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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24541 | # Math Help - equation of tangent line on curve
1. ## equation of tangent line on curve
find an equation of the tangent line to the curve at the given point
(hyperbola)
$\frac{x^2}{16}-\frac{y^2}{9} = 1\ \left(-5,\frac{9}{4}\right)$
using the quotient rule $\frac{vu'-uv'}{v^2}$
$\frac{16(2x)-x^2(0)}{16^2}-\frac{9(... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24542 | # integral hodge classes of the Calabi-Yau 3-fold
I have been read many papers,But I don"t know a integral hodge class of the calabi-Yau 3-fold is algebraic or non-algebraic?Hope give some help and nice reference. Calabi-Yau 3-fold is a Kahler 3-fold with trival canonical bundle.Is it a open question？
-
I think we do... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24543 | # Sum
Calculus Level 4
$\large s = \sum^\infty_{n=1}\left(\frac{n^2+2n+3}{2^n}\right)$
Compute the value of $$1^3 + 2^3 + 3^3 + \cdots + s^3$$. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24528 | ### Spherical Volume Formula
Spherical Volume Formula
The sphere is a perfectly round shape. The following formula is given to determine the volume of a sphere:
$$V=\frac{4}{3}.\pi . r^3$$
Example:
What is the volume of a sphere with a diameter of 20 cm?
Solution: $$V=\frac{4}{3}\pi . r^3$$ $$V=\frac{4}{3}\pi.(10)^3$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24530 | # Need a hint proving that f is bijective
Regard 0 (zero) as an even number and define f : N → N by
f(n) = \begin{cases} n + 1, & \text{if $n$ is even} \\ n -1, & \text{if $n$ is odd} \end{cases}
Prove that f is bijective
My solution:
(1) show that the function is injective:
f(n1)= f(y1)
n + 1 = y + 1
n = y
f(... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24536 | # Discrete math: Is the survey accurate?
A library has conducted a survey of its readers. The survey asked its $10,000$ readers about their reading habits and the number of books that they have borrowed from the library in $2012$. It has found that its readers claimed to have borrowed $75,000$ books in $2012$. The lib... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24540 | # Internal Energy question
1. Oct 24, 2014
### CaptainOfSmug
1. The problem statement, all variables and given/known data
A 1200-kg car is backing out of a parking space at5.5m/s . The unobservant driver of a 1900-kgpickup truck is coasting through the parking lot at a speed of 4.0m/s and runs straight into the rear... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5712 | ## Intermediate Algebra for College Students (7th Edition)
$|a|$ represents the distance of the real number $a$ from $0$ on the number line.
$|a|$ represents the distance of the real number $a$ from $0$ on the number line. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5713 | # function composition and inverse function
• November 9th 2009, 01:03 PM
sbankica
function composition and inverse function
Let A={1,2,3,4,5} and B={6,7,8,9,10,11,12}.
How many functions f:A->B are such that f -1({6,7,8})={1,2}?
• November 9th 2009, 01:29 PM
Plato
Quote:
Originally Posted by sbankica
Let A={1,2,3,4,... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5714 | 11
1
1
4
# SphericalHarmonicExpansions
Build Status
The purpose of this package is to provide methods to numerically handle real spherical harmonics expansions in Cartesian coordinates.
## Mathematical Background
### Definition of the Spherical Harmonics
The normalized real spherical harmonics on the unit sphe... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5715 | # Handbook of Homotopy Theory
It seems there’s a new book in preparation dedicated to collating survey articles on various topics in contemporary homotopy theory. The chapters are slowly turning up on the arXiv. There are also odd chapters only on people’s webpages (eg this one by Paul Balmer). I haven’t seen a webpag... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5716 | # Where does the 3-velocity live?
Imagine a four-dimensional affine space $\mathcal{M}$ with the standard metric $\eta = \text{diag} (1,-1,-1,-1)$. Let $\mathcal{C}$ be a worldline of a point particle parametrized by an affine parameter $\tau$ (proper time). If we introduce some (Cartesian) coordinates $\{x^\mu\}$, th... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5717 | The theorem in Sec. 6 is incorrect. This is due to the mistaken assumption that the coupling matrices of Chazottes et al. and of Kontorovich-Ramanan are the same. They are not, as shown in detail here (see Remark 5.2). |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5719 | ## Introduction:
Less than two months ago I had an exchange with Barak Pearlmutter, a neuroscientist who has made seminal contributions to the field of automatic differentiation, on the relation between Cauchy’s Integral Formula for derivatives and forward mode automatic differentiation. In particular, he mentioned th... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5720 | My Math Forum Waiting time for n buses (pdf)
Probability and Statistics Basic Probability and Statistics Math Forum
December 23rd, 2016, 07:58 AM #1 Newbie Joined: Dec 2016 From: US Posts: 6 Thanks: 0 Waiting time for n buses (pdf) In order to go from city A to city B you have to take n buses. For each of them yo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5721 | Subjects -> MATHEMATICS (Total: 1013 journals) - APPLIED MATHEMATICS (92 journals) - GEOMETRY AND TOPOLOGY (23 journals) - MATHEMATICS (714 journals) - MATHEMATICS (GENERAL) (45 journals) - NUMERICAL ANALYSIS (26 journals) - PROBABILITIES AND MATH STATISTICS (113 journals) MATHEMATICS (714 journals) ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5722 | GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 17 Nov 2018, 13:44
# Join here
### 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 emai... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5724 | # Find the absolute value
• Apr 6th 2010, 11:41 AM
wopashui
Find the absolute value
Find the absolute value and the argument $\theta$ in the range $0 <= \theta < 2\pi$ for $(1 - i\sqrt{3})^9$
I dun remember how to do this type of question, I wonder if someone can show me the process
• Apr 6th 2010, 03:20 PM
Drexel28
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5726 | # Thread: Determining whether a function is 1-to-1 &/or onto
1. ## Determining whether a function is 1-to-1 &/or onto
For purposes of the problem, let Z=the set of all integers. Here goes:
"Define f: Z x Z --> Z by f(n,m)=nm"
I found f to NOT be 1-to-1. Now I need to determine whether or not it is onto (i.e. ran(f)... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5718 | # The general solution of the differential equation $$\frac{{{\rm{dy}}}}{{{\rm{dx}}}} = \frac{{1 + {\rm{cos}}2{\rm{y}}}}{{1 - \cos 2{\rm{x}}}}$$ is
This question was previously asked in
GATE EC 2015 Official Paper: Shift 2
View all GATE EC Papers >
1. $${\rm{tan\;y\;}}-{\rm{\;cot\;x\;}} = {\rm{\;c}}\left( {{\rm{c\;is\... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5725 | ## Real Analysis Exchange
### Rearrangeable Functions on the Real Line
#### Abstract
A function $f$ on the real line is rearrangeable if there exists a bijection $\gamma$ on its domain such that $f\circ\gamma$ is continuous. Combinatorial and analytic aspects of the problem are investigated.
#### Article informatio... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5727 | Overview - Maple Help
Iterator
Description
• A mixed-radix tuple is a sequence of integers $\left({a}_{1},{a}_{2},\dots ,{a}_{n}\right)$, with $0\le {a}_{k}<{m}_{k}$, for $1\le k\le n$, where the radices are the positive integers $\left({m}_{1},\dots ,{m}_{n}\right)$. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5723 | The values of a and b, for which the system of equations
Question:
The values of $a$ and $b$, for which the system of equations
$2 x+3 y+6 z=8$
$x+2 y+a z=5$
$3 x+5 y+9 z=b$
has no solution, are :
1. $a=3, b \neq 13$
2. $a \neq 3, b \neq 13$
3. $a \neq 3, b=3$
4. $a=3, b=13$
Correct Option: 1
Solution:
$D=\... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6656 | # How do you simplify (2sqrt6)/sqrt5?
$\frac{2 \sqrt{30}}{5}$
#### Explanation:
Multiply by $\sqrt{5}$.
$\frac{2 \sqrt{6}}{\sqrt{5}} = \frac{2 \sqrt{30}}{5}$
Other than that, I really don't think there is anymore to do. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6657 | # 2 by 2 matrices with a fixed determinant
Fix a complex number $$z$$ with modulus at most one. What are all examples of non-triangular $$2\times 2$$ matrices with $$z$$ as its determinant? The question has satisfactory answer in the triangular matrix situation because of two reasons: (1) every matrix can be (say) upp... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6658 | ## Essential University Physics: Volume 1 (3rd Edition)
$\omega = \frac{mgr}{L }$
Examining the values of omega and the angular displacement, we find the following equation: $\omega = \frac{\Delta L}{Lsin\theta \Delta t}$ We know that the value of torque is $\tau=\frac{\Delta L}{\Delta t}$. Thus: $\omega = \frac{\tau}... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6659 | • Create Account
Like
2Likes
Dislike
# Bitwise Operations in C
By Joseph Farrell | Published Oct 30 2001 11:34 AM in General Programming
bitwise c lang
If you find this article contains errors or problems rendering it unreadable (missing images or files, mangled code, improper text formatting, etc) please contact ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6660 | # How do you simplify -20/(sqrt6 - sqrt2)?
Feb 24, 2016
Rationalize the denominator to find that
$- \frac{20}{\sqrt{6} - \sqrt{2}} = - 5 \left(\sqrt{6} + \sqrt{2}\right)$
#### Explanation:
We will use the fact that $\left(a - b\right) \left(a + b\right) = {a}^{2} - {b}^{2}$ to rationalize the denominator.
-20/(sq... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6663 | # Generalized eigenvector for product of commuting matrices
Suppose $$A,B$$ are commuting invertible matrices with a common generalized eigenvector $$v$$ with eigenvalues $$a,b$$ respectively. That is, suppose there exist positive integers $$K,L$$ such that $$(A-aI)^K v= 0$$ and $$(B-bI)^Lv=0$$. Is it true that there ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6664 | Inequality of convex plus concave function
Given $\displaystyle f(x) = \sqrt[x]{1+x}$, prove:
$$f(x)+f\left(\frac{1}{x}\right)<4 \quad \forall x>0$$
My reduction so far: it is sufficient to show the inequality holds for $\displaystyle x \in (0,1]$
Jensen's Inequality can't provide an estimate since the LHS is a sum... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6666 | # Diophantus of Alexandria/Arithmetica/Book 1/Problem 8
Jump to navigation Jump to search
## Problem
What number must be added to $100$ and to $20$ (the same number added to each) so that the sums are in the ratio $3 : 1$?
## Solution
$20$
## Proof
Let $x$ be the number added.
Then we have:
$\ds 100 + x$ $=$ ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6667 | # How many solutions does the equation $2i+j+3k=l$ have in nonnegative integers?
Let $i,j,k$ be nonnegative integers and $l$ be a positive integer.
How many solutions does the equation $2i+j+3k=l$ have?
For low enough $l$, I can easily find the number of solutions, but is there a general formula which gives, for arb... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6668 | # A Little Quiz -truth, existence, proof
1) Does the number 1 exist?
2) Is it true that 1 + 1 = 2?
3) Is it possible that 1 + 1 = 2 is false?
4) Can you doubt that 1 + 1 = 2?
5) Can you doubt that 1 exists?
6) Can you prove that a statement is true without knowing the meaning of the statement? [For example, Prove... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6670 | # Laplace Transform (Linear Algebra)
1. Apr 23, 2013
### yesiammanu
1. The problem statement, all variables and given/known data
Evaluate the laplace transform of {t2e7tsinh(3t)}
2. Relevant equations
Laplace transform of {tnf(t)}=(-1)ndn/ds2 * F(s)
3. The attempt at a solution
I've replaced it with (-1)2d2L{e7tsi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6671 | Journal topic
Ann. Geophys., 38, 331–345, 2020
https://doi.org/10.5194/angeo-38-331-2020
Ann. Geophys., 38, 331–345, 2020
https://doi.org/10.5194/angeo-38-331-2020
Regular paper 16 Mar 2020
Regular paper | 16 Mar 2020
# Global total electron content prediction performance assessment of the IRI-2016 model based on em... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6661 | # Rotational Energy, ball on a loop
1. Mar 13, 2016
### bigguccisosa
1. The problem statement, all variables and given/known data
Imagine a ball with moment of inertia $I_{cm} = \beta MR^2$ encountering a circular loop of radius $R_0 > R$ after rolling on a level surface at a speed of $v_0$. Assume that the ball doe... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6665 | Magyar Information Contest Journal Articles
Problem P. 3759. (December 2004)
P. 3759. Subscribers can reach the complete after signing in. The text will be public from 10 December 2004.
(4 pont)
Deadline expired on 11 January 2005.
Statistics:
>
225 students sent a solution. 4 points: 102 students. 3 points: 21 ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6669 | # Finite sum of the fractional type
Some special manipulations involving finite sums. How to solve this sum?
$\displaystyle{\sum_{k=1}^{n}}\frac{1}{4k^2 - 1}$
-
Hint 1: the denominator can be factorised. Hint 2: Partial fractions. Hint 3: It telescopes. – ShreevatsaR Oct 16 '11 at 17:09
The following problem below ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6662 | # forall a b, a -> b [duplicate]
This question already has an answer here:
I know for pretty sure that there is a function with the type $f: \forall \alpha, \beta . \alpha \rightarrow \beta$ (at least in a Hindley-Milner type system), but I can't wrap my head over it. Neither could I think of an actual function with ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9856 | # Particle Physics Planet
## May 23, 2013
### Emily Lakdawalla - The Planetary Society Blog
Charles Bolden stopped by JPL to highlight research being done on advanced propulsion techniques that would be used in the proposed asteroid retrieval mission.
### John Baez - Azimuth
Category Theory for Scientists
At last... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9857 | • anonymous
I need to show a linear equation involving a seasonal pass of $219.50 and a daily pass of$21.95. I need to show my results in a graph while at the same time explain how I got my answers. Can you help?
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-00003-of-00114-e7fc257ef044bc03_doc_9859 | # zbMATH — the first resource for mathematics
Compact metric spaces and weak forms of the axiom of choice. (English) Zbl 0968.03057
A topological space is Loeb (weakly Loeb) if the family of the closed nonempty subsets admits a choice function (a multiple choice function which chooses nonempty finite subsets). Since t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9860 | # Definition:Filter Basis
## Definition
Let $S$ be a set.
Let $\mathcal P \left({S}\right)$ be the power set of $S$.
Let $\mathcal B \subset \mathcal P \left({S}\right)$.
Then $\mathcal F := \left\{{V \subseteq X: \exists U \in \mathcal B: U \subseteq V}\right\}$ is a filter on $S$ if and only if the following con... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9861 | # Number of non-negative integer solutions of an equation using generating functions
I have question. Can anyone able to solve this problem or figure out the idea how non negative integer solution $x_1+5x_2=n$ and $x_1+5x_2=60$ Using the convolution thank you so much
-
I don't know what generating functions, combinat... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9862 | # Geodesics in a 2D embedded space
1. Feb 5, 2008
### Brinx
For a course on tensor analysis, we were asked to perform some calculations regarding a 2D space embedded in 'regular' Euclidean 3D space. I've gotten some results, but I've hit a snag...
1. The problem statement, all variables and given/known data
The fo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9865 | Question
# A wire of length r feet is bent into a rectangle whose width is 2 times its height. Write the area A of the rectangle as a function of the wire's leng
Solid Geometry
A wire of length r feet is bent into a rectangle whose width is 2 times its height. Write the area A of the rectangle as a function of the wi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9866 | ## Search
Regulations are current to 2021-02-15 and last amended on 2021-01-01. Previous Versions
## Part X — Greenhouse Gas Emissions from International Aviation — CORSIA (continued)
### Division III — Offsetting (continued)
#### Calculation of Reductions from Use of CORSIA Eligible Fuels
• (1) A private operato... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9867 | Disaster
``````:"_OO3_OO_O3_O_2O_2O->Str1
:"_->Str2
:For(F,1,length(Str1
:sub(Str1,F,1->Str3
:If inString("123456789",Str3
:Then
:For(G,1,expr(Str3
:Str2+sub(Str1,F+1,1->Str2
:End
:Else
:Str2+Str3->Str2
:End
:End```
```
You can use a technique known as Run-length encoding (RLE) to compress a string. In the example abo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9868 | Dot Product, what's wrong with my method?
1. Jan 19, 2008
rocomath
Find the three angles of the triangle with given vectors.
A(1,0)
B(3,6)
C(-1,4)
I found that AB & BC are congruent, so this ends up being an Isosceles triangle and the only angle I need to find is B.
BC=<3+1,6-4>=<4,2>
AB=<3-1,6-0>=<2,6>
$$\angle... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9869 | # zbMATH — the first resource for mathematics
##### Examples
Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "strai... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9870 | Home Arrays [Leetcode] : Find All Duplicates in an Array Solution
# [Leetcode] : Find All Duplicates in an Array Solution
Let us try to understand the problem statement first. You have an array of integers, where some of the elements are duplicated. Find all the duplicates present in the array and give them as an out... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9863 | ## Ice Cube and Time Varying Force
An ice cube with a mass of 10 kg is acted upon by a horizontal force dependent on time. This dependence is described with the formula Fx = p(q − t) , where p = 100 N·s−1, q = 1 s. At time t = 0 s the ice cube was at the beginning of our frame of reference, its speed was 0.2 m·s−1 and... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9864 | # Chapter 10 - Analytic Geometry - 10.1 Parabolas - 10.1 Exercises - Page 966: 5
domain is $\left[ -4,\infty \right] ;$ and the range is $\left[ -\infty ,\infty \right]$
#### Work Step by Step
$x-k=a\left( y-c\right) ^{2}\Rightarrow vertex=\left( k,c\right) \Rightarrow x+4=y^{2}\Rightarrow x-\left( -4\right) =1\time... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9871 | # The Unapologetic Mathematician
## The Differential Mean Value Theorem
Let’s say we’ve got a function $f$ that’s continuous on the closed interval $\left[a,b\right]$ and differentiable on $(a,b)$. We don’t even assume the function is defined outside the interval, so we can’t really set up the limit for differentiabi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9858 | Evaluate the following definite integrals as limit of sums.int_0 | Filo
Class 12
Math
Calculus
Integrals
562
150
Evaluate the following definite integrals as limit of sums.
562
150
Connecting you to a tutor in 60 seconds. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12192 | ## anonymous 5 years ago What is the solution of the equation (3x-4)/5=(2x+1)/10? Use Cross multiplication and show all work.
1. anonymous
$\frac{3x-4}{5}=\frac{2x+1}{10}$
2. anonymous
$10(3x-4)=5(2x+1)$
3. anonymous
$30x-40=10x+5$ $20x=45$ $x=\frac{45}{20}=\frac{9}{4}$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12194 | # zbMATH — the first resource for mathematics
Distribution of zeros of solutions of $$y''=q(t)y$$ in relation to their behaviour in large. (English) Zbl 0286.34050
##### MSC:
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34A30 Linear ordinary differential equ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12195 | # All Publications
B ZAIDMAN, A KISILEV, Y SASSON, and N Garti. 1988. “Double bond oxidation of unsaturated fatty acids.” JAOCS, J. Am. Oil Chem. Soc., 65, 4, Pp. 611–615. Abstract
Different oxidizing agents for performing the cleavage oxidn. of the double bond of the unsatd. fatty acids are presented, and their econo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12197 | transpose matrix properties
# transpose matrix properties
0 1
The result depends on rule parameter. Terms in this set (4) The transpose of the transpose of some matrix equals that matrix. As luck would have it, the matrix transpose has both. When we take the transpose, element (i, j) goes to position (j, i). Learn. ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12198 | Endomorphisms of a finite dimensional vector space
From Humphreys' Introduction to Lie Algebras and Representation Theory:
If $V$ is a finite dimensional vector space over $F$, denote by $\text{End }V$ the set of linear transformations $V\rightarrow V$. As a vector space over $F$, $\text{End }V$ has dimension $n^2$ (... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12199 | , 07.11.2019 16:31, bm42400
# Which line is parallel to a line that has a slope of 3 and a y-intercept...
Which line is parallel to a line that has a slope of 3 and a y-intercept at (0, 0)?
line ab
line cd
line fg
line hj
### Other questions on the subject: Mathematics
Mathematics, 21.06.2019 17:30, Hilljos018
The ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12200 | # Wigner-Eckart theorem and reduced matrix element
1. Apr 6, 2012
### Tilde90
Wigner-Eckart theorem and "reduced matrix element"
Hello,
I am studying the Wigner-Eckart theorem and I have found some difficulties understanding the reduced matrix element of a spherical tensor.
In fact, a spherical tensor is commonly ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12202 | # Maximality with respect to inclusion
• November 26th 2012, 09:31 AM
math8
Maximality with respect to inclusion
Let $g(x)=max_{i=1,...,m} f_{i}(x)$ where $f_{i}$ are continuous concave functions and
let $X = \{x: a_{j}^T x \geq b_{j} \}$ ; $M(x) = \{i: f_{i}(x) = g (x) \}$ and $J(x) = \{j: a_{j}^T x = b_{j} \}$.
We ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12203 | # Equal Matrices
Equality of two matrix: Two matrices [aij] and [bij] are said to be equal when they have the same number of rows and columns and aij = bij for all admissible values of i and j.
Definition of Equal Matrices:
Two matrices A and B are said to be equal if A and B have the same order and their correspond... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12205 | # Combination (combinatorics)
A combination (from Latin combinatio 'summary' ) or disordered sample is in combinatorics a selection of objects from a given basic set which (in contrast to permutation ) does not have to contain all objects of the basic set and in which (in contrast to permutation and variation ) the or... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12206 | ## Intermediate Algebra (6th Edition)
$\sqrt[3] (2m)$
$(2m)^{\frac{1}{3}}=\sqrt[3] (2m)$ Since the term $2m$ is in parentheses, we apply the exponent to both the $2$ and the $m$. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12207 | # Math Help - couple math 95 problems
1. ## couple math 95 problems
[SIZE=3]& # 8 7 3 0 ;
x-2(√(x-3) = 3
so I substract the x from both sides but then what? do I square both sides or do I divide by 2 and make the other side a fraction?
√(5x+1) = x+1
I can get it down to x(x-3) but then I am stuck. So yeah ok 3 works... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12196 | ### 2007 Workshop for Young Researchers in Mathematical Biology (WYRMB): Abstracts and Lecture Materials
#### Plenary Speakers
Biofluidmechanics of reproduction
Lisa Fauci, Department of Mathematics, Tulane University
Complex fluid-structure interactions are central to mammalian fertilization. Motile spermatozoa, mu... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12201 | ## mathmath333 one year ago Math/Reasoning type question
• This Question is Open
1. mathmath333
\large \color{black}{\begin{align} & \normalsize \text{A piece of paper is folded and cut as shown below in the question figures }\hspace{.33em}\\~\\ & \normalsize \text{From the given answer figures,indicate how it will a... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12204 | # Difference between revisions of "1993 AHSME Problems/Problem 20"
## Problem
Consider the equation $10z^2-3iz-k=0$, where $z$ is a complex variable and $i^2=-1$. Which of the following statements is true?
$\text{(A) For all positive real numbers k, both roots are pure imaginary} \quad\\ \text{(B) For all negative r... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12193 | # Convex subset
Let $A$ be the subset of $\mathbb{R}^2$ given by
$A = \{(x,y) \hspace{1mm} | \hspace{1mm} y\leq x, y\leq 2\}$. Show that A is convex.
Please help me check the steps below which shows that A is indeed convex by using the fact that the intersection of two convex subsets is convex.
Answers can be viewed... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2624 | # Find Fourier transform of triangular function based on a Fourier results of rectangular
I have a triangular pulse given by $$x\left(\frac{t}T\right) = \begin{cases} 1-\frac {|t|}T, & \text{if T\ge t} \\ 0, & \text{otherwise} \end{cases}$$
Given that $F\left(\operatorname{rect}\left(\frac{t}T\right)\right)=T\operato... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2625 | # Does emf (electromotive force) exist between the points A and B in the image? If it exists what is the value?
The battery has no internal resistance and the wire doesn't have any resistance.The circuit is in ideal conditions.
I know that current won't flow in the circuit because,if it flows, the potential differenc... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2626 | Particle in gravitational field
1. Nov 28, 2008
Math Jeans
1. The problem statement, all variables and given/known data
Consider a particle of mass m constrained to move on the surface of a paraboloid whose equation (in cylindrical coordinates) is $$r^2=4az$$. If the particle is subject to a gravitational force, sh... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2627 | # Thread: Difference equation - recurrence relation
1. ## Recursive sequence - Need help
Hello,
I am stuck with the following recursive sequence (please see pdf attached image):
Is the particular solution of the equation that I have trouble solving.
Any detailed explanation would be greatly appriciate it.
2. Well,... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2628 | <meta http-equiv="refresh" content="1; url=/nojavascript/"> Magnetism | CK-12 Foundation
Chapter 18: Magnetism
Difficulty Level: At Grade Created by: CK-12
Credit: User:Evan-Amos/Wikimedia Commons
Source: http://commons.wikimedia.org/wiki/File:Plastic-compass.jpg
We are familiar with magnets mostly as devices to st... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2629 | Select Page
Try this problem from IIT JAM 2014 exam. It requires knowledge of the exact differential equation and partial derivative.
## Differential Equation | IIT JAM 2014 | Problem 4
For $a,b,c \in \mathbb R$, If the differential equation $(ax^2+bxy+y^2)\mathrm d x+(2x^2+cxy+y^2)\mathrm d y=0$ is exact then
• $b... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2630 | # Absolute value of a function integrable?
1. Nov 23, 2008
### tomboi03
this is the question,
Prove that if f is continuous on (a,b] and if |f| is bounded on [a,b] then f is integrable on [a,b]. (note: it is not assumed that f is continuous at a.)
I know you have to use the upper and lower bounds to prove this stat... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2632 | # On the hardness of finding minimal-weight codewords in a QC-MDPC code
Problem 1 (Knapsack)
We want to maximize the value of a subset of items such that the weight of the set is no larger than weight $W$.
$\sum_{i \in \mathcal{S}} w_i x_i \leq W$
$\max \sum_{i \in \mathcal{S}} v_i x_i$
Let us first study another ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2633 | # Thread: Vector space basic proof
1. ## Vector space basic proof
Hi everyone,
how can I show that:
1. F=C,V ={f∈C[t]|f(0)∈R},
2. F=R,V ={f∈C[t]|f(0)∈R}.
are or aren't vectorial spaces? I know the 8 axioms that I'm supposed to use to show it but I don't see how I can use them here.
2. Originally Posted by sunmalu... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2634 | 2. If the new currencies of one day are not changed with the new currencies of the following days, then you need to solve $30n=5000(90/100)$. The solution is $n=150$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2635 | # Number Theory
## This Prime Generating Product generates successive prime factors
Any integer greater than 1 is called a prime number if and only if its positive factors are 1 and the number p itself. The basic ideology involved in this post is flawed and the post has now been moved to Archives. – The Editor Prime ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2636 | Differential and Integral Equations
Positive solutions of an elliptic system depending on two parameters
Flavio Dickstein
Abstract
We consider the Dirichlet problem associated to a $2\times 2$ semilinear elliptic system of equations in a bounded domain of $\mathbb R^n$. This system depends on two parameters $(\eta,... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2638 | # Give me my fancy math 𝒳 from mathptmx back!
In the old times of mathptmx, we wrote stuff such as
\documentclass{article}
\pagestyle{empty}
\usepackage{mathptmx}
\begin{document}
Let $$\mathcal{X}=\{X_1,\ldots,X_n\}$$.
\end{document}
and got from pdflatex a fancy calligraphic math 𝒳, which was sufficiently fancy... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2639 | # Rotation: mass transfer and angular momentum conservation
1. Jul 5, 2013
### Avi Nandi
1. The problem statement, all variables and given/known data
a drum of mass M$_{a}$ and radius a rotates freely with initial angular velocity ω$_{a}$(0). A second drum with mass M$_{b}$ and radius b greater than b is mounted on... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2631 | # Properties
Label 845.2.m.g Level $845$ Weight $2$ Character orbit 845.m Analytic conductor $6.747$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$
# Related objects
## Newspace parameters
Level: $$N$$ $$=$$ $$845 = 5 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 845.m (of ord... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2637 | # How to formally define what a reading comprehension question answering problem is?
I'm trying to formally define what Intelligent Agents with Reading Comprehension Question Answering agents are in mathematical terms for a dissertation.
To my mind we can say we have on the one hand $P=\{p_1,...,p_i\}\neq\varnothing$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21296 | 1. ## Inverse Proportion
it is know that variable A is inversely proportional to the square of variable B. For a particular value of B, A is 64. When B is doubled, what happens to A?
2. Originally Posted by Punch
it is know that variable A is inversely proportional to the square of variable B. For a particular value ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21297 | # Definition:Fractional Calculus/Historical Note
The field of fractional calculus was initiated by Joseph Liouville when he assigned meaning to the concept of the derivative $\dfrac {\mathrm d^n} {\mathrm d x^n}$ for $n$ not a positive integer. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21299 | # Return to Answer
2 deleted 2 characters in body edited Jul 24 '15 at 18:30 dsaxton 10.2k11 gold badge1717 silver badges3939 bronze badges One reason this function might seem more "natural" than others is that it happens to be the inverse of the canonical parameter of the Bernoulli distribution: \begin{align} f(y) &... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21302 | #### Posts
2019-05-16: Glow worms return
2019-04-11: Original memetic sin
2019-01-31: The theory of weight
2018-11-06: Origins of telephone network theory
2018-10-24: Modern thought
2018-09-10: Feeding a controversy
2018-06-11: Glow worm distribution
2018-04-23: Outlawing risk
2017-08-22: A rebuttal on the bea... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21303 | # Definition:Supremum
## Disambiguation
This page lists articles associated with the same title. If an internal link led you here, you may wish to change the link to point directly to the intended article.
Supremum may refer to:
## Also known as
Particularly in the field of analysis, the supremum of a set $T$ is o... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21304 | ## Logic in Proofs
If man is five, then the devil is six.
And if the devil is six, then god is seven.
This monkey’s gone to heaven.
Black Francis, Monkey Gone to Heaven
[/callout]
Logic as a game of pushing symbols is fun, but our purpose with it is to construct arguments. In fact, classically an advanced educati... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21305 | # GMAT: Math 30
## Video transcript
We're on problem 154. An empty pool being filled with water at a constant rate takes 8 hours to fill to 3/5 of its capacity. So you could say you can fill 3/5 of a pool every 8 hours, which is just another way of saying that you can fill, let's see, 3/5 divided by 8 is 3 over-- wha... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21306 | Problem 29E
19-29 Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative.
29. $f(x)=x^{4}$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21307 | ## College Algebra (11th Edition)
$(-2+i)^2+4(-2+i)+5=0$
In order to see that $-2+i$ is a solution, we plug it in and make sure the equation remains true. $(-2+i)^2+4(-2+i)+5=0?$ Expand the left hand side. $4-4i+i^2-8+4i+5$ Combine like terms using the fact that $i^2=-1$. $(-2+i)^2+4(-2+i)+5=0$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21308 | # Relationship between eigendecomposition and singular value decomposition
Let $A \in \mathbb{R}^{n\times n}$ be a real symmetric matrix. Please help me clear up some confusion about the relationship between the singular value decomposition of $A$ and the eigen-decomposition of $A$.
Let $A = U\Sigma V^T$ be the SVD o... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21310 | # Given a Horizontal Derivative Kernel What Would Be the Output Image?
Hi, im solving this problem and everything went well until i went and solved the position p(5,3) and i got the answer of 0. However, the solution guide lists the solution as 150 which is pointed at in blue. I don't understand this since the pixel a... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21311 | # Questions Asked onJanuary 23, 2010
1. ## College chemistry
Butane (C4H10) has a heat of vaporization of 22.44 kJ/mol and a normal boiling point of -0.4 C. A 250 mL sealed flask contains 0.5 g of butane at -22 C. How much butane is present as a liquid? If the butane is warmed to 25 C, how much is present as a
2. ##... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21298 | Please use this identifier to cite or link to this item: http://hdl.handle.net/2445/95817
Title: Some moduli spaces for rank 2 reflexive sheaves on ${{\mathbf{P}}^3}$ Author: Miró-Roig, Rosa M. (Rosa Maria) Keywords: Geometria algebraicaHomologiaAlgebraic geometryHomology Issue Date: 1987 Publisher: American Mathemati... |
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