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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18988 | Harvard Astronomy 201b
Accretion Luminosity
In Uncategorized on April 27, 2011 at 5:05 pm
Let $m = \dot{M} t$ be the orbiting mass entering and leaving the ring. $dE = \frac{dE}{dr} dr = \frac{d}{dr} \left(-G \frac{M_* m}{2 r}\right) dr = G \frac{M_* \dot{M} t }{2 r^2} dr$. In the steady state, conservation of ene... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18990 | ## angular momentum of a two-particle system
angular momentum of a two-particle system
um heres where i get but idk what to do from here some stuff must be perpendicular always and stuff a lil help would be awesome
$$\Sigma_i L_i = \Sigma_i \vec{r_i} \times m_i \vec{v_i} = \Sigma_i (\vec{r_i}+\vec{r_{cm}}) \times m_i ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18991 | # how to write the general formula for a telescoping series
Im trying to check if the series
$$\sum_{k=2}^{\infty} \frac{1}{\sqrt{k-1}} - \frac{1}{\sqrt{k+1}}$$
is converging or not.
I have divided the series into two parts with the series with even k >= 2 and the series with the odd k >= 3.
For the series with ev... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18982 | Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.
A. INTRODUCTION
When building statistical models, the goal is to define a compact and parsimonious mathematical representation of some data generating process. Many of these techniques require that one make assumptions abou... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18985 | ## c++ simpson's method --loop doesn't stop
Hello, i have done the simpson's method and it works fine.My problem is that it doesn't stop when it gives me the desired result but the loop continues for ever..
Code:
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <iomanip>
#include <cmath>
using names... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18989 | Applications 2: Marginal rate of subsitution
Introduction: If the value of a variable changes, then usually the function value changes as well. For a function of two variables it is however possible that there are combinations of changes of both variables that do not result in a change of the function value.
Property... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18976 | # Show that conditions of second derivative test for $g:\mathbb{R}^2 \to \mathbb{R}$ implies that its Hessian is positive definite
The following is extracted from Second Derivative Test.
To optimize a function $$f:\mathbb{R}^3\to\mathbb{R},$$ one can use Second Derivative Test, that is,
$$(1)$$ if its Hessian matrix... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4528 | # Minimum distance of a code
Is there a way to compute minimum distance of a code given a systematic parity check matrix? I know that min dist is smallest number $$d$$ such that there exists $$d$$ linearly dependant columns. I am looking in particular to find minimum distance of binary (codes over $$\mathbb{F}_{2^l}$$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4529 | Consecutive Numbers
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
14 Divisors
What is the smallest number with exactly 14 divisors?
Summing Consecutive Numbers
Many numbers can be expressed as the sum of two or more consecutive integers. For examp... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4530 | # Determine the number of perfect pairings in a complete bipartite graph Kn,n, in which n disjoint edges are removed.
Determine the number of perfect pairings in a complete bipartite graph Kn,n, in which n disjoint edges are removed.
• This question is admittedly easy, but it still takes some time to write down a pol... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4531 | GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 18 Jun 2018, 00:56
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customize... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4533 | # How do you factor 24x^2-76x+40?
May 15, 2015
First, let's simplify this dividing the equation by $4$.
$6 {x}^{2} - 19 x + 10$
Then, we have to find its roots: ${x}_{1} = \frac{2}{3}$ and ${x}_{2} = \frac{5}{2}$. But in order not to work with these fractions, we can multiply both sides by the denominator of the fr... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4534 | # How to integrate twice of this viscous term?
I am reading a paper, and I do not understand why the author said the following term when integrated twice will become,
$\int\limits_\Omega {{\rm{d}}\Omega {{\bf{\psi }}^{\bf{u}}}\cdot\nabla \cdot\left( {2\nu D\left( {{\bf{u}}} \right)} \right)} = - \int\limits_\Gamma {{... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4535 | 1. ## complex numbers
if w is a non real cube root of unity prove that (2+5w+2w^2)^6 =729
i am not really sure how to do this
2. ## Re: complex numbers
$w$ is a cube root of unity so we know it's magnitude is $1$
Thus we can write $w = e^{i \theta}$
let $f(w) = 2 + 5w + 2w^2$
a little work shows that
$f(e^{i\th... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4537 | Mathematics
Complex Analysis in one Variable
Author: NARASIMHAN
Publisher: Springer Science & Business Media
ISBN: 1475711069
Category: Mathematics
Page: 268
View: 2717
This book is based on a first-year graduate course I gave three times at the University of Chicago. As it was addressed to graduate students wh... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4538 | # Exterior Point of a Set
Let $\left( {X,\tau } \right)$ be a topological space and $A$ be a subset of $X$, then a point $x \in X$, is said to be an exterior point of $A$ if there exists an open set $U$, such that
In other words, let $A$ be a subset of a topological space $X$. A point $x \in {A^c}$ is said to be an e... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4539 | # t-test as Mahalanobis distance
Our tutor once said that the t-test applies Mahalanobis distance. Could you please explain how it does so?
• I think a good answer to this question would also mention Hotelling's T-squared distribution, which in a sense generalises Student's t to multiple dimensions, which is the situ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4540 | # Scalar product
The scalar product of a vector v in Rn by a real number k is a vector u in Rn obtained by multiplying each component of v by k. $$u = v \cdot k = \begin{pmatrix} v_1 \\ v_2 \\ ... \\ v_n \end{pmatrix} \cdot k = \begin{pmatrix} v_1 \cdot k \\ v_2 \cdot k \\ ... \\ v_n \cdot k \end{pmatrix}$$
It is als... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4541 | # Pulley Torque Question
1. Homework Statement
You have been given a pulley for your birthday. It is 12 cm in diameter and has a mass of 2 kg. You get to wondering whether the pulley is uniform. That is, is the mass evenly distributed, or is concentrated toward the center of near the rim? To find out, you hang the pul... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4543 | # Nullable nonterminals and recursion
I have two questions regarding nullable nonterminals in a grammar. Often a simple algorithm is described to find nullable nonterminals:
1. Basis: if $A \rightarrow \epsilon$ is a production, $A$ is nullable.
2. Induction: if $A \rightarrow X_1X_2\ldots X_n$ is a production, and $... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4536 | location: Publications → journals
Search results
Search: MSC category 22D05 ( General properties and structure of locally compact groups )
Expand all Collapse all Results 1 - 1 of 1
1. CMB 2008 (vol 51 pp. 60)
Janzen, David
F{\o}lner Nets for Semidirect Products of Amenable Groups For unimodular semidirec... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4532 | ## AryaVegapunk one year ago For the first 60 miles of a 120-mile trip, a person drive 50 mph. What speed would he have to travel for the last half of the trip so that the average speed for the entire trip would be 61 mph. The answer is supposed to be 78 8/39 miles. How can this be?
1. AryaVegapunk
Here's my logic: 6... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4542 | Feeds:
Bài viết
Bình luận
## Apollonius of Perga
Born: about 262 BC in Perga, Pamphylia, Greek Ionia (now Murtina, Antalya, Turkey)
Died: about 190 BC in Alexandria, Egypt
Apollonius of Perga was known as ‘The Great Geometer’. Little is known of his life but his works have had a very great influence on the developme... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8624 | # Carbon diffuses in iron via an interstitial mechanism—for FCC iron from one octahedral site to an adjacent one. Two general sets
###### Question:
Carbon diffuses in iron via an interstitial mechanism—for FCC iron from one octahedral site to an adjacent one. Two general sets of point coordinates for this site are 0 ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8625 | Law of Large Numbers when expectation is infinite and random variable not identical
I am trying to prove the following question:
Let $$X_i$$ be sequence of indepedent non-negative random variables with $$E(X_i) = \infty$$ and $$X_i$$ having different distributions.
Is it true that $$\frac{X_1 + \cdots + X_n}{n} \to ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8626 | # Polynomial equal to polynomial of lower degree
I am studying Linear Algebra Done Right, chapter 2 problem 6 states:
Prove that the real vector space consisting of all continuous real valued functions on the interval $[0,1]$ is infinite dimensional.
My solution:
Consider the sequence of functions $x, x^2, x^3, \do... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8627 | # Thread: Equations of tangents through point (curve)
1. ## Equations of tangents through point (curve)
Determine the exact equations of the tangents to the curve which pass through point P
curve = (8-x)^(1/2)
point = 5,2
I'd like to see how you would solve this. What I tried to do is set the variables of the point... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8628 | # Which functors between multicategories that come from monoidal categories are monoidal?
Given any monoidal category $(\mathcal{C}, \otimes, I)$ we have an associated multicategory $M_{\mathcal{C}}$ with underlying category $\mathcal{C}$, and $k$-morphisms $M_{\mathcal{C}}(A_1,\ldots,A_k; B) = \mathcal{C}(A_1\otimes\... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8629 | # Remainder Theorem Problem
When the polynomial $p(x)$ is divided by $(x^2+3x+2)$ the remainder is $5x+1$. Find the remainder when $p(x)$ is divided by $(x+2)$.
I get that $(x+2)$ is a factor of $(x^2+3x+2)$ but I'm not sure how to use that fact to get the question's answer.
• The remainder when 10 is divided by 6 i... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8631 | # Expected eigenvalues of a Wishart Matrix
I consider a $n\times n$ Wishart Matrix with expected value $p \cdot I_n$, i.e. a matrix of the form $$W = XX'$$ with $X$ a $n\times p$ matrix with independent standard normal entries.
It is easy to find in the literature the joint distribution of its eigenvalues $\lambda_1 ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8633 | +0
# What is the remainder of 5^2010 when it is divided by 7?
0
283
2
What is the remainder of 5^2010 when it is divided by 7?
Guest Aug 9, 2017
Sort:
#1
0
5^2010 when it is divided by 7?
5^2010 mod 7 =1 The remainder.
Guest Aug 9, 2017
#2
+19344
0
What is the remainder of 5^2010 when it is divided by 7?
$$\b... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8634 | # Math Help - Integral
1. ## Integral
$\int \frac{(x^3+x-1)dx}{(x^2+2)^2}$
2. Expand it out and then integrate:
$\int\frac{x}{x^{2}+2}dx-\int\frac{x}{(x^{2}+2)^{2}}dx-\int\frac{1}{(x^{2}+2)^{2}}dx$
3. thank you |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8635 | Home > Standard Error > What Does Standard Error Of The Mean Measure
# What Does Standard Error Of The Mean Measure
## Contents
When the finding is statistically significant but the standard error produces a confidence interval so wide as to include over 50% of the range of the values in the dataset, then If the pop... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8636 | # Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty
## Distinguished subspaces of $L_p$ of maximal dimension
### Tom 215 / 2013
Studia Mathematica 215 (2013), 261-280 MSC: 46E30, 46A45, 46A16, 46B45. DOI: 10.4064/sm215-3-4
#### Streszczenie
Let $(\varOmega ,\varSigma ,\mu )$ be a measure spac... |
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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8639 | # zbMATH — the first resource for mathematics
## Order
### A Journal on the Theory of Ordered Sets and its Applications
Short Title: Order Publisher: Springer Netherlands, Dordrecht ISSN: 0167-8094; 1572-9273/e Online: http://link.springer.com/journal/volumesAndIssues/11083 Comments: Indexed cover-to-cover
Documen... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8632 | `
Timezone: »
Poster
On Top-k Selection in Multi-Armed Bandits and Hidden Bipartite Graphs
Wei Cao · Jian Li · Yufei Tao · Zhize Li
Thu Dec 10 08:00 AM -- 12:00 PM (PST) @ 210 C #92 #None
This paper discusses how to efficiently choose from $n$ unknowndistributions the $k$ ones whose means are the greatest by a certa... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8630 | # Definition:Triangle (Geometry)/Equilateral
## Definition
An equilateral triangle is a triangle in which all three sides are the same length:
That is, a regular polygon with $3$ sides.
Thus it can be seen that an equilateral triangle can be considered to be a special case of an isosceles triangle.
## Euclid's Def... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8637 | # Math Help - [SOLVED] Expanding Cubic Brackets
1. ## [SOLVED] Expanding Cubic Brackets
I'm stuck on a particular maths question which asks;
Write $(1 + \sqrt{5})^3$ in the form $a + b\sqrt{5}$, where a and b are integers.
I do have a worked solution to this problem, but it isn't much help, as I'm uncertain as to h... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_23008 | 0
97
# Averages and Percentage Questions for SSC CHSL and MTS
Here you can download the Averages and Percentages Questions for SSC CHSL and MTS PDF with solutions by Cracku. These are the most important Averages and Percentages questions PDF prepared by various sources also based on previous year’s papers. Utilize th... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_23009 | Question
# You have to divide a pack of $$52$$ cards equally among $$4$$ players. In how many ways the cards can be divided in $$4$$ sets, $$3$$ of them having $$17$$ cards each & the $$4^{th}$$ with $$1$$ card
A
52!4!3!(17!)3
B
52!(3!)3(17!)
C
52!(3!)(17!)
D
52!(17!)3
Solution
## The correct option is A $$\display... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_23010 | ## Algebra and Trigonometry 10th Edition
$a_1=0$ $a_2=a_1+3=0+3=3$ $a_3=a_2+3=3+3=6$ $a_4=a_3+3=6+3=9$ $a_5=a_4+3=9+3=12$ $a_6=a_5+3=12+3=15$ The first differences: $a_2-a_1=a_3-a_2=a_4-a_3=a_5-a_4=a_6-a_5=3$ The second differences: $3-3=3-3=3-3=3-3=0$. The first differences are constant; thus it is linear. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_23011 | E04 Chapter Contents
E04 Chapter Introduction
NAG Library Manual
# NAG Library Routine DocumentE04PCF
Note: before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.
## 1 Purpose
E04PCF solves a l... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_23012 | Courses
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# A bag contains 3 red balls, 5 black balls and 4 white balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is:$(a)$ White$(b)$ Red$(c)$ Black$(d)$ Not red
Last updated date: 25th Mar 2023
Total views: 308.7k
Vi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_23013 | ## 11 May 2014
### The Carvallo paradox - part II
I mentioned the Carvallo paradox in a previous post. Here, I will give a simpler version and some comments. Consider that, instead of using a spectrometer, we only use the dispersive element (e.g. a prism). After refraction, the signal components (the various colors) ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_23015 | # $L_1$-Estimates for Eigenfunctions of the Dirichlet Laplacian
For $d \in {\bf N}$ and $\Omega \ne \emptyset$ an open set in ${\bf R}^d$, we consider the eigenfunctions $\Phi$ of the Dirichlet Laplacian $-\Delta_\Omega$ of $\Omega$. We do {\it not} require $\Omega$ to be of finite volume. % If $\Phi$ is associated wit... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_23016 | # math
use the properties of logarithms to write the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)
In 3sqrt t
1. 👍 0
2. 👎 0
3. 👁 243
1. ln (3 *t^(1/2))
ln 3 + ln t^(1/2)
ln 3 + (1/2) ln t
How did you do with the Peruvian fish?
1. 👍 0
2. 👎 0
## S... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_23017 | # 5.5: Orthologistic solution
Finally, let s be positive. This creates a vertical asymptote and orthologistic growth. The position in time of the vertical asymptote is the “singularity” mentioned earlier. The interesting question is, when s is positive, what is the time of the singularity? That is, when will the popu... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_23019 | # Difference between revisions of "1985 AJHSME Problem 25"
## Problem
Five cards are lying on a table as shown.
$$\begin{matrix} & \qquad & \boxed{\tt{P}} & \qquad & \boxed{\tt{Q}} \\ \\ \boxed{\tt{3}} & \qquad & \boxed{\tt{4}} & \qquad & \boxed{\tt{6}} \end{matrix}$$
Each card has a letter on one side and a whole ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_23020 |
• 9.1: The Square Root Function
In this section we turn our attention to the square root function, the function defined by the equation f(x)=√x. We begin the section by drawing the graph of the function, then we address the domain and range. After that, we’ll investigate a number of different transformations of the f... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_23021 | ## Algebra 1
Three points on the curve: $y=3x^2-7$ Line of symmetry: $x=-b/2a$ $x=-1*0/2*3$ $x=0/6 = 0$ $y=3x^2-7$ $y=3*(0^2)-7$ $y=3*0-7$ $y=-7$ $(0,-7)$ Let $x=3$: $y=3x^2-7$ $y=3*3^2-7$ $y=3*9-7$ $y=27-7$ $y=20$ $(3,20)$ Since $(3,20)$ is three units from the axis of symmetry, we also know that $(-3,20)$ is also th... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_23022 | ## September 30, 2006
### Dimensional Analysis and Coordinate Systems
#### Posted by John Baez
We had a nice conversation on dimensional analysis. Here are some things I learned.
As Terry Tao pointed out, systems of units are like coordinates. They’re both systems of arbitrary choices that let us describe reality u... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_23023 | Emmanuel Pace
2022-07-18
How do you find the exact value of $\mathrm{cos}$ 180 degrees - $\mathrm{sin}$ 180 degrees?
grocbyntza
Expert
Within the unit circle, cosine provides the x coordinate of a point on the surface of the circle. Sine provides the y coordinate of a point on the surface of the circle.
At ${180}^... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_23014 | # Thread: Integrals - test tomorrow
1. ## Integrals - test tomorrow
hey,
i have a calc test tomorrow and i can't solve these practice problems. help please!!!
Compute the following definite integrals:
(a) integral from -1 to 1 of sin(x)sin(x^2)dx
(b) integral from 0 to pi of cos(x) / (2 + sin(x)^2
Given two curves... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_23018 | # How do you solve x^2-1>=4x using a sign chart?
Dec 14, 2016
The answer is x in ] -oo,(2-sqrt5) ] uu [(2+sqrt5), +oo[
#### Explanation:
Let's rewrite the equation
${x}^{2} - 4 x - 1 \ge 0$
Let $f \left(x\right) = {x}^{2} - 4 x - 1$
We need the values of $x$, when $f \left(x\right) = 0$
that is, ${x}^{2} - 4 x ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2928 | Proving an inequality or finding a counter example
I'm trying to prove that the following inequality holds for any $0\leq a_1,a_2,b_1,b_2\leq 1$:
$$|a_1a_2-b_1b_2|\leq |a_1-b_1|+|a_2-b_2|$$
Does anybody have an idea for proving this, or has a counter-example.
Thanks,
Hint: $$|a_1a_2-b_1b_2|=|a_1a_2-a_2b_1+a_2b_1-b... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2929 | How do you convert -2 - 2sqrt3i to polar form?
You can simplify this as $- 2 \left(1 + \sqrt{3} i\right)$. This is not needed, but I like to work with easier terms. Next, you remember that $z = r \left(\cos \left(\theta\right) + i \sin \left(\theta\right)\right)$. $r$ is called the modulus of $z$ and it is defined as... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2930 | Question
# $$AB$$ is parallel to $$QR$$, such that $$\dfrac { PA }{ AQ } =\dfrac { PB }{ BR }$$. $$PB =2$$ cm, $$EC =4$$ cm and $$QR =9$$ cm, then find the length of $$AB$$.
Solution
## $$6AB=2\times 9\quad or\quad AB\quad =\quad 3cm$$Mathematics
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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2931 | # How do you find the zeroes for -2x^6 + 2x^5 - 4x^4 - 44x^3 + 120x^2?
May 30, 2015
$- 2 {x}^{6} + 2 {x}^{5} - 4 {x}^{4} - 44 {x}^{3} + 120 {x}^{2}$
$= - 2 {x}^{2} \left({x}^{4} - {x}^{3} + 2 {x}^{2} + 22 x - 60\right)$
The $- 2 {x}^{2}$ factor means that $\textcolor{red}{x = 0}$ is a zero of the polynomial.
Using... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2932 | 5
# StdchioyEiRTIdentifying the limiung rcactant in drawing ol mixtureThe drawing below shoivsmixmntmoleculescarbonhycrogennitrogensulfuroxygcnchlorineSuppose the follo...
## Question
###### StdchioyEiRTIdentifying the limiung rcactant in drawing ol mixtureThe drawing below shoivsmixmntmoleculescarbonhycrogennitroge... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2933 | # Wrong Inflection point
I have the next function: $$f(x)=x^3-3x^2+4$$.
I need to find an inflection point so I had done the following steps:
I found the first derivative: $$f'(x)=3x^2-6x$$
Then the second one: $$f''(x)=6x-6$$
Comparative to zero: $$6x-6=0$$
$$6x=6\rightarrow x=1$$
I checked values before and afte... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2934 | Space Calc
Doing the math, so you don't have to.
# Multi-Stage Rocket Delta-V Optimizer
## Introduction
When building a rocket, it is advantageous to do staging. Staging is throwing away big, expensive parts of your rocket while the rest continues on. The advantage is that you aren't carrying all that dead weight. F... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2935 | # Derivatives of Logarithmic Functions -Fractions-
• Oct 23rd 2008, 06:44 PM
GirouxCalder
Derivatives of Logarithmic Functions -Fractions-
Hello everyone.
I got a question regarding the derivatives of a log but in a fraction. Here is an example:
3x^2 / ln(x)
This isnt a homework problem but im studying for a quiz t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2936 | # [FOM] Re: Consistency of Formal Theories
Richard Zach rzach at ucalgary.ca
Fri Jun 20 13:54:47 EDT 2003
> Also, a yes answer would appear to contradict the information that
> was tacit in Richard Zach's response to my original query, for he
> seems to indicate that the Church-Kleene ordinal is countable, as if
> t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2937 | # How to use Weierstrass test?
How can I use Weierstrass test to determine a set $I$ on which the series $\displaystyle \sum_{n=1}^{\infty} nx^n(1-x)^n$ converges uniformly?
Weierstrass test: Let $f_n : I \to \mathbb{R}$ be a sequence of functions with $|f_n(x)| \le M_n$ for all $x \in I$ and $k=1,2, \dots$. If $\sum... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2938 | # Black-Scholes PDE
The Black-Scholes partial differential equation is the partial differentiation equation:
$\displaystyle rf=\frac{\partial f}{\partial t}+rx\,\frac{\partial f}{\partial x% }+\frac{1}{2}\sigma^{2}x^{2}\,\frac{\partial^{2}f}{\partial x^{2}}\,,\quad f=f% (t,x)\,,$ (1)
on the domain $0\leq x<\infty\,... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2939 | # What is 64 ounces in pounds?
Dec 11, 2015
There are 4 pounds in 64 ounces.
#### Explanation:
There are 16 ounces in one pound, so you have to divide 64 ounces by the 16 ounces per pound.
$\text{1 pound"="16 ounces}$
$\text{64 ounces" * "1 pound"/"16 ounces}$
$\text{64 oz lb"/"16 oz}$
$\text{64 oz lb"//"16 oz"... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2940 | Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.
A few days ago, http://www.futilitycloset.com/ published a short post based on the fourth problem of the 1987 Canadian Mathematical Olympiad (from on a problem from the 6th All Soviet Union Mathematical Competition in Vorone... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2941 | ### myHandle's blog
By myHandle, history, 2 months ago, ,
I have studied the Push-Relabel algorithm, the main difference between Augmenting path algorithms and Push-Relabel is that:
• Augmenting path algorithms maintain a flow(capacity constraints and conservation constraints are valid) and augment it some s-t path ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2943 | # Errata for Hands-On Machine Learning with Scikit-Learn and TensorFlow
The errata list is a list of errors and their corrections that were found after the product was released. If the error was corrected in a later version or reprint the date of the correction will be displayed in the column titled "Date Corrected".
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2942 | # Unions
Calculate how much money per year would go to the treasury of unions if 218 thousand employee join unions with an average net salary of 407 euros and if memberhip in union cost 1% of the net monthly salary.
Correct result:
x = 10647120 Eur
#### Solution:
Our examples were largely sent or created by pupil... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24480 | # Calculator issues?
by yumito
Tags: calculator
Share this thread:
P: 17 1. The problem statement, all variables and given/known data To save money you put $3000 at the end of each year in an annuity that pays 6.8% compounded annually. Use the formula for the value of an annuity. The Given Formula: A=P[(1+(r/n)nt)-1... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24481 | ## Precalculus (6th Edition) Blitzer
a)The value of $h\left( 5 \right)$ is $8$. b)The value of $h\left( 0 \right)$ is $3$. c)The value of $h\left( 3 \right)$ is $6$.
(a) As $5\ne 3$. So, the first part of the piecewise function will be applicable for $x=5$. \begin{align} & h\left( x \right)=\frac{{{x}^{2}}-9}{x-3} \\ ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24482 | # Calculating percentages with weights
I've done a search for the answer but still couldn't figure it out.
Say for example:
Year 1 Result = 80% (Weight:20%)
Year 2 Result = 70% (Weight:10%)
Year 3 Result = Unknown (Weight:70%)
I've not yet got my results for year 3. I want to calculate what my average percentage ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24483 | Deepak Scored 45->99%ile with Bounce Back Crack Course. You can do it too!
# The corner points of the feasible region determined by the following system of linear inequalities:
Question:
The corner points of the feasible region determined by the following system of linear inequalities:
$2 x+y \leq 10, x+3 y \leq 15... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24484 | # If i = √-1, then how many values does i-2n have for different n ϵ Z?
1. One
2. Two
3. Four
4. Infinite
Option 2 : Two
## Detailed Solution
Concept:
The value i or the concept of i is used in explaining and expressing complex numbers. Complex numbers are numbers with a real and imaginary part. The imaginary part ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24485 | # Backrunning Private Transactions Using MPC
This article examines the use of secure multi-party computation in allowing searchers to backrun users’ transactions while preserving transaction and search strategy confidentiality.
Thanks to Alejo Salles, Jonathan Passerat-Palmbach, Mateusz Morusiewicz, Quintus Kilbourn,... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24486 | # Equation involving complex conjugate
Can someone show me how $$\frac{1-\bar{z}}{(1-z)(1-\bar{z})}=\frac{1-\bar{z}}{2(1-Re(z))}.$$
-
If you did any work at all (like, perhaps, multiplying out the bottom) it would be good to include it to convince readers you made some progress :) – rschwieb Nov 6 '12 at 17:38
Do yo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24488 | # Are 'lists' and vectors the same thing?
1. ### autodidude
333
I've just been reading through the first few pages of 'Linear Algebra Done Right' by S. Axler and so far, the concept of a 'list' seems a lot like a vector. Are they one and the same?
If so, is there a reason why Axler chose to call it a list? Perhaps m... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24490 | # Math Help - Indefinite Integral
1. ## Indefinite Integral
How would you put 10((x^7/3)/(7/3) back in radical form?
I think it would be 30(cube root of x^?)/7....?
2. $\frac{10\cdot x^{\frac{7}{3}}}{\frac{7}{3}} = \frac{30}{7}\cdot x^{\frac{7}{3}}$
3. Originally Posted by tradar
How would you put 10((x^7/3)/(7/3)... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24491 | # Formula
2010 Mathematics Subject Classification: Primary: 03BXX Secondary: 68P05 [MSN][ZBL]
Formulas are syntactically correct expressions in a formalized language defined over a signature, a set of variables, and a logics. In this way, formulas are quite similar to terms. Since predicates and logics symbols are in... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24492 | # What is the dot product of <3,4,1 > and <5,-1,2 >?
Dec 19, 2015
13
#### Explanation:
1. Dot product is distributive.
(e.g. $a \cdot \left(b + c\right) = a \cdot b + a \cdot c$)
2. Dot product of 2 vectors that are perpendicular is zero
(e.g. $\hat{i} \setminus \cdot \hat{j} = 0$)
$\left(3 \hat{i} + 4 \hat{j} + ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24494 | ### Engineering Mathematics - Combinatorics
#### Question - 1
How many ways are there to arrange the nine letters in the word ALLAHABAD?
• A 7500
• B 7560
• C 4000
• D 2000
#### Question - 2
The number of diagonals which can be drawn by joining the angular points of a heptagon is
• A 14
• B 7
• C 10
• D 12
#### ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24495 | My Math Forum Finding the radius
Geometry Geometry Math Forum
February 23rd, 2017, 01:47 PM #1 Newbie Joined: Jan 2017 From: London Posts: 10 Thanks: 0 Finding the radius I'm struggling to find the radius of the circle in the image (the only other given length is the length between B and the right angle below, wh... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24493 | Model Theory Seminar
Isaac Goldbring and Jonathan Wolf
UIC
Introduction to Positive Bounded Logic (continued)
Abstract: We will continue introducing the model theory associated to the positive bounded logic introduced last time. We will also introduce the notions of $(1+\epsilon)$-isomorphism and $(1+\epsilon)$-equiva... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24487 | # The number of zeros of a function regular on the closure on $U$ and the max of $\operatorname{Re}\frac{zf'(z)}{f(z)}$
Suppose that $f(z)$ is holomorphic on the closed unit disk $\bar U$ and never vanishes on the boundary $\partial \bar U$. Prove that the maximum of $\displaystyle \operatorname{Re}\frac{zf'(z)}{f(z)}... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24489 | # L1-penalized likelihood asymptotics
selective inference
Generalizing Lasso penalty to non-linear model, e.g. a binomial model.
Author
Kenneth Hung
Published
April 10, 2017
Following a paper by Lee et al. (2016) on the correcting for the selection bias after lasso-based selection, a natural progression is to cons... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24688 | # Homework help: Ratios in Mathematics [closed]
I'm trying to solve this ratio problem. Can't seem to get around in solving it.
$750g$ of salt is to be divided between three storage cans $A, B$ and $C$ in the ratios $A:B = 5:2$ and $B:C = 3:2$. What mass of salt will be stored in each can?
A quick solution would be ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24689 | ## Monday, 2 September 2013
### Mann-Whitney U test
The Mann-Whitney U (MWU) test is a non-parametric statistical test that is widely used in many fields (e.g in medical statistics and psychology), and tests whether two groups (a.k.a datasets or populations) are the same (the null hypothesis) against the alternative ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24691 | # Elitmus previous questions - 1
1. If a number x is in octal form and having zero as unit place then if we change that number x in decimal form then what is the probability that number x having zero as unit place?
Explanation:
When you convert a decimal number into octal form, think which numbers end with zero. The ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24692 | My watch list
my.chemeurope.com
# Bose–Einstein statistics
Particle statistics
Maxwell-Boltzmann statistics
Bose-Einstein statistics
Fermi-Dirac statistics
Parastatistics
Anyonic statistics
Braid statistics
edit
In statistical mechanics, Bose-Einstein statistics (or more colloquially B-E statistics) determines the s... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24693 | Proof That the Cartesian Product of a Countable Product of Second Countable Metric Spaces is Second Countable
Theorem
Letbe a countable set of second countable metric spaces.
The cartesian productis second countable.
Proof
Since eachis second countable, a countable basisexists for the topology onfor eachA basis fo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24694 | # Weakly closed implies relatively normal
Suppose $H \le K \le G$ are such that $H$ is a Weakly closed subgroup (?) of $K$ relative to $G$. Then, $H$ is a Normal subgroup (?) of $K$. In other words, $H$ is a Relatively normal subgroup (?) in $K$ with respect to $G$. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24696 | # Tag Archives: kind
Prove that $$\sum_{k=1}^\infty \frac{(H_k)^2}{k^2} = \frac{17\pi^4}{360}$$ $$\textit{proof}$$ Start by the following which can be proved by induction $$\frac{\left[n\atop 3\right]}{n!} =\frac{ (H_{n-1})^2-H^{(2)}_{n-1}}{2n}$$ And the generating function proved here $$-\sum_{n=3}^\infty \left[n\ato... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24699 | Basin of attraction of triangular maps with applications afootnote aafootnote aThe authors are supported by Ministry of Economy and Competitiveness grants MTM2008-03437 (first and second authors); DPI2011-25822 (third author). GSD-UAB and CoDALab Groups are supported by the Government of Catalonia through the SGR progr... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24700 | # How do you solve 2x - 3 >21?
$x > 12$, written in Interval form, $x \in \left(12 , \infty\right) .$
Adding $3$ on both sides, we get, $2 x - 3 + 3 > 21 + 3$, i.e., $2 x > 24$
Next to isolate $x$ on $L H S$, we multiply throughout by $\frac{1}{2}$, keeping in mind that as $\frac{1}{2}$ is $+ v e$, the order will not ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24702 | ## Journal of Symbolic Logic
### On Minimal Structures
#### Abstract
For any countable transitive complete theory T with infinite models and the finite model property, we construct a minimal structure M such that the theory of M is small if and only if T is small, and is $\lambda$-stable if and only if T is $\lambda... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24703 | 2020
Activity report
Project-Team
MINGUS
RNSR: 201822635E
Research center
In partnership with:
CNRS, Université Rennes 1, École normale supérieure de Rennes
Team name:
MultI-scale Numerical Geometric Schemes
In collaboration with:
Institut de recherche mathématique de Rennes (IRMAR)
Domain
Applied Mathematics, Computat... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24695 | 1
JEE Main 2021 (Online) 25th February Evening Shift
+4
-1
The shortest distance between the line x $$-$$ y = 1 and the curve x2 = 2y is :
A
0
B
$${1 \over 2{\sqrt 2 }}$$
C
$${1 \over {\sqrt 2 }}$$
D
$${1 \over 2}$$
2
JEE Main 2021 (Online) 25th February Evening Shift
+4
-1
A hyperbola passes through the foci of the el... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24697 | ## anonymous 5 years ago Eep. Halp! Identify the vertical and horizontal asymptotes of the following functions!
1. anonymous
$f(x) = ( x\ x-2)$
2. anonymous
Oh, that turned out badly. x over x - 2.
3. anonymous
g (x) = x over x + 4 plus 7. I've no idea how to code this.
4. anonymous
There's, like, five more, bu... |
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