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![]() So, this is the point negative 1, negativeĥ. And, you'll see the symmetry around it inĪ second. Negative, when x is negative 1, f of x is Fair enough? Then, we have this point that we have this Y is negative 2 so that is that right overģ. When x is negative 2, this is the x axis. You have the point negative 2, negative 2. We're going to set y equal to whatever our output of I could keep going, this is in the y, and That's negative five over there on the yĪxis, y axis and then it will go to positive 7. So, let's say this is negative 1,2,3,4,5. X is equal to, this is x is equal to 0 and then this is x is equal toġ right over there and then when x is equal to, we go from negative 2Īll the way to positive. This is x is equal to negative 1, this is What the graph of the function would look And, that I think is enough points to give us a scaffold of what this graph will look When x is equal to 1, you have 3 times one So, we have, we could try, x is equal toġ. We could try, let's do one more point over ![]() ![]() If you go one x value below the vertex, orīelow the x value of the vertex, f of x is equal to If you go one above the vertex, f of x isĮqual to negative 2. And, this is where you can see that this is the vertex, and you start seeing the So, what happens when x is equal to 0? These first two terms are 0, you're just That's the coefficient on this term right And, you know the formula for the vertex, So, this is 3 minus 6 is negative 3 minus 2 is equal negative 5, and that actually Is minus 6 and then minus 2, and then minusĢ. Squared, which is just 1, minus, or I should say plus 6 times negative 1 which Negative 1? So, this is going to be 3 times negative 1 Which is 4, plus 6 times negative 2, which is 6 times negative 2, Two? Then f of x is 3 times negative 2 squared, So, let's try, well this the values we'veīeen trying the last two videos. Lets try some x values and lets see what f It comes straight out of the quadratic formula, which you get from completing the Negative b over 2a is the formula for it. There's other ways to directly compute the To calculate the vertex exactly, but let's see how we can This and maybe get a sense of its vertex. Has a shape like this, it won't take on any valuesīelow its vertex when it's upward opening, and it won't take on any values above Right over here, it is a quadratic- you might already know And, if you're familiar with quadratics- and that's what this function is I'm going to try to graph this function right over here. On a graph, it's a set of all the possible y values. Now, the range, at least the way we'veīeen thinking about it in this series of videos- The range is set of possible, So, you take any real numberĪnd you put it here, you can square it, multiply it by 3, It's pretty muchĮverything but complex numbers. Numbers that you know of, they are part of When you first learn them, called imaginary numbersĪnd complex numbers. There is a class of numbers, that are a little bit bizarre You know, aren't all numbers real? You may or may not know that And, for those of you who might say, well, Of valid inputs, the set of inputs over which this function So essentially any number if we're talkingĪbout reals when we talk about any number. Square it, multiply it by 3, then add 6 times that real numberĪnd then subtract 2 from it. What is a set of all of the valid inputs, or all of the valid x valuesįor this function? And, I can take any real number, Determine the domain and range of the function f of x is equal toģx squared plus 6x minus 2. With cutting-edge features, a full FX suite, and more, this modular system delivers the highest quality sound with user-friendly controls. 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It can process audio at much higher bit rates than most internal sound cards can handle route to different outputs (such as headphones and studio monitors) as well as record vocals, instruments, and more directly into your DAW.Ī DJ audio interface does all the above, and also includes the specific controls and features that DJs need, such as portability to get you to your gigs, pro-grade faders, tactile EQ knobs, and the ability to preview and cue tracks in your headphones.ĭJ AUDIO INTERFACE – FROM BEDROOMS TO BOOTHS ![]() Often connected via USB, a DJ audio interfac e is a piece of hardware that allows the input and output of high-quality audio signals to and from a computer. X = linsolve(A,B) = linsolve(A,B) Description. The calculator will use the Gaussian elimination or Cramer’s rule … ![]() Writing simultaneous equations in matrix form Consider the simultaneous equations x+2y = 4 3x− 5y = 1 Provided you understand how matrices are multiplied together you will realiseģ×3 system of equations solvers This calculator solves system of three equations with three unknowns (3×3 system). On this leaflet we explain how this can be done. Using the inverse matrix to solve equations Introduction One of the most important applications of matrices is to the solution of linear simultaneous equations. Let’s solve this one: First, find the determinant of the coefficient matrix: Solving a system of 3 equations and 4 variables using matrix row-echelon form Matrices for solving systems by elimination Solving a system of 3 equations and 4 variables using matrix row-echelon formįigure 3 – Solving linear equations using Gaussian elimination Since A transforms into the identity matrix we know that the transform of C is the unique solution to the system of linear equations, namely x = 0, y = 2 and z = -1.Īrab israeli conflict summary speech and language calendar glencoe mcgraw hill geometry homework practice workbook answer key pay for literature review, child drug addiction in india creative writing workshops gold coast holt mcdougal mathematics course 1 pdf child observation report sample pride and prejudice sparknotes network basedĬramer’s Rule for 3 x 3’s works, pretty much, the same way it does for 2 x 2’s - it’s the same pattern. On this leaflet we explain how this can be done. 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![]() ![]() "I knew it had to be fake! No real country would wear that many jean jackets!"įun thing to do if locked in the mall overnight "The Legend of Zelda's Ass, in which you go on a long journey, only to discover that the treasure trunk is filled with junk."Ĭome up with the name of a country that doesn't exist I don't."Ĭome up with a title for an adult version of any classic video game "Ew, I don't want to know what the mayonnaise is for. "Ugh, dammit! Always being measured against the yard stick that is Word Spud!" "Wow, you actually typed Hitler? Huh, I did Nazi that coming!"Īn angry review you'd give this game (Quiplash). "You know what's even scarier? I'm right behind you, in bed!" "The name's Girly, see? I came here for one thing and one thing only? I forgot my dollies! I need to grab my dollies and I'll be on my way." "The USS SS! Okay, I'm not gonna touch that one. Pee clear, that would be a healthy color."Ī rejected name for a ship in the U.S. "Pee yellow? Yep, pee yellow would be a very sick color. "Yeah, but you know when Judge Scalia goes pants-less, it's not really so much a prank, it's just really hard to find Scalia-sized pants." But he's still my favorite character created by Tim Burton"Ī prank the Supreme Court Justices probably play on each other Johnny Depp would be a terrible pirate name. "I wanna buy Abercrombie and Sh*ts, but the shirtless mall model in diapers intimidates me." 'Psychedelic baby, yeah!' "Ī name for a brand of designer adult diapers "Well, at least by saying 'I see dead people', you let people know that they'll be suffering through a night of references from 2001. "Have you gotten so lazy that you won't spend the energy to scratch your own butt? Me too! Welcome to the club."Ī great opening line to start a conversation with a stranger at a party "Yeah, Cookie Masterson sounds like a convincingly real name to me, not made up at all."Ī great new invention that starts with "Automatic" "You know what? You should only go to work naked if you're a stripper, or the host of a video game. "Honestly, I'd take the color of bleeding walls over eggshell white any day." "Boogie in your butt? What are you, Eddie Murphy?" "Just be careful not to yell out 'Winter is coming!'"Ī good fake name to use when checking into a hotel "Pudding pants? You bet! It will change your life."Ī fun thing to think about during mediocre sex "Did you not understand what we were asking? Or you did, and you just couldn't bring yourself to do it? What are you, some kind of video game perfectionist? Lighten up!" That's not the whole reason but."Ī completely wrong way to spell "Jennifer Aniston" It reminds them that despite being smarter than dogs, many pigs are treated cruelly by the meat industry. uh, second, if you count Taft."Ī bad thing to say to a cop as he writes you a speeding ticket "Yeah, I'd imagine America is is still quite a ways away from it's first openly satanist president. Unless they were using reverse psychology, then it's brilliant!"Ī bad first line for your presidential inauguration speech "Don't Vote for Me! That would be a horrible slogan. Starting from Quiplash, if a certain word or phrase is said, Schmitty will have something to say about it (this doesn't apply to all prompts).Ī bad campaign slogan for a congressperson The game selects a random player (other than the Audience or the player(s) given the scenario to complete) to fill this spot. Berserk: Guts only cares about one thing aside from slicing monsters apart and that is former love of his life and former Hawks Captain Casca.When Suzu objects to Matsuri sacrificing himself, he reluctantly complies and lets Shirogane live. While their first meeting was hostile, after Casca grudgingly keeps his body warm with her own, Guts forms strong feelings for her. He was more than ready to fall off a cliff with her and had no qualms blocking arrows shot at her with his body, it's these acts that ultimately cause Casca to fall for him, as she claimed no man had ever shed blood for her in battle before. Guts goes above and beyond protecting her, brutally defending her from violating monsters and going near when he couldn't save her from Griffith in the Eclipse Guts becomes borderline insane. Guts saves the now insane Casca from being burned at the stake as a witch by Bishop Mozgus and his henchmen, who are being backed by all of the citizens who blindly follow whatever he says just to save themselves from damnation. They want to burn her because they think she is responsible for the influx of monsters and evil spirits around St. Albion (and technically they're correct, since the Brand of Sacrifice on Casca's breast attracts evil spirits that are nearby that want to eat her). Guts doesn't really give a damn about what will happen to the innocents caught up in the attack so long as he and Casca survive at the end of it all, and indeed is disgusted that all that these people are even doing is praying and clinging to Mozgus's every word instead of trying to get the hell out of Dodge. He tells Mozgus and the refugees to suck it up and deal with it.
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