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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8020 | # Addition and Subtraction of Rational Expressions
Tip: This isn't the place to ask a question because the teacher can't reply.
## Key Questions
• $\frac{A}{B} + \frac{C}{D} = \frac{A D + B C}{B D}$
and
$\frac{A}{B} - \frac{C}{D} = \frac{A D - B C}{B D}$
• You can keep the same denominator and add or subtract the... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8021 | ## Algebra 1
Published by Prentice Hall
# Chapter 7 - Exponents and Exponential Functions - 7-3 Multipying Powers with the Same Base - Practice and Problem-Solving Exercises: 63
#### Answer
$-12x^6 + 40x^4$
#### Work Step by Step
(i) $a^m \cdot a^n = a^{m+n}$ (ii) $x(y-z) = xy - xz$ Use rule (ii) above by multipl... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8022 | # Set Union/Examples/3 Arbitrarily Chosen Sets
Jump to: navigation, search
## Example of Set Union
Let:
$\displaystyle A_1$ $=$ $\displaystyle \set {1, 2, 3, 4}$ $\displaystyle A_2$ $=$ $\displaystyle \set {1, 2, 5}$ $\displaystyle A_3$ $=$ $\displaystyle \set {2, 4, 6, 8, 12}$
Then:
$A_1 \cup A_2 \cup A_3 = \se... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8023 | Math Help - Linear programming question
1. Linear programming question
DuPhos produces two chemicals: Formula S and Formula T.
14. Re: Linear programming question
Thanks for your help but I still have no idea.
I'll put this one in the too hard basket for now and come back to it when I practise these a bit more.
T... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8024 | Franklin Pezzuti Dyer
Analysis of growth orders of sequences, continued
This post is a continuation of my previous post, in which we constructed equivalence classes of sequences of real numbers in order to formalize the notion of a "growth order". We also defined a couple of simple operations on these growth orders, ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8025 | # Using Undetermined Coefficients to solve an equation for a particular solution?
1. Oct 18, 2014
### KevinD6
1. The problem statement, all variables and given/known data
$y'' + 9y = 3sin(3x) + 3 + e^{3x}$
2. Relevant equations
3. The attempt at a solution
This is my first post here so let me know if I've done any... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8026 | Lagrange spectrum
2010 Mathematics Subject Classification: Primary: 11J06 [MSN][ZBL]
The set of Lagrange constants in the problem of rational approximation to real numbers. The Lagrange spectrum is strictly contained in the Markov spectrum (see Markov spectrum problem).
Given positive real $\alpha$, define the homog... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8027 | # Finite Complement Space is T1
## Theorem
Let $T = \struct {S, \tau}$ be a finite complement topology on any set $S$ which contains at least two points.
Then $T$ is a $T_1$ (Fréchet) space.
## Proof
Let $x, y \in S$.
Then:
$S \setminus \set x$ is an open set of $T$ containing $y$ but not $x$.
$S \setminus \set ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8028 | # Valid metric on a hyperbolic space
Note: cross-posted to mathoverflow.net
I'm looking at the distance that's defined in this paper on Poincaré Embeddings:
$$d(\mathbf{u}, \mathbf{v}) = \operatorname{arccosh} \left(1 + 2\frac{\left\| \mathbf{u} - \mathbf{v} \right\|^2}{(1 - \left\| \mathbf{u} \right\|^2)(1 - \left\... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8029 | # Family of 3's
Level 2
$\large \sqrt[a_1]{3 \ \sqrt[a_2]{3^2 \ \sqrt[a_3]{3^3 \ \sqrt[a_4]{\cdots}}}}= \ ?$
where $a_n=3n+1$. Report your answer to two decimal places.
× |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8030 | # Galois Solvable Group
Galois Group
Is $$G$$ realizable over $$\mathbb{Q}$$ given that $$|G|=p^n$$ ?
Last edited:
Related Linear and Abstract Algebra News on Phys.org
Is it possible to have this in pdf? Thank you.
(Note: Shafarevich's theorem and work will be worthless if the Inverse Galois Problem is true. (Unle... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8031 | ### Home > INT2 > Chapter 8 > Lesson 8.1.1 > Problem8-16
8-16.
Examine the triangle at right..
1. What is the perimeter of the triangle?
Use the Pythagorean Theorem.
1. What is the measure of each of the acute angles in the triangle?
You have learned many different trigonometry tools. Which is appropriate to the ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8032 | # Laplace transform and fractional moments.
Is there any "easy" way to calculate fractional moments from Laplace transform. To be more specyfic let us consider the following example. Let $X$ be a positive random variable and $L(\theta) := E \exp (-\theta X)$ be its Laplace transform. Of course it is easy to calculate ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8033 | Journal article
### Counting homomorphisms to K4-minor-free graphs, modulo 2
Abstract:
We study the problem of computing the parity of the number of homomorphisms from an input graph $G$ to a fixed graph $H$. Faben and Jerrum [Theory Comput., 11 (2015), pp. 35--57] introduced an explicit criterion on the graph $H$ a... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8034 | # A non-convex meta-frontier Malmquist index for measuring productivity over time
A non-convex meta-frontier Malmquist index for measuring productivity over time Abstract This article proposes a non-convex meta-frontier Malmquist index for measuring productivity over time, where the panel data comprise groups of decis... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8035 | # How do you subtract 1/(x-6) - 3/(x+6) + (3x)/(36-x^2)?
Jun 25, 2016
$\frac{1}{x - 6} - \frac{3}{x + 6} + \frac{3 x}{36 - {x}^{2}} = \frac{24 - 5 x}{{x}^{2} - 36}$
#### Explanation:
$\frac{1}{x - 6} - \frac{3}{x + 6} + \frac{3 x}{36 - {x}^{2}}$
= $\frac{1}{x - 6} - \frac{3}{x + 6} - \frac{3 x}{{x}^{2} - 36}$
As ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8036 | # Discrete Probability Distributions
${15 \choose 7}(s)^7(1-s)^{15-7}$
Where $s$ is the probability of success. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8037 | # Straightforward differentiation, but think I have wrong sign somewhere
1. Feb 18, 2009
### phyzmatix
1. The problem statement, all variables and given/known data, attempt at a solution
Please see attached. I'm actually busy with a physics problem, but solving it requires that I complete this part correctly. It's ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8038 | ## Limit profiles and uniqueness of ground states to the nonlinear Choquard equations.(English)Zbl 1419.35066
Summary: Consider nonlinear Choquard equations $\begin{cases}-\Delta u+u=(I^\alpha * \vert u\vert^{p})\vert u\vert^{p-2}u\quad\text{in }\mathbb R^N,\\ \lim_{x\to\infty}u(x)=0,\end{cases}$ where $$I_{\alpha}$$ ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8039 | # Tag Info
## Hot answers tagged quantum-spin
4
The options 1,2 are actually physically identical because the electrons are identical particles. Once we have two electrons, we can't say which of them is "Paul" and which of them is "Peter". When the addition is slow etc., the option 1=2 violates the conservation law ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8040 | # Given that $\tan 2x+\tan x=0$, show that $\tan x=0$
Given that $\tan 2x+\tan x=0$, show that $\tan x=0$
\begin{align} \tan 2x & = \frac{2\tan x}{1-\tan ^2 x} \\ \Rightarrow \frac{2\tan x}{1-\tan ^2 x}+\tan x & = 0 \\ \ 2\tan x+\tan x(1-\tan ^2 x) & = 0 \\ 2+1-\tan ^2 x & = 0 \\ \tan ^2 x & = 3 \end{align}
This is ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8041 | ACT Math : How to find compound interest
Example Questions
Example Question #1 : How To Find Compound Interest
Ashley makes a bank deposit of at annual interest, compounded monthly. About how many years will it take her deposit to grow to ?
years
years
year
years
years
years
Explanation:
The formula for co... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8042 | # |a| < 1 show lim |a|^n ->0
1. Nov 26, 2013
### kingstrick
1. The problem statement, all variables and given/known data
given |a| < 1, show that the limit of |a|^n goes to 0 as n goes to infinity.
2. Relevant equations
3. The attempt at a solution
let |a|<1 and n>0 (n is a natural number, a is a real number)
t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8043 | # Hyperboloid
Hyperboloid of one sheet
Hyperboloid of two sheets
In mathematics, a hyperboloid is a quadric, a type of surface in three dimensions, described by the equation:
[itex]{x^2 \over a^2} + {y^2 \over b^2} - {z^2 \over c^2}=1[itex] (hyperboloid of one sheet),
or
[itex]{x^2 \over a^2} + {y^2 \over b^2} - ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8044 | MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).
2 (corrected some more typos)
Here is another proof of the same result (it is probably the same as the one given by darij grinberg but I do not understand all the wo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8045 | # Math Help - Quick ? : Identifying function from series
1. ## Quick ? : Identifying function from series
Hello! Does anyone know offhand the function that the Maclaurin series given by [(-1)^n * x^(2n) / (n+1)], n=0..., represents? Thanks!!
2. Originally Posted by pi_cubed
Hello! Does anyone know offhand the functi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8046 | # Math Help - Not by separating variables
1. ## Not by separating variables
Here's the equation $\frac{dx}{\frac{ay}{x^2+y^2}}=\frac{dy}{\frac{ax}{ x^2+y^2}}$
how is this one done separating variables seems impossible
2. Originally Posted by phycdude
Here's the equation $\frac{dx}{\frac{ay}{x^2+y^2}}=\frac{dy}{\frac... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8047 | # What is the remainder when (2x^3 – 8x^2 + 6x – 6) ÷ (x – 4)?
The Remainder Theorem states that the remainder when a polynomial $P \left(x\right)$ is divided by $x - a$ is equal to $P \left(a\right)$.
Applying this, we get that the remainder is just $2 {\left(4\right)}^{3} - 8 {\left(4\right)}^{2} + 6 \left(4\right) ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15968 | # Geometric series involving logarithms
1. Jan 28, 2014
### sooyong94
1. The problem statement, all variables and given/known data
A geometric series has first term and common ratio both equal to $a$, where $a>1$
Given that the sum of the first 12 terms is 28 times the sum of the first 6 terms, find the exact value ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15969 | # Equation - Exponential Function
#### Alvy
Hello guys.
I know this must be pretty basic. But, I don't get it.
How do I solve 0,6 = 0,95^x ?
This is from an equation. I got up to this point, but I can't finish it. Any help would be appreciated.
#### earboth
MHF Hall of Honor
Hello guys.
I know this must be pret... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15970 | # What are he intercepts of y=(x+1)^2-2?
Jul 25, 2018
The $x$-intercepts are at $\left(\sqrt{2} - 1\right)$ and $\left(- \sqrt{2} - 1\right)$ and the $y$-intercept is at $\left(0 , - 1\right)$.
#### Explanation:
To find the $x$-intercept(s), plug in $0$ for $y$ and solve for $x$.
$0 = {\left(x + 1\right)}^{2} - 2$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15971 | ## Calculus 8th Edition
$-80 \pi$
When the surface is orientable then the flux through a surface is defined as: $\iint_S F \cdot dS=\iint_S F \cdot n dS$ where, $n$ is the unit vector. Since, we have $\iint_S f(x,y,z) dS \approx \Sigma_{i=1}^n f[\overline{x}, \overline{y}, \overline{z}] AS_i$ Since, $\iint_S f(x,y,z) ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15972 | # Parametric Equations of the Parabola
Equations can also be written in parametric form. In this form, x and y are both written in terms of a third variable called a parameter.
An example of a parametric equation is $x=2t, y=t-2$.
Try to write $y=3x+1$ in a parametric form.
Given parameter p:
Let x = p
Then y = 3... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15973 | # zbMATH — the first resource for mathematics
Thom’s lemma, the coding of real algebraic numbers and the computation of the topology of semi-algebraic sets. (English) Zbl 0689.14006
Summary: Thom’s lemma, a very simple and basic result in real algebraic geometry, and explained in section 1, has a lot of interesting co... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15974 | Question on Ordinary Differential Equation (ODE)
1. Aug 25, 2013
a150daysflood
1. The problem statement, all variables and given/known data
Find the ODE of the following
(1) du/dy = -u
(2) d^2u/dxdy = -du/dx
2. Relevant equations
For question 1, the answer is u= A(x)e^(-y)
while for question 2, the answer is u= e... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15975 | GMAT Changed on April 16th - Read about the latest changes here
It is currently 24 May 2018, 14:09
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
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15976 | # Resources tagged with: Mathematical reasoning & proof
Filter by: Content type:
Age range:
Challenge level:
### There are 172 results
Broad Topics > Mathematical Thinking > Mathematical reasoning & proof
### Thousand Words
##### Age 16 to 18 Challenge Level:
Here the diagram says it all. Can you find the diagram... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15977 | Chapter 14 - Review - True-False Quiz - Page 982: 5
False
Work Step by Step
False It may be the case that as ${ (x,y)\to (a,b)}$ along a curve, not along a straight line through $(a,b)$. Then, $\lim\limits_{ (x,y)\to (a,b)}f (x,y)\ne L$
After you claim an answer you’ll have 24 hours to send in a draft. An editor wi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15978 | 7.5k views
How many $3$-to-$8$ line decoders with an enable input are needed to construct a $6$-to-$64$ line decoder without using any other logic gates?
1. $7$
2. $8$
3. $9$
4. $10$
edited | 7.5k views
0
To get $6:64$ we need $64$ $o/p$
We have $3:8$ decode with $8$ $o/p$. So, we need $64/8=8$ decoders.
Now, to ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15979 | Rigorous delta potential – a formulation using distributions?
It is common in QM, even in mathematical physics, to consider Hamiltonians with a Dirac delta in the potential: $$\hat H = -\frac{\mathrm{d}^2}{\mathrm{d}x^2} + V(x) + \delta(x-a) \: .$$ The most common interpretation of this is the self-adjoint operator $$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15980 | # Math Help - Determine which primes > 3 divide...
1. ## Determine which primes > 3 divide...
Determine which primes > 3 divide some number of the form 3n^2 - 5n + 1 and which do not.
2. Since $p>3, \; (3,p)=1 \implies 3^{-1}$ exists. Let $a_p\equiv3^{-1} \bmod{p}$.
Set $3n^2+5n-1\equiv0\bmod{p}\implies n^2+5a_pn-a... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15981 | # Which of these methods is correct to solve this work and energy problem? [closed]
The question is:
The lower end of a spring of spring constant $k$ is fixed on the ground and its other end passes through a light pulley and is connected to a block of mass $m$ after passing through the pulley. The system is released ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15982 | # Find the area enclosed by the curve x=t^2-2t,\ y=\sqrt{t} and
Find the area enclosed by the curve $$\displaystyle{x}={t}^{{2}}-{2}{t},\ {y}=\sqrt{{{t}}}$$ and the y-axis
• Questions are typically answered in as fast as 30 minutes
### Solve your problem for the price of one coffee
• Math expert for every subject
•... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15983 | • April 3rd 2006, 02:28 PM
miss_lolitta
Sup{lnε/ln {abs(x)}; x#0 , x on(-1,1)}=???
Thank in advance to anyone that can help
Miss_Lolitta
• April 3rd 2006, 03:39 PM
ThePerfectHacker
Quote:
Originally Posted by miss_lolitta
Sup{lnε/ln {abs(x)}; x#0 , x on(-1,1)}=???
Thank in advance to anyone that can help
Miss_Lo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7952 | # Complexity of the Two-Variable Fragment with Counting Quantifiers
@article{PrattHartmann2005ComplexityOT,
title={Complexity of the Two-Variable Fragment with Counting Quantifiers},
author={Ian Pratt-Hartmann},
journal={Journal of Logic, Language and Information},
year={2005},
volume={14},
pages={369-395}
}
• I. Prat... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7953 | What is the equation of the tangent line of f(x)=sinpix at x=3 ?
Dec 30, 2015
$y = \pi \left(3 - x\right)$
Explanation:
$\textcolor{b l u e}{\text{Graph of } f \left(x\right)}$
graph{sin(pix) [-10, 10, -5, 5]}
To construct a straight line, one needs either two points, or a point and the gradient. In this case, ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7954 | HomeEnglishClass 12MathsChapterComplex Numbers
bb"statement-1" Locus of z sat...
# bb"statement-1" Locus of z satisfying the equation abs(z-1)+abs(z-8)=5 is an ellipse. <br> bb"statement-2" Sum of focal distances of any point on ellipse is constant for an ellipse.
Updated On: 17-04-2022
Get Answer to any question, ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7955 | ## FANDOM
153 Pages
The FRW metric is the generic form of a metric for a matter distribution that is homogeneous and isotropic. We begin the derivation with an equation for a four dimensional sphere
$x^2 + y^2 + z^2 + w^2 = r^2 + w^2 = R^2$
where $R$ is a constant. Taking the differential of this equation yields
$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7956 | x
## Piecewise-Defined Functions and Periodic Functions
important note: f ( x) = - f ( - x) → anti-symmetric → cos-trans are zero! ∫ 0 2 π f ( x) cos ( k x) d x = 0 b k = 1 π ∫ 0 2 π f ( x) sin ( k x) d x = 1 π ∫ 0 π 1 sin ( k x) d x + 1 π ∫ π 2 π ( - 1) sin ( k x) d x = 1 π ( - cos ( k x) k | 0 π - - cos ( k x) k | ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7957 | # How do you factor f(x)=2x^3-10x^2-8x+40?
May 14, 2016
$\left(x - 2\right)$ $\left(2 x - 10\right)$ $\left(x + 2\right)$
#### Explanation:
First, find a factor of $f \left(x\right)$
try $f \left(1\right)$
$f \left(1\right)$ = 24 therefore is not a factor
next try $f \left(2\right)$
$f \left(2\right)$ = 0 there... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7958 | # Math Help - Stumped on a simple harmonic motion question
1. ## Stumped on a simple harmonic motion question
$mg = k\Delta\l$
And I obtained 5314 N/m.
After that, I calculated $v_{max}$ by using:
$v_{max} = A\sqrt{\frac{k}{m}}$
2. Originally Posted by xxlvh
A proud deep-sea fisherman hangs a 65.0 kg fish from an id... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7959 | # Why are G and H used for feedback block diagrams?
The symbols $G$ and $H$ are typically used for the forward gain and feedback fraction in negative feedback block diagrams like this:
The choice of $G$ is, I suppose, an obvious one, meant to be mnemonic for gain.
But $H$ I don't get. Is it just because it's the nex... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7960 | # In the Gas-Up problem, how is the amount of gas the same up to a cyclic shift regardless of starting city?
I'm working through Elements of Programming Interviews as practice for finding a job. I've spent a ridiculous amount of time on Problem 18.7.
In the gas-up problem, $n$ cities are arranged on a circular road. ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7961 | # Real Analysis (Set Theory) Proof
1. Jan 16, 2006
### playboy
Let A and B be subsets if a universal set U. Prove the following.
a) A\B = (U\B)\(U\A)
To do this, show it both ways.
1) A\B contains (U\B)\(U\A)
2) (U\B)\(U\A) contains A\B
if x is in (U\B)\(U\A),
then x is in (U\B) and x is NOT in (U\A).
then (x is i... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7962 | ## 2009年8月31日 星期一
### AM-GM 不等式的幾個證明（一）
$AM=\frac{x_1+x_2+\cdots+x_n}n$ 和 $GM=\sqrt[n]{x_1x_2\cdots x_n}$
AM-GM 不等式指出，n 個正數的算術平均必定大於或等於幾何平均，而且等號成立當且僅當該 n 個數皆相等。例如：2003、3、14 的算術平均約是 673.33，幾何平均約是 43.82。
## 2009年8月16日 星期日
============================================================
Topic: A leisurely introduction t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7963 | # 8.4 Building rational expressions and the lcd (Page 3/4)
Page 3 / 4
To add or subtract two or more rational expressions they must have the same denominator .
Building rational expressions allows us to transform fractions into fractions with the same denominators (which we can then add or subtract). The most conv... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7964 | # make horizontal curly brace underlying parts of a equation so that I could write another formula under that part of specific equation
how could i make horizontal curly brace underlying parts of a equation so that I could write another formula under that part of specific equation . PS: i do not want to add a text und... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7965 | § Whalesong hyperbolic space in detail
We can build a toy model of a space where velocity increases with depth. Let the x-y axis be: left-to-right (→) is positive x, top-to-bottom (↓) is positive y. Now let the velocity at a given location $(x^\star, y^\star)$ be $(y^\star+1, 1)$. That is, velocity along $y$ is consta... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7966 | # How do I calculate the limit of this integral?
Using an appropriate probability distribution or otherwise show that
$$\lim_{n\to\infty} \int_0^n e^{-x}{x^{n-1}\over(n-1)!}dx =0.5$$
-
Hey if you are a new user please know that to get an answer you must first show/explain what you have tried. – Lyapunov Jul 16 '12 ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7967 | ## Closure Operators
Often in mathematics there is the idea of taking the closure of some elements under a particular operation. For instance if you have several vectors you may take the span of them, if you have a field and want to add the zeros of a particular polynomial you want to consider the corresponding extens... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_25040 | +0
0
220
5
+47
Hi please help me fast! I have attempted this many different ways and I can't cracked it
Aug 26, 2021
#1
0
-9x^2 - 3x + 2 factors as -(3x - 2)(3x + 1), so x = 2/3.
Aug 26, 2021
#2
+47
0
Sorry that's incorrect:(
Correct answer was 1/3 you were so close!
SmartCookiezZ Aug 26, 2021
edited by Smart... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_25041 | MathSciNet bibliographic data MR251992 (40 #5217) 81.46 Segal, Irving Notes towards the construction of nonlinear relativistic quantum fields. III. Properties of the \$C\sp{\ast} \$$C\sp{\ast}$-dynamics for a certain class of interactions. Bull. Amer. Math. Soc. 75 1969 1390–1395. Article
For users without a MathSciNe... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_25042 | Math Help - integration
1. integration
$\int\sqrt{cosec^{-1}{x}^{2}} d{x}$
2. Re: integration
Wolphram alpha says it's not possible to solve this integral in terms of mathematical standard mathematical functions:
integrate sqrt(arcosec(x)x^2)dx - Wolfram|Alpha |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_25043 | # Wold's decomposition
(Redirected from Wold decomposition)
In mathematics, particularly in operator theory, Wold decomposition or Wold–von Neumann decomposition, named after Herman Wold and John von Neumann, is a classification theorem for isometric linear operators on a given Hilbert space. It states that every iso... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_25044 | # Tunnelling in Total Internal Reflexion and Evanescent Fields
When an electromagnetic wave is totally internally reflected, it takes on a phase shift. Inside the optically less dense medium, where ray optics tells us there is no field, there is rather an evanescent field. This field is wholly analogous to quantum mec... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_25045 |
6.4: Summary
• Important Definitions:
• Recursively-defined Sequence
• Initial Conditions
• Recursive Relation
• Fibonacci Sequence
• Proof by Induction
• Base Case
• Inductive Step
• Inductive Hypothesis
• Strong Induction
• Induction with Multiple Base Cases
• Notation:
• $$(\text{IH})$$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_25046 | Can someone provide an example of a discontinuous Young function
Let me first define the notion of a Young function:
A convex function $$\Phi: \mathbb{R} \to \mathbb{R}^+$$ which satisfies the following conditions
(1) $$\Phi(0)=0$$
(2) $$\Phi(-x)=\Phi(x)$$
(3) $$\lim_{x\to \infty}\Phi(x)=\infty$$
is called a Young ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_25047 | # PCA, test for eigen values
Let's say I have a matrix $$X$$ with $$4$$ variables and $$n$$ observations and I run PCA, so I compute the eigenvalues/eigenvectors of the sample covariance matrix, and then I test $$H_0: \lambda_1=\lambda_2=\lambda_3=\lambda_4$$, and I find that I don't reject $$H_0$$. So I don't have ev... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8704 | ## The Journal of Analysis
Short Title: J. Anal. Publisher: Springer, Singapore; Forum d’Analystes, Chennai, Tamil Nadu, India ISSN: 0971-3611; 2367-2501/e Online: http://link.springer.com/journal/volumesAndIssues/41478http://www.springer.com/mathematics/analysis/journal/41478http://sites.google.com/site/journalofana... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8705 | # conditional expectation?
I'm trying to solve an expected value problem where a biased coin is flipped until a run of five heads is achieved. I need to compute the $E(X)$ where $X$ is the number of tails expected before the run of five heads.
Would this require conditional expectation, since $E(X)$ is dependent on $... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8706 | # Conservation of Energy initial velocity
1. Sep 28, 2008
### vesperaka
I know if there was no initial velocity, the velocity at the bottom would just be sqrt(2gh), but I'm not sure how the initial velocity impacts the velocity at the bottom. I thought just adding the x-component of the velocity would be enough but ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8707 | # 10. If p is a sublinear functional on a real vector space X, show that there exists linear functional f
###### Question:
10. If p is a sublinear functional on a real vector space X, show that there exists linear functional f on X such that ~p(-x)sfkx)sp(x)
#### Similar Solved Questions
##### Prob. 13-12 13-13. De... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8708 | Solutions of ϕ (n) = ϕ (n + k) and σ (n) = σ (n + k)
Abstract We show that for some even $k\leqslant 3570$ and all $k$ with $442720643463713815200|k$, the equation $\phi (n)=\phi (n+k)$ has infinitely many solutions $n$, where $\phi$ is Euler’s totient function. We also show that for a positive proportion of all $k$, ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8709 | # How is the Euler Equation for Consumption derived from from intertemporal budget constraint and lifetime utility function in basic macroeconomics
I suspect that what I'm actually asking here is just a basic calculus question, which I have overwrought, but I wanted to ask it here to make sure before taking it to SEMa... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8710 | ## Algebra 1
$\frac{1}{18}$
To subtract fractions with unlike denominators, we must first make them have the same denominator. We do this by multiplying by fractions that are equivalent to $1$. $\frac{5}{9}\times\frac{10}{10}=\frac{50}{90}$ $\frac{5}{10}\times\frac{9}{9}=\frac{45}{90}$ We can now subtract the two frac... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8711 | # General Second Order Circuit
• Engineering
## Homework Statement
Refer Attachment.
I am trying to derive the second order equation using the natural response of the circuit
Refer Attachment
## The Attempt at a Solution
Nodal Analysis:
v1+$\frac{1}{2}$$\frac{dv1}{dt}$+$\frac{1}{3}$$\frac{dv2}{dt}$=0
Mesh Analysi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8712 | ## Posts Tagged ‘new results’
### Progress! (Apollonian Sphere Packings)
August 12, 2010
Since giving the recent talk, I had a bit of a breakthrough. Two of the problems I mentioned are no longer open! I now know (and can prove) the following:
Theorem: If $a,b,c$ are nonzero integers, at most one of which is nega... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8713 | # Stereo plotting in R
## 2020/01/06
Here’s another neat trick I picked up from Julien Sprott’s book on Strange Attractors: that good ole’ 90s 3D effect you get if you focus outside of the image and frustratingly wait for that image to appear.
The technique I will use is called Cross-eyed stereo viewing, which works... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8714 | • # question_answer A prism of ${{6}^{o}}$ is made of material of refractive index $\frac{5}{3}$. The deviation caused by it is: A) ${{2}^{o}}$ B) ${{8}^{o}}$C) ${{4}^{o}}$ D) none of these
The relation between $\delta$ and $\mu$ is $\delta =(\mu -1)\,A$ $\Ri... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8715 | # Some important summations
When studying number theory, you’ll soon realize that some familiarity with certain formalisms is required. In particular, some kinds of summations are so common that it’s worth treating them separately, before applying them in various contexts. This is what we’ll do in this post, which can... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8716 | # Torus Chessboard
Probability Level 5
A token is placed on the corner square of a $3 \times 3$ chess board. The token is moved either up, down, left, or right, with equal probability. If the token would move off the edge of the board it "wraps around'' the board and moves to the opposite side instead. For example, i... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8717 | # Determine noise distribution [closed]
I'm trying to solve the following least squares problem:
$\underset{x}{\text{min}} ||Ax - \tilde{b}||_2$
where $Ax = b$ and $\tilde{b} = b + w$
### Question:
How do I determine which probability distribution fits $w$ best?
Also, $A \in \mathbb{R}^{n\times n}$ is a large, an... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8718 | # Dimension of a Lie algebra
1. Jan 25, 2017
### Kara386
1. The problem statement, all variables and given/known data
Show the (real) dimension of su(n) is $n^2-1$.
2. Relevant equations
3. The attempt at a solution
$su(n) = \{ A \in M_n(\mathbb{C}) | A+A^T = 0, tr(A) =0 \}$
Maybe the solution is obvious, because ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_8719 | # How many cards must be picked to guarantee you have 10 cards of the same suit?
Assume you pick cards from a deck of cards at random without replacement (i.e. don't put it back in the deck once you pick it). How many cards must be picked to guarantee you have 10 cards of the same suit?
Standard deck of 52 cards. 13 ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_16736 | ## Relaxation of the Anisotropic Perimeter – Part 1
I have discussed in a previous post how Modica-Mortola theorem can provide a good framework for relaxing the perimeter functional in the single and multi-phase cases. The ideas can be extended further to a more generalized notion of perimeter, the anisotropic perimet... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_16737 | # Which term of the series 5, 8, 11, 14,...is 320 ?
1. 106th
2. 105th
3. 107th
4. 104th
Option 1 : 106th
## Detailed Solution
Concept:
Let us consider sequence a1, a2, a3 …. an is an A.P.
Common difference “d”= a2 – a1 = a3 – a2 = …. = an – an – 1
nth term of the A.P. is given by
Tn = a + (n – 1) d
Where,
a =... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_16738 | SEARCH HOME
Math Central Quandaries & Queries
Question from Kenneth: What does the following indicate? "A percent is another way of expressing the ratio or fractional relationship of two numbers." I know what a ratio is, but the term "fractional relationship" confuses me. I thank you for your reply.
Hi Kenneth,
Sup... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_16739 | Try out our new practice tests completely free!
Solved
# A Test Is Made Of $H _ { 0 } : \mu = 60 \text { versus } H _ { 1 } : \mu \neq 60$
Question 10
Multiple Choice
Question 10
Multiple Choice
## A test is made of $H _ { 0 } : \mu = 60 \text { versus } H _ { 1 } : \mu \neq 60$$\bar { x } = 66$ The population stand... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_16740 | 1. ## Problem 49
(minor variant of a problem due to Roy Barbara)
Let $a,\ b,\ c$ be three positive real numbers.
Find necessary and sufficient conditions on $a,\ b,\ c$ for there to exist an interior point $P$ in the equilateral triangle $ABC$ with unit side, such that $|PA|=a,\ |PB|=b,\ |PC|=c$.
I have a solution ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_16741 | #### Vol. 304, No. 2, 2020
Recent Issues Vol. 310: 1 Vol. 309: 1 2 Vol. 308: 1 2 Vol. 307: 1 2 Vol. 306: 1 2 Vol. 305: 1 2 Vol. 304: 1 2 Vol. 303: 1 2 Online Archive Volume: Issue:
The Journal Subscriptions Editorial Board Officers Contacts Submission Guidelines Submission Form Policies for Authors ISSN: 1945... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_16742 | # Few problems with sequences
1. Mar 10, 2006
### rahl__
i have a few problems with sequences
1. show, that if:
$$\lim_{n\to\infty}a_{n}=L$$
than sequence:
$$b_{n}=\frac{a_{1}+...+a_{n}}{n}$$
is convergent to L
2. show that the sequence$$a_{n}$$ is monotone, bounded and find out its limit, if:
$$a_{1}=2$$
$$a_{n+1}... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_16743 | # Re: Some thoughts about the revised provenance Model document
From: James Cheney <jcheney@inf.ed.ac.uk>
Date: Thu, 29 Sep 2011 12:07:00 +0100
Cc: W3C provenance WG <public-prov-wg@w3.org>
Message-Id: <2CA55FA5-2E88-4152-8200-AF728EAB1546@inf.ed.ac.uk>
To: Graham Klyne <GK@ninebynine.org>
> <aside>
> My suggested def... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_16744 | ### (18) If a , b , c are in A.P then prove that (1/bc),(1/ca),(1/ab) are also in A.P
Solution:
a , b , c are in A.P
Divide each term by abc, so we get
(a/abc),(b/abc),(c/abc) are also an A.P
By simplifying this we get,
(1/bc),(1/ca),(1/ab) are also in A.P |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_16745 | # Question on Compact operators: Suitable definition of a sequence of compact operators
Let $$H$$ denote a separable Hilbert space with an orthonormal basis $$\{e_k\}_k\in \mathbb N$$ and consider a linear, bounded operator $$A:H \to H$$ such that: $$Ae_k=\lambda_k e_k$$. Show that $$T$$ is a compact operator provided... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_16746 | Least squares problem with constrained solution [closed]
If $a_{m\times 1}$ and $Q_{m\times n}$ ($m<n$) are known, and we know every element of $b$ is between $[-1\ \ 1]$, how to determine $b$ to minimize $\|a+Qb\|_2$?
closed as off-topic by Suvrit, Stefan Kohl, user1688, Wolfgang, Alex DegtyarevSep 18 '16 at 21:09
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_16747 | # Totally symmetric tensor
by ehrenfest
Tags: symmetric, tensor, totally
P: 1,996 1. The problem statement, all variables and given/known data If t_{ab} are the components of a symmetric tensor and v_a are the components of a vector, show that if: $$v_{(a}t_{bc)} = 0$$ then either the symmetric tensor or the vector =... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_16748 | ## Tuesday, January 13, 2009
### Euler
Leonhard Euler was one of the great mathematicians of all time, and arguably the most prolific. (Only Paul Erdős has published more papers, but Euler published more pages.) Euler's greatest contributions were to number theory, but he also did important work in algebra, calculus,... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_16749 | # Parallelism implies Equal Corresponding Angles
## Theorem
Given two infinite straight lines which are cut by a transversal, if the lines are parallel, then the corresponding angles are equal.
In the words of Euclid:
A straight line falling on parallel straight lines makes the alternate angles equal to one another... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_16750 | # §36.9 Integral Identities
36.9.1 $\displaystyle|\mathop{\Psi_{1}\/}\nolimits\!\left(x\right)|^{2}$ $\displaystyle=2^{5/3}\int_{0}^{\infty}\mathop{\Psi_{1}\/}\nolimits\!\left(2^{2% /3}(3u^{2}+x)\right)du;$ equivalently, 36.9.2 $\displaystyle(\mathop{\mathrm{Ai}\/}\nolimits\!\left(x\right))^{2}$ $\displaystyle=\frac{... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_16751 | # Determine whether this polynomial form a vector space
I'm doing a question asking "A set of all polynomials with degree exactly 5. Does it form a vector space?" I'm a bit confusing showing multiplication part. If say the polynomial is ax^5+b, when the scalar is 0, then the polynomial is 0 degree. Does this prove thi... |
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