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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_1800 | # Do linear combinations of two efficient portfolios cover the entire efficient frontier?
Note : We are considering the case of N risky assets.
I think the answer is 'Yes', although I am not sure as I am unable to prove it.
The reasons for me thinking that the answer is 'Yes' are -
1) The two portfolios being consi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_1801 | '
# Random Question & Answer
Select Category:
### Differentiation Question 10z
10. Differentiate with respect to the given variable.
z)
10. Differentiate with respect to the given variable.
10. Differentiate with respect to the given variable.
z)
Solution:
z)
Remember
The derivative of .
We choose so that ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_1802 | # Is $\ln |f|$ harmonic?
I'd like to show that $\ln |f|$ is harmonic, where $f$ is holomorphic defined on a domain of the complex plane and never takes the value 0. My idea was to use the fact that $\ln |f(z)| = \operatorname{Log} f(z) - i*\operatorname{Arg}(f(z))$, but $Log$ is only holomorphic on some part of the co... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_1803 | # The modulus and amplitude of the complex number $[e^{3-i \pi/4}]^{3}$ is respectively
$\begin{array}{1 1}(1)e^{9},\frac{\pi}{2}&(2)e^{9},\frac{-\pi}{2}\\(3)e^{6},\frac{-3\pi}{4}&(4)e^{9},\frac{-\pi}{4}\end{array}$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_1804 | # 5.2 Periodic functions (Page 5/5)
Page 5 / 5
If “a” and “b” are non-zero real number and functions g(x) and h(x) are periodic functions having periods, “ ${T}_{1}$ ” and “ ${T}_{2}$ ”, then function $f\left(x\right)=ag\left(x\right)±bh\left(x\right)$ is also a periodic function. The period of f(x) is LCM of " ${T... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_1805 | # Trouble understanding Electric flux and gauss law
Well, i know that the electric flux is the number of field lines passing a certain area, but (1)what does that mean? I can't the concept itself. I know it have many applications, gauss law one of them, but (2)what information does it reflect?
Gauss law states that t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_1806 | Algebra i Analiz
RUS ENG JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB
General information Latest issue Archive Impact factor Subscription Search papers Search references RSS Latest issue Current issues Archive issues What is RSS
Algebra i Analiz: Year: Volume: Issue: ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_1807 | 11-Apr-2021
# A brief look at the toy
I recently bought my daughter a fishing toy.
It looks like this:
It’s just a spinning disc with little fishes in it. These fishes sometimes open their mouth, during which you can put hook from the given fishing rod. If the timing is right, you can hook them out of the disc.
Th... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10880 | # Definition:Binomial Coefficient/Integers/Definition 1
## Definition
Let $n \in \Z_{\ge 0}$ and $k \in \Z$.
Then the binomial coefficient $\dbinom n k$ is defined as:
$\dbinom n k = \begin{cases} \dfrac {n!} {k! \paren {n - k}!} & : 0 \le k \le n \\ & \\ 0 & : \text { otherwise } \end{cases}$
where $n!$ denotes t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10881 | ## anonymous 4 years ago Calculate an integral
1. anonymous
2. anonymous
Have you tried u-sub?
3. anonymous
try u = 9-x^2
4. anonymous
No, sub u=x^2
5. anonymous
I'm pretty sure mine still works... Both are fine...
6. anonymous
my substitution become like this...
7. anonymous
Well you can trig sub if you w... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10882 | My Math Forum law of sines
Geometry Geometry Math Forum
October 5th, 2018, 07:00 AM #1 Senior Member Joined: Nov 2011 Posts: 248 Thanks: 3 law of sines Why the author use the law of sines? What is goal to use it? In the link: https://www.maa.org/external_archive...n/Polygon.html
October 5th, 2018, 07:43 AM #2 Gl... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10883 | # Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2004 | May-Jun | (P1-9709/01) | Q#6
Question
The curve and the line intersect at two points. Find
i.
the coordinates of the two points,
ii. the equation of the pe... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10884 | # Find the Sum of the Infinite Geometric Series 2 , 10 , 50 , 250
, , ,
This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by gives the next term. In other words, .
Geometric Sequence:
The series given has a value of such that or . ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10885 | Narrowing the difficulty gap for the Celis-Dennis-Tapia problem
We study the {\em Celis-Dennis-Tapia (CDT) problem}: minimize a non-convex quadratic function over the intersection of two ellipsoids. In contrast to the well-studied trust region problem where the feasible set is just one ellipsoid, the CDT problem is no... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10886 | # Variational Gaussian Processes¶
## The Variational Free Energy¶
Often, the log marginal likelihood of the data can be costly or intractable to compute. To circumvent this difficulty, one solution is to optimise an alternative objective instead of the log-marginal. This objective should be chosen such that (1) it i... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10887 | # Algebraic structure of Gaussian PDFs
The answer to this question shows that the product of two Gaussian PDFs is also a Gaussian PDF.
My questions are:
• Is there a multiplicative identity for this product?
• More generally what algebraic structure (e.g. semigroup/monoid/ring/field) do Gaussian PDFs belong to?
• OK... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10888 | ## Precalculus (6th Edition) Blitzer
Published by Pearson
# Chapter 9 - Section 9.3 - The Parabola - Exercise Set - Page 997: 27
#### Answer
$x=\dfrac{1}{8}(y-2)^2+1$
#### Work Step by Step
General form of a horizontal parabola is given as: $(y-k)^2=4p(x-h)$...(1) Here, $\text{Vertex}=(h,k)$ and focus is: $(h+p, ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10889 | Find the sum of all the four digit numbers formed using the : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack
It is currently 28 Feb 2017, 07:14
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estim... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10890 | # Algebra Examples
,
Consider the difference quotient formula. Use this formula to solve for the slope of the secant line .
Find the components of the definition.
Evaluate the function at .
Replace the variable with in the expression.
Simplify the result.
Rewrite as .
Expand using the FOIL Method.
Apply the distributi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10891 | Matrix Variate Normal Distributions with MixMatrix
2021-11-15
library(MixMatrix)
Matrix Variate Distributions
Suppose there is a two-dimensional grid of observations: each observation is randomly distributed somehow, perhaps each spot on the grid has its own mean, there’s a covariance relation across the rows that ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10892 | # Parity (physics)
In quantum mechanics, a parity transformation (also called parity inversion) is the flip in the sign of one spatial coordinate. In three dimensions, it can also refer to the simultaneous flip in the sign of all three spatial coordinates (a point reflection):
${\displaystyle \mathbf {P} :{\begin{pma... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10893 | # Singular Value Decomposition (SVD). Show equality.
I have to show the following equality:
$WW^{T} = USUS$, where $W = USV^{T}$; $U,V$ are orthogonal matrices and $S$ is a diagonal matrix, where all entries but the diagonal are $0$.
I think I am missing just one step to finish the proof. I am this far: $WW^{T} = (U... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10894 | Home > Standard Deviation > Computer Standard Deviation From Standard Error
# Computer Standard Deviation From Standard Error
## Contents
For instance we would provide the mean age of the patients and standard deviation, the mean size of tumors and standard deviation, etc. What is missing from a non-afterburning eng... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10895 | # The magnetic indyction field due to magnetic north pole of strength 10Am and 5cm away from the pole in weber /metre square
Arun
25758 Points
2 years ago
Magnitude of magnetic induction due to a pole of strength m at a distance r from it is
B = (\mu0 / 4\pi)(m / r2) , \mu0 / 4\pi = 10–7 H.
m = 10 Am, r = 5 cm = 5 x 1... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6896 | #### Closed-Form Expressions for the n-Queens Problem and Related Problems
##### Kevin Pratt
In this paper, we derive simple closed-form expressions for the $n$-queens problem and three related problems in terms of permanents of $(0,1)$ matrices. These formulas are the first of their kind. Moreover, they provide the ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6897 | # Determining Rank and Nullity
Suppose $L: M(4,3) \to R^7$ is linear and onto.
1. Determine the rank L.
2. Determine the nullity L.
I know that rank is equal to the leading 1's in a reduced row echelon matrix, and the nullity is equal to the number of columns corresponding to free variables. So if I was given an act... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6898 | # Cubic equation's determinant
Algebra Level 3
If $$\alpha , \beta \text{ & } \gamma$$ are the roots of the equation
$x^3 + ax^2 + b = 0$
find the value of $$\begin{vmatrix} \alpha & \beta & \gamma \\ \beta & \gamma & \alpha \\ \gamma & \alpha & \beta \\ \end{vmatrix}$$.
× |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6899 | # Working with phi function with larger numbers?
I've been recently learning about Phi function(Euler's totient function). I am attempting to efficiently find the $\phi(n)$ of higher numbers.
$$\frac{30}{\phi(30)} = 3.75,$$
would I be able to now know that for every multiple of $30$?
$$\frac{180}{\phi(180)} = 3.75,... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6900 | # Questions Asked onNovember 1, 2010
1. ## chemistry
What volume of HCl gas is produced by the reaction of 2.4 liters of H2 gas with 1.5 liters of Cl2 gas? (Volumes are at the same T and P.) 1. 3.0 liters 2. 4.8 liters 3. 0.75 liters 4. 2.4 liters 5. 1.5 liters
2. ## Chemistry
If 4.0 L of a 4.8 M SrCl2 solution is ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6901 | • Save
• Share
# Permutations Combinations and Probability Quiz SBI PO 2018
4 months ago .
Are you preparing for Banking, Insurance and other Competitive Recruitment or Entrance exams? You will likely need to solve a section on Quant for sure. Permutations Combinations and Probability Quiz SBI PO 2018 will help you ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6902 | ## petegutz Whats the difference between diverge and converge??? one year ago one year ago
1. hba
go to the physics portion
2. TuringTest
what? no it's a math Q
3. petegutz
but its in algebra 2
4. hba
k sorry
5. pratu043
Diverge means separate, converge means meet.
6. TuringTest
converge is to "settle down"... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6903 | # How to decide the convergence or divergence of a positive term series under the given information? [duplicate]
Possible Duplicate:
Positive series problem
If $a_n > 0$ for each $n = 1, 2, 3, \cdots$ such that the series $\sum_{n=1}^{\infty} a_n$ diverges, then how to determine if the series $$\sum_{n=1}^{\infty} \f... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6904 | Newtonian limit FRW
1. Sep 18, 2008
astromandi
The newtonian limit for general relativity exists only for the asymptotically flat spacetimes.
FRW case definitely not asymptotically flat. SO the newtonian limit should not exist for it.
However we have Newtonian theory of cosmology in homogeneous and isotropic univers... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6905 | ### Compound Depreciation Calculator
She promised Ankita that she will pay it back in two equal installments. If we calculate the present value of that future $10,000 with an inflation rate of 7% using the net present value calculator above, the result will be$7,129. To calculate reducing balance depreciation, you wil... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6906 | Choosing the algebraic independent elements in Noether's normalization lemma
Given a field $k$ and a finitely generated $k$-algebra $R$ without zero divisors, one knows that there exist $x_1, \ldots, x_n$ algebraically independent such that $R$ is integral over $k[x_1, \ldots, x_n]$. How can one choose actually the $x... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6907 | # zbMATH — the first resource for mathematics
Infima in the recursively enumerable weak truth table degrees. (English) Zbl 0909.03038
The following interesting results are given:
1. For any nonrecursive, $$W$$-incomplete r.e. $$W$$-degree $${\mathbf c}$$, there is an r.e. $$W$$-degree $${\mathbf a} |_W {\mathbf c}$$ s... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6908 | ### Tail behavior of randomly weighted sums
#### Abstract
Let {Xt, t ≥ 1} be a sequence of identically distributed and pairwise asymptotically independent random variables with regularly varying tails, and let {Θt, t ≥ 1} be a sequence of positive random variables independent of the sequence {Xt, t ≥ 1}. We will disc... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6909 | Home » Statistics » Probability Distributions » Chebyshev’s Inequality
# Chebyshev’s Inequality
## Chebyshev’s Inequality
Chebyshev’s Inequality is a very powerful inequality, because it applies to any probability distribution.
Chebyshev’s Inequality is used to estimate the probability that a random variable $X$ is ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6910 | ## [USACO Jan07]干草塔
Grade 0 Open Time Friday, 18 January 2013, 1:30 pm Discount 0.8 Time Discount Friday, 18 January 2013, 1:30 pm Allow late Yes Close Time Friday, 18 January 2013, 1:30 pm Input file btwr.in Output file btwr.out
Always bored with cud-chewing, the cows have invented a new game. One cow retrieves a s... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6911 | FearOfPhysics.com: Home
Fearofphysics: Physics problem of the week
# Physics Problem of the Week for Dec 08 2014
Truck and BoulderA truck is moving at 21 m/s. The driver sees a boulder in the road, directly ahead 110 m away. After a reaction time (during which the truck continues at 21 m/s), the driver applies the ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9952 | # Propositional Logic: Atomic Statements
In Propositional Logic most books I read say - Atomic Statements are statements which can't be simplified further.
I find the above definition ambiguous or maybe based on intuition (i.e. what is 'simple')
Is there a more rigorous definition? For e.g. how do I go about proving... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9953 | # What is known about the sets enumerated by primitive recursive functions?
Let's say that a set of natural numbers $$S \subseteq \mathbb{N}$$ is primitive recursively enumerable if there exists some primitive recursive function $$f$$ such that $$S$$ is the range of $$f$$. That is, we can enumerate $$S$$ by calculatin... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9954 | Reduced Cohomology
Get Reduced Cohomology essential facts below. View Videos or join the Reduced Cohomology discussion. Add Reduced Cohomology to your PopFlock.com topic list for future reference or share this resource on social media.
Reduced Cohomology
In mathematics, reduced homology is a minor modification made to... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9955 | # error of linear interpolation
I have two points $x_1, x_2$ between which I would like to have a linear interpolation $P_1$. Those two points are just points where I know the value of the underlying function $f$. I know that the error at any point between the two will be bounded by the second derivative of the functi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9956 | Question
# True or False? Justify your answer with a proof or a counterexample. You can explicitly solve all first-order differential equations by separation or
Differential equations
True or False? Justify your answer with a proof or a counterexample. You can explicitly solve all first-order differential equations b... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9957 | # Properties of Rectangle
## What is Rectangle?
A rectangle is a four-sided two-dimensional plane figure. A rectangle is a four-sided polygon with opposing sides that are parallel and equal in length. It is one of the types of quadrilateral in which all four angles are right angles or equal to 90 degrees. A rectangle... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9958 | # Finding conjugacy classes and normal subgroups of $D_8$, the dihedral group of order $16$ [duplicate]
What are the conjugacy classes for the dihedral group $D_8$ of order 16?
What are its subgroups of order $4$, and which of them are normal subgroups?
I know that $\{e\} ,\{r^2,r^6\},\{r,r^7\},\{r^3,r^5\},\{r^4\},\... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9959 | • anonymous
The probability density function $f(x) = \left(\begin{matrix}2x-4 \\ 0\end{matrix}\right)$$2 \le x \le 3 - otherwise -$ Sketch the graph of f(x).
Mathematics
Looking for something else?
Not the answer you are looking for? Search for more explanations. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9960 | # In the figure, DE || QR and AP and BP are the bisectors of ∠EAB and ∠RBA.
14 views
closed
In the figure, DE || QR and AP and BP are the bisectors of ∠EAB and ∠RBA. Find the value of ∠APB.
by (35.6k points)
selected
DE || QR (given)
∴∠EAB + ∠RBA = 180°
(Sum of the interior angles on the same side of a transvers... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9961 | ## Elementary Algebra
$(5x-6)^2$
RECALL: A perfect square trinomial can be factored using either of the following formulas: (i) $a^2+2ab+b^2=(a+b)^2$ (ii) $a^2-2ab+b^2=(a-b)^2$ The given trinomial can be written as: $=(5x)^2-2(5x)(6)+6^2$ The trinomial above is a perfect square trinomial of the form $a^2-2ab+b^2$, whe... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9962 | ## How to find the future value of an annuity compounded quarterly
Find the present value of $40, 000 due in 4 years at the given rate of interest. interest at the rate of 9%/year compounded quarterly? Section 5.2 Annuities. Calculates a table of the future value and interest using the compound interest method. Presen... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9963 | # Calculate percentages
1. Sep 24, 2006
### sublime
I have a ti-89, does anyone know how to calculate percentages of teh normal model on it? I am not sure what the function is, and using the table in the back of my book is a pain. The problem's I mean are, for example-
given N(80,5) what percentage of the data is ab... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9964 | # show that $\Sigma _{n \leq x} \mu(n) \lfloor \frac{x}{n} \rfloor ^2 = \frac{x^2}{\zeta(2)} + \mathcal{O}(x\log(x))$
Basically the problem asks to show that $$\Sigma _{n \leq x} \mu(n) \lfloor \frac{x}{n} \rfloor ^2 = \frac{x^2}{\zeta(2)} + \mathcal{O}(x\log(x))$$ where $x$ is a real number and $n$ integer
I might b... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9965 | From this definition it follows that the sine of any angle is always less than or equal to one. Together with the law of cosines, the law of sines can help when dealing with simple or complex math problems by simply using the formulas explained here, which are also used in the algorithm of this law of sines calculator.... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9966 | ×
# Lines, lines, lines galore
Let $$n$$ be a positive integer. On each side of a square $$n$$ points are chosen. (No point is at a vertex of the square.)
(a) How many segments are there whose endpoints are two of the above points and such that no segment lies along a side of the square?
(b) What is the maximal pos... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9967 | In the previous post, we were trying to show that any homology class of a space $X$ in dimension at most six can be represented by a smooth oriented manifold mapping to $X$. This statement is a geometric one, but it can be proved via homotopy-theoretic means. In the previous post, we interpreted it in terms of homotopy... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6912 | ]> Simple Differential Equations
### Chapter 2: Integration; Section 1: Indefinite Integrals; page 4
Previous topic: page 3 Special Methods
Next topic: section 2 Definite Integrals, page 1 Fundamentals
# Simple Differential Equations
## Introduction
A differential equation is a mathematical representation of a re... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6913 | ## Algebra 1
$0$
We start with the given expression: $(\frac{4}{3}\times0)\times(-20)$ The zero property of multiplication states that the product of any real number an $0$ is $0$. We use this property to simplify the expression: $0\times(-20)=0$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6914 | Thread: Cauchy sequence convergence in a general metric space
1. Cauchy sequence convergence in a general metric space
Hello!
My question is one from Baby Rudin... Chapter 3, Question 23.
The question is, given two Cauchy sequences $\{p_n\}$ and $\{q_n\}$, in a metric space X (with a metric "d"), we want to show th... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6915 | C. Dima and Staircase
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
Dima's got a staircase that consists of n stairs. The first stair is at height a1, the second one is at a2, the last one is at an (1 ≤ a1 ≤ a2 ≤ ... ≤ an).
Dima decided to play with the ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6916 | # Automorphism on the unit interval compatible with a measure preserving set function
Cross-posting from math stack-exchange since it's not getting any visibility there.
I am given a function $F: \{[0, y]: y \in I\} \to \Sigma(I)$, such that $\lambda(F([0, y])) = y$, and $F([0, y]) \subseteq F([0, z])$ for $y \le z$.... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6917 | # Trignometry prove question
I am new to this website so Please forgive me for my mistakes.
I have a question of trigonometry to prove and it is as (I dont know how to write theta symbol sorry for it)
$(1-\sin \theta)/(1-\sec \theta) = 2\cot \theta(\cos \theta- \csc\theta)$
• Enclose the gray box inbetween \$\$ and... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6918 | Question
Which of the following gives the correct relation between the acceleration due to gravity and period of a pendulum?
1. $g=\dfrac{2\pi L}{T^2}$
2. $g=\dfrac{4\pi^2 L}{T^2}$
3. $g=\dfrac{2\pi L}{T}$
4. $g=\dfrac{2\pi^2 L}{T}$
(b)
Solution Video
# OpenStax College Physics Solution, Chapter 16, Problem 11 (Test... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6919 | 1. Prove equation
cosh2$\displaystyle theta$= 2sinh^2$\displaystyle theta$
I did this = 2.(e^theta -e^-theta)/2 x(e^theta -e^-theta)/2
=2 x 1/4(e^2theta + e^-2 theta)
=(e^2theta +e^-2theta)/2
= cosh2$\displaystyle theta$
I am trying to get the hang of this Latex
2. Originally Posted by Jaffa
cosh2$\displaystyle thet... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6920 | GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 18 Sep 2019, 21:57
### GMAT Club Daily Prep
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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6921 | # Parametric Plane Equation
• April 21st 2008, 11:55 AM
Del
Parametric Plane Equation
Find the parametric equations for the line through the point P = (0, 1, -3) that is perpendicular to the plane https://webwork.math.lsu.edu/webwork...c0ae5b1b41.png
Use "t" as your variable, t = 0 should correspond to P, and the velo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6922 | # Mittag-Leffler function
An entire function $E _ \rho ( z)$ of a complex variable $z$, introduced by G. Mittag-Leffler [1] as a generalization of the exponential function:
$$E _ \rho ( z) = \sum _ { k= } 0 ^ \infty \frac{z ^ {k} }{\Gamma ( 1 + k / \rho ) } ,\ \ 1 \leq \rho < \infty .$$
Since the Mittag-Leffler func... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6923 | ## Precalculus (6th Edition) Blitzer
To get the value of $f\left( x+h \right)$, put $x+h$ in place of x, and then substitute in the given expression: So, \begin{align} & f\left( x+h \right)=8\left( x+h \right)-11 \\ & =8x+8h-11. \end{align} Now, \begin{align} & \frac{f\left( x+h \right)-f\left( x \right)}{h}=\frac{8x+... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6924 | k The eigenvalues are immediately found, and finding eigenvectors for these matrices then becomes much easier. {\displaystyle A} ψ {\displaystyle {\tfrac {d}{dt}}} {\displaystyle \psi _{E}} Therefore, for matrices of order 5 or more, the eigenvalues and eigenvectors cannot be obtained by an explicit algebraic formula, ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6925 | you are viewing a single comment's thread.
[–] -1 points0 points
sorry, this has been archived and can no longer be voted on
Is the set B finite here?
Not necessarily. You'll have to prove it yourself.
wouldnt
That's not a word. At least in English.
[–][S] 0 points1 point
sorry, this has been archived and can n... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6926 | # Math Help - Help with simple internal line segments of triangles proof.
1. ## Help with simple internal line segments of triangles proof.
Prove that if $D$ is internal to $\overline{AB}$, $E$ is internal to $\overline{AC}$ and $\frac{DB}{ DA} = \frac{EC}{EA}$ then ${BC}$ is parallel to ${DE}$
I'm having a tough ti... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6927 | # How do you find the midpoint of (–2, 5) and (–4, –6)?
Mar 15, 2016
$M = \left(- 3 , - \frac{1}{2}\right)$
#### Explanation:
The midpoint of a line created by the coordinates of the endpoints of the line can be determined using the formula
$M = \left(\frac{{x}_{1} + {x}_{2}}{2} , \frac{{y}_{1} + {y}_{2}}{2}\right... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18800 | Home/Other Classes/Other Subjects/
## Question
The table shows the number of cups of four different beverages sold by a coffee shop. What is the angle of sector representing tea in a pie chart?
Beverage Number of cups Coffee 60 Tea 75 Hot chocolate 25 Milk 40
(A) $$40^o$$
(B) $$135^o$$
(C) $$108^o$$
(D) $$72^o$$
$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18801 | # Manfred Scheucher
## Contact
Email:
lastname[at]domain, math.tu-berlin.de = domain
Address:
Technische Universität Berlin
Institut für Mathematik
Sekretariat MA 5-1
Strasse des 17. Juni 136
D-10623 Berlin, Germany
## About Me
I'm a postdoctoral researcher in the group of Stefan Felsner at TU Berlin (Arbeitsgrupp... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18802 | ## Proceedings of the Japan Academy, Series A, Mathematical Sciences
### New results on slowly varying functions in the Zygmund sense
#### Abstract
Very recently Seneta [15] has provided a characterization of slowly varying functions $L$ in the Zygmund sense by using the condition, for each $y>0$, $$x\left(\frac{L(x... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18803 | It is currently 15 Jul 2019, 14:59
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.
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we will pick new questions that match your level based on your Ti... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18804 | Introduction
In this section,we will introduce a new learning algorithm for density estimation, namely Expectation-Maximization (EM) algorithm. Before we introduce what EM is, I will first talk about mixture of Gaussian model and build the intuition on that.
Let’s denote ${x^{(1)},\dots,x^{(m)}}$ the training dataset... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18805 | Survival function of accumulated hazard in Cox model
I have this setup:
Independent subjects following a Cox model $$\lambda_i(t,X_i) = \lambda_0(t) \exp(X_i^T \beta )$$
the observed right censored survival data $$(T_i, \delta_i, X_i)$$ are i.i.d. and $$T_i = min( \tilde{T}_i,C_i)$$ and $$\delta_i = 1(\tilde{T_i}\le... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18806 | # Integrating $\int e^{x^2}dx=e^{x^2}F(x)+c$ [duplicate]
This might be a duplicate but I couldn't find it. Anyhow I'm having trouble integrating $$\int^t_0 e^{x^2}dx$$ I found it in an introductory chapter of a differential equations book and perhaps it assumes I know an integration technique I haven't been introduced... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18807 | # Formation of real image using a biconvex lens is shown below If the whole set up is immersed in water without disturbing the object and the
Formation of real image using a biconvex lens is shown below:
If the whole set up is immersed in water without disturbing the object and the screen position, what will one obse... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18808 | # How do you use the trapezoidal rule with n=4 to approximate the area between the curve sqrt(x) sinx from pi/2 to pi?
Nov 9, 2016
${\int}_{\frac{\pi}{2}}^{\pi} \sqrt{x} \sin x \mathrm{dx} \approx 1.430$ (3dp)
#### Explanation:
The values of y are tabulated as follows (using Excel)
Using the trapezoidal rule:
${\i... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18809 | Symbol
Problem
$3$ Solve the following problems involving logarithmic functions. $1$ Suppose that the earthquake released approximately $10^{12}$ Joules of energy. /Formula: $R-23logk$ $o$ $\left(a$ What is its magnitude on a Richter scale? (b) How much more energy does this earthquake release than the reference earthq... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18810 | ## App Windows – Tweak Software RV 7.3.3 | NulledTeam UnderGround
File size: 139.6 MB
RV is the next step in our efforts to develop great tools for VFX and animation artists. It is based on the RVX Core, a new GPU-accelerated image processing architecture that combines fast I / O, resolution-independent image handlin... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18811 | # ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 8 Matrices Ex 8.2
## ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 8 Matrices Ex 8.2
These Solutions are part of ML Aggarwal Class 10 Solutions for ICSE Maths. Here we have given ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 8 Matrices Ex 8.2
Mo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18812 | ## Related Articles
• CBSE Class 12 Syllabus
• CBSE Class 12 Maths Notes
• CBSE Class 12 Physics Notes
• CBSE Class 12 Chemistry Notes
• CBSE Class 12 Accountancy Notes
• CBSE Class 12 Computer Science (Self-Paced Course)
# Determinant of a Matrix
• Last Updated : 20 Jan, 2023
Determinant of a Matrix is defined as ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18813 | Characterization of ^ϕ-amenability and ^ϕ-module amenability of semigroup algebras
Document Type : Research Paper
Author
Esfarayen University of Technology, Esfarayen, North Khorasan,Iran
Abstract
For every inverse semigroup $S$ with subsemigroup $E$ of idempotents, necessary and sufficient conditions are obtained... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18814 | # Prove $\lfloor x + n \rfloor= \lfloor x\rfloor + n : n \in \mathbb{Z}$
Prove $$\lfloor x + n \rfloor= \lfloor x\rfloor + n : n \in \mathbb{Z}$$
So far I have used that $$\lfloor x + n \rfloor - n \leq x < \lfloor x + n \rfloor - n + 1$$, but I don't know how to continue.
## 2 Answers
Just use the definition of $$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18815 | # Homework Help: Fourier series of a function
1. Sep 18, 2011
### estro
I'm trying to find Fourier series for the following function:
$$f(x) = \begin{cases}1, & \mbox{if x \in (-\frac{\pi}{2}+2\pi n,\frac{\pi}{2}+2\pi n) } \\ -1, & \mbox{if x \in [\frac{\pi}{2}+2\pi n,\frac{3\pi}{2} + 2\pi n]} \end{cases}$$
This is... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10112 | # How do you write an exponential function whose graph passes through (0,-0.3) and (5,-9.6)?
Nov 3, 2016
#### Explanation:
An exponential function is:
$y = C {e}^{\alpha \left(x\right)}$
We can find the value of C, using the point $\left(0 , - 0.3\right)$
$- 0.3 = C {e}^{\alpha \left(0\right)}$
${e}^{\alpha \lef... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10113 | # Topological boundary of a specific manifold.
Let $\emptyset\neq X\subset\mathbb{R}^n$, $n\ge2$, be an $(n-1)$-dimensional differentiable submanifold, i.e. for every $p\in X$ there is an open $U_p\subset\mathbb{R}^n$ with $p\in U_p$, and a differentiable map $f:U_p\to\mathbb{R}$ such that $f^{-1}(0)=X\cap U_p$ and $r... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10114 | ## Solving a homogeneous ODE by first-order substitution methods
Calculating analytically solutions to differential equations can be hard and sometimes even impossible. Methods exist for special types of ODEs. One method is to solve the ODE by separation of variables. The idea of substitution is to replace some variab... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10115 | # A challenging sum series
## Homework Statement
Let
$$P(x) = \displaystyle\sum\limits_{k=1}^\infty arctan (\frac{x-1}{(k+x+1)sqrt(k+1) + (k+2)sqrt(k+x)})$$ (infite sum from K=1 to infinity)
a) Simplify the expression for P(n), where n is a non-negative integer
## Homework Equations
$$tg(a-b)=\frac{tg(a)-tg(b)}{1... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10116 | Language: Search: Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.
Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 1011.35100
Henrot, Antoine; Oudet, Edouard
The stadium does not minim... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10117 | # Consequences of VP = VNP on randomness
According to the answers in posting it is possible that $\mathsf{VP} = \mathsf{VNP}$ and $\mathsf{P} \neq \mathsf{NP}$ are simultaneously correct.
$\mathsf{VP} = \mathsf{VNP}$ implies $\mathsf{P/poly} = \mathsf{PH/poly}$ (assuming the Generalized Riemann Hypothesis). This mean... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10118 | # Adjoints of the interval topology functor
Given a poset $(P,\leq)$ the interval topology $\tau_i(P)$ on $P$ is generated by $$\{P\setminus{\downarrow x} : x\in P\} \cup \{P\setminus{\uparrow x} : x\in P\},$$ where $\downarrow x = \{y\in P: y\leq x\}$ and $\uparrow x = \{y\in P: y\geq x\}$.
It turns out that every o... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10119 | ## calculusxy one year ago Solving equation with quadratic formula. Question will be given below
1. calculusxy
$\large 2x^2 - 5x = 52$
2. calculusxy
I know that the quadratic formula is: $\large x = \frac{ -b \pm \sqrt{b^2 - 2ac} }{ 2a }$
3. amistre64
a quadratic equation of the form: ax^2 + bx + c = 0 has roots ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10120 | Question 426219
<font face="Times New Roman" size="+2">
You replace the variable(s) with the value(s) and do the indicated arithmetic. If the result is a true statement, then the value is a solution, otherwise not.
A potential solution to an equation is tested the same way.
John
*[tex \LARGE e^{i\pi} + 1 = 0]
My ca... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10121 | # How do you combine (5a + 9b) - (2a + 4b)?
Regroup with the terms that include the variable $a$ in one group and the terms that include the variable $b$ in the other.
$\left(5 a + 9 b\right) - \left(2 a + 4 b\right)$
$= \left(5 a - 2 a\right) + \left(9 b - 4 b\right)$
$= 3 a + 5 b$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10122 | # You put 500 pieces of paper in a copy machine. When you check back 6 days later, there are only 320 pieces left. How many pieces of paper are being used each day?
Oct 30, 2016
The mean usage over 6 days is 30 per day
#### Explanation:
Realistically you do not know. One day may use more than another. For example: ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10123 | Another Way to Sum a Series: Generating Functions, Euler, and the Dilog Function
Year of Award: 2013
Award: Halmos-Ford Award
Publication Information: The American Mathematical Monthly, Vol. 119, 2012, pp. 42-51
Summary: (Adapted from the MathFest 2013 Prizes and Awards Booklet)
About the Author: (From the MathFes... |
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