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Geometry notation: what does $m\\angle ABC$ mean? @Hilbert: As blf points out, ∠ABC ∠ A B C denotes the angle, itself, while m∠ABC m ∠ A B C is its measure For example, suppose we have an equilateral triangle with vertices A, B, C A, B, C Then ∠ABC ∠ A B C occurs at the intersection of the segments AB A B and BC B C, while m∠ABC m ∠ A B C is the measure of that angle The distinction isn't always important, but sometimes it is
How to simplify $a^n - b^n$? - Mathematics Stack Exchange How to simplify an −bn a n − b n? If it would be (a + b)n (a + b) n, then I could use the binomial theorem, but it's a bit different, and I have no idea how to solve it Thanks in advance
The idea behind the sum of powers of 2 - Mathematics Stack Exchange I know that the sum of powers of 2 2 is 2n+1 − 1 2 n + 1 − 1, and I know the mathematical induction proof But does anyone know how 2n+1 − 1 2 n + 1 − 1 comes up in the first place For example, sum of n numbers is n(n+1) 2 n (n + 1) 2 The idea is that we replicate the set and put it in a rectangle, hence we can do the trick What is the logic behind the sum of powers of 2 2 formula?
What is the formula for the difference between CI and SI? If principal, time and rate are given how,do I find the difference between Compound interest and Simple Interest? p=12,000 n=1 and a 1 2 yrs r=10% per year Formulae that I know: CI - SI for 2 y
How to add and subtract values from an average? I know that's an old thread but I had the same problem I want to add a value to an existing average without having to calculate the total sum again to add a value to an exisitng average we only must know for how many values the average was calculated for:
quadratics - Newtons Identity - Mathematics Stack Exchange While reading about quadratic equations, I came across Newton's Identity formula which said we can express αn +βn α n + β n in simpler forms but not given any explanation They wrote Sn = αn +βn S n = α n + β n and plugged in the quadratic equation f(x) = ax2 + bx + c f (x) = a x 2 + b x + c to write:
Do We Actually Calculate Inverse Laplace Transforms? As requested by OP in the comment section, I am writing this answer to demonstrate how to calculate inverse Laplace transform directly from Mellin's inversion formula It is known that for a> 0 a> 0 if f(t) =ta−1 f (t) = t a − 1 then F(s) = Γ(a) sa F (s) = Γ (a) s a Now we are going to verify this result using Mellin's inversion formula It suffices to prove that for any c> 0 c> 0