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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7380 | # Show how the sequence of terms f(n) = n^2, n = 5, 6, 7... can be written using the domain n = 1, 2, 3?
5. Show how the number 4 can be written as a sum of ... n 1 2 3 4 ... n tn 2 5 8 ... The first term is b andthe final term is f. There are n terms in the sequence ... - Read more
Analysis and Complex Analysis: ...... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7381 | Make many "Morrie's Laws"
Geometry Level 5
Richard Feynman was fascinated by the equation $$\cos(20^\circ)\cos(40^\circ)\cos(80^\circ)=\dfrac1{2^3}$$, which he named "Morrie's Law" after a childhood friend, Morrie Jacobs, who told him the rule. More generally, how many positive integers $$n<90$$ are there such that $... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7382 | # relationship between convergence of a sequence and its corresponding series.
I'm preparing for my calculus exam and I'm unsure how to approach these type of questions .
• If the sequence $a_n$ is convergent/divergent what can we about the corresponding series $\sum_{n}a_n$? Is it convergent or divergent?
• If the s... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7383 | # Do you know your definitions on set theory? - Part (1)
Discrete Mathematics Level pending
Let $$S$$ be an an uncountable set and $$A$$ the collection of all countable and cocountable subsets of S.
Then:
× |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7384 | # Generalizations of the Convex Hull
I am aware of generalizations of the convex kernel, via the addition of more polygonal line segments between points in a set. However, I wonder if there are similar generalizations for the convex hull. If they exist, what papers exist on them, and in essence, what are they?
-
Per... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7385 | # Factorization of Quadratic Expressions with Negative Coefficients
## Factor quadratics with positive and negative coefficients
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Factorization of Quadratic Expressions with Negative Coefficients
### Factorization of Quadrati... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7386 | Uniform circular motion
1. May 1, 2004
LD_90
I've been working on this for awhile. I think I've got it. Ok here's the problem:
A particle moves in a circle of radius r completing one cycle in time T. What is the magnitude of the average acceleration over time T and over time T/2?
It seems to me that over time T th... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7387 | # How do you solve using the quadratic formula: x^2+x+1=0?
Nov 20, 2015
See explanation...
#### Explanation:
${x}^{2} + x + 1$ is of the form $a {x}^{2} + b x + c$ with $a = b = c = 1$
This has zeros given by the quadratic formula:
$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a} = \frac{- 1 \pm \sqrt{{1}^{2} - \... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7388 | # Newton's Sums with pi?
Algebra Level 5
$x+y+z=1\\ { x }^{ 2 }+{ y }^{ 2 }+{ z }^{ 2 }=\pi\\ { x }^{ 3 }+{ y }^{ 3 }+{ z }^{ 3 }={ \pi }^{ 2 }+3{ z }^{ 2 }-3z+1\\$
This set of equations is true for three complex numbers $$x, y, z$$.
If $$xyz-xy=\frac { A }{ B } {\pi }^{ C }$$ for positive integers $$A, B, C$$ and ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7389 | # Real Analysis/Introduction
The subject of real analysis is concerned with studying the behavior and properties of functions, sequences, and sets on the Real number line, which we denote ${\displaystyle \mathbb {R} }$. Concepts that we wish to examine through real analysis include properties like Limits, Continuity, ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7390 | Lemma 37.28.3. Let $f : X \to Y$, $s : Y \to X$ be as in Situation 37.28.1. Assume $f$ of finite type. Let $y \in Y$ be a point. Then there exists a nonempty open $V \subset \overline{\{ y\} }$ such that the inverse image of $X^0$ in the base change $X_ V$ is open and closed in $X_ V$.
Proof. Let $Z \subset Y$ be the ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7391 | # What is the martingale measure requirement when $\mu(t,S(t)) = \mu(t)$?
It is known that if the numeraire is the bank account, then the martingale measure is determined by the fact that every asset has $r$ as its local rate of return.
However, the local rate of return is the "multiplier" of the stock price in the d... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2272 | ## Differential Geometry Seminar: A polyhedron comparison theorem for 3-manifolds with positive scalar curvature
Seminar | January 22 | 2:10-3 p.m. | 939 Evans Hall
Chao Li, Stanford
Department of Mathematics
We establish a comparison theorem for polyhedra in 3-manifolds with nonnegative scalar curvature, answering... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2273 | Physics
Atoms and Nuclei
Previous Years Questions
## Numerical
In a radioactive decay chain reaction, ${ }_{90}^{230} \mathrm{Th}$ nucleus decays into ${ }_{84}^{214} \mathrm{Po}$ nucleus. The ratio of the number ...
Suppose a $$_{88}^{226}Ra$$ nucleus at rest and in ground state undergoes $$\alpha$$-decay to a $$_{8... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2274 | ### Entropy Change Formula
A pointwise bound 3. Entropy of fusion. The state function entropy S puts the foregoing discussion on a quantitative basis. The general expression can be given as: $$ΔS_{total}$$ = $$ΔS_{sys}~+~ΔS_{surr}~\gt~0$$ For more information on entropy formula and the effect of entropy on the spontan... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2275 | If f(x)=3x-4 and g(x)=x^2, how do you find the value of f(3)-g(2)?
1 Answer
Jan 5, 2017
See complete process below:
Explanation:
First, we can find the formula for the subtraction without substitution:
$f \left(\textcolor{red}{x}\right) - g \left(\textcolor{b l u e}{x}\right) = \left(3 \textcolor{red}{x} - 4\right... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2276 | # zbMATH — the first resource for mathematics
## Hájek, Petr
Compute Distance To:
Author ID: hajek.petr Published as: Hajek, P.; Hajek, Peter; Hajek, Petr; Hájek, P.; Hájek, Petr External Links: MGP · Wikidata · dblp · GND
Documents Indexed: 197 Publications since 1963, including 17 Books Biographic References: 9 P... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2277 | # Which is the solution to the equation 0.5x+4.2= 5.9?
Dec 20, 2016
I got $x = \frac{17}{5} = 3.4$
#### Explanation:
We can write it as:
$\frac{5}{10} x + \frac{42}{10} = \frac{59}{10}$
Cancel all the $10$ and we can solve:
$5 x + 42 = 59$
$5 x = 59 - 42$
$5 x = 17$
$x = \frac{17}{5} = 3.4$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2278 | # multiply by reciprocal
• November 28th 2008, 09:16 AM
brentwoodbc
multiply by reciprocal
To get rid of the 1/2 how is it done?
2d+4c=1/2 4b+2a
is it
2/1(2d+4c)=2/1(1/2 4b+2a)
so
4d+8c=4b+2a
or
2/1(2d+4c)= (2/1)1/2 4b+2a
so
4d+8c=4b+2a
or something different?
• November 28th 2008, 09:49 AM
TheEmptySet
Quote:
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2279 | # Thread: Find the value of each variable. Can someone help?
1. ## Find the value of each variable. Can someone help?
Find that value of each variable.
I don't know what the heck I am doing.
Also, what is wrong with this problem?
3(x-5)=28
3(x-5)+5=28+5
3x=33
3x/3=33/3
x=11
2. For your first question, equate each... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2280 | You can Download Samacheer Kalvi 10th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.
## Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 3 Algebra Ex 3.7
10th Maths Exercise 3.7 Samacheer Kalvi Question 1.
Find the square... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2281 | # Group Direct Product of Cyclic Groups/Examples/C2 x C3
## Examples of Use of Group Direct Product of Cyclic Groups
Let $C_2$ denote the cyclic group of order $2$.
The group direct product $C_2 \times C_3$ is a cyclic group.
## Proof
Let us represent $C_2$ as the group $\struct {\Z_2, +_2}$:
$\begin {array} {r|r... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2282 | ## The Annals of Probability
### The Rate of Escape of Random Walk
William E. Pruitt
#### Abstract
Let $\{X_k\}$ be an i.i.d. sequence and define $S_n = X_1 + \cdots + X_n$. The problem is to determine for a given sequence $\{\beta_n\}$ whether $P\{|S_n| \leq \beta_n \mathrm{i.o.}\}$ is 0 or 1. A history of the pro... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2283 | # On the moments of Lévy processes
For a Brownian motion $B_t$, the evolution of the moments with $t$ obeys the simple rule: $$\mathbb{E}[|B_t|^p] = \kappa_p |t|^{p/2},$$ with $\kappa_p<\infty$. The proof only requires to remark that the random variables $\frac{B_t}{\sqrt{t}}$ are Gaussian with variance 1.
I am inter... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2284 | # Hurst exponent
The Hurst exponent is used as a measure of long-term memory of time series. It relates to the autocorrelations of the time series, and the rate at which these decrease as the lag between pairs of values increases. Studies involving the Hurst exponent were originally developed in hydrology for the prac... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2285 | # Exponential functions (Page 9/16)
Page 9 / 16
Access these online resources for additional instruction and practice with exponential functions.
## Key equations
definition of the exponential function definition of exponential growth compound interest formula continuous growth formula $t$ is the number of unit ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2286 | # What is the unit vector that is normal to the plane containing (- 3 i + j -k) and ( i +k )?
Nov 29, 2016
The unit vector is:
$\hat{C} = \frac{\sqrt{6}}{6} \hat{i} + \frac{\sqrt{6}}{3} \hat{j} - \frac{\sqrt{6}}{6} \hat{k}$
#### Explanation:
Let $\overline{A} = - 3 \hat{i} + \hat{j} - \hat{k}$
Let $\overline{B} = ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2287 | # Tag Info
377
I think the Wikipedia articles $\mathsf{P}$, $\mathsf{NP}$, and $\mathsf{P}$ vs. $\mathsf{NP}$ are quite good. Still here is what I would say: Part I, Part II [I will use remarks inside brackets to discuss some technical details which you can skip if you want.] Part I Decision Problems There are variou... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10976 | # Identity involving a recursive product
Here is yet another problem related to plane partitions. Given the recursive formula
\begin{align*} F(0)&=1,\\ F(r)&=\prod_{i=1}^r\frac{i+2r-1}{2i+r-2}F(r-1). \end{align*}
How can we prove
$$F(n)=\prod_{1\leq i\leq j\leq k\leq n}\frac{i+j+k-1}{i+j+k-2}\ ?$$
EDIT: The soluti... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10977 | # zbMATH — the first resource for mathematics
An interpretation of $$\text{Ext}_{\Lambda^ e}^ 2 (\Lambda,M)$$. (English) Zbl 0142.28102
##### Keywords:
associative rings
Full Text:
##### References:
[1] Cartan, H., andS. Eilenberg: Homological algebra. Princeton University Press 1956. · Zbl 0075.24305 [2] Hochschild... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10978 | MathSciNet bibliographic data MR1783791 (2001j:57044) 57R85 (57R75) Pergher, Pedro L. Q. \$(Z\sb 2)\sp k\$$(Z\sb 2)\sp k$-actions whose fixed data has a section. Trans. Amer. Math. Soc. 353 (2001), no. 1, 175–189. Article
For users without a MathSciNet license , Relay Station allows linking from MR numbers in online m... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10979 | ## anonymous 5 years ago determine two values of b that will make 64xcubed+bx+16 a perfect square trinomial
1. anonymous
$64x^3+b*x+16$
2. anonymous
a perfect square trinomial is a square of a binomial: $(a+b)^2$
3. anonymous
if i assume the equation to be 64x^2 + b*x + 16 --> (a + b)^2 = a^2 + 2*a*b + b^2
4. an... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10980 | How do you find vertical, horizontal and oblique asymptotes for (3x^2+2x-1 )/(x^2-4)?
1 Answer
Apr 22, 2018
$\text{vertical asymptotes at } x = \pm 2$
$\text{horizontal asymptote at } y = 3$
Explanation:
$\text{the denominator of "f(x)" cannot be zero as this would}$
$\text{make "f(x)" undefined. Equating the denom... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10981 | # Solve for the positive values of $x$ in $\ln(e^{\frac{1}{2}}+\sin x) = \frac{1}{2}$
I tried:
$$\ln(e^{\frac{1}{2}}+\sin x) = \frac{1}{2} \Leftrightarrow \\ e^{\frac{1}{2}}+\sin x = e^{\frac{1}{2}} \Leftrightarrow \\ 0 = \sin x \Leftrightarrow \\ x = \arcsin(0) +2k\pi \lor x = \pi-\arcsin(0)+2k\pi \Leftrightarrow \\... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10982 | Research
# Applications of differential subordinations for certain classes of p-valent functions associated with generalized Srivastava-Attiya operator
MK Aouf, AO Mostafa, AM Shahin and SM Madian*
Author Affiliations
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt
For al... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10983 | QUESTION
# Find the values of K, for which the following pair of linear equations has infinitely many solutions.${\text{K}}x + 4y + \left( {\mu + 8} \right) = 0 \\ 4x + {\text{K}}y + 4 = 0 \\$
Hint: Here, we will proceed by using the condition for two linear equations which are ${a_1}x + {b_1}y + {c_1} = 0$ and ${a_2... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10984 | # Lazarus Fuchs
Lazarus Fuchs
Lazarus Immanuel Fuchs (1833–1902)
Born 5 May 1833
Moschin, Prussia
Died 26 April 1902 (aged 68)
Berlin, German Empire
Residence Germany
Nationality German
Institutions University of Greifswald
University of Heidelberg
University of Berlin
University of Göttingen
Alma mater University of ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10985 | # The number of non-trivial polynomial solutions of the differential equation $x^3y'(x)=y(x^2)$
I came across the following problem that says:
The number of non-trivial polynomial solutions of the differential equation $x^3y'(x)=y(x^2)$ is which of the following?
$(1)0\space (2)1 \space (3)3 (4)\infty.$
Can someone ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10986 | # Planet Evidence Module¶
This tutorial will provide instructions on using the nested sampling implementation to compute the evidence of a detection obtained with the KLIP-FM technique being a true point source or just residual noise along with posterior distributions of the source parameters. This module is useful fo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10987 | # condskeel
condskeel(M, [x, p])
$$\kappa_S(M, p) & = \left\Vert \left\vert M \right\vert \left\vert M^{-1} \right\vert \right\Vert_p \ \kappa_S(M, x, p) & = \left\Vert \left\vert M \right\vert \left\vert M^{-1} \right\vert \left\vert x \right\vert \right\Vert_p$$
Skeel condition number $\kappa_S$ of the matrix M, o... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10988 | # State space equations
I am stuck on this exercise. I don't know how to deal with this squared y in the denominator. What am I supposed to do to obtain state space equations?
ex.1 Simplified dynamic model of the steel ball kept in the magnetic field has the following form: $$my'' = mg - C{u^2 \over y^2}.$$
u – volt... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10989 | Double negation
topos theory
Double negation
Idea
In logic, double negation is the operation that takes $P$ to $\neg{\neg{P}}$, where $\neg$ is negation. In other words, double negation is the composite of negation with itself. This is a closure operator/modality and as such a special case of a continuation monad.
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10990 | # Food weight
Stacie is a resident at the medical facility where you work. You are asked to chart the amount of solid food that she consumes. For the noon meal, today she ate 1/2 of a 3-ounce serving of meatloaf, 3/4 of her 3-ounce serving of mashed potatoes, and 1/3 of a 2-ounce serving of green beans. How many ounce... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10991 | # zbMATH — the first resource for mathematics
On the Erdős-Rényi maximum of partial sums. (English. Russian original) Zbl 0928.60008
Theory Probab. Appl. 42, No. 2, 254-270 (1997); translation from Teor. Veroyatn. Primen. 42, No. 2, 274-293 (1997).
Let $$\{X_i, i\geq 1\}$$ be i.i.d. r.v.’s satisfying the conditions $$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14768 | # A Simple probability question
Suppose you are correct 90% of the time.
But in a particular case of 30 questions, you only get 15 correct. What are the odds of that?
-
The question can be answered if we model it by thinking of $30$ rolls of a $10$-sided die. That may not be a reasonable model, if many of the questi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14769 | Page 1 / 3
## Introduction
Geometry (Greek: geo = earth, metria = measure) arose as the field of knowledge dealing with spatial relationships. It was one of the two fields of pre-modern mathematics, the other being the study of numbers. In modern times, geometric concepts have become very complex and abstract and are... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14770 | Introduction
A significant amount of focus in statistics is on making inference about the averages or means of phenomena. For example, we might be interested in the average number of goals scored per game by a football team, or the average global temperature or the average cost of a house in a particular area.
The tw... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14771 | # Math 204: Linear Algebra
Think-it-through: Michael Cary Offered: Spring 2016 Instructor: Kevin J. Mitchell Office: Lansing 305 Phone: (315) 781-3619 Fax: (315) 781-3860 E-mail: mitchell@hws.edu Office Hours: Mon & Wed 2:30 to 4:00, Tues 2:00 to 3:30, Thurs 1:00 to 2:30, and Fri 1:30 to 2:30. Available at other time... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14772 | # Write a proportion to solve each problem
## Write A Proportion To Solve Each Problem
First, we need to write a proportion to solve each problem construct our proportion, so we need two ratios.A recipe uses 5 cups of flour for every 2 cups of sugar.The Example of Proportion image shows that 1/2 = 2/4.Set up the rati... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14773 | # A Degree of Gauss normal map
1. Nov 30, 2016
### spaghetti3451
If $M^{2} \subset \mathbb{R}^{3}$ is a surface with given normal field, we define the Gauss (normal) map
$$n:M^{2} \rightarrow \text{unit sphere}\ S^{2}$$
by
$$n(p) = \textbf{N}(p), \qquad \text{the unit normal to M at p}.$$
-----------------------... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14774 | # zbMATH — the first resource for mathematics
Maximal outerplanar graphs with perfect face-independent vertex covers. (English) Zbl 0808.05042
Let $$G = (V, E)$$ be a 2-connected planar graph, embedded in the plane. A subset $$W \subseteq V$$ is called perfect face-independent vertex cover (FIVC) of $$G$$ if every fac... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14775 | It is currently 17 Oct 2017, 01:02
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based o... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14776 | # Could someone explain derivatives of delta function?
I am studying Signals and Systems.
The textbook told me $\delta'(t)$ has the following properties.
$1$. $x(t)\delta'(t-t_0)=x(t_0)\delta'(t-t_0)-x'(t_0)\delta(t-t_0)$
$2$. $\displaystyle\int_{-\infty}^t\delta'(\tau-t_0)d\tau=\delta(t-t_0)$
$3$. $\displaystyle\... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14777 | # Uniform distribution (discrete)
34,117pages on
this wiki
Probability mass functionn=5 where n=b-a+1 Cumulative distribution functionn=5 where n=b-a+1. The convention is used that the cumulative mass function $F_k(k_i)$ is the probability that $k>=k_i$ Parameters $a \in (...,-2,-1,0,1,2,...)\,$$b \in (...,-2,-1,0,1... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14778 | # Prove that if $g^{(p-1)/2} \equiv -1 (mod \mbox{ } p)$ then its smaller power can't be congruent to 1.
Let $p$ be a prime greater than $2$. Show that $g^{(p-1)/2} \equiv -1 (mod \mbox{ }p)$ implies $g^{k} \not\equiv 1 (mod \mbox{ }p)$ for every $1≤k≤(p-1)/2$.
• Try $p = 7$, it doesn't follow. – Daniel Fischer Nov 2... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14779 | # Standard deviation of sampling distribution when n=1
#### Frodo/Sociology
##### New Member
Hi everyone,
I'm reading this when it comes to the theory around the sampling distribution: "The standard deviation of the sample means (known as the standard error of the mean) will be smaller than the population standard d... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14780 | # Cauchy's Mean Theorem
## Theorem
Let $x_1, x_2, \ldots, x_n \in \R$ be real numbers which are all positive.
Let $A_n$ be the arithmetic mean of $x_1, x_2, \ldots, x_n$.
Let $G_n$ be the geometric mean of $x_1, x_2, \ldots, x_n$.
Then $A_n \ge G_n$.
## Proof
The arithmetic mean of $x_1, x_2, \ldots, x_n$ is def... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14781 | # How do you find the solution to 5(costheta+1)=5 if 0<=theta<360?
Jun 8, 2018
$\frac{\pi}{2}$ and $\frac{3 \pi}{2}$
#### Explanation:
I assume you know $0 \le \theta < 360$ is the same thing as $0 \le \theta < 2 \pi$
I will solve in Radians which are easier than degrees.
$5 \left(\cos \theta + 1\right) = 5$ on $... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14782 | User jeremy bradford - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T03:16:51Z http://mathoverflow.net/feeds/user/9727 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/4422/is-a-torsion-free-abelian-group-finitely-generated-if-all-of-its-localizations-a/40805... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14783 | # How do you differentiate z=w^(3/2)(w+ce^w)?
Apr 28, 2017
$\textcolor{red}{\frac{\mathrm{dz}}{\mathrm{dw}} = \frac{\sqrt{w}}{2} \left[5 w + c {e}^{w} \left(2 w + 3\right)\right]}$
#### Explanation:
$z = {w}^{\frac{3}{2}} \left(w + c {e}^{w}\right)$
Assuming that c is a constant,
$\frac{\mathrm{dz}}{\mathrm{dw}} ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18352 | # Property of complex numbers.
Let $z \in \mathbb{C}$ such that $Re(z^{n})\geq0, \forall n\in\mathbb{N}$, where $Re(z^{n})$ is the real part of $z^{n}$. Show that $z\in\mathbb{R}^{+}$.
If $z=a+bi$, $a,b\in\mathbb{R}$, then for $n=1\Rightarrow Re(z)\geq0\Rightarrow a\geq0$. So $a\in\mathbb{R}^{+}$, now we only need sh... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18353 | # JEE Main & Advanced Mathematics Applications of Derivatives Length of Intercept Made on Axes by The Tangent
## Length of Intercept Made on Axes by The Tangent
Category : JEE Main & Advanced
Equation of tangent at any point $({{x}_{1}},\,{{y}_{1}})$ to the curve $y=f(x)$ is ${{G}_{2}}$, then x-intercept $={{x}_{1}}... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18354 | If the distance of the point P (1,2,1) from the plane x + 2y - 2z =alpha where alpha> 0, is 5, then the foot o
### Question Asked by a Student from EXXAMM.com Team
Q 1114491359. If the distance of the point P (1,2,1) from the plane x + 2y - 2z =alpha where alpha> 0, is 5, then the foot of the perpendicular to the... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18355 | zbMATH — the first resource for mathematics
On the zeros of the Wronskian of an entire or meromorphic function and its derivatives. (English) Zbl 0865.30044
Let $$g$$ be a meromorphic function in the complex plane, and define the homogeneous differential polynomial $$\psi$$ by $$\psi= W(g, g^{(k_1)}, g^{(k_2)}, \dots,... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18356 | # Tag: Clearly Explained
## A Simple Proof for the Chebyshev Inequality: Clearly Explained!
In the Appendix A of this book: Statistics: Principles and Methods written by Giuseppe Cicchitelli, Pierpaolo D’Urso and Marco Minozzo published by Pearson in 2021, I found the…
## Skewness in Wolfram Alpha: Clearly Explained... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18357 | 3: kilogram per meter 3 (kg/m 3) 2. In radians, one complete counterclockwise revolution is 2 π and in degrees, one complete counterclockwise revolution is 360 °. Trigonometry (10th Edition) answers to Chapter 3 - Radian Measure and the Unit Circle - Section 3. 9) The minute hand of a clock is 8 inches long. To find a ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18358 | Question
# A ladder is $$2$$m long has lower end on the ground and the other end in contact with a vertical wall. The lower end slips along the ground. If upper end is moving downward at the rate of $$25$$ cm/sec and when upper end of ladder is $$1$$m above the ground, then the rate at which lower end of the ladder is... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18359 | # Difference between revisions of "2010 AMC 12A Problems/Problem 23"
## Problem
The number obtained from the last two nonzero digits of $90!$ is equal to $n$. What is $n$?
$\textbf{(A)}\ 12 \qquad \textbf{(B)}\ 32 \qquad \textbf{(C)}\ 48 \qquad \textbf{(D)}\ 52 \qquad \textbf{(E)}\ 68$
## Hints and Method of Attack... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18360 | # Finding a function, given its derivative.
At the start of day zero during the summer, the temperature is $y(0) = 15$ degrees Celsius. Over a 50 day period the temperature increases according to the rule $$y'(t) = {y(t) \over 50}$$. With time $t$ measured in days. Find the formula for $y$
I not sure how to start her... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18361 | # Rewriting Fractions: Factoring, Rationalizing, Embedded.
## Presentation on theme: "Rewriting Fractions: Factoring, Rationalizing, Embedded."— Presentation transcript:
Rewriting Fractions: Factoring, Rationalizing, Embedded
Simplifying Rational Expressions Simplify: Can NOT cancel since everything does not have a ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18362 | # Tag Info
Depending on the context, the use of the complex form could be for mathematical convenience or for a no-kidding need for both real and imaginary parts. When you factor the expression, you get $$u(t) = e^{{\eta}t^2}e^{j{\beta}t^2}$$ Where the first exponential is a generic magnitude envelope, in this case Ga... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18363 | Zed
Written by Jerry Ratzlaff on . Posted in Plane Geometry
• Three rectangles, two that intersect at a 90° angle to the third one at end each at different directions.
• A zed is a structural shape used in construction.
area of a Zed formula
$$\large{ A = t \; \left[ l + 2 \; \left( w - t \right) \right] }$$
Where... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18364 | # ISSN: Wikis
Note: Many of our articles have direct quotes from sources you can cite, within the Wikipedia article! This article doesn't yet, but we're working on it! See more info or our list of citable articles.
# Encyclopedia
(Redirected to International Standard Serial Number article)
An International Standard... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18365 | # Cartesian Product Space with dependent event in probability!
It's a question on sample space for dependent event and; as a precursor, I've first used independent events. So prepare for a lengthy question!
Suppose there is an urn with 3 white and 2 red balls. Two balls are picked randomly with replacement. To find o... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18366 | Python Course homework 5
Exercise 1
Previously we discussed the concept of recursive function calls
Write a recursive implementation of the bisection function described above, which we repeat here for convenience
def bisect(f, a, b, tol=10e-5):
"""
Implements the bisection root finding algorithm, assuming that f is... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18367 | anonymous 5 years ago another question on limits
1. anonymous
$\lim_{x \rightarrow \infty} (\int\limits_{0}^{x}e ^{x}dx)^{2}/\int\limits_{0}^{x}e ^{2x ^{2}}dx$
2. apples
The numerator easily simplifies to $\left(e^x - 1\right)^2$ but the lower integral has no elementary antiderivative, so I'm not too sure.
3. appl... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6528 | # Eigenfunctions orthogonal in Hilbert space
Gold Member
Hello,
I am having a question regarding how eigenfunctions are orthogonal in Hilbert space, or what does that even mean (other than the inner product is zero). I mean, I know in ##\mathbb {R^{3}}##, vectors are orthogonal when they are right angles to each othe... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6529 | ## A community for students. Sign up today
Here's the question you clicked on:
## anonymous one year ago Find the quotient of quantity of 3 times x to the 3rd power plus 9 times x to the 2nd power minus 6 times x all over negative 3 times x. x^2 − 9x + 6 −x^2 − 3x − 2 x^2 + 9x − 6 −x^2 − 3x + 2
• This Question is Op... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6530 | # Thread: How do I find area between functions using integrals if...?
1. ## How do I find area between functions using integrals if...?
How do I find area between functions using integrals if there are more than two functions as shown in the attached pdf as #15?
Any input would be greatly appreciated!
2. Your points... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6531 | # Resulting velocity of 2 particles
1. Dec 29, 2008
### disclaimer
[solved] resulting velocity of 2 particles
1. The problem statement, all variables and given/known data
2. Relevant equations
conservation of momentum
$$m_Av_A'=m_Bv_B'$$
$$v_A'=\frac{m_B}{m_A}v_B'$$
conservation of energy
$$V=\frac{1}{2}m_A(v... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6532 | # Simple assignment notation question
this is an elementary question, but I haven't encountered this notation before:
S, and T are being assigned but what does "/" signify here?
Thanks
• – vadim123 Jan 25 '17 at 2:29
These both signify a quotient of $\mathbb{R}$ with respect to certain group actions. The group $(\... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6533 | # Step-by-step Solution
## Find the higher order derivative of $2xy^2$
Go
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
2
e
π
ln
log
lim
d/dx
Dx
>
<
>=
<=
sin
cos
tan
cot
sec
csc
asin
acos
atan
acot
asec
acsc
sinh
cosh
tanh
coth
sech
csch
asinh
acosh
atanh
acoth
asech
acsch
### Videos
$0$
## Step-by-step explanation
Proble... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6534 | Let $G$ be any simple and undirected graph. Let $A$ be the adjacency matrix of $G$.
1) Let $B$ be the number $\tfrac16\mathrm{tr}(A^3)$. What does $B$ count? That is $B$ counts the number of....?
2) Suppose that $M$ is adjacency matrix of a tree. Explain why every element of the diagonal of $M^3$ must be zero.
3) Mu... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6535 | ## jroop 2. Divide. (2x3 – x2 – 24x + 12) ÷ (2x – 1) (1 point)x2 – 1 x2 – 12 2x – 1 3. Simplify. (1 point) –2 4. What is the undefined value of ? (1 point)4 0 –3 –4 5. Multiply. (1 point) 6. Add. (1 point) 7. Add (1 point) 8. Subtract. (1 point)1 0 –1 9. Solve. (1 point)x = x = x = x = 10. Solve. (1 point)x = –4 x = 8 ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6536 | # Homework Help: Integrating trig
1. Mar 7, 2006
### QueenFisher
integrate with respect to x: (sinx)^3 * cosx
i have no idea where to start, can anyone help me? i've looked at differentials of other trig functions but i can't see any that would help
2. Mar 7, 2006
### benorin
Use a "u substitution".
3. Mar 7, 2... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6537 | # American Institute of Mathematical Sciences
November 2016, 10(4): 895-919. doi: 10.3934/amc.2016048
## Variation on correlation immune Boolean and vectorial functions
1 School of Computer Software, Tianjin University, Tianjin 300072, China 2 Department of Mathematics, University of Paris VIII, CNRS, UMR 7539 LAG... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6538 | # Angular Momentum Problem
1. Aug 9, 2010
### Karol
1. The problem statement, all variables and given/known data
A ladder is leaning against a smooth wall and a smooth floor (no friction). it's starting to slide
down. The initial angle between the ladder and the floor is $$\theta$$0, according to the drawing. The ma... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6539 | # Shortest distance between lines and the lines
1. May 29, 2012
### ezsmith
1. The problem statement, all variables and given/known data
Find the shortest distance between the lines r = (0,7,6) + t (-3,2,2) and the line r = (-3,6,-4) + s (2,-5,6)
3. The attempt at a solution
What I did was I cross product s(2,-5,6)... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6540 | multiplicative order of 2 mod p^N
Does there exist a positive integer N such that for all odd primes p the multiplicative order of 2 mod p is strictly less than the multiplicative order of 2 mod p^N ? Once again, references would be greatly appreciated as this pertains to ongoing graduate research.
• Since only two W... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6541 | # Tag Info
0
Your approach is correct. For better clarity, I suggest proving the relation $$\overline{\operatorname{Im} T^*} = (\ker T)^\perp$$ separately (it's useful on other occasions too). The proof uses the fact that the closed linear span of $A$ is $(A^\perp)^\perp$: $$\overline{\operatorname{Im} T^*} = ((\oper... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6542 | # How do you solve (x - 3)^2 = 25?
Mar 6, 2016
#### Answer:
$- 2 \mathmr{and} 8$.
#### Explanation:
$x - 3 = \sqrt{25} = \pm 5$
x = 3 + 5 and x = $3 - 5$. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6543 | # How do you solve 6x^2+x>1?
Sep 2, 2016
$\textcolor{g r e e n}{x < - \frac{1}{2}}$ or $\textcolor{g r e e n}{x > \frac{1}{3}}$
#### Explanation:
$6 {x}^{2} + x > 1$ is equivalent to $6 {x}^{2} + x - 1 > 0$
Factoring $6 {x}^{2} + x - 1$
we have $\left(3 x - 1\right) \left(2 x + 1\right)$
which will be equal to zer... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_1792 | ### Select your language
Suggested languages for you:
Americas
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4 P
Expert-verified
Found in: Page 177
### Physics For Scientists & Engineers
Book edition 9th Edition
Author(s) Raymond A. Serway, John W. Jewett
Pages 1624 pages
ISBN 9781133947271
# The record number of boat lifts, including the boat and i... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_1793 | # Fields
A fundamental component of many cryptographic protocols is the algebraic structure known as a field. Fields are sets of objects (usually numbers) with two associated binary operators and such that various field axioms hold. The real numbers are an example of a field with uncountably many elements.
Halo makes... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_1794 | # Riemann Sums for computing $\int_0^3 x^3 dx$
Answer the attached questions for the integral
$$\int_0^3x^3 dx$$
• Use the right hand rule for Riemann sums.
• Sure, thanks for the additional info. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_1795 | # Games
You are currently browsing the archive for the Games category.
## ROI in Games – Part 1
There are many games that have an investment phase followed by an exploitation phase including the card game Dominion, Terraforming Mars, Slay the Spire (during a combat), Saint Petersburg, Roll for the Galaxy, Master of ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_1796 | What is the definition of magnetic moment in quantum mechanics?
• The general formula for the magnetic moment of a charge configuration is defined as $$\vec{\mu} = \frac{1}{2} \int \vec{r} \times \vec{J} \,d^3r$$
• For an electron it's said that the correct equation relating it's spin and magnetic moment is is $$\vec... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_1797 | ## Abstract
This article proposes a hierarchical energy management strategy for power-split hybrid electric vehicles (HEVs) in presence of driving cycle uncertainty. The proposed hierarchical controller exploits long-term and short-term decision making via a high-level pseudospectral optimal controller and a low-level... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_1798 | Homework Help: Central Limit Theorem
1. Dec 15, 2009
cse63146
1. The problem statement, all variables and given/known data
Each of 180 students in an evening stats and methods class is asked to generate 64 random numbers with a "spinner" that selects numbers from 1 to 50, and then compute the mean of the 64 numbers... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_1799 | # <mtext>Content</mtext> ( f g ) </mrow> ⊂<!-- ⊂ -->
$\text{Content}\left(fg\right)\subset \text{Content}\left(f\right)\text{Content}\left(g\right)\subset \text{rad}\left(\text{Content}\left(fg\right)\right)$
to deduce that if $\text{Content}\left(f\right)$ contains a nonzerodivisor of $R$, then $f$ is nonzerod... |
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