• Articles

    Properties of the Derivatives of Vector Valued Functions

    Welcome to a review of the properties of the derivative of a vector-valued function, part one. In this video, we’ll take a look at proving the property involving the derivative of a dot product. So here we have the six properties of the derivative of a vector-valued function we’re gonna take a look at. These will look very familiar to some of the properties that we reviewed when we were finding derivatives of basic functions. This first property just states that if we want to find the derivative of a constant times a vector-valued function R of T, that’ll just equal the constant times the derivative of that vector-valued function.…

  • Articles

    Ex 2: The Distributive Property

    – HERE ARE SOME MORE EXAMPLES OF USING THE DISTRIBUTIVE PROPERTY TO SIMPLIFY EXPRESSIONS. IN THE FIRST EXAMPLE WE HAVE -9P x THE QUANTITY P + 2. SO, WE WANT TO DISTRIBUTE -9P, WHICH MEANS WE WANT TO MULTIPLY -9P AND P AS WELL AS -9P AND 2. SO, WE’D HAVE -9P x P + -9 x 2. WELL, -9P x P IS GOING TO BE -9P TO THE SECOND OR -9P SQUARED, AND THEN WE’LL HAVE + (-18), BUT INSTEAD OF LEAVING IT IN THIS FORM AS + AND -, IT’S MORE COMMON TO WRITE THIS AS SUBTRACTING A POSITIVE. SO, THIS IS EQUIVALENT TO -9P SQUARED – (+18).…

  • Slow Motion Flipping Cat Physics | Smarter Every Day 58
    Articles,  Blog

    Slow Motion Flipping Cat Physics | Smarter Every Day 58

    Hey it’s me Destin Welcome back to SmarterEveryDay So you’ve probably observed that cats almost always land on their feet Today’s question is why. Like most simple questions there’s a very complex answer For instance let me reword this question How does a cat go from feet up To feet down In a falling reference frame without violating the conservation of angular momentum Now I’ve studied free falling bodies, my own in fact in several different environments and once i get my angular rotation started in one direction, I can’t stop it. Today, we’re going to use a high speed camera- we’re not going to use Alley because this is…

  • EMPTY HOUSE TOUR 2018!
    Articles,  Blog

    EMPTY HOUSE TOUR 2018!

    Hi sister! James Charles here and welcome back to my house! Oh my God! Come in! Come In! Come in! okay You guys, for today’s brand-new video We’re going to be doing a sister sanctuary tour – but you guys know about two years ago now, I officially moved to Los Angeles to pursue make up as a career and *thank god* it has really really taken off! And when I moved here, I moved to downtown LA Because, a lot of the work I was doing was in Hollywood, But my really close family and friends were all in Orange County and Whittier, So, it was kind of right…

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    Best Friends Build A Gingerbread Dream House ft. Emma Chamberlain & Dolan Twins

    – Hi sisters. – James Charles here, welcome back to our Youtube channel. Merry Christmas to you guys. Today I’ve joined with some very very special guests, the sister squad. – That’s what we’re called. – Hey. – As you can tell we are not in our normal filming location and that’s because we’re in my kitchen. So we are not doing makeup, thank god. – Thank Santa. – But what we are doing– – Thank Saint Nick. – I’m going to kill you. – Thank Kris Kringle. – Thanks Kris. – Thanks Jack Frost. – You’re getting coal in your stocking if you don’t shut up. – Jack Frost…

  • Properties of Exponents
    Articles,  Blog

    Properties of Exponents

    – WELCOME TO THE PRESENTATION ON THE PROPERTIES OF EXPONENTS. THE GOAL OF THIS VIDEO IS TO USE THE PROPERTIES OF EXPONENTS TO SIMPLIFY EXPRESSIONS. HERE IS A LIST OF THE PROPERTIES OF EXPONENTS WE WILL BE DISCUSSING TODAY. YOU MAY WANT TO PAUSE THE VIDEO NOW AND WRITE THESE DOWN. WE WILL CONSIDER THEM ONE AT A TIME. THE FIRST PROPERTY IS A PRODUCT PROPERTY. IT STATES IF YOU’RE MULTIPLYING AND THE BASES ARE THE SAME, YOU ADD THE EXPONENTS. LET’S TAKE A LOOK AT WHY THAT MAKES SENSE. IF WE WANT TO MULTIPLY 5 TO THE SECOND x 5 TO THE FOURTH, WE KNOW THAT 5 TO THE…

  • Ex: Property of Definite Integral Addition
    Articles,  Blog

    Ex: Property of Definite Integral Addition

    – WELCOME TO TWO EXAMPLES INVOLVING THE ADDITION PROPERTY OF DEFINITE INTEGRALS. TO HELP ILLUSTRATE THESE EXAMPLES WE’LL ASSUME F OF X IS THIS FUNCTION HERE, GRAPHED IN RED, WHICH IS A NONNEGATIVE FUNCTION. WE’RE GIVEN THE DEFINITE INTEGRAL OF F OF X FROM 1 TO 6=THE DEFINITE INTEGRAL OF F OF X FROM 1 TO 4 + THE DEFINITE INTEGRAL OF F OF X FROM “A” TO B, AND WE’RE ASKED TO FIND “A” AND B. BECAUSE F OF X IS NONNEGATIVE, IF WE INTEGRATE F OF X FROM 1 TO 6 IT WOULD GIVE US THE AREA OF THIS BLUE SHADED REGION, WHICH MEANS THE SUM OF THESE…