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Rightmost Non-zero Digit of \(n!\) | Brilliant Math & Science Wiki
n!
Tapas Mazumdar, Rahil Sehgal, Ben A, and
Finding the number of trailing zeroes in
n!
is an elementary and standard approach which gives us the number of zeroes at the end of
n!
. But finding the rightmost non-zero digit is one such commonly asked pro... |
Inverse Laplace Transform without using equations I'm stuck with a question
Inverse Laplace Transform without using equations
I'm stuck with a question about Inverse Laplace Transform here, but the use of inverse laplace transform equation is forbidden.
Y\left(s\right)=\frac{{e}^{-\pi s}}{s\left[{\left(s+1\right)}^{2}+... |
Quadratic Formula - Course Hero
College Algebra/Solving Quadratic Equations and Inequalities/Quadratic Formula
The quadratic formula is used to solve a quadratic equation of the form
ax^2+bx+c=0
a\neq0
, by using its coefficients:
x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}
The quadratic formula can be used to solve any quadratic... |
\mathrm{LerchPhi}\left(z,a,v\right)=\sum _{n=0}^{\mathrm{\infty }}\frac{{z}^{n}}{{\left(v+n\right)}^{a}}
|z|<1
|z|=1\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{and}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}1<\mathrm{ℜ}\left(a\right)
z
and
v
v
are positive integers, LerchPhi(z, a, v) has a branch cut in the
z
z=1
z=1
a
z
... |
Frequency (statistics) - Wikipedia
(Redirected from Frequency distribution)
Number of occurrences in an experiment or study
In statistics, the frequency (or absolute frequency) of an event
{\displaystyle i}s the number
{\displaystyle n_{i}}
of times the observation occurred/recorded in an experiment or study.[1]: 12–19... |
Title: Quantum Matrix Algebras and their applications
Quantum Matrix Algebras are very interesting objects from algebraic viewpoint. Particular examples of these algebras are related to Drinfeld-Jimbo Quantum Groups. Some of these QMA admit defining analogs of partial derivatives. In a limit it is possible to develop a... |
Understanding Excess Returns
Excess Return vs. Riskless Rates
Excess Return & Risk Concepts
Excess Return & Optimal Portfolios
Excess returns are returns achieved above and beyond the return of a proxy. Excess returns will depend on a designated investment return comparison for analysis. Some of the most basic return c... |
Online exam in Data representation | Online Exam
Online exam in Data representation,Computer for Competitive exams like UPSC & State Level PSCs Exams, SSC, Railways, IBPS, SBI & Its Associates, RBI, Bank PO/MT, Clerical, RRBs, MBA, MCA, BBA, BCA, BBS
A hexadecimal number is represented by
Decimal number system is the g... |
Polynomial satisfying p(x)=3^{x} for x\in\mathbb{N}
haguemarineo6h 2022-04-25 Answered
Polynomial satisfying
p\left(x\right)={3}^{x}
x\in \mathbb{N}
p\left(x+1\right)=3p\left(x\right)
\mathbb{N}⇒p\left(x+1\right)=3p\left(x\right)⇒p\left(-1\right)=\frac{1}{3}
p\left(x\right)\in \mathbb{Z}\left[x\right]
Or, continuing,
\... |
Quantitative Aptitude Exam papers | Online Exam
Home Quantitative Aptitude Mensuration Mensuration-Test 1
Mensuration-Test 1
Chapter :- Mensuration-Test 1
The perimeter of a rectangle is 42 m. If the area of the square formed on the diagonal
of the rectangle as its side is 1 1/12 % more than the area of the rectangle, ... |
Revision as of 09:08, 29 July 2013 by NikosA (talk | contribs) (→Automatising Conversions: units="..." was too long in the script)
{\displaystyle {\frac {W}{m^{2}*sr*nm}}}
{\displaystyle L\lambda ={\frac {10^{4}*DN\lambda }{CalCoef\lambda *Bandwidth\lambda }}}
{\displaystyle \rho _{p}={\frac {\pi *L\lambda *d^{2}}{ESU... |
===== in Python =====
A custom python script, performing the operations of interest, might be like [https://github.com/NikosAlexandris/i.quickbird.toar i.quickbird.toar (for GRASS 7.x)]
===== in bash =====
Am example bash shell script, might look like the one that follows. '''Note,''' however, constants, band parameter... |
Combine terms of identical algebraic structure - MATLAB combine - MathWorks Deutschland
Powers of the Same Base
Powers of the Same Exponent
Terms with Logarithms
Terms with Sine and Cosine Function Calls
Terms with Integrals
Terms with Inverse Tangent Function Calls
Terms with Calls to Gamma Function
Multiple Input Exp... |
Revision as of 09:06, 29 July 2013 by NikosA (talk | contribs) (→Deriving Physical Quantities: bash scripted conversions from to DN to Radiances & Reflectances)
{\displaystyle {\frac {W}{m^{2}*sr*nm}}}
{\displaystyle L\lambda ={\frac {10^{4}*DN\lambda }{CalCoef\lambda *Bandwidth\lambda }}}
{\displaystyle \rho _{p}={\f... |
Write a multivariable function (i.e z=f(x,y)) for a linear function that contains the points (−1,0),
Write a multivariable function (i.e z=f(x,y)) for a linear function that contains the points (−1,0),(0,2),(1,−1). Ive
chukizosv
The general form of a linear function of two variables is given by
f\left(x,y\right)=Ax+By+... |
The symmetric difference of A and B, denoted
The symmetric difference of A and B, denoted by A B, is the set containing those elements in
either A or B, but not in both A and B.
a) Find the symmetric difference o f { 1, 3 , 5 } and { 1, 2, 3 } .
b) Determine whether the symmetric difference is associative; that is, if ... |
What is P ( A ∪<!-- ∪ --> ( B ∩<!-- ∩ --> C ) ) ?
P\left(A\cup \left(B\cap C\right)\right)
The question says it all. I know
P\left(A\cap \left(B\cup C\right)\right)=P\left(A\cap B\right)+P\left(A\cap C\right).
Would this mean,
P\left(A\cup \left(B\cap C\right)\right)=P\left(A\cup B\right)+P\left(A\cup C\r... |
IsSupersoluble - Maple Help
Home : Support : Online Help : Mathematics : Group Theory : IsSupersoluble
attempt to determine whether a group is supersoluble
IsSupersoluble( G )
IsSupersolvable( G )
G
is supersoluble if it has a normal series with cyclic quotients. That is, there is a normal series
G={G}_{0}▹{G}_{1}▹\dot... |
Marmo G. A Manifold view point of Lie Algebras (abstract) - Geometry of Differential Equations
Marmo G. A Manifold view point of Lie Algebras (abstract)
Title: A Manifold view point of Lie Algebras
Lie algebra brackets play a prominent role in the description of evolution (equations of motion) for any physical system, ... |
This question concerns the vector field F = −xy2
This question concerns the vector fieldF = −xy2 i − x2y j + z(x2 + y2) k.(a) Calculate the divergence of F. Use the divergence theorem to show thatthe flux of F over any closed surface is equal to zero. (b) A cylinder of height h and radius R has its base in the xy... |
String metric - Wikipedia
"String distance" redirects here. For the distance between strings and the fingerboard in musical instruments, see Action (music).
In mathematics and computer science, a string metric (also known as a string similarity metric or string distance function) is a metric that measures distance ("in... |
How to solve a cyclic quintic in radicals? Galois theory tells us that \frac{z^{11}-1}{z-
\frac{{z}^{11}-1}{z-1}={z}^{10}+{z}^{9}+{z}^{8}+{z}^{7}+{z}^{6}+{z}^{5}+{z}^{4}+{z}^{3}+{z}^{2}+z+1
{\zeta }^{1},{\zeta }^{2},\dots ,{\zeta }^{10}
\begin{array}{rl}{A}_{0}& ={x}_{1}+{x}_{2}+{x}_{3}+{x}_{4}+{x}_{5}\\ {A}_{1}& ={x}_... |
Revision as of 20:43, 4 August 2013 by NikosA (talk | contribs) (→Automatising Conversions: some "wrong" comment removed from script)
{\displaystyle {\frac {W}{m^{2}*sr*nm}}}
{\displaystyle L_{\lambda {\text{Pixel, Band}}}={\frac {K_{\text{Band}}*q_{\text{Pixel, Band}}}{\Delta \lambda _{\text{Band}}}}}
{\displaystyle ... |
Convert transfer function filter parameters to zero-pole-gain form - MATLAB tf2zp - MathWorks Nordic
Zeros, Poles, and Gain of Continuous-Time System
[z,p,k] = tf2zp(b,a) finds the matrix of zeros z, the vector of poles p, and the associated vector of gains k from the transfer function parameters b and a. The function ... |
Karleigh Moore, Ethan W, Ejun Dean, and
An Enigma machine is a famous encryption machine used by the Germans during WWII to transmit coded messages. An Enigma machine allows for billions and billions of ways to encode a message, making it incredibly difficult for other nations to crack German codes during the war — for... |
The Effect of China’s Family Structure on Household Nutrition
1Department of Agribusiness and Applied Economics, North Dakota State University, Fargo, ND, USA
2Beijing Food Safety Policy & Strategy Research Base, College of Economics and Management, China Agricultural University, Beijing, China
3Department of Food an... |
Social return on investment (SROI) is a method for measuring values that are not traditionally reflected in financial statements, including social, economic, and environmental factors. They can identify how effectively a company uses its capital and other resources to create value for the community. While a traditional... |
1 How many lines can be drawn through a given point 2 In how many points - Maths - Introduction to Euclid\s Geometry - 8144955 | Meritnation.com
1. How many lines can be drawn through a given point ?
2. In how many points two distinct lines can intersect ?
3. In how many lines tow distinct planes can intersect ?
4. In ... |
How do you evaluate 10P8 using a calculator?
using the definition for
\text{using the definition for}\phantom{\rule{1ex}{0ex}}{\text{}}^{n}P{\text{}}_{r}
\text{that is}\phantom{\rule{1ex}{0ex}}{\text{}}^{n}P{\text{}}_{r}=\frac{n!}{\left(n-r\right)!}
\text{where}\phantom{\rule{1ex}{0ex}}n!=n\left(n-1\right)\left(n-2\rig... |
xy'ln(y/x)=x+yln(y/x) find general solution of the homogenous equation
\cap \cup
\left(a,b\right)\in R
\left(A-B\right)-C=\left(A-C\right)-\left(B-C\right)
3n+1
A 5-card hand is dealt from a perfectly shuffled deck of playing cards. What is the probability that the hand is a full house? A full house has thre... |
Gaussian elimination - Wikipedia
(Redirected from Gauss–Jordan elimination)
Algorithm for solving systems of linear equations
Swapping two rows,
Multiplying a row by a nonzero number,
Adding a multiple of one row to another row. (subtraction can be achieved by multiplying one row with -1 and adding the result to anothe... |
1.4 Flow Geometry
The Application Challenge TA 2 - AC 7, "Confined Double Annular Jet" proposed by the VUB, Belgium, is an axisymmetric double annular flow field generated by a burner, and discharging into a confined combustion chamber (see Fig. 1 below). The flow is studied in cold conditions, and in a nozzle region g... |
Solve this: Draw the sign scheme1) x - 22 x - 3x - 1 02) x - - Maths - Linear Inequalities - 12660113 | Meritnation.com
Draw the sign scheme\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}1\right) \frac{{\left(x - 2\right)}^{2} \left(x - 3\right)}{x - 1} > 0\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}2\right) \... |
Mathematics in medieval Islam - Wikipedia
(Redirected from Islamic mathematics)
Overview of the role of mathematics in medieval Islam
1.7 Double false position
2 Other major figures
Omar Khayyám's "Cubic equations and intersections of conic sections" the first page of the two-chaptered manuscript kept in Tehran Univers... |
Use the Divergence Theorem to calculate the surface
Use the Divergence Theorem to calculate the surface integral F · dS, that is, calculate the flux of F across S.
F\left(x,y,z\right)={x}^{3}+cosyi+{y}^{3}sinxzj+{z}^{3}+2ek
S is the surface of the solid bounded by the cylinder
{y}^{2}+{z}^{2}=4
x=0
x=4
a. The work requ... |
The function g is related to one of
jamesvivian911 2022-02-08 Answered
g\left(x\right)={x}^{2}+6
The parent function,
f\left(x\right)={x}^{2}
⇒
g\left(x\right)=f\left(x\right)+6
f\left(x\right)=\text{ }-\frac{1}{{x}^{2}}
f\left(x\right)={\mathrm{log}}_{2}x
y=\mathrm{cos}x
, sketch the function of
y=-\mathrm{cos}\left(3... |
Find the discriminant b2−4acb2-4ac, and use it to determine
Find the discriminant b2−4acb2-4ac, and use it to determine the number of real solutions to the equation. a2+8=4aa2+8=4a Discriminant: Real Solution:
{a}^{2}+8=4a
{a}^{2}-4a+8=0
D={b}^{2}-4ac
=\left(-4{\right)}^{2}-4\cdot 1\cdot 8=16-32=-16
x... |
Transforming Linear Graphs - Course Hero
College Algebra/Linear Functions and Modeling/Transforming Linear Graphs
Translations of Linear Functions
A translation of a linear function shifts its graph vertically or horizontally.
The parent function, or most basic function in the linear family, is the linear function
f(x)... |
Revision as of 10:36, 24 October 2014 by NikosA (talk | contribs) (Added link to working script i.fusion.hpf (for GRASS-GIS ver. 6.4))
{\displaystyle {\frac {W}{m^{2}*sr*nm}}}
{\displaystyle L\lambda ={\frac {10^{4}*DN\lambda }{CalCoef\lambda *Bandwidth\lambda }}}
{\displaystyle \rho _{p}={\frac {\pi *L\lambda *d^{2}}{... |
Disc Method | Brilliant Math & Science Wiki
Mei Li, Beakal Tiliksew, Aditya Virani, and
Given a region under a curve
y=f(x)
a \leq x \leq b
, revolving this region around the
x
-axis gives a three-dimensional figure called a solid of revolution.
To find the volume of this solid of revolution, consider a thin vertical s... |
Discrete Random Variables - Definition | Brilliant Math & Science Wiki
Alexander Katz, Ognjen Vukadin, and Jimin Khim contributed
A random variable is a variable that takes on one of multiple different values, each occurring with some probability. When there are a finite (or countable) number of such values, the random... |
Egyptian Fractions | Brilliant Math & Science Wiki
Ameya Daigavane, Worranat Pakornrat, Geoff Pilling, and
An Egyptian fraction is the sum of finitely many rational numbers, each of which can be expressed in the form
\frac{1}{q},
q
For example, the Egyptian fraction
\frac{61}{66}
\frac{61}{66} = \frac12 + \frac13 + \fr... |
Using Exponential Decay to Explain Amplitude Decreases | Brilliant Math & Science Wiki
Consider the equation of motion of the underdamped harmonic oscillator:
x(t) = Ae^{-\frac{b}{2m} t} e^{ i\sqrt{\frac{k}{m} - \frac{b^2}{4m^2} }t} + Be^{-\frac{b}{2m} t} e^{ -i\sqrt{\frac{k}{m} - \frac{b^2}{4m^2} }t}.
This solution de... |
Heat Transfer | Brilliant Math & Science Wiki
Ashish Menon, Andrew Ellinor, Sravanth C., and
This wiki is the subject of a wiki collaboration party set to be held on Saturday, April 9th at 8:30pm IST (8:00am PST). Please add examples to the appropriate headings or under the examples heading.
Contribute wherever you wou... |
Seminar talk, 11 May 2022 - Geometry of Differential Equations
Seminar talk, 11 May 2022
Speaker: Ilia Gaiur
Title: Hamiltonian reduction and rational Calogero system
In my talk I am going to give an introduction to the theory of the moment map for the Hamiltonian group action on the symplectic manifolds with the focus... |
VisualEditor:Test - MediaWiki
3World languages
6Shape of this world
This photo of this world is called The Blue Marble.
This world is a planet where a society of people has formed.
Authors sometimes invent new worlds. The authors use these worlds as the setting for their stories. Some authors invent worlds that have ma... |
Lando S. Polynomial graph invariants and the KP hierarchy (abstract) - Geometry of Differential Equations
Lando S. Polynomial graph invariants and the KP hierarchy (abstract)
Title: Polynomial graph invariants and the KP hierarchy
We describe a large family of polynomial graph invariants whose average value is a
{\disp... |
Fees - Balancer
There are a few different types of fees on Balancer, each collected to support a healthy ecosystem. For example, Liquidity Providers collect swap fees as users trade with pools; this acts as an incentive for them to continue providing liquidity, which is useful to facilitate trades.
Traders pay swap fee... |
Vulnerability Assessment of Climate Change on Sea Level Rise Impacts on Some Economic Sectors in Binh Dinh Province, Vietnam
Department of Climate Change, Ministry of Natural Resources and Environment (MoNRE), Hanoi, Vietnam
V=f\left(E,S,AC\right)
↑
{x}_{ij}=\frac{{X}_{ij}-\underset{i}{\mathrm{min}}\left\{{X}_{ij}\ri... |
Shemyakova E. On super Plücker embedding and cluster algebras (abstract) - Geometry of Differential Equations
Shemyakova E. On super Plücker embedding and cluster algebras (abstract)
Speaker: Ekaterina Shemyakova
There has been active work towards definition of super cluster algebras (Ovsienko, Ovsienko-Shapiro, and Li... |
If u, v, w ∈ R n ,
Let u and v be vectors in
{\mathrm{ℝ}}^{n}
. span(u,v) is defined as the set of a linear combinations of vectors u and v
w\in span\left(u,v\right)
This implies that the vector w can be written as a Linear Combination of vectors u and v
w={c}_{1}u+{c}_{2}v
span\left(u,v\right)=span\left(u,v,w\right)
C... |
Makna lagu Bungong Jeumpa
Video Seni Budaya SMP Teknik dan Gaya Bernyanyi dalam Musik Tradisi
Gaya Bernyanyi Lagu Daerah Teknik dan Gaya Bernyanyi dalam Musik Tradisi Seni Budaya Kurikulum 2013 K13
This is Louville, one of the downtown areas in London. There are many buildings in this district. The buildings are mostly... |
Triple Angle Identities | Brilliant Math & Science Wiki
Pranshu Gaba, Mei Li, Pi Han Goh, and
\sin 3 \theta = 3 \sin \theta - 4 \sin ^3 \theta
\cos 3\theta = 4 \cos ^ 3 \theta - 3 \cos \theta
To prove the triple-angle identities, we can write
\sin 3 \theta
\sin(2 \theta + \theta)
\begin{aligned} \sin 3 \theta & = \sin ... |
Prove instability using Lyapunov function x' = x^3 + xy y' =
hadaasyj 2022-05-01 Answered
{x}^{\prime }={x}^{3}+xy
{y}^{\prime }=-y+{y}^{2}+xy-{x}^{3}
{x}^{6}+{x}^{3}y+{y}^{2}
. This term is positive (complete the square). All other terms are small when x,y, are small, so they can be controlled. Here are the details.
{... |
Hidden Markov Models | Brilliant Math & Science Wiki
John McGonagle, Ayush G Rai, and Eli Ross contributed
A simple hidden Markov model with 3 states and 4 observation tokens. The states are represented by the labels
x_1
x_2
x_3
, while the transition probabilities between states are represented by the edge label
a_{ij... |
Peak of Electron Density in F2-Layer Parameters Variability at Quiet Days on Solar Minimum
Peak of Electron Density in F2-Layer Parameters Variability at Quiet Days on Solar Minimum
Emmanuel Nanéma1,2*, Moustapha Konaté2, Frédéric Ouattara2
1Centre National de la Recherche Scientifique et Technologique (CNRST), Insti... |
How to prove that the inverse Laplace Transform
Emilia Hoffman 2022-04-06 Answered
{L}^{-1}\left\{0\right\}=0
Buizzae77t
L\left(f\right)=F
{L}^{-1}\left(F\right)=f.\phantom{\rule{1em}{0ex}}L\left(0\right)=0
because L is a linear operator. Or you can actually compute L(0) using the definition.
{y}^{″}+2{y}^{\prime }+y=4... |
An Analysis of the Effect of Lower Extremity Strength on Impact Severity During a Backward Fall | J. Biomech Eng. | ASME Digital Collection
Reuben Sandler,
Biomechanics Laboratory, Department of Orthopaedic Surgery, San Francisco General Hospital and University of California, San Francisco, San Francisco, CA 94110
Cont... |
Convert geocentric latitude to geodetic latitude - Simulink - MathWorks Switzerland
Output altitude
The Geocentric to Geodetic Latitude block converts a geocentric latitude (λ) into geodetic latitude (μ). The function uses an iteration-method of Bowring's formula is used to calculate the geodetic latitude. For more inf... |
Change in Entropy of Spinning Black Holes Due to Corresponding Change in Mass in XRBs
Dipo Mahto1, Anuradha Kumari2
1 Department of Physics, Marwari College, T. M. B. University, Bhagalpur, India.
2 Department of Physics, T. M. B. University, Bhagalpur, India.
Abstract: The present paper gives a theoretical model for t... |
Dyadic analysis filter bank - MATLAB - MathWorks Switzerland
dsp.DyadicAnalysisFilterBank
Subband Ordering For Asymmetric Tree Structure Using Dyadic Analysis Filter Bank
Subband Ordering For Symmetric Tree Structure Using Dyadic Analysis Filter Bank
The dsp.DyadicAnalysisFilterBank System object™ decomposes a broadban... |
Proving single solution of initial value problem is increasing Given the
Libby Boone 2022-05-01 Answered
Proving single solution of initial value problem is increasing
{y}^{\prime }\left(x\right)=y\left(x\right)-\mathrm{sin}\left\{y\left(x\right)\right\},y\left(0\right)=1
wellnesshaus4n4
We use the simple fact that
v\l... |
Interpreting the Return on Investment (ROI)
An Alternative Return on Investment (ROI) Calculation
Investments and Annualized ROI
Combining Leverage With Return on Investment (ROI)
The Problem of Unequal Cash Flows
Return on investment (ROI) is a financial metric that is widely used to measure the probability of gaining... |
Electrostatic Mechanism for Depolymerization-Based Poleward Force Generation at Kinetochores
Electrostatic Mechanism for Depolymerization-Based Poleward Force Generation at Kinetochores ()
L. John Gagliardi1, Daniel H. Shain2
1Department of Physics, Rutgers The State University of New Jersey, Camden, NJ, USA.
2Departme... |
Home : Support : Online Help : Mathematics : Calculus : Transforms : inttrans : Examples : addtable
addtable (inttrans Package)
The integral transforms package contains functionality that allows great flexibility in the patterns that can be entered into the tables, as well as the ability to match these patterns quickly... |
Unit Circle | Brilliant Math & Science Wiki
Akshay Yadav, Andy Hayes, Aareyan Manzoor, and
Contribute to this wiki by adding relevant examples! For more information, see here.
The unit circle is a circle of radius 1 unit that is centered on the origin of the coordinate plane.
The unit circle is fundamentally related to... |
How would you use permutations to find the arrangements possible
Line of 4 boys:
4×3×2×1=4!=24
Line of 4 girls: also
4!=24
Combination of the two:
4!×4!={24}^{2}=576
posibilities.
If it doesn't matter whether the first is a boy or a girl, we'll have to double that to
2×576=1152
A card is drawn randomly from a deck of c... |
Let f be the function from R to
DAWIT BERIHUN 2022-04-02
We want to prove that
\left({Z}_{7},\oplus \right)
is group. I have difficulty proving associativity axiom. The solution reads
a\in {\mathbb{Z}}_{7},b\in {\mathbb{Z}}_{7}
c\in {\mathbb{Z}}_{7}
. By Theorem 3.4.10 we only need to show
\left(a+\left(b+c\right... |
Quotient rule - Wikipedia
Formula for the derivative of a ratio of functions
In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions.[1][2][3] Let
{\displaystyle f(x)=g(x)/h(x),}
where both g and h are differentiable and
{\displaystyle h(x)\ne... |
Revision as of 16:19, 29 July 2013 by NikosA (talk | contribs) (→Importing data: creating another Mapset, copying over material and optionally renaming)
{\displaystyle {\frac {W}{m^{2}*sr*nm}}}
{\displaystyle L\lambda ={\frac {10^{4}*DN\lambda }{CalCoef\lambda *Bandwidth\lambda }}}
{\displaystyle \rho _{p}={\frac {\pi... |
Proved that question: S(n) = \sum_{k \geq 1} \frac{n!}{k (n-k)! n^k}
Proved that question:
S\left(n\right)=\sum _{k\ge 1}\frac{n!}{k\left(n-k\right)!{n}^{k}}=\sum _{k\ge 1}\frac{{n}^{\underset{―}{k}}}{k{n}^{k}}\approx \frac{1}{2}\mathrm{log}\left(n\right)
Cloplerotly1gu
Here is a rough argument. Filling in the details ... |
tobeint39r 2022-04-30 Answered
M\in End\left(V\right)
M\otimes M
End\left(V\right)\otimes End\left(V\right)
This looks like it can get complicated. Generically, at least over an algebraically closed field, a matrix M will have distinct eigenvalues
{m}_{1},\dots ,{m}_{n}
, and generically
M\otimes M
will have distinct e... |
In many cases, MATSim uses a terminology that is different from the mainstream terminology. In most cases, the reason is that the concepts are only similar, but not identical, and we wanted to avoid the confusion of using the same term for aspects that are similar but not identical. The following attempts some commente... |
Fenwick Tree | Brilliant Math & Science Wiki
Agnishom Chattopadhyay, Pranjal Jain, Debarghya Adhikari, and
A Fenwick tree or binary indexed tree is a data structure that helps compute prefix sums efficiently. Computing prefix sums are often important in various other algorithms, not to mention several competitive progr... |
-7x=-a-4
Divide each term in -7x=-a-4 by -7 and simplify.
x=\frac{a}{7}+\frac{4}{7}
P\left(x\right)=-12{x}^{2}+2136x-41000
x=r\mathrm{cos}\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}y=r\mathrm{sin}
\underset{\left(x,y\right)\to \left(0,0\right)}{lim}\frac{{x}^{2}-{y}^{2}}{\sqrt{{x}^{2}+{y}^{2}}}
{y}^{\p... |
1.1 Solution 1a
1.1.3 Step functions approximate L^1 functions well
1.2 Problem 1b
1.3 Solution 1b
Prove the following version of the Riemann-Lebesque Lemma: Let
{\displaystyle f\in L^{2}[-\pi ,\pi ]\!\,}
. Prove in detail that
{\displaystyle {\frac {1}{2\pi }}\int _{-\pi }^{\pi }f(x)e^{-inx}dx\rightarrow 0\!\,}
{\disp... |
Linearization around the equilibrium point for a system of differential equations \frac{dN}{d
pacificak8m 2022-05-01 Answered
Linearization around the equilibrium point for a system of differential equations
\frac{dN}{dt}=\mu N\left(1-\frac{N}{K}\right)+N{\int }_{0}^{\mathrm{\infty }}p\left(a,t\right)da
\frac{\partial ... |
Find the Laplace transform of \(\displaystyle{f{{\left({t}\right)}}}={10}{t}{e}^{{-{5}{t}}}\)
Jakobe Norton 2022-04-15 Answered
f\left(t\right)=10t{e}^{-5t}
stecchiniror7
\mathcal{L}\left(t\right)=\frac{1}{{s}^{2}}
\mathcal{L}\left(10t{e}^{-5t}\right)=10F\left(s+5\right)=\frac{10}{{\left(s+5\right)}^{2}}
Note: we made ... |
Discrete Random Variables - Cumulative Distribution Function | Brilliant Math & Science Wiki
The cumulative distribution function of a random variable
X
F_X
that, when evaluated at a point
x
, gives the probability that the random variable will take on a value less than or equal to
x:
\text{Pr}[X \leq x]
. For example,... |
Optimization of Bleaching Process of Crude Palm Oil by Activated Plantain (Musa paradisiaca) Peel Ash Using Response Surface Methodology
Optimization of Bleaching Process of Crude Palm Oil by Activated Plantain (Musa paradisiaca) Peel Ash Using Response Surface Methodology ()
Wuraola Abake Raji*, Rowland Ugochukwu Azik... |
Khudaverdian H. Non-linear homomorphisms of algebras of functions are induced by thick morphisms (abstract) - Geometry of Differential Equations
Khudaverdian H. Non-linear homomorphisms of algebras of functions are induced by thick morphisms (abstract)
Speaker: Hovhannes Khudaverdian
Title: Non-linear homomorphisms of ... |
Algebra Shortcuts Warmup Practice Problems Online | Brilliant
\large \frac{ \color{#20A900}{2015} \times \color{#3D99F6}{1999} -\color{#20A900}{2015} \times \color{#D61F06}{1379}} { \color{#3D99F6}{1999} - \color{#D61F06}{1379} } .
Hint: Use the distributive property.
a = 2 , b = 7, c = 9
1 + a + b + c + ab + bc + ca +... |
Want to know more about Green's, Stokes', and the divergence theorem?
Determine the lowest common multiple (LCM) of the following 4𝑥2𝑦2 , 6𝑥𝑦 , 10𝑥𝑦2
A nonhomogeneous second-order linear equation and a complementary function
{y}_{c}
are given. Find a particular solution of the equation.
4{x}^{2}y{ }^{″}-4x{y}^{\p... |
Abstract algebra questions, solved and explained
Abstract algebra questions and answers
Recent questions in Abstract algebra
Paula Good 2022-03-25 Answered
How can I show these polynomials are not co'?
x,\text{ }x-1
x+1
{\mathbb{Z}}_{6}\left[x\right]
siliciooy0j 2022-03-24 Answered
Let k be a field, V a finite-dimensio... |
Monte-Carlo Simulation | Brilliant Math & Science Wiki
Beakal Tiliksew, Alex Chumbley, Ethan W, and
Mayle Dump
Monte Carlo simulations define a method of computation that uses a large number of random samples to obtain results. They are often used in physical and mathematical problems and are most useful when it is dif... |
Compare accuracies of two classification models by repeated cross-validation - MATLAB testckfold - MathWorks Italia
{e}_{crk}
{\stackrel{^}{\delta }}_{rk}={e}_{1rk}-{e}_{2rk}.
{\overline{\delta }}_{r}=\frac{1}{K}\sum _{k=1}^{K}{\stackrel{^}{\delta }}_{kr}.
\overline{\delta }=\frac{1}{KR}\sum _{r=1}^{R}\sum _{k=1}^{K}{\... |
Free solutions to counting principles problems
Counting principles problems and answers
Recent questions in Counting Principles
N\left(A\cup B\cup C\right)=N\left(A\right)+N\left(B\right)+N\left(C\right)-N\left(A\cap B\right)-N\left(A\cap C\right)-N\left(B\cap C\right)+N\left(A\cap B\cap C\right)
21=9+10+7-N\left(A\cap... |
Rubtsov V. Lie algebroid cohomology: from Der to Lie algebroid non-abelian extensions (abstract) - Geometry of Differential Equations
Rubtsov V. Lie algebroid cohomology: from Der to Lie algebroid non-abelian extensions (abstract)
Title: Lie algebroid cohomology: from Der to Lie algebroid non-abelian extensions
After a... |
Pitchfork bifurcation - Wikipedia
Bifurcation from a system having one fixed point to three fixed points
In bifurcation theory, a field within mathematics, a pitchfork bifurcation is a particular type of local bifurcation where the system transitions from one fixed point to three fixed points. Pitchfork bifurcations, l... |
1.2.7 CFD12
Numerical simulation of the flow around the wing RAE M2155 have been performed at QINETIQ, for case 1-2-3-4, and at CIRA, only for case 2, with the main aim of validation and assessment of the turbulence models employed.
QINETIQ [3] has used the following turbulence models :
1) A k-ω based variant of the Me... |
Proving the generator of A = \{154a + 210b : a,b
A=\left\{154a+210b:a,b\in \mathbb{Z}\right\}
\left(154,\text{ }210\right)
For the further proof , you just need to show that
154a+210b
just generates all the common multiples of 154 and 210 for different values of a and b where
a,\text{ }b\in \mathbb{Z}
and even HCF can ... |
ca foundation mock test in indices in Business Mathematics | Online Exam
Home Quantitative Aptitude ca foundation mock test-indices
ca foundation mock test in indices in Business Mathematics
If A = B/2 = C/5, then A : B : C is
If a/3 = b/4 = c/7, then a+b+c/c is
If p/q = r/s = 2.5/1.5, the value of ps:qr is
If x : y = ... |
Directions : In each of these questions a number series is given. In each series only one number is wrong. Find out the wrong number.
The series is 50 + 1^2 = 51, 51 – 2^2 = 47, 47 + 3^2 = 56, 56 – 4^2 = 40, 40 + 5^2 = 65, 65 –
6^2 = 29.
Hence, there should be 40 in place of 42.
The series is 3 × 2 + 3 = 9, 9 × 3 – 4 =... |
Work | Brilliant Math & Science Wiki
July Thomas, Sravanth C., Anish Harsha, and
Work is done when a force is applied, at least partially, in the direction of the displacement of the object. If that force is constant then the work done by the force is the dot product of the force with the displacement:
W=\vec{F} \bulle... |
If y=\arctan(\frac{2x−1}{1+x−x^2}), then \frac{dy}{dx} at x=1 is equal to? I have
stropa0u 2022-01-24 Answered
y=\mathrm{arctan}\left(\frac{2x-1}{1+x-{x}^{2}}\right)
\frac{dy}{dx}
bekiffen32
In the derivative of
y=\mathrm{arctan}\left(x\right)-\mathrm{arctan}\left(1-x\right)+k\pi
\frac{dy}{dx}=\frac{1}{1+{x}^{2}}-\left... |
Kunshan First People’s Hospital, Kunshan, China.
Abstract: Background: To explore the therapeutic effect of Tongxinluo capsule (Tongxinluo) on patients with Syndrome X and Affective Disorder. Methods: Fifty-six patients with Syndrome X and Affective Disorder were randomly divided into a Tongxinluo capsule group and a p... |
A geometric representation, showing the relationship between a whole and its part, is from Class 12 TET Previous Year Board Papers | Mathematics 2018 Solved Board Papers
\sqrt{784}
\sqrt{\overline{2\times 2}\times \overline{2\times 2}\times \overline{7\times 7}}
2\times 2\times 7
28
{\left(\frac{5}{7}\right)}^{4}\tim... |
xvYCC - Wikipedia
Sony's x.v.Color logo
xvYCC or extended-gamut YCbCr is a color space that can be used in the video electronics of television sets to support a gamut 1.8 times as large as that of the sRGB color space.[1][2][3] xvYCC was proposed by Sony,[4] specified by the IEC in October 2005 and published in January... |
Nonlinear regression model class - MATLAB - MathWorks Italia
NonLinearModel class
Fit a Nonlinear Regression Model
Nonlinear regression model class
An object comprising training data, model description, diagnostic information, and fitted coefficients for a nonlinear regression. Predict model responses with the predict ... |
Autoregressive Moving Average Model - MATLAB & Simulink - MathWorks Switzerland
Stationarity and Invertibility of the ARMA Model
For some observed time series, a very high-order AR or MA model is needed to model the underlying process well. In this case, a combined autoregressive moving average (ARMA) model can sometim... |
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