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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23312 | # Homework Help: Permutation question
1. Nov 16, 2008
### TTob
1. The problem statement, all variables and given/known data
prove that there are not permutations of order 18 in S_9.
2. Relevant equations
3. The attempt at a solution
let t=c_1,...,c_k is cycle decomposition of such permutation. let r_1,...,r_k the ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23313 | # How long is one second?
Classical Mechanics Level 2
Usain Bolt is a Jamaican sprinter who holds the world record for the $$100$$ meters of $$9.58$$ seconds, which is the highest since the start of fully automatic time measurements. The second (symbol: s) is the base unit of time in the International System of Units... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23314 | ## The Annals of Statistics
### Bayesian Sequential Estimation
Mayer Alvo
#### Abstract
For fixed $\theta$, let $X_1, X_2, \cdots$ be a sequence of independent identically distributed random variables having density $f_\theta(x)$. Using a sequential Bayes decision theoretic approach we consider the problem of estim... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23315 | # Math Help - Finding x & y intercepts (found the y-intercept)
1. ## Finding x & y intercepts (found the y-intercept)
I need help please with finding the x-intercept for the following:
$y = -2x^2 +4$
I got the y-intercept (0,4) by setting x = 0
However, when I set y = 0 and attempt to solve I get stuck
$0 = -2x^2... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23316 | Someone's Intermediate Representation
0%
# Keywords
• Hypothetical Judgments: an entailment between one or more hypotheses and a conclusion.
• Entailment has 2 notions:
• derivability
• General Judgment: the universality or genericity of a judgment.
• General Judgment has 2 forms:
• generic
• parametric
# Hypotheti... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23317 | Linear Algebra eigenvalue proof question?
Let A be an nxn matrix, and let v be an eigenvector of A with eigenvalue λ. Prove that if f(t) is any polynomial, then f(A)v=f(λ)v.
Relevance
• Eugene
Lv 7
7 years ago |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23318 | ## Essential University Physics: Volume 1 (4th Edition)
We use the equation that relates the decibel level to intensity to find: $\beta_1 - \beta_2 = 10logP_2-10logP_1$ $\beta_1 - \beta_2 = 10log\frac{P_2}{P_1}$ $\frac{\beta_1 - \beta_2}{10} = log\frac{P_2}{P_1}$ $\frac{P_2}{P_1} = 10^{\frac{\beta_1 - \beta_2}{10}}$ $... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23319 | # Rayleigh distribution function pdf
Given the single shot rayleigh distribution, calculate the single shot cumulative distribution function cdf for the rayleigh distribution. To shift andor scale the distribution use the loc and scale parameters. The rayleigh distribution is one of the most popular distributions in a... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23320 | Question
# A particle moves in a circular path of radius r. In half the period of revolution its displacement and distance covered are.\begin{align} & \text{A}\text{. }2r,\pi r \\ & \text{B}\text{. }r,\pi r \\ & \text{C}.\text{ }2r,2\pi r \\ & \text{D}\text{. }r\sqrt{2},\pi r \\ \end{align}
Hint: We know that basical... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23321 | # NO VENN DIAGRAMS!
Discrete Mathematics Level 2
Let $$X$$, $$Y$$ and $$Z$$ be three distinct subsets of the universal set $$U$$, no two of which are disjoint.
WITHOUT USING VENN DIAGRAMS, find $$n(X)$$, given: $$n(X \cap Y \cap Z) = 5$$, $$n[X \cap (Y - Z)]=20$$, $$n[X \cap (Z - Y)]=25$$, and $$n[(X-Y)-Z]=50$$.
##... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23322 | # Tag Info
0
We can use Master Theorem to solve this : If a Recurrence Relation is of the Form $$T(n)=aT\bigg(\frac{n}{b}\bigg)+{n^k}({\log(n)})^p$$ Then, as per Master Theorem, we have Six Conditions depending on value of $a,b,k$ and $p$ If $\log_ba>k$ Answer is $\theta(n^{\log_ba})$ If $log_ba=k$ and $p>-1$ Answer ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23323 | # Derivatives of a series of monotone functions
Suppose that $(f_n)$ is a sequence of monotone non-decreasing functions on $[a,b]$ such that $f(x) = \sum_{n=1} ^\infty f_n (x)$ is finite for each $x\in [a,b]$. By Lebesgue's theorem on monotone functions, each $f_n$ is differentiable almost everywhere, and it is clear ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23324 | ## Derivative of cos(ln(tan(x^3)) ?
Derivative of cos(ln(tan(x^3)) ? I get lost at the end of the chain rule
• Anonymous commented
Kindly Rate the Best Answer FIRST.................... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23325 | # 1.9 Waves (Page 2/7)
Page 2 / 7
${v}_{\text{w}}=\frac{\lambda }{T}$
or
${v}_{\text{w}}=\mathrm{f\lambda }.$
This fundamental relationship holds for all types of waves. For water waves, ${v}_{\text{w}}$ is the speed of a surface wave; for sound, ${v}_{\text{w}}$ is the speed of sound; and for visible light, ${v}... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23326 | Click to Chat
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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23327 | # ''Incomplete'' expression
Algebra Level 4
In the expansion of $$(1 - x- kx^2)^8$$, the coefficient of $$x^3$$ is 3.5 times the sum of the coefficients of $$x$$ and $$x^2$$.
$$k$$ can be expressed as $$\frac{a}{b}$$ where a and b are coprime positive integers. What is the value of $$a+b$$?
× |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10784 | # Metric Spaces and Topology
• Oct 13th 2009, 03:07 PM
CollegeMathKid
Metric Spaces and Topology
A and B are any sets in a metric space (X, d)
Prove that
(A U B )' = A' U B'
' meaning interior.
And then prove that
(A U B ) closure = A closure U B closure
I know that you have to prove it both ways, and that the pro... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10785 | # Some questions about differential forms
• If $A$ is a differential one form then $A\wedge A .. (more\text{ }than\text{ }2\text{ }times) = 0$ Then how does the $A\wedge A \wedge A$ make sense in the Chern-Simon's form, $Tr(A\wedge dA + \frac{2}{3} A \wedge A \wedge A)$ ?
I guess this anti-commutative nature of wedge... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10786 | Infoscience
Journal article
# Coloring some classes of mixed graphs
We consider the coloring problem for mixed graphs, that is, for graphs containing edges and arcs. A mixed coloring $c$ is a coloring such that for every edge $[x_{i},x_{j}]$, $c(x_{i})\neq c(x_{j})$ and for every arc $(x_{p},x_{q})$, $c(x_{p})<c(x_{... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10787 | ## College Algebra (11th Edition)
$\frac{1}{2}$
Divide the inside of each radical with one radical over both of them. $\sqrt{\frac{-10}{-40}}$ Simplify. $\sqrt{\frac{-10}{-40}}=\sqrt{\frac{1}{4}}$ Pull the negative inside the radical into an imaginary number outside of the radical. $\sqrt{\frac{1}{4}}=\frac{1}{2}$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10788 | # Hadwiger number of total graph
Let $G=(V,E)$ be a finite, simple, undirected graph, and let $T(G)$ be its total graph. The Hadwiger number $\eta(G)$ is the maximum $n\in\mathbb{N}$ such that $K_n$ is a minor of $G$.
Is there an example of a graph $G$ such that $\eta(T(G)) > \Delta(G) + 2$ (where $\Delta(G)$ is the ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10789 | # Tasty Logarithm 6
$\large \lambda(\lambda(\lambda(10))) = 10^n$
Let $\lambda(m)$ denote the product of all positive integers that divides $m$ (inclusive of 1 and itself). What is the value of $n$ such that it satisfy the product above?
× |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10790 | ## Textbooks & Solution Manuals
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## Holooly Tables
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## Holooly Help Desk
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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10791 | ## Moduli of representations of the fundamental group of a smooth projective variety. I.(English)Zbl 0891.14005
This is a step by step construction with full proofs of moduli spaces and associated objects of representations of the fundamental group of a smooth projective variety. It leads to various incarnations:
(1) ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10792 | ## Monday, December 21, 2015
### Prove $a(a-c)^2+b(b-c)^2\ge (a-c)(b-c)(a+b-c)$ for all real $a,\,b,\,c\ge 0$: First Attempt
For reals $a,\,b,\,c\ge 0$, prove the inequality
$a(a-c)^2+b(b-c)^2\ge (a-c)(b-c)(a+b-c)$
and state when the equality holds.
It's hard not to relate the LHS of the inequality with the AM-GM ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10793 | 4 retag
3 fixed discriminant 12 error; added 11 characters in body
Suppose $f \in \mathbb{Q}[x]$ has is monic, with roots $\alpha_{1},\dots,\alpha_{n}$. Define the discriminant of $f$ to be the number $\Delta = \Pi_{i<j} (\alpha_{i} - \alpha_{j})^2$. Let $D(f) = \sqrt{\Delta} = \Pi_{i<j} (\alpha_{i} - \alpha_{j})$ be ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10794 | # If you have 100J of total mechanical energy in a closed system, if the object is at rest how much potential energy is in the system? A. 50 J B. 200 J C. 100 J D. There is not enough information to solve this problem
###### Question:
If you have 100J of total mechanical energy in a closed system, if the object is at... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10795 | NEW
New Website Launch
Experience the best way to solve previous year questions with mock tests (very detailed analysis), bookmark your favourite questions, practice etc...
## GATE CE 1999
Exam Held on Thu Jan 01 1970 00:00:00 GMT+0000 (Coordinated Universal Time)
Click View All Questions to see questions one by one ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10796 | # Quick way of showing an $n\times n$ Jordan block associated to $1$ is similar to the companion matrix of $(x-1)^n$
Is there a quick, clean way of proving that the $n\times n$ Jordan block with $1$'s on the diagonal and the Frobenius companion matrix corresponding to the polynomial $(x-1)^n$ are similar matrices?
Ap... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10797 | # Basis for topology of weak convergence of probability measures
Let $S$ be a metric space with be Borel $\sigma$-algebra $\Sigma$. Let $\boldsymbol{P}(S)$ be the set of probability measures on $(S,\Sigma)$. According to wikipedia, "the weak topology is generated by the following basis of open sets:
$$\left\{ U_{\phi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10798 | # Find the regression equation, letting the first variable be the predictor (x) variable. Using the listed...
###### Question:
Find the regression equation, letting the first variable be the predictor (x) variable. Using the listed actressactor ages in various years, find the best predicted age of the Best Actor winn... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10799 | # Tag Archives: irreducible representations
## Polynomials and Representations XXXVIII
Determinant Modules We will describe another construction for the Schur module. Introduce variables for . For each sequence we define the following polynomials in : Now given a filling T of shape λ, we define: where is the sequence... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2128 | SEARCH HOME
Math Central Quandaries & Queries
Question from gordon, a parent: What is the formula to find out how many gallon of water in a length of pipe tried your answer on 8inch at 50feet did not work out
Hi Gordon,
The formula for the volume of a circular cylinder is $\pi \; r^2 h$ where $\pi$ is approximately... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2129 | Now showing items 1220-1239 of 1524
• #### 1332 - Partial Differential Equations
[OWR-2013-40] (2013) - (04 Aug - 10 Aug 2013)
The workshop dealt with partial differential equations in geometry and technical applications. The main topics were the combination of nonlinear partial differential equations and geometric... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2130 | # Samacheer Kalvi 7th Maths Solutions Term 3 Chapter 3 Algebra Ex 3.3
Students can Download Maths Chapter 3 Algebra Ex 3.3 Questions and Answers, Notes Pdf, Samacheer Kalvi 7th Maths Book Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2131 | Difference between revisions of "2017 AMC 10A Problems/Problem 20"
Problem
Let $S(n)$ equal the sum of the digits of positive integer $n$. For example, $S(1507) = 13$. For a particular positive integer $n$, $S(n) = 1274$. Which of the following could be the value of $S(n+1)$?
$\textbf{(A)}\ 1 \qquad\textbf{(B)}\ 3\q... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2132 | # Thread: Absolute value of Legendre polynomials ??
1. ## Absolute value of Legendre polynomials ??
Hi guys,
I would like to ask for some help regarding a problem with Legendre polynomials:
P_n(x) is an arbitrary Legendre polynomial (0<=n and -1<x<1). Prove the following
$\left| P_{n}(x) \right | \le \sqrt{\pi/(1-x... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2133 | # Empty Set as Subset
## Theorem
Let $S$ be a set.
Let $A$ be a subset of $S$.
Then:
$A = \O \iff \forall x \in S: x \notin A$
## Proof
Sufficient condition follows by definition of empty set.
For necessary condition assume that:
$\forall x \in S: x \notin A$
Let $x$ be arbitrary.
Aiming for a contradiction,... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2134 | # Polygon Formula
Polygon is a word derived from The Greek language, where poly means many and gonna means angle. So we can say that in a plane, closed figure with many angles is called a polygon. The given diagram is how a polygon looks like:
There are many properties in a polygon like sides, diagonals, area, angles... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2135 | # A model train with a mass of 4 kg is moving along a track at 6 (cm)/s. If the curvature of the track changes from a radius of 32 cm to 48 cm, by how much must the centripetal force applied by the tracks change?
Jul 29, 2017
The answer is $\text{1500 dyn}$.
Jul 29, 2017
Ans:1500dyn. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2136 | # Does every Riemannian manifold has a local orthonormal divergence free frame of vector fields?
Let $$(M,g)$$ be a smooth Riemannian manifold, and let $$p \in M$$.
Is there an open neighbourhood $$U$$ of $$p$$ that admits an orthonormal frame of divergence-free vector fields?
Edit: At least for dimension $$2$$, $$M... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2137 | # Symmetric relation and definition of even numbers
Let a relation $$\rho$$ be defined on $$\mathcal{Z}$$(set of integers) by '$$a \rho b$$ if and only if $$a-b$$ is even' for $$a,b \in \mathcal{Z}$$.
Then, is the above relation symmetric or anti-symmetric?
Can the negative integers be treated as even or odd numbers... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2138 | Math Calculators, Lessons and Formulas
It is time to solve your math problem
mathportal.org
# Determinant Calculator
This calculator computes determinant of a square matrix. The calculator shows all steps and detailed explanation.
Determinant calculator (shows all steps)
show help ↓↓ examples ↓↓
Input matrix
worki... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2139 | # PROBLEM LINK:
Author: Abhinav Sharma
Tester: Satyam
Editorialist: Nishank Suresh
To be calculated
# PREREQUISITES:
Sorting, prefix sums
# PROBLEM:
There are N cans lying on the x-axis, the i-th at position X_i. The i-th can can be moved one step in either direction for a cost of B_i.
There is also a green zone... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2140 | Lemma 38.20.4. In Situation 38.20.3.
1. If $A' \to A''$ is a flat morphism in $\mathcal{C}$ then $F_{lf}(A') = F_{lf}(A'')$.
2. If $A \to B$ is essentially of finite presentation and $M$ is a $B$-module of finite presentation, then $F_{lf}$ is limit preserving: If $\{ A_ i\} _{i \in I}$ is a directed system of object... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2141 | Transmission Coefficient through a delta potential
Homework Statement
Consider an uni-dimensional scattering by a delta function at the origin, given by the potential $V(x) = g \delta(x)$, with $g>0$.
Using the following result, with $G(x)$ being the green function:
$$\Psi (x) = e^{ikx} + g \dfrac{2m}{\hbar}\dfrac{... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2142 | Research
# Existence of nontrivial solutions to perturbed p-Laplacian system in ℝ N involving critical nonlinearity
Huixing Zhang* and Wenbin Liu
Author Affiliations
Department of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu 221116, People's Republic of China
For all author emails, pleas... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2143 | # Derive some facts of the negative binomial distribution
The previous post called The Negative Binomial Distribution gives a fairly comprehensive discussion of the negative binomial distribution. In this post, we fill in some of the details that are glossed over in that previous post. We derive the following points:
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6496 | # American Institute of Mathematical Sciences
• Previous Article
A perturbation-based approach for continuous network design problem with emissions
• NACO Home
• This Issue
• Next Article
A smooth QP-free algorithm without a penalty function or a filter for mathematical programs with complementarity constraints
2015, ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6497 | Chapter 6: Polynomials
# 6.9 Pascal’s Triangle and Binomial Expansion
Pascal’s triangle (1653) has been found in the works of mathematicians dating back before the 2nd century BC. While Pascal’s triangle is useful in many different mathematical settings, it will be applied to the expansion of binomials. In this appli... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6498 | # Distance and fractional isomorphism in Steiner triple systems
Forbes, Anthony; Grannell, Mike and Griggs, Terry (2007). Distance and fractional isomorphism in Steiner triple systems. Rendiconti del Circolo Matematico di Palermo Serie II, 56, pp. 17–32.
## Abstract
Quattrochi and Rinaldi introduced the idea of - is... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6499 | # Free Energy of BiPolytrope with $~(n_c, n_e) = (0, 0)$
Here we present a specific example of the equilibrium structure of a bipolytrope as determined from a free-energy analysis. The example is a bipolytrope whose core has a polytropic index, $~n_c = 0$, and whose envelope has a polytropic index, $~n_e = 0$. The det... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6500 | ## (Lobachevskii Journal of Mathematics, Vol.13, pp.39-43)
An $L^{1}$--convergence property of the complex form $g_{n}(c,t)=S_{n}(c,t)- \left[ c_{n}E_{n}(t)+c_{-n}E_{-n}(t) \right]$ of the modified sums introduced by Garrett and Stanojevi\'{c} [3] is established and a necessary and sufficient\ condition for $L^{1}$-co... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6501 | ### Home > CC3 > Chapter 4 > Lesson 4.1.2 > Problem4-21
4-21.
Kelso’s mom wants to put a floating blanket over the family’s circular wading pool to keep the heat in and the leaves out. The pool has a diameter of $10$ feet. Homework Help ✎
1. How many square feet of blanket will Kelso’s mother need?
The formula to f... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6502 | Method of Variation of parameters
1. Jan 21, 2009
s7b
Hi,
When using the method of variation of parameters to solve something like;
y'' + y' = 2^x
I got the aux. equation: r^2 - r =0 which gives the roots r=0,1
How do I find the complementary equation yc?
2. Jan 22, 2009
ice109
what is the aux. eqn? did you s... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6503 | Simulating 15C RAN # on 35s
02-14-2015, 05:13 PM (This post was last modified: 02-15-2015 08:01 AM by Tugdual.)
Post: #1
Tugdual Senior Member Posts: 756 Joined: Dec 2013
Simulating 15C RAN # on 35s
This 35s program will return the exact same RAN # values as the 15C (Don't even ask me why I did that...). Fun fact: the... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6504 | Article | Open | Published:
Probing the growth and melting pathways of a decagonal quasicrystal in real-time
Scientific Reportsvolume 7, Article number: 17407 (2017) | Download Citation
Abstract
How does a quasicrystal grow? Despite the decades of research that have been dedicated to this area of study, it remains ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6505 | # Entire extension of the Fouier transform of a smooth compactly supported function
The statement which is not very clear is this: if $\phi \in C^{\infty}_0$ then its Fourier transform extends to a complex-analytic function.
Of course the candidate extension is $\hat{\phi}(z)=\int e^{-i<x,\xi+i\eta>}\phi(x) dx$ where... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6506 | ## Penalised regression
On regression estimation with penalties on the model.
Practically this means choosing appropriate smoothing to do good model selection, and possibly using some clever optimisation method.
Related to compressed sensing but here we consider sampling complexity,
the effect of measurement noise, an... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6507 | # A calculus problem by neelesh vij
Calculus Level 4
$\large \int_{0}^{1} \dfrac{x^2 e^{\arctan(x)}}{\sqrt{1+x^2}} \, dx$
Find the value of the closed form of the above integral.
Give your answer to 1 decimal place.
× |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6508 | How do you solve ln(-m)=ln(m+10)?
Dec 21, 2016
$m = - 5$
Explanation:
Given:
$\ln \left(- m\right) = \ln \left(m + 10\right)$
Take exponents of both sides to find:
$- m = {e}^{\ln \left(- m\right)} = {e}^{\ln \left(m + 10\right)} = m + 10$
Add $m - 10$ to both ends to get:
$- 10 = 2 m$
Divide both sides by $2... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6509 | ## Elliptic Curves
Author: Dale Husemoller
Publisher: Springer Science & Business Media
ISBN: 1475751192
Category: Mathematics
Page: 350
View: 5316
The book divides naturally into several parts according to the level of the material, the background required of the reader, and the style of presentation with respe... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6510 | ### Math Notes
Subjects
#### Algebra Solutions
##### Topics || Problems
Algebra
When A and B both work, they can paint a certain house in 8 days. Also, they could paint this house if A worked 12 days and B worked 6 days. How long would it take each to paint the house alone? Solution:
Rate of A: $$\frac{1}{A}$$
Ra... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6511 | ## anonymous 3 years ago what is the arcsin(sin3pi)
• This Question is Open
1. zepdrix
The range of arcsine is restricted from $$\large -\pi/2$$ to $$\large \pi/2$$. $\large \arcsin\left(\sin(3\pi)\right)\qquad = \qquad \arcsin\left(0\right) \qquad = \qquad 0$
2. anonymous
Those domain restrictions always find a wa... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9520 | # It is given that the events A and B are such that $P(A) = \large\frac{1}{4}\: \: P \bigg( \large\frac{A}{B} \bigg) \large\frac{1}{2}\: and \: P \bigg( \large\frac{B}{A} \bigg) = \large\frac{2}{3}$ Then $P(B)$ is
$\begin {array} {1 1} (A)\;\large\frac{1}{6} & \quad (B)\;\large\frac{1}{3} \\ (C)\;\large\frac{2}{3} & \... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9521 | # Are there more convenient ways of getting the number of digits of a positive integer?
I want to define $n$th power of $10$ for a positive integer. Say for $43$ it would be $2$, for $5$ it would be $1$, for $9999$ it would be $4$. As for $1$, $10$, $100$, ... I am still shifting between two options. $10$ would result... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9522 | # Status of a conjecture about powers of 2
I recently saw a conjecture on a blog ( http://blog.tanyakhovanova.com/?p=311 ) which the author refers to as the 86 conjecture. The conjecture claims that all powers of 2 greater than $2^{86}$ have a zero in their base 10 representation.
At first glance this seems like a nu... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9523 | # Excercise 1.2 Rational Numbers- NCERT Solutions Class 8
Go back to 'Rational Numbers'
## Chapter 1 Ex.1.2 Question 1
Represent these numbers on the number line.
(i) \begin{align}\;\frac{7}{4}\end{align}
(ii) \begin{align}\;\frac{{ - 5}}{6}\end{align}
### Solution
Reasoning:
The positive numbers are on the ri... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9524 | How do you solve 2 ln x = 1?
May 3, 2016
$x = \sqrt{e}$
Explanation:
$2 \ln \left(x\right) = 1$
$\ln \left({x}^{2}\right) = 1$
${x}^{2} = {e}^{1}$
$x = \pm \sqrt{e}$
Since $\ln \left(x\right)$ is not defined for $x < 0$
$x = \sqrt{e}$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9525 | # Jordan matrix
In the mathematical discipline of matrix theory, a Jordan block over a ring $R$ (whose identities are the zero 0 and one 1) is a matrix composed of 0 elements everywhere except for the diagonal, which is filled with a fixed element $\lambda\in R$, and for the superdiagonal, which is composed of ones. T... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9526 | Let R be a ring. An ideal of R is a subring I of R such that if a I, r R, then a · r I and r · a I. Let R be a ring with identity 1, and let a R. If a has an inverse with respect to multiplication, then we say that a is a unit of R. A commutative ring R is an integral domain if R contains no zero divisors. In other wor... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9527 | # How to prove a complete binary tree of depth N has $2^{N+1} - 1$ nodes?
Here is the description of a proof problem:
A complete binary tree of depth N is a binary tree in which every node on levels $0,1,2,...,N-1$ is a parent and has two children, and each node on level N is a leaf.
It's asking for proving binary t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9528 | Persistence of boundary punctured holomorphic curves
Given a Legendrian $\Lambda$ in a contact manifold $(Y,\alpha)$, suppose one has a rigid J-holomorphic curve into the symplectization $(M,\omega)=(Y\times\mathbb{R},\mathrm{d}(e^t\alpha))$. As considered in Legendrian contact homology, the domain of the curve should... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9529 |
Inside every non-Bayesian, there is a Bayesian struggling to get out.
—Dennis V. Lindley (quoted by E. T. Jaynes)
Significance testing is all about whether the outcome would be too much of a coincidence for the hypothesis to be true. But how much of a coincidence is too much? Should we reject a hypothesis when we fin... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9530 | # Math Help - what will be the determinant of the matrix A
1. ## what will be the determinant of the matrix A
Let A be 3 by 3 matrix over real numbers satisfying A⁻¹= I -2A. Then what will be the
determinant of the matrix A?
2. ## Re: what will be the determinant of the matrix A
Originally Posted by sorv1986
Let A... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9531 | # What is the derivative of x^(lnx)?
Aug 9, 2015
$\frac{d}{\mathrm{dx}} {x}^{\ln x} = 2 {x}^{\ln x - 1} \ln x$
#### Explanation:
Let $y = {x}^{\ln x}$
Taking the natural logarithm:
$\ln y = {\left(\ln x\right)}^{2}$
Taking the derivative with respect to x:
$\frac{1}{y} \frac{\mathrm{dy}}{\mathrm{dx}} = \frac{2 \ln... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9532 | # Are all degenerate d-orbitals identical?
This discussion spun off from the comments to another question. The basic idea of that question was that electrons don't have a preferred order of filling in $p$ orbitals, i.e. the first electron will fill in the $p_x$ orbital just as well as it will fill in the $p_y$ or $p_z... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9533 | Bob's Followers
Level pending
Bob had 10 followers on Brilliant the first week, 15 followers the second week, 25 followers the third week, and 45 followers the fourth week(now). How many followers will Bob have next week(the fifth week) if the number of followers Bob has is $$5+5(2^{x-1})$$?
("x" is the xth week, ex... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9534 | Category:Complex Conjugates
Jump to navigation Jump to search
This category contains results about Complex Conjugates.
Definitions specific to this category can be found in Definitions/Complex Conjugates.
Let $z = a + i b$ be a complex number.
Then the (complex) conjugate of $z$ is denoted $\overline z$ and is defi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9535 | Flux and nonconducting shells
Homework Statement
Flux and nonconducting shells. A charged particle is suspended at the center of two concentric spherical shells that are very thin and made of nonconducting material. Figure (a) below shows a cross section. Figure (b) below gives the net flux Φ through a Gaussian spher... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19248 | 1. ## Arc Length question
It says...
Find the length fo the graph and compare it to the straight-line distance between the endpoints of the graph.
f(x)=ln[sex(x)] x E [0,(pi/4)]
how would you do this?
2. ln(sex)?. That's everyone's favorite integral. What is E?.
Do you mean arc length of $\displaystyle ln(sec(x))... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19249 | Question Info
This question is public and is used in 1 group and 10 tests or worksheets.
Type: Multiple-Choice
Category: Nonlinear Equations and Functions
Standards: HSG-GPE.A.3
Author: nsharp1
Created: 3 years ago
View all questions by nsharp1.
Nonlinear Equations and Functions Question
View this question.
Add t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19250 | # Solve the differential equation: $-x^2 y'' = \lambda y$
I need to solve the differential equation $-x^2 y'' = \lambda y$ by transforming the differential equation to a equation with constant coefficients. I need to do this by using $f(x) = y(e^x)$. If I do this, I become the equation: $y''(e^x) + \frac{y'(e^x)}{e^x}... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19251 | 💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!
# Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct to six decimal places).$\displaystyle \lim_{t \to 0}\frac{e^{5t} - 1}{t}$, $t = \pm 0.5, \pm 0.1, \pm 0... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19252 | An example of covariant functor.
Let $F$ be the following covariant functor from the category of sets to the category of left module over a ring $R$ with identity. For each set $X$, $F\left(X\right)$ is the free $R$-module on $X$. If $f : X\rightarrow X'$ is a function, let $F\left(f\right) : F\left(X\right)\rightarro... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19253 | # Simple Question: Units and volume of DNA - Can't get formula correct?
## Homework Statement
Deoxyribonucleic acid (DNA) is thought to be the chemical compound
responsible for the process of heredity. A sample of DNA was found to have
density 1.10 g/cm3 and its molecular weight was estimated to be
3.04 × 108 g. What... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19254 | Calculating the flux of a vector field
Calculate the flux of F=$<xy,yz,xz>$ out of $S$, ,which is the part of the paraboloid $x^2+y^2+z=4$ that lies above the square $[0,1]\times[0,1]$.
I know we need to solve $\iint_{s}F\cdot ds$ which can be written as $\iint_{D}F(u,v)\cdot (r_u\times r_v)dA$, where $r(u,v)$ is the... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19255 | +0
# geometry problem. help requested :(
0
69
2
Let $$ABCD$$ be an isosceles trapezoid, with bases $$\overline{AB}$$ and $$\overline{CD}.$$ A circle is inscribed in the trapezoid, as shown below. (In other words, the circle is tangent to all the sides of the trapezoid.) The length of base $$\overline{AB}$$ is $$2x$$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19256 | # help on proof
• June 6th 2006, 01:49 PM
Judi
help on proof
if Bk>0, then prove the following:
B1+B2+.....+Bn-B1B2....Bn<=n-1
(sum-product is less than equal to n-1)
When my instructor was talking about Bernoulli's inequalities, he gave us this problem to prove.
• June 6th 2006, 02:01 PM
ThePerfectHacker
Quote:
Ori... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19257 | # What fraction denominator is 100?
## What fraction denominator is 100?
A percent is a special type of fraction where the denominator is 100.
How do you compare fractions with denominators?
To compare improper fractions with different denominators, first write each fraction as its equivalent fraction so that they ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19258 | # Linear regression with redundant features (perfect multicolinearity)
Suppose $X \sim N(0,1)$, $Z=X$, and $Y=X$. An ordinary least squares regression problem is solved:
$min_{(b1,b2)} \|Y-(b1*X+b_2*Z)\|_{2}^2$
This is a strictly convex function which must have a unique solution. But this example has three solutions... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19259 | # Sphere
• Radius of a sphere: $$R$$
Height of a spherical cap/segment: $$h$$
Radius of the base of a spherical cap: $$r$$
Area of the base of a spherical cap: $${S_B}$$
Area of the spherical surface of a cap: $${S_C}$$
Radii of the bases of a spherical segment: $${r_1},$$ $${r_2}$$
Areas of the bases of a spherical s... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19260 | # Linear Algebra
Free Version
Moderate
LINALG-MXK4VD
Given the vectors:
\begin{align*} \vec{x}_1&=\begin{pmatrix} 1 \\\ 1\\\ 1 \end{pmatrix} \\\ \vec{x}_2&=\begin{pmatrix} 1 \\\ 0\\\ \!\!-\!1 \end{pmatrix} \\\ \vec{x}_3&=\begin{pmatrix} -1\\\ 0\\\ 1 \end{pmatrix} \\\ \end{align*}
...then $\mathcal{B}=\{\vec{x}_1,\... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19261 | ## anonymous 5 years ago [y^2-2y/y^2+7y-18] X [y^2-81/y^2-11y+18] Simplify the rational expression.
1. anonymous
break the denominators off into factored squares, and cancel terms to simplify.
2. anonymous
i did that and got y(y-9)/(x-2) (y+2)
3. anonymous
4. anonymous
$\frac{y(y - 2)}{(y+9)(y-2)} * \frac{(y+9)(... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19262 | # CW complex
In topology, a CW complex is a type of topological space introduced by J. H. C. Whitehead to meet the needs of homotopy theory. This class of spaces is broader and has some better categorical properties than simplicial complexes, but still retains a combinatorial nature that allows for computation (often ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19263 | # A test for quantifier eliumination
In David Marker's "Model Theory: An Introduction" book I was trying to prove Corollary 3.1.12 which is left for the reader, but I couldn't reach any solution. The aforementioned corollary states:
Suppose that $T$ is an $\mathcal{L}-$theory such that:
$i)$ $T$ has algebraically pr... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7376 | # Past exam question: probabilistic method to prove a partition of a graph exists
The following is a question from a past paper:
Let $G$ be a graph with an even number of vertices. Show that the vertices of $G$ can be partitioned into two parts $A$ and $B$ of equal size such that the number of edges between $A$ and $... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7377 | ## viernes, 6 de mayo de 2011
### Integration by Sustitution
Lets start by understanding that this method of integration comes from the rule chain method for example,
$\frac{d[f[g(x)]}{dx}=f'[g(x)]g'(x)$ (1)
lets integrate both sides of equation 1
\begin{align*} \int \frac{d[f[g(x)]}{dx}\; dx&=\int f'[g(x)]g'(x)\;... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7378 | Location of Repository
## The cohomology of λ-rings and ψ-rings
### Abstract
In this thesis we develop the cohomology of diagrams of algebras and then apply this to the cases of the λ-rings and the ψ-rings. A diagram of algebras is a functor from a small category to some category of algebras. For an appropriate cate... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7379 | # Math Help - mapping homomorphism and subgroup
1. ## mapping homomorphism and subgroup
1) Describe explicitly all homomorphisms h: C_6 maps to Aut(C_12)
Firstly, I have to find what group Aut(C_12) is isomorphic to, and then find the order of that group. Is this the right track?
If it is, then I don't know how to ... |
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