1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
seen from Canada
seen from Greece
seen from United States
seen from United States
seen from Türkiye
seen from United States
seen from China
seen from United States
seen from United Kingdom
seen from India
seen from United States
seen from Indonesia
seen from Malaysia
seen from Malaysia
seen from Malaysia
seen from United States
seen from China
seen from China
seen from United States
seen from Maldives
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
Inspired by the notion that Bruce hates internet slang.
And everyone takes advantage of it.
Everyone.
(ﾉ◕ヮ◕)ﾉ*.✧(ﾉ◕ヮ◕)ﾉ*.✧(ﾉ◕ヮ◕)ﾉ*.✧(ﾉ◕ヮ◕)ﾉ*.✧
Steph, after finding out Bruce has a doc of people's embarrassing photos and moments, getting breakfast (he refused to share the doc with her): See how I respect people's privacy and share? Very cutesy, very mindful. I'm not someone people hesitate to ask for help from, they can trust me. Very demure.
Bruce exhales, long and loud, through his nose
₍₍◞( •௰• )◟₎₎⁽⁽◝( •௰• )◜⁾⁾₍₍◞( •௰• )◟₎₎⁽⁽◝( •௰• )◜⁾⁾
Alfred lecturing Bruce in the batcave about safety and how he shouldn't 'prioritise' during missions or bench anyone in the middle of a mission: You could even call your actions crazy.
Tim, the one who got benched, taking this golden opportunity: Crazy? I was crazy once,
Jason, after spotting The twitch in B's left eyebrow, because he can: They locked me in a room
Steph, suspiciously avoiding looking at the ceiling: a rubber room with rats
T,J,S: and rats make me crazy
They repeat this about three more times, at the perfect volume as Alfred does all but hide his smirk
Only later, when he's collecting the multitude of speakers playing the recording from earlier does he realise that Conner Kent was meant to be at the manor that day.
Tim had let him into the batcave to record from the ceiling.
And maybe Cass had a hand in hiding the speakers, but he won't know.
༼;´༎ຶ ༎ຶ༽༼;´༎ຶ ༎ຶ༽༼;´༎ຶ ༎ຶ༽༼;´༎ຶ ༎ຶ༽༼;´༎ຶ ༎ຶ༽
Duke, humming and murmuring under his breath: but when you're gone I feel incomplete-
A pissed Dick Grayson, not so quiet: And if you want the truth-
Bruce: no, god, please no
Jason whipping his phone camera out as fast as possible:
Tim and Cass giving Duke, Alfred, and Jason earplugs:
Dick, with a megaphone: I just wanna be part of your SYMPHONYYYYYY YEAH! WILL YOU HOLD ME TIGHT AND NOT LET GOO!! SYMPHONYYEEEEEE-
Bruce's mug shatters.
And if Damian gave Dick the megaphone to sneak Jon Kent and a stray cat in, he was doing his binomial expansion homework.
A blog about mathematics.
Finished Chapter 2: Basic Counting Rules!
Note that the next notes will be Chapter 7, so many chapters will be skipped.
MIT grad shows how to do a binomial expansion with the Binomial Theorem and/or Pascal's Triangle. Nancy of mathbff explains the steps on YouTube’s NancyPi channel:
1) HOW TO START A BINOMIAL EXPANSION: If your binomial is something like (x + 3) raised to a power like (x + 3)^5, you have two parts of your binomial: x and 3. You're going to take each of those and raise them to different powers in each term of the expansion. You can start your expansion just by writing these powers out.. For the FIRST PART of your binomial, x, it will start with a power of 5 (your power number) in the first term of the expansion (x^5), and then in each term after the power will go down by 1 (x^4, x^3, etc. all the way down to a zero power, x^0). Then you take the SECOND PART of the binomial, 3, and multiply each term by a power of 3. The 3 factor will start with a power of 0 in the first term, so 3^0, and then will increase by 1 power in each term after.
2) HOW TO FIND THE COEFFICIENTS (with the FACTORIAL or COMBINATION method): Then there's one more number to find, a number that gets multiplied in front of each term, or a binomial coefficient. There are two ways to find the coefficients (for the Pascal's Triangle way, see below). To find the coefficients using the factorial, combination ("n choose k") formula of n!/(k!(n-k)!, each term has a coefficient number you find using an n value equal to the power number, 5, and a k value that runs from 0 for the first term up through 5 for the last term. This number gets multiplied by the other factors in each term, and then simplify for your final expansion.
3) HOW TO FIND THE COEFFICIENTS (with PASCAL'S TRIANGLE): You can instead use Pascal's Triangle to find the binomial coefficients. Whichever row of Pascal's Triangle has your power number in it, as the second number, is the row that gives you all the coefficient numbers you'll need for your expansion. Each coefficient is multiplied with its term, and then you can simplify the expansion.
4) WHAT IF THE BINOMIAL HAS SUBTRACTION? It's very similar. It's easier to think of the subtracted term as "adding a negative number", and then all of the negative number (in parentheses) will be raised to the power in each term of the expansion. Note: if the binomial have something like 2x - y instead of x - y, make sure that all of (2x) is raised to each power.
For more: check out the NancyPi channel on YouTube at: https://www.youtube.com/channel/UCRGXV1QlxZ8aucmE45tRx8w
AS LEVEL PURE MATHEMATICS 1 (PAPER 1)
PURE MATHEMATICS 1 (2002-2010) C1 Quadratics /C2 Functions /C3 Coordinate Geometry C4 Circular Measure C5 Trigonometry C6 Vectors C7 Series C8 Differentiation C9 Integration PURE MATHEMATICS 1 (2010-2013) C1 Quadratics C2 Functions C3 Coordinate Geometry C4 Circular Measure C5 Trigonometry C6 Vectors C7 Series C7 Binomial C8 Differentiation C9 Integration
View On WordPress
Binomial Theorem: Expansion & Divisibility (Question taken from Putnam)
Binomial Theorem: Expansion & Divisibility (Question taken from Putnam)
View On WordPress
Question on Properties of Binomial Coefficients (Algebra)
RP 108 Formulation of Solutions of Standard Congruence of Higher Degree modulo a Multiple of Composite Power Integer
by Prof B M Roy "RP-108: Formulation of Solutions of Standard Congruence of Higher Degree modulo a Multiple of Composite Power Integer"
Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-2 , February 2020,
URL: https://www.ijtsrd.com/papers/ijtsrd30151.pdf
Paper Url : https://www.ijtsrd.com/mathemetics/other/30151/rp-108-formulation-of-solutions-of-standard-congruence-of-higher-degree-modulo-a-multiple-of-composite-power-integer/prof-b-m-roy
internationaljournalsofcomputerscience callforpapercomputerscience ugcapprovedjournalsforcomputerscience
In this study, the solutions of a standard congruence of higher degree modulo a multiple of composite power integer is considered for formulation and is formulated. The formula developed is proved and verified true. Oral calculation of solutions are also possible. Formulation is the merit of the paper.