This Pre-Algebra video tutorial explains the process of simplifying algebraic fractions with exponents and variables. It discusses how to simplify algebraic expressions with powers & exponents by factoring.

_______________________________________________________________________________________________
Algebra For Beginners: https://www.youtube.com/watch?v=MHeirBPOI6w
Algebra 2 - Basic Introduction: https://www.youtube.com/watch?v=i6sbjtJjJ-A
Algebra 1 Review Study Guide: https://www.youtube.com/watch?v=TbJ5gqLRpeM
Algebra Final Exam Review: https://www.youtube.com/watch?v=U0Y8nSmEpNM
________________________________________________________________________________________________
Basic Math Review: https://www.youtube.com/watch?v=T_6Mq6PWoGc
How To Evaluate Algebraic Expressions: https://www.youtube.com/watch?v=-VCUcRtQjx8
Percentages Made Easy: https://www.youtube.com/watch?v=WYWPuG-8U5Q
Fractions - Basic Introduction: https://www.youtube.com/watch?v=GvLIEiqxS6s
How To Solve Linear Equations: https://www.youtube.com/watch?v=7DPWeBszNSM
Linear Equations - Test Review: https://www.youtube.com/watch?v=Ft2_QtXAnh8
How To Factor Trinomials: https://www.youtube.com/watch?v=-4jANGlJRSY
Systems of Linear Equations - 2 Variables: https://www.youtube.com/watch?v=oKqtgz2eo-Y
Quadratic Equations - Test Review: https://www.youtube.com/watch?v=fFFA7Q4eVuY
________________________________________________________________________________________________
Fundamental Theorem of Algebra: https://www.youtube.com/watch?v=cAfRgqEOURw
Rational Expressions - Basic Intro: https://www.youtube.com/watch?v=0Gq3uw2p6fA
Simplifying Rational Expressions: https://www.youtube.com/watch?v=uVpsz-xpnPo
Multiplying Rational Expressions: https://www.youtube.com/watch?v=RROSgr4oXjU
Dividing Rational Expressions: https://www.youtube.com/watch?v=rMVOdIDNjpA
Adding & Subtracting Rational Expressions: https://www.youtube.com/watch?v=WWwG2uh4OUE
Rational Expressions - Unlike Denominators: https://www.youtube.com/watch?v=1KGVwaUhR-s
Simplifying Complex Rational Expressions: https://www.youtube.com/watch?v=ifDEetTq8bM
How To Solve Rational Equations: https://www.youtube.com/watch?v=1fR_9ke5-n8
Rational Equations - Extraneous Solutions: https://www.youtube.com/watch?v=PvMYq9JD724
Graphing Rational Functions: https://www.youtube.com/watch?v=bWVhwYdSnfk
Horizontal and Slant Asymptotes: https://www.youtube.com/watch?v=kvhpu1TkSjI
Finding Rational Functions Given 2 Points: https://www.youtube.com/watch?v=ODs3t1vX1GY
Rational Functions - X and Y Intercepts: https://www.youtube.com/watch?v=ebpEDR4-Q3Y
Graphing Advanced Rational Functions: https://www.youtube.com/watch?v=GxynsEIvjRA
______________________________________________________________________________________________
Square Roots and Cube Roots: https://www.youtube.com/watch?v=IWzPle0KDPo
Simplifying Radical Expressions: https://www.youtube.com/watch?v=U7AXF75rC00
Multiplying Radical Expressions: https://www.youtube.com/watch?v=i0TMNeOwpSg
Adding & Subtracting Radicals: https://www.youtube.com/watch?v=83wXAgwcWH0
Simplifying Cube Root Expressions: https://www.youtube.com/watch?v=VdUNTsf14qs
Rationalizing The Denominator: https://www.youtube.com/watch?v=5j8a75aHaSE
Multiplying Radicals With Different Indices: https://www.youtube.com/watch?v=onOQMAcnj8U
How To Solve Radical Equations: https://www.youtube.com/watch?v=0gicD4STzpg
Solving Equations With Cube Roots: https://www.youtube.com/watch?v=mg8aS58vsN8
Solving Complex Radical Equations: https://www.youtube.com/watch?v=laEeUSZr83s
How To Graph Radical Functions: https://www.youtube.com/watch?v=8t9_IXFzH_M
Domain of Radical Functions: https://www.youtube.com/watch?v=fOlon31vEU4
How To Graph Cube Root Functions: https://www.youtube.com/watch?v=qxR6p_xDnho
Radical Expressions - Test Review: https://www.youtube.com/watch?v=wOcc5EoOojE
______________________________________________________________________________________________
Imaginary Numbers - Basic Intro: https://www.youtube.com/watch?v=vRJqPo_zcnQ

Crash Course Black American History explores arts and culture! Learn about the art, literature, and political thought innovations of the Harlem Renaissance, the literature of Toni Morrison and Zora Neale Hurston, the origins of rap and hip-hop, and the poetry of Phillis Wheatley.

***
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Thanks to the following patrons for their generous monthly contributions that help keep Crash Course free for everyone forever:
DL Singfield, Ken Davidian, Stephen Akuffo, Toni Miles, Steve Segreto, Kyle & Katherine Callahan, Laurel Stevens, Burt Humburg, Perry Joyce, Scott Harrison, Mark & Susan Billian, Alan Bridgeman, Breanna Bosso, Matt Curls, Jennifer Killen, Jon Allen, Sarah & Nathan Catchings, team dorsey, Bernardo Garza, Trevin Beattie, Eric Koslow, Indija-ka Siriwardena, Jason Rostoker, Siobhán, Ken Penttinen, Nathan Taylor, Barrett & Laura Nuzum, Les Aker, William McGraw, Vaso, ClareG, Rizwan Kassim, Constance Urist, Alex Hackman, Pineapples of Solidarity, Katie Dean, Stephen McCandless, Thomas Greinert, Wai Jack Sin ,Ian Dundore, Caleb Weeks

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🍎 Sing a fun fruit song (with pictures!) with your kids and learn the names of different fruits in English! ✨ Animated friends Lucas, Ruby, Lily, and Brody present a fantastic and active way to educate children about apples 🍎, bananas 🍌, grapes 🍇, strawberries 🍓, oranges 🍊, and other fruits 🍉🥝🍍🍒🥑, all in an entertaining environment. 🤩 Kids will love singing along with the lyrics, and parents will love that everyone's learning the names of the fruits!

Watch this fantastic fruit sing-along in ultra HD 4K for a better experience. 🎓 You and your children will learn the names of many of the most popular fruits in the world, including apples, bananas, kiwi, watermelon, strawberries, oranges, pineapple, and cherries. 🎉 It's fun, it's catchy, and it's educational! It's great for preschoolers, kindergarteners, and children of all ages, and parents will enjoy it! 🥳

🎤 Fruit Song Lyrics:

I eat my fruits Everyday
Yummy yummy yummy fruits
Fruits are so healthy
Eat your fruits everyday

Apples, Bananas, Grapes, kiwi, watermelon
Strawberry, Orange, Pineapple, Cherry, Avocado

Yummy Yummy Yummy Fruits

Apples are my favorite
Juicy juicy red apples
Bananas are my favorite
Yummy yummy yellow bananas,

Hey Lucas,
What fruit is this?
"It's a red apple"

Apples, Bananas, Grapes, Kiwi, Watermelon
Strawberry, Orange, Pineapple, Cherry, Avocado

mmm Yummmyyy

Grapes are my favorite
Juicy juicy purple grapes
Watermelons are my favorite
Yummy yummy green watermelons

Hey Ruby
Can you guess what fruit this is?
"It is my favorite watermelon"

Apples, Bananas, Grapes, Kiwi, Watermelon
Strawberry, Orange, Pineapple, Cherry, Avocado

Yummy Yummy Yummy Fruits

Orange is my favorite
Juicy juicy round orange
Strawberries are my favorite
Yummy yummy red strawberries

Hey Brody
What fruit is this?
"It is a red strawberry"

Apples, Bananas, Grapes, Kiwi, Watermelon
Strawberry, Orange, Pineapple, Cherry, Avocado

mmm Yummmyyy

Cherries are my favorite
Juicy juicy red cherries
Pineapple is my favorite
Yummy yummy yellow pineapple

Hey Lilly
Can you guess what fruit this is?
"It is my favorite cherry"

Apples, Bananas, Grapes, Kiwi, Watermelon
Strawberry, Orange, Pineapple, Cherry, Avocado

Kiwis are my favorite
Yummy yummy brown kiwis
Avocados are my favorite
Yummy yummy green avocados

Apples, Bananas, Grapes, Kiwi, Watermelon
Strawberry, Orange, Pineapple, Cherry, Avocado

⭐ If our video entertains your child and makes them happy, please hit the LIKE button. SHARE it with your friends and family members so that more and more kids can sing and have fun. 👍 SUBSCRIBE to our channel to watch our other nursery rhymes, kids songs, and educational videos for children and parents. 🔔 And make sure you turn on the bell icon to get notified as soon as our new videos come up. 🔥

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🌟 More fun nursery rhymes and kids songs by RV AppStudios:
🥳 Put Your Hands In the Air Song - https://youtu.be/lKemaWQif4g
🦁 Lucas Song RV AppStudios - https://youtu.be/jpSMPm-DFUs
🎂 Birthday Song for Children - https://youtu.be/naWirAMrE5c
🥰 Humpty Dumpty Kids Song - https://youtu.be/mE1W-IE3_Dc

Copyright © RV AppStudios

#Fruits #KidsSong #NurseryRhymes

“Bloomberg: The China Show” is your definitive source for news and analysis on the world's second-biggest economy. From politics and policy to tech and trends, David Ingles and Stephen Engle give global investors unique insight, delivering in-depth discussions with the newsmakers who matter.

Chapters:
00:00:01 - Bloomberg: The China Show opens
00:03:00 - What to watch in China today
00:04:15 - Trump in dispute with Colombia over deported migrants
00:09:01 - Trump's tariffs, Chinese AI startup DeepSeek in focus
00:15:33 - China boosts index investments
00:21:44 - Breaking: China's factory activity slows ahead of Lunar New Year
00:27:39 - Hang Lung Properties' Adriel Chan on company earnings
00:39:20 - 'Magnificent Seven' set to report Earnings
00:43:55 - Breaking: US stock futures sink as China's DeepSeek sparks tech worries
00:50:15 - Capital's Kyle Rodda on DeepSeek, US tech stocks outlook
01:02:54 - DeepSeek spurs rally in Chinese AI shares with advanced model
01:10:49 - China Decoded: Distressed developers in focus
01:13:41 - Blue Mountain Bridge Capital's Raymond Chan on China's distressed developer debt
--------
More on Bloomberg Television and Markets

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1,000 years from now, the length of a solar day on Earth will increase by 1/30 of a second. Leap seconds will have to be added multiple times during the month.

30,000 years from now, Niagara Falls will have eroded the remaining 32 km to Lake Erie and will cease to exist.

100,000 years from now, the proper motion of stars across the celestial sphere, which results from their movement through the Milky Way, renders many of the constellations unrecognizable.

500,000 years from now, Earth will likely have been hit by an asteroid of roughly 1 km in diameter, assuming that it cannot be averted.

1 million years from now, Betelgeuse will have exploded in a supernova, making it visible on Earth in daylight.

50 million years from now is the earliest estimated time for Earth to naturally replenish its fossil fuel reserves.

180 million from now, due to the gradual slowing down of Earth's rotation, a day on Earth will be one hour longer than it is today.

250 million years from now, the west coast of North America, the coast of California will collide with Alaska.

1.2 billion years from now is the high estimate until all plant life dies out.

2 billion years from now is the first close passage of the Andromeda Galaxy and our Milky Way galaxy.

5.4 billion years from now, the sun begins to evolve into a red giant, engulfing the Earth and moon.

150 billion years from now, the Universe's expansion causes all galaxies beyond the former Milky Way's Local Group to disappear beyond the cosmic light horizon, removing them from the observable universe.

1 trillion years from now, star formation ends in galaxies as galaxies are depleted of the gas clouds they need to form stars.

120 trillion years from now, stars in the universe will have exhausted their fuel.

In One gazillion, quadrillion, trillion, billion, million, thousand years from now - we start all over again.

#astronomy​​​ #astrophotography​​​

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


Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilon-delta definition of limits.

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 Differential Calculus channel:
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How Many Faces, Edges And Vertices Does A Sphere Have?
Here we’ll look at how to work out the faces, edges and vertices of a sphere.
We’ll start by counting the faces, these are the flat surfaces that make the sphere. A sphere has 0 faces altogether - but it does have a curved surface.
Next we’ll work out how many edges the sphere has, which are where two faces meet. A shere has 0 edges.
Next we’ll count the corners of the sphere (the corners). No surprises, a sphere does not have any vertices.

For the full playlist for the faces, edges and Vertices of a whole lot of 3D shapes go to https://www.youtube.com/playli....st?list=PLjbxBzUM6SL

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e

Discover what the four types of sentences are with Oliver, Chloe, Bella, and Elvis, as they take you around the petting zoo. The declarative Oliver never stops making simple statements and doling out information, while the interrogative Chloe has a never-ending list of questions. The imperative Bella can’t stop commanding or requesting, and the Exclamatory Elvis is a hoot with his excited utterances. With loads of examples briskly hopping in from every nook and cranny of the petting zoo in this video, identifying the types of sentences or differentiating between them will no longer be a Herculean task for kids. Learn to use appropriate punctuation marks: a period for declarative sentences, a question mark for interrogative sentences, and an exclamation point for exclamatory sentences. Get on board right away, ‘coz there’s so much to do at the petting zoo!
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#TypesOfSentences #SentencesForKids #TutoringHour #4KindsOfSentences #EnglishGrammar #SentencesForBeginners #DeclarativeSentences #InterrogativeSentences #ImperativeSentences #ExclamatorySentences #SentenceStructure #Statements #Questions #Commands #Exclamations #AssertiveSentences #SentenceTypes #DefinitionsAndExamples #SentencesForKindergarten #TypesOfSentencesForGrade1 #2ndGradeKindsOfSentences #ELA #ELS

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Esther is an American teacher from California.
It is the best video course for beginner students. Esther teaches English articles, pronouns, prepositions, adjectives, etc. This video is perfect to help you improve your English speaking, listening, writing, and reading.
0:00 - Beginner English Introduction
0:57 - Vowels and Consonants
5:57 - a/an + Noun
11:26 - Singular / Plural Nouns
20:45 - Subjective Pronouns
26:53 - Subjective Pronouns + Be
33:44 - Subjective Pronouns + Be + Not 38:43 - 'be' Verb Pronoun Questions
49:54 - Review #1 - Subjective Pronouns 53:12 - Grammar Check Up #1
58:55 - What + Be Verb Questions
1:03:43 - This / That
1:07:32 - These / Those
1:11:58 - This / That / These / Those Practice
1:13:47 - Possessive Adjectives
1:21:46 - Possessive Pronouns
1:27:04 - Grammar Check Up #2
1:34:16 - Articles + Noun
1:40:47 - Prepositions: in / on / under 1:45:44 - Beginner Adjectives
1:50:13 - Grammar Check Up #3
1:57:41 - Have / Has
2:01:59 - Don't / Doesn't Have Questions 2:06:26 - Do / Does Have Questions
2:10:42 - Grammar Check Up #4
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This is a full lesson video on 3D shapes for children! It is a re-release of my first video ever, titled "3D Shapes for Kids". I used to re-release shortened versions of videos that could be used in classrooms.

Thanks for watching! I hope you have an AMAZING day!

Daniel
"Homeschool Pop"

Today is July the 3rd. And for us humans on earth, today is the day that we're the furthest away from the sun that we’ll be all year. So why is it so warm? Where I live, it's summertime and we've just gone through our first heatwave of the year, and you'd think it would be cold when you're far away from the sun and warm when you're close to the sun. On the 3rd of January. But it's the other way around. This can all be explained by the fact the earth has a tilted axis like my head. Right now, in the summer, we're tilted towards the sun, so we're getting more heat from it. Just to give you some concrete numbers. We're getting about 7% less energy from the sun by being far away now compared to January the 3rd, when we're closer, we get 7% more. But the difference in tilt means tilting towards the sun gives about 500 percent as much energy as being tilted away. For here in London. It obviously varies depending on how high up or down in latitude you are. And obviously everything's flipped for the southern hemisphere because it's their winter at the moment, so it does kind of make sense for them. But it's interesting. This combination means that in the Northern Hemisphere we have slightly longer summers and slightly shorter winters, whereas in the southern hemisphere it's the opposite way around. They have slightly shorter summers and slightly longer winters. So in conclusion, as they always say, nobody cares how far away you are from the sun. If you've got a wonky axis.

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

Parametric Representations of Lines in R2 and R3

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/linear_combinations/v/linear-combinations-and-span?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/vectors/v/intro-unit-vector-notation?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.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channe....l/UCGYSKl6e3HM0PP7QR
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In no time my bot will be beating the best players in the world. Stay tuned to see how I built it :).

Lemme know what you guys wanna see next. If u liked the video subscribe OR ELSE.

Anyways heres the chapters:
0:00 - Intro
0:15 - How the AI Works
1:48 - Building the Bot
3:10 - Training the Bot
4:10 - Playing the Bot
6:15 - Closing Thoughts

Shoutout to JuinorBuilds and Kian Brose for the inspiration.

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

Generalizing the technique of approximating area under a curve with rectangles. Created by Sal Khan.

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/ap-calculus-ab/ab-accumulation-riemann-sums/ab-riemann-sums-in-summation-notation/e/riemann-sums-and-sigma-notation?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-accumulation-riemann-sums/ab-riemann-sums-in-summation-notation/v/practice-approximating-area-under-curve?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-accumulation-riemann-sums/ab-summation-notation/v/summation-notation-worked-examples?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
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Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/hu....manities/us-governme

Federalism in the United States. Exclusive and concurrent federal and state powers.

View more lessons or practice this subject at https://www.khanacademy.org/humanities/ap-us-government-and-politics/foundations-of-american-democracy/relationship-between-states-and-the-federal-government/v/federalism-in-the-united-states?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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I’m guessing you’re pretty familiar with ice. We use it in our drinks, slip on it, skate on it, worry about climate change melting it. But have you ever stopped to really think about this stuff? The freezing and melting of water affects so much of our world. It’s ice crystals in thunderclouds that create lightning. Ice is powerful enough crack boulders, float stones, and alter entire landscapes. Ice is such a common substance, you'd think we'd know everything about it by now. But it has some secrets and weird properties we’ve only just begun to figure out. One question about ice that's, still not totally answered, is one of the most obvious: why is ice slippery? It's a more complicated answer than it seems!


References: https://sites.google.com/view/....why-is-ice-slippery-

Special thanks to our Brain Trust Patrons:
AlecZero
Bob Rosset
Brent M.
Diego Lombeida
Ron Kakar


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Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/vectors/e/scaling_vectors?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/vectors/v/linear-algebra-vector-examples?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/vectors/v/adding-vectors?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.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channe....l/UCGYSKl6e3HM0PP7QR
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/algebra2/x2ec2f6f

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/precalculus/imaginary_complex_precalc/complex_num_precalc/e/the_complex_plane?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus

Watch the next lesson: https://www.khanacademy.org/math/precalculus/imaginary_complex_precalc/complex_num_precalc/v/complex-number-addition?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus

Missed the previous lesson?
https://www.khanacademy.org/math/precalculus/imaginary_complex_precalc/complex_num_precalc/v/complex-number-intro?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus

Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!

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 Precalculus channel:
https://www.youtube.com/channe....l/UCBeHztHRWuVvnlwm2
Subscribe to Khan Academy: https://www.youtube.com/subscr....iption_center?add_us

DeepSeek-R1 is a strong performing, open source reasoning model with several distilled versions that can be run locally. Here, we walk through the DeepSeek-R1 paper to review the details of the training methodology, download the 14b distilled model via Ollama, test generation / JSON-mode, and then test it in a fully local "deep research" assistant that performs web-research / summarization w/ an iterative reflection step to improve its results.

Video notes:
https://mirror-feeling-d80.not....ion.site/DeepSeek-R1

Code repo:
https://github.com/langchain-a....i/ollama-deep-resear

Related video on reasoning models:
https://www.youtube.com/watch?v=f0RbwrBcFmc

Prior build-from-scratch video for an earlier version of this research assistant:
https://www.youtube.com/watch?v=XGuTzHoqlj8

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