/mcat/cells/cellular-division/v/interphase?utm_source=YT&utm_medium=Desc&utm_campaign=mcat

Missed the previous lesson? https://www.khanacademy.org/test-prep/mcat/cells/cellular-division/v/fertilization-haploid-diploid-gamete-zygote-homologous?utm_source=YT&utm_medium=Desc&utm_campaign=mcat

MCAT on Khan Academy: Go ahead and practice some passage-based questions!

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

Subscribe to Khan Academy’s MCAT channel: https://www.youtube.com/channe....l/UCDkK5wqSuwDlJ3_nl
Subscribe to Khan Academy: https://www.youtube.com/subscr....iption_center?add_us

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/cc-seventh-grade-

Sometimes when you convert a fraction to a decimal you have to do some long division and rounding.

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/decimal-to-fraction-pre-alg/e/converting_fractions_to_decimals?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/decimal-to-fraction-pre-alg/v/converting-fractions-to-decimals-ex2?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/dividing-decimals-pre-alg/v/dividing-decimal?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!

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

Subscribe to KhanAcademy’s Pre-Algebra channel:: https://www.youtube.com/channe....l/UCIMlYkATtXOFswVoC
Subscribe to KhanAcademy: https://www.youtube.com/subscr....iption_center?add_us

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/sc....ience/electrical-eng

Finding Fourier coefficients for square wave

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/ap-statistics/den

Discussion of how "normal" a distribution might be

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/probability/statistics-inferential/normal_distribution/e/empirical_rule?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Watch the next lesson: https://www.khanacademy.org/math/probability/statistics-inferential/normal_distribution/v/ck12-org-normal-distribution-problems-empirical-rule?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Missed the previous 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

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.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Probability and Statistics channel:
https://www.youtube.com/channe....l/UCRXuOXLW3LcQLWvxb
Subscribe to KhanAcademy: https://www.youtube.com/subscr....iption_center?add_us

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/ap-calculus-bc/bc

Sometimes the value of an infinite integral is, well, infinite. Created by Sal Khan.

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/ap-calculus-bc/bc-antiderivatives-ftc/bc-improper-integrals/e/improper-integrals?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-bc/bc-antiderivatives-ftc/bc-u-substitution/v/u-substitution?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-bc/bc-antiderivatives-ftc/bc-improper-integrals/v/improper-integral-with-two-infinite-bounds?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC

AP Calculus BC on Khan Academy: Learn AP Calculus BC - everything from AP Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP Test

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.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy's AP Calculus BC channel: https://www.youtube.com/channe....l/UC5A2DBjjUVNz8axD-
Subscribe to Khan Academy: https://www.youtube.com/subscr....iption_center?add_us

What it means for triangles to be congruent

Watch the next lesson: https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/v/sss-to-show-a-radius-is-perpendicular-to-a-chord-that-it-bisects?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Missed the previous lesson?
https://www.khanacademy.org/math/geometry/congruent-triangles/transformations-congruence/v/another-example-of-rigid-transformations-for-congruence?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

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

Subscribe to Khan Academy’s Geometry channel:
https://www.youtube.com/channe....l/UCD3OtKxPRUFw8kzYl
Subscribe to Khan Academy: https://www.youtube.com/subscr....iption_center?add_us

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/ap-calculus-ab/ab

Washer method when rotating around a horizontal line that is not the x-axis. Created by Sal Khan.

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-definite-integrals/ab-washer-method/e/the-washer-method?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-washer-method/v/part-2-of-washer-for-not-axis-rotation?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-definite-integrals/ab-washer-method/v/generalizing-the-washer-method?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.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channe....l/UCyoj0ZF4uw8VTFbml
Subscribe to Khan Academy: https://www.youtube.com/subscr....iption_center?add_us

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/sc....ience/biology/human-


More free lessons at: http://www.khanacademy.org/video?v=YdBXHm3edL8