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Can't cancel (x-2)! And (x-2) The right answer: x(x-1)(x-2)(x-3)!=3(x-1)(x-2) After cancel x(x-3)!=3 If check x=3 that is 3(3-3)!=3 This right (x=3) Can't check x<3 that is road to Gama Function.
You should've written x! as x(x-1)(x-2)(x-3)! and then cancel the (x-1) and (x-2) factors with their corresponding ones on the right side of the equation and that would've left only x(x-3)!=3 wich is only possible if x=3 or, to answer the original question: "find x!", the answer would've been x!=6, because 3!=6.
"x (x-1) (x-2)!" does have pretty obvious meaning and makes sense. What makes 0 sense is cancelling the terms like that. wouldnt even be dumb to cancel them, but the (x-2) is factorial on the left side, so you would actually be left with x(x-3)! = 3 which I dont really know how you're supposed to solve.
or maybe I'm the one who doesnt understand factorials. Either way, the video is dumb and hopefully a joke. Didn't even solve for "x" !! (hard to use exclamation marks while talking about factorials lol)
You need to state that x and y are whole numbers. The lower bound on x is 13, given that restriction. If you decide to let x and y be non-negative real numbers, you'll get an infinite number of solutions with a lower-bound of x = 4*(log(40))^2/9/(log(2)^2) and y=0.
Faster way would be: set 3^x = 2 * 3, then log base of 3 on both sides. x * log3(3) = log3(2) + log3(3) , replacing log3(3) with 1 gives you the final result x = log3(2) + 1
1 Implicitly connected GROUPS of factors and coefficients are treated as single values throughout mathematics. Distance divided by circumference is equal to revolutions. D÷2πr=D÷πd must be calculated as D÷(2πr)=D÷(πd) to avoid failing dimensional analysis. It can be shown that the viral equations 8"÷2(2"+2")=? And 6"÷2(2"+1")=? Are both, in fact, forms of D÷2πr= revolutions. And must be calculated as 8"÷[2(2"+2")]=1. And 6"÷[2(2"+1")]=1 Or arrive at experimentally, verifiably false results of 16in²and 9in² respectively. Even, or especially, when the radius dimensions are a sum of hub and tread thickness. 120"÷[2π(11"+1")]=120"÷[π(22"+2")]=1.59 revolutions. Volume divided by area to determine depth of contents, V÷πr²=depth must be evaluated as V÷(πr²)=depth, to avoid failing dimensional analysis. 1000ft³÷[π(13'-1')]=2.21' deep Volume divided by spherical volumes V÷4/3πr³=number of flasks filled And must be calculated as V÷[4/3πr³] in order to pass dimensional analysis and not arive at 6 dimensional space in the spurious results. 300in³÷4/3π(3in-0.12in)³= 300in³÷[4/3π(3in-0.12in)³]=3 This is also a good example of how the different division notations are used differently. V÷4/3πr³=V÷[4(1/3)(π)(r³)]=quantity D÷2πr is interpreted as D÷[2πr] a quotient with an implicit grouping of factors and coefficients in the denominator. While D/2πr represents a product of the factors D(1/2)(π)(r) that would not be equal to rotations made by a wheel. In fact, each and every instance of Implicitly joined groups of factors and coefficients must be resolved prior to even acknowledging any other explicit operations in the rest of an equation. To omit this grouping relationship means to arrive at spurious results each and every time. The implicit grouping relationship is inherent in the implicit notation and cannot simply be ignored, without expecting incorrect results. So PEMDAS must be interpreted as Parenthetical expressions(including coefficients) First, also using PEMDAS. Then, Exponents Multiplication Division Addition Subtraction The example problem is in no way excluded from these mathmatical behaviors.