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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24449 | Let f(x) be a polynomial of degree 3 such that
Question:
Let $f(x)$ be a polynomial of degree 3 such that $f(-1)=10$, $f(1)=-6, f(x)$ has a critical point at $x=-1$ and $f^{\prime}(x)$ has a critical point at $x=1$. Then $f(x)$ has a local minima at $x=$
Solution:
Let $f(x)=a x^{3}+b x^{2}+c x+d$
$f(-1)=10$ and $f(... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24450 | Mathematics Part I Solutions Solutions for Class 9 Maths Chapter 3 Polynomials are provided here with simple step-by-step explanations. These solutions for Polynomials are extremely popular among Class 9 students for Maths Polynomials Solutions come handy for quickly completing your homework and preparing for exams. Al... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24451 | ## arXiv.org: Quantum Physics
Quantum Physics (quant-ph) updates on the arXiv.org e-print archive
Updated: 17 hours 5 min ago
### Coexistence of vortex arrays and surface capillary waves in spinning prolate superfluid He-4 nanodroplets. (arXiv:2104.06712v1 [cond-mat.mes-hall])
Thu, 2021-04-15 08:45
Within Density F... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24452 | # Random variable on product space as product of random variables
Let $\left(\Omega_i,\mathcal{A}_i,P_i\right)$ for $i=1,2$ a probability space and assume that $\mathcal{A}_1$ is independent of $\mathcal{A}_2$. Define the probability space $\left(\Omega,\mathcal{A},P\right)$ where $\Omega=\Omega_1\times\Omega_2$, $\ma... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24453 | # Counting monomials in cyclotomic polynomials
Let $$\Phi_n(x)$$ denote the $$n$$-th cyclotomic polynomial. There are numerous properties and utilities of these polynomials. My interest is more basic and in the spirit of
Tewodros Amdeberhan and Richard P. Stanley, Polynomial Coefficient Enumeration, preprint (2008) a... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24454 | # Definition:Logical Argument
## Definition
A logical argument (or just argument) is a process of creating a new statement from one or more existing statements.
An argument proceeds from a set of premises to a conclusion, by means of logical implication, via a procedure called logical inference.
An argument may hav... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24457 | ## Thinking Mathematically (6th Edition)
On${{15}^{th}}$ day the person puts aside$\16,384$.
: The provided information can be modelled as a geometric progression with the following parameters: $a=1,\,r=2,\,n=15$ The fifteenth term is, \begin{align} & {{a}_{n}}=a{{r}^{n-1}} \\ & {{a}_{15}}=1\times {{2}^{\left( 15-1 \r... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24458 | Chapter 10.6, Problem 17E
### Single Variable Calculus: Early Tr...
8th Edition
James Stewart
ISBN: 9781305270336
Chapter
Section
### Single Variable Calculus: Early Tr...
8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem
# (a) Find the eccentricity and directrix of the conic r = 1/(1 − 2 sin θ) and ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24459 | # Large Numbers, Infinities & God (2/3)
This post is continuing on from my discussion on large numbers and notation. I am going to assume some knowledge of Set Theory for this post as there really is a lot to write about and I have found it hard to cut it down to a nice size.
2. Infinities
Infinity as a concept has s... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24461 | <img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
# Fractional Exponents
## Relate fractional exponents to nth roots
%
Progress
MEMORY METER
This indicates how strong in your memory this concept is
Progress
%
Rational Exponents and Ro... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24462 | # Show that non-singular is necessary for the Inverse Function Theorem
I am attempting the following problem:
Show that the condition that $$dF(a)$$ be non-singular is necessary in the inverse function theorem by showing that if a function $$F$$ from a neighborhood of $$a$$ in $$\mathbb{R}^p$$ to $$\mathbb{R}^p$$ is ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24463 | # Find the work done by the force field in moving the particle from one point to another
Find work done by the force field F in moving the particle from $(-1, 1)$ to $(3, 2)$
This sounds good till we are given that $\textbf{F} = \dfrac{2x}{y}\textbf{ i }- \dfrac{x^2}{y^2}\textbf{ j }$
Can someone explain how to unde... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24455 | # Equation substitution
1. Jul 18, 2011
### exidez
In the attached image, how are equations 1, 2, 3 and 4 used to come to the final equation of 5 and 6? Im suspecting it has something to do with the derivative with respect to t, but I dont know how they remove it to get the final solution. Am I missing something inc... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24456 | - Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnline Submission ㆍMy Manuscript - For Reviewers - For Editors
Multipliers in th... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24460 | # LCM Dilemma
\begin{align*} A &= \text{lcm} (1, \, 2, \, 3, \, \dots, \, 2018) \\\\ B &= \text{lcm} (1010, \, 1011, \, 1012, \, \dots, \, 2018) \end{align*}
Which is true?
Notation: $$\text{lcm}(\cdot)$$ denotes the lowest common multiple function.
× |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6000 | # I Lagrangian Equation with Generalized Force term
1. Sep 8, 2016
### KT KIM
In basic level classical mechanics I've known so far
The Lagrangian Equation is
Like this
But in the little deeper references, they covers Lagrangian Equation is
Like this
Qi is Generalized force, and Qi also contains frictions that's wh... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6003 | ## Prealgebra (7th Edition)
1.2= 12% $\times$ x 1.2= 0.12 $\times$ x $\frac{1.2}{0.12}$ = $\frac{0.12\times x}{0.12}$ $\frac{1.2}{0.12}$ $\times$ $\frac{100}{100}$=x $\frac{120}{12}$ =x x=10 |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6004 | # Exact Value of Trig Functions Calculator
Created by Davide Borchia
Reviewed by Komal Rafay
Last updated: Feb 02, 2023
Use our exact value of trig functions calculator to quickly find the values of the trigonometric functions of some selected angles. Keep reading this short article to learn:
• How to find the exact... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6005 | # How do you solve \frac { 5x } { 6} = 7x - 3?
Apr 16, 2018
$x = \frac{18}{37}$
#### Explanation:
Multiply both sides by 6 to remove the fraction.
$5 x = 42 x - 18$
$5 x + 18 = 42 x$
Subtract $5 x$ from both sides
$18 = 37 x$
$x = \frac{18}{37}$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6006 | # Math Help - Summation
1. ## Summation
My textbook states.
$-2\sum_{i=k-4}^{2}i=-(7-k)(k-2)$
But I got the summation to equal -2k+4. I don't see how the textbook got the LHS to equal to the RHS. Thanks in advance.
2. Originally Posted by Simplicity
My textbook states.
$-2\sum_{i=k-4}^{2}i=-(7-k)(k-2)$
But I got... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6007 | How 9 Cheenta students ranked in top 100 in ISI and CMI Entrances?
# Understand the problem
The multiplicative group $F^*_7$ is isomorphic to a subgroup of the multiplicative group $F^*_{31}$.
[/et_pb_text][et_pb_tabs active_tab_background_color="#0c71c3" inactive_tab_background_color="#000000" _builder_version="3.2... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6008 | # Integrating Cosecant
Calculus Level 3
$\begin{eqnarray} I_1 &=&\int \csc x \, dx = \int \dfrac{\csc x (\csc x - \cot x)}{\csc x - \cot x} \, dx = \ln | \csc x - \cot x | \\ I_2 &=&\int \csc x \, dx = \int \dfrac{-\csc x (\csc x + \cot x)}{\csc x + \cot x} \, dx = - \ln | \csc x + \cot x | \\ \end{eqnarray}$
If bot... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6011 | Search by Topic
Resources tagged with Visualising similar to Triangle Island:
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Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle o... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6013 | 7 views
Draw the recursion tree for $T(n)=4T(\lfloor n/2\rfloor) +cn$, where $c$ is a constant,and provide a tight asymptotic bound on its solution. Verify your bound by the substitution method.
| 7 views |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6014 | # Isomorphism of relatively prime groups
1. Mar 8, 2012
### PennState666
1. The problem statement, all variables and given/known data
Allow m,n to be two relatively prime integers. You must prove that Z(sub mn) ≈ Z(sub m) x Z(sub n)
2. Relevant equations
if two groups form an isomorphism they must be onto, 1-1, and... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6002 | # A question in Probability, resignations from stores
"Stores A,B and C have 50,75 and 100 employees and respectively, 30, 60 and 70 percent of these are women. Resignations are equally likely among all employees, regardless of sex. One employee resigns and this is a woman. What is the probability that she works in st... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6010 | # Duality of an Ample invertible sheaf has no non-trivial global section?
This is EXERCISE 7.1 of Chapter III in Hartshorne's AG:
[Q] Let $$X$$ be an integral projective scheme of dimension $$\geq1$$ over a field $$k$$, and let $$\mathscr{L}$$ be an ample invertible sheaf on $$X$$. Then $$H^0(X,\mathscr{L}^{-1})=0$$.... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6015 | 1
### JEE Main 2017 (Online) 8th April Morning Slot
A potentiometer PQ is set up to compare two resistances as shown in the figure. The ammeter A in the circuit reads 1.0 A when two way key K3 is open. The balance point is at a length $\ell$1 cm from P when two way key K3 is plugged in between 2 and 1, while the bala... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6001 | # Perimeter of Squares
#### formula
Perimeter of a square = 4 × length of a side.
# Perimeter of a Square:
Perimeter of the Square = Sum of the lengths of its four sides.
= AB + BC + CD + DA
= AB + AB + AB + AB....(All the four side of square are equal)
= 4 × AB
= 1m + 1 m + 1 m + 1 m = 4 × 1 m
= 4 m
Perimete... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6009 | # Adjoint of derivative operator on polynomial space
I was working on a problem when I made the following reasoning.
I know that every linear operator $T:V \longrightarrow V$ on a Hilbert space $(V,\langle.,.\rangle)$ such that $\dim(V)<\infty$ has one (unique) adjoint operator $T^*:V \longrightarrow V$ (that is, $\l... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6012 | # The Normal Distribution
A LevelAQAEdexcelOCRAQA 2022Edexcel 2022OCR 2022
## The Normal Distribution
The normal distribution is a bell shaped curve that is symmetric about the mean. It is defined by its mean $\mu$ and its standard deviation $\sigma$. If $X$ is normally distributed, we write $X\sim N(\mu,\sigma^{2})... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_304 | \< 1.625 = 1 \frac58 \>Showing the workRewrite the decimal number together a portion with 1 in the denominator\< 1.625 = \frac1.6251 \>Multiply to eliminate 3 decimal places. Here, you main point top and bottom through 103 = 1000\< \frac1.6251\times \frac10001000= \frac16251000 \>Find the Greatest typical Factor (GCF) ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_305 | # Probability wave speed of dispersion and interference
I'm a layperson learning about quantum mechanics and probability waves. My understanding is that the probability wave for the position of a particle disperses throughout all of the universe.
I have two questions about probability waves:
1) Does the probability ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_306 | This category contains definitions related to Adherent Points.
Related results can be found in Category:Adherent Points.
A point $x \in S$ is an adherent point of $H$ if and only if every open neighborhood $U$ of $x$ satisfies:
$H \cap U \ne \O$
## Pages in category "Definitions/Adherent Points"
The following 4 pag... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_308 | ## FANDOM
16 Pages
The article will discuss the probability of obtaining two heads in a row in n tosses with heads and tails having different probablilities.
## Derivation Edit
to come soon...
$P(n) = P(n-1) + (1-P(n-1))P(H) - (1-P(n-2) )P(H)P(T)$
where P(H) is the probability of heads and P(T) is the probabili... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_311 | Definitions
# De Bruijn notation
In mathematical logic, the de Bruijn notation is a syntax for terms in the λ calculus invented by the Dutch mathematician Nicolaas Govert de Bruijn (). It can be seen as a reversal of the usual syntax for the λ calculus where the argument in an application is placed next to its corres... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_312 | # 12.3 Stress, strain, and elastic modulus (Page 5/26)
Page 5 / 26
$\text{bulk strain}=\frac{\text{Δ}V}{{V}_{0}}.$
The bulk strain results from the bulk stress, which is a force ${F}_{\perp }$ normal to a surface that presses on the unit surface area A of a submerged object. This kind of physical quantity, or press... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_313 | GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 17 Oct 2019, 06:08
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-00003-of-00114-e7fc257ef044bc03_doc_314 | # Ring of Integers Modulo Prime is Field
## Theorem
Let $m \in \Z: m \ge 2$.
Let $\struct {\Z_m, +, \times}$ be the ring of integers modulo $m$.
Then:
$m$ is prime
$\struct {\Z_m, +, \times}$ is a field.
### Corollary
Let $m \in \Z: m \ge 2$.
Let $\struct {\Z_m, +, \times}$ be the ring of integers modulo $m$.... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_315 | # The prime number that comes just after 47 is
(a) 57
(b) 53
(c) 49
(d) 51
Solution:
A prime number is a number that has only two factors, that is, 1 and the number itself.
53 is the prime number that comes just after 47.
Hence option b is the answer. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_316 | # How do you find the inflection points of f(x)= 12x^5+45x^4-80x^3+6?
Jun 22, 2018
Maximum: x=-4
Inflection: x=0
Minimum: x=1
#### Explanation:
In general, this is a hard problem for a quintic equation. But this particular quintic has some missing low order terms that help us a great deal.
To find the inflection a... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_317 | # Putnam Perimeter!
Geometry Level 5
What is the minimum perimeter of the triangle with one vertex at $$(4\sqrt{2}, 3\sqrt{2})$$, one on the $$x$$-axis and one on the line $$y=x$$?
This problem appeared in the Putnam Examination.
× |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_318 | ## In search of an isomorphism
I’m working on some group-theoretic stuff related to n copies of a unital quantum channel and am in search of some isomorphism between the dihedral group $\textrm{D}_n$ and the unitary group U(n).
Now, what’s interesting is that the unitary group U(1) is isomorphic to the circle group, ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_319 | By using the substitution $p=x+\frac{1}{x}$, show that the equation $$2x^4+x^3-6x^2+x+2=0$$ reduces to $2p^2+p-10=0$.
I can't think of anything that produces a useful result, I tried writing p as $p=\frac{x^2+1}{x}$ and finding areas to substitute but have come with no progress. Could someone offer a slight hint on ho... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_309 | # Using Solve[] to find Eigenstates of a 1D Double Dirac Potential
I’d like to Solve
$$k^2 \equiv – \frac{2mE}{\hbar^2} = (- \frac{mA}{\hbar^2} (1+ e^{-2ka}))^2$$
for E, in terms of m, $$\hbar$$, A, a.
I tried using the following command:
Solve[-((2 m ene)/h^2) == (m^2 A^2)/h^4 (1 + E^(-2 a*Sqrt[-((2 m ene)/h^2)])... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_310 | # 2003 USAMO Problems/Problem 3
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
## Problem
Let $n \neq 0$. For every sequence of integers
$A = a_0,a_1,a_2,\dots, a_n$
satisfying $0 \le a_i \le i$, for $i=0,\dots,n$, define another sequence
$t(A)= t(a_0), t(a_1), t(a_2), \dots, t(a_n)$
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_307 | ##### Activity2.1.2
In this activity, we will look at linear combinations of a pair of vectors,
\begin{equation*} \vvec = \left[\begin{array}{r} 2 \\ 1 \end{array}\right], \wvec = \left[\begin{array}{r} 1 \\ 2 \end{array}\right] \end{equation*}
with weights $$a$$ and $$b\text{.}$$
LINEAR-COMBINATIONS
1. The weight... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4592 | # Box Integrals
### Description
By a "box integral" we mean here an expectation $\langle|\vec r - \vec q|^s \rangle$ where $\vec r$runs over the unit $n$-cube,with $\vec q$ and $s$ fixed, explicitly:\begin eqnarray*&&\int_01 \cdots \int_01 \left((r_1 - q_1)2 + \dots+(r_n-q_n)2\right)^ s/2 \ dr_1 \cdots dr_n.\end eqna... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4593 | # How do you solve the following system?: y=4x- 6 , y=x-2
$x - 2 = 4 x - 6 \to 3 x = 4 \to x = \frac{4}{3}$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4595 | # Finding the point of differentiability of a real valued function.
Let $f:(0,2)\rightarrow \mathbb{R}$ be defined by
$f(x)=x^2$ if $x\in (0,2)\cap \mathbb{Q}$ and
$f(x)=2x-1$ if $x\in (0,2)- \mathbb{Q}$
Check for the points of differentiability of $f$ and evaluate the derivative at those points.
My attempt: I kno... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4597 | # Lesson 21
The Slope of a Fitted Line
### Problem 1
Which of these statements is true about the data in the scatter plot?
A:
As $$x$$ increases, $$y$$ tends to increase.
B:
As $$x$$ increases, $$y$$ tends to decrease.
C:
As $$x$$ increases, $$y$$ tends to stay unchanged.
D:
$$x$$ and $$y$$ are unrelated.
#... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4598 | Non-ZFC set theory and nonuniqueness of the hyperreals: problem solved? - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T23:30:18Z http://mathoverflow.net/feeds/question/88292 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/88292/non-zfc-set-theory-and-nonuni... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4599 | # Algebraic equation -- six degree polynomial
Tags:
1. May 5, 2016
### gruba
1. The problem statement, all variables and given/known data
Solve the equation for $r,r>0,r<R$.
$$\frac{-2\pi R^3}{3}-\frac{8\pi r^2\sqrt{R^2-r^2}}{3}+2r^2R+\frac{2\pi}{3}R^2\sqrt{R^2-r^2}=\frac{2\pi R^3}{3}$$
2. The attempt at a solution... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4600 | # Finding the order of another element of a group
If in a group $G$, $a^5 = e$ , $e$ is the identity element of $G$. If $a,b \in G$ and $aba^{-1}=b^2$ then find the order of b
I have got no clue how to go forward with it, except that perhaps we can construct a cyclic group of order 5 with a and thus the order of $G$ ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4601 | # How do you solve -3<x-3<0?
to solve for $- 3 < x - 3 < 0$
we would just need to add $3$ to each element in the equation.
$- 3 + 3 < x - 3 + 3 < 0 + 3$
$0 < x < 3$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4602 | # Killing form explained
In mathematics, the Killing form, named after Wilhelm Killing, is a symmetric bilinear form that plays a basic role in the theories of Lie groups and Lie algebras. Cartan's criteria (criterion of solvability and criterion of semisimplicity) show that Killing form has a close relationship to th... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4603 | # How do you prove tan^2xsin^2x=tan^2x + cos^2x-1?
${\tan}^{2} x . {\sin}^{2} x = {\tan}^{2} x \left(1 - {\cos}^{2} x\right) = {\tan}^{2} x - {\tan}^{2} x \left({\cos}^{2} x\right)$
$= {\tan}^{2} x - \frac{{\sin}^{2} x . {\cos}^{2} x}{{\cos}^{2} x} = {\tan}^{2} x - {\sin}^{2} x =$
$= {\tan}^{2} x - 1 + {\cos}^{2} x$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4604 | 🎉 Announcing Numerade's $26M Series A, led by IDG Capital!Read how Numerade will revolutionize STEM Learning Numerade Educator ### Problem 51 Easy Difficulty # A machine part consists of a thin, uniform$4.00-\mathrm{kg}$bar that is 1.50$\mathrm{m}$long, hinged perpendicular to a similar vertical bar of mass 3.00$\math... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4605 | # Theories of Everything: Ideas in Profile
Ideas in Profile. Small introductions to big topics is a series published by Profile Books that give short introductions to important socio-cultural or scientific topics. The book under review is the only one so far on a mathematical-physical topic: the theories of everything... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4606 | Department of
Mathematics
Seminar Calendar
for events the day of Tuesday, November 1, 2016.
.
events for the
events containing
Questions regarding events or the calendar should be directed to Tori Corkery.
October 2016 November 2016 December 2016
Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4607 | # Incorrect answer supplied to one of the Quiz problems
One of the quiz problems presented is to investigate whether 90!/(30!)^3 is a whole number. The answer is supposedly true: it is a whole number and a very weak argument is provided to show that. The argument given for proof is incorrect. it starts out with a proo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4594 | # Odds Ratio Calculator
Instructions: This calculator computes the Odds Ratio (OR) for a 2x2 crosstabulation, which measures the ratio of the odds of exhibiting a condition (or disease) for those in an exposed group, versus the the odds of exhibiting the condition (or disease) for those in the non-exposed group. Pleas... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4596 | D
Differentiation question
16 viewed last edited 1 year ago
Timothy Lee
1
I have two functions here: H(p) = 0,03p^(10) + 1,2p^(6) - p This would then be H'(p) = 0,3p^(9) + 7,2p^(5) - 1 And I think I understand this because -p is -1p But in this function: K(x) = 5x^(7) + ax^(2) + b The answer is K'(x) = ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3424 | Working with formulas > Using formulas
1234Using formulas
## Theory
A formula is a sentence containing variables. Formulas often describe a relation between those variables, but not always.
Formulas often look like an equation, i.e. a sentence with an equals sign.
If a formula describes a relation between two variabl... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3425 | # The Complex Power Function
The generalized complex power function is defined as: \begin{eqnarray}\label{gcp} f(z) = z^c = \exp(c\log z), \quad \text{with}\quad z\neq 0. \end{eqnarray}
Due to the multi-valued nature of $\log z$, it follows that (\ref{gcp}) is also multi-valued for any non-integer value of $c$, with ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3428 | If A is an I.e., it will be an eigenvector associated with {\displaystyle |v_{i,j}|^{2}={\frac {p_{j}(\lambda _{i}(A))}{p'(\lambda _{i}(A))}}}. λ {\displaystyle \mathbf {v} } j While a common practice for 2×2 and 3×3 matrices, for 4×4 matrices the increasing complexity of the root formulas makes this approach less attr... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3429 | ## Saxon Math
##### v1
###### Usability
Our Review Process
Title ISBN Edition Publisher Year
9780547729169
9781600325342
9780547746951
9781600327216
9780547729183
9781600325465
9780547746975
9781600327179
9780547746937
9781600327193
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9781600325403
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### Overall Summary
The instructional material... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3433 | Here's the question you clicked on:
## kobe24 Group Title what is the derivative of ln(1+1/x)? they say the answer is xsquared-1/ xcubed+x now can someone explain how you find the answer one year ago one year ago
• This Question is Open
1. dpaInc Group Title
the answer given is correct but not simplified.... use the... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3435 | The Logarithm is the inverse operation to exponentiation. Suppose we have the exponentiation $N=x^a$, then the logarithm of N with base a equals to x, or $x=log_{a}{N}$
To compute the logarithm with an arbitrary base just enter your number and base in the corresponding calculator fields:
##### Logarithm
The calculato... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3437 | # Math Help - Differentiation - I thought I had finally got it, but im stuck again!
1. ## Differentiation - I thought I had finally got it, but im stuck again!
Ok, the question is:
Differentiate: five over the square root of four + x
2. ## Re: Differentiation - I thought I had finally got it, but im stuck again!
$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3438 | # Getting integer solutions for equation $x^{2}-y^{4}=336$
I need to get integer solutions for the next equation: $$x^{2}-y^{4}=336$$ I know equations that look like $x^{2}-y^{2}=n$ have solutions $x$ and $y$ where $x=\frac{a+b}{2}$ and $y=\frac{a-b}{2}$, $a$ and $b$ being both odd or even. But I can not figure out ho... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3439 | # Is this question proper? “Solve $\log_{10}x\in\mathbb{R}$.”
Is this question proper? "Solve $\log_{10}x\in\mathbb{R}$."?
I know that $\log_{10}x\in\mathbb{R}$ means $x\in(0,\infty)$, but can we write "Solve $\log_{10}x\in\mathbb{R}$." as a question alone? Thank you.
-
What are you trying to solve? What would the c... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3426 | # Math Help - Orbit of a geostationary satellite
1. ## Orbit of a geostationary satellite
Hi,
Question is: compute the radius of a geostationary satellite's orbit in units of the Earth's radius.
Earth's radius R = 6378.1 km approx
Satellite is 35,786km above ground so radius of the orbit in terms of earth's radius ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3427 | scroll identifier for mobile
main-content
## Über dieses Buch
At the intersection of mathematics, engineering, and computer science sits the thriving field of compressive sensing. Based on the premise that data acquisition and compression can be performed simultaneously, compressive sensing finds applications in imag... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3430 | Theo Raedschelders
RESEARCH INTERESTS
My research is in noncommutative algebraic geometry and related topics in deformation theory, homological algebra and representation theory. More specifically, I like to think about Hochschild-type invariants for enhanced triangulated categories, and am also particularly interest... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3434 | # he masses and radii of the earth and moon are M1 , R1 and M2 , R2 respectively. Their centres are distance d apart. The minimum velocity with which a particle of mass m should be projected from a point midway between their centres so that it escapes to infinity is
Q: The masses and radii of the earth and moon are M1... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3436 | # If T is an infinite subset of $\mathbb{N}$ show that there is a 1-1 mapping of T onto $\mathbb{N}$ [duplicate]
Like the title says: If T is an infinite subset of $\mathbb{N}$, show that there is a 1-1 mapping of T onto $\mathbb{N}$.
I get the idea (like for evens and odds) but I don't know how to prove it for ANY i... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3431 | # Strange region
Algebra Level 5
How many solutions to the set of inequalities $$sinx<log(cosy)$$
$$xsec(y)<log(tanx)$$ In the region from $$x\epsilon(3,9.8)$$
$$y\epsilon(5,19.8)$$
× |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3432 | Home > Algebra, IMO, Olympiad, Problem Solving > Miklos Schweitzer 2013 Problem 8
## Miklos Schweitzer 2013 Problem 8
Problem 8. Let ${f : \Bbb{R} \rightarrow \Bbb{R}}$ be a continuous and strictly increasing function for which
$\displaystyle f^{-1}\left(\frac{f(x)+f(y)}{2}\right)(f(x)+f(y)) =(x+y)f\left(\frac{x+y}{... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11936 | # American Institute of Mathematical Sciences
• Previous Article
Improving whale optimization algorithm for feature selection with a time-varying transfer function
• NACO Home
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On the bang-bang control approach via a component-wise line search strategy for unconstrained optimization
March 2... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11937 | # Homework Help: Vector Spaces
1. Apr 20, 2010
### joemama69
1. The problem statement, all variables and given/known data
Determine if the following sets are vector spaces
Part A) R^2; u+v = (u1 + v1, u2 + v2); cu = (cu1,cu2)
part b) M_2,2
A + B = |(a_11 + b_11) (a_12 + b_12)| & cA = |ca_11 ca_12|
|(a_21 + b_21) ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11938 | # Came up with a problem that I can't solve
Tags:
1. May 11, 2016
### guv
Imagine a hoop with mass M and radius R that will only roll without slipping on the floor. Place a point object with mass m on top of the hoop and then the system starts from at rest. Question: where does m leave M?
If one fixes the hoop or l... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11939 | # Math Help - Feynman Path Integral and Free Particle
1. ## Feynman Path Integral and Free Particle
can someone show me how to calculate a simple path integral so i can see how they work? more specifically, can it be a problem that involves free particles, preferably a "classic" problem?
I want to understand the con... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11941 | Thread: "Eigenpair" Fundamental Matrix
1. "Eigenpair" Fundamental Matrix
I came across this problem in my class notes. I can't solve this one and I was wondering how to solve it.
Use the "eigenpair" method to find a fundamental matrix for the differential equation system. Use your answer to find e^At
x'=Ax [0 1]
[-... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11942 | Gravitational Forces in 2D Video Lessons
Example
# Problem: Consider the earth following its nearly circular orbit (dashed curve) about the sun. The earth has mass 5.98 x 1024 kg and the sun has mass 1.99 x 1030 kg. They are separated, center to center, by r = 93 million miles = 150 million km. What is the magnitude... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11943 | factory-0.3.0.0: Rational arithmetic in an irrational world.
Factory.Math.Precision
Description
AUTHOR
Dr. Alistair Ward
DESCRIPTION
Defines the unit with which precision is measured, and operations on it.
Synopsis
# Types
## Type-synonyms
A number of decimal digits; presumably positive.
# Constants
Linear con... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11944 | # Matematički blogovi
### Holomorphic images of disks
Terrence Tao - Sub, 2020-11-28 21:11
Consider a disk in the complex plane. If one applies an affine-linear map to this disk, one obtains
For maps that are merely holomorphic instead of affine-linear, one has some variants of this assertion, which I am recording ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11945 | 3 added 42 characters in body
Posting this as an answer at Colin's request. The second paragraph of the question is addressed at this other MO question.
The answer to the question in the first paragraph is delicate, it depends on how much of the ground model we decide to preserve: $\alpha$ and $\alpha^+$? $\rm{cof}(\... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11946 | # Finding equation of equlibrium for rod and two blocks
1. Jul 3, 2009
### KEØM
1. The problem statement, all variables and given/known data
A slender rod AB of weight W is attached to blocks A and B which move freely in the guides shown. The constant of the spring is k, and the spring is unstretched when $$\theta$$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11948 | # Focused Electric Field
Electricity and Magnetism Level 5
In the $$xy$$ plane, there is a parabola described by $$y = x^{2}$$. The parabola has a uniform linear charge density $$\sigma$$.
The magnitude of the electric field at the focus of the parabola can be expressed as $$\dfrac{a}{b}k\sigma$$, where $$k$$ is the... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11949 | ### Two Squares and Four Squares
Diophantus of Alexandria wrote a collection of books called Arithmetica in the 3rd century AD. He noted that natural numbers of the form cannot be expressed as the sum of two square numbers. He also [more…]
### How about sending me a fourth gimbal for Christmas?
Part of a conversat... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11950 | Probability of modifying $\alpha$ and $\beta$ in $\beta = a \alpha + b$ such that the equality still holds
Let $a ,$ $b ,$ $\alpha ,$ and $\beta$ be non-zero binary strings of length exactly $n$ where $$\beta = a \alpha + b.$$
Now, consider the following scenario. Fix $a$ and $b.$ I give you $\alpha$ and $\beta,$ but... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11940 | MathSciNet bibliographic data MR814689 57R42 (57R45) Levine, Harold Classifying immersions into ${\bf R}\sp 4$${\bf R}\sp 4$ over stable maps of $3$$3$-manifolds into ${\bf R}\sp 2$${\bf R}\sp 2$. Lecture Notes in Mathematics, 1157. Springer-Verlag, Berlin, 1985. v+163 pp. ISBN: 3-540-15995-9 Article
For users without... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11951 | 289 views
Consider a square of side length $2$. We throw five points into the square. Consider the following statements:
1. There will always be three points that lie on a straight line.
2. There will always be a line connecting a pair of points such that two points lie on one side of the line and one point on the ot... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11947 | # The noncommutative $$H^{(r,s)}_{p}({\mathcal A};\ell _{\infty })$$ H p ( r , s ) ( A ; ℓ ∞ ) and $$H_{p}({\mathcal A};\ell _{1})$$ H p ( A ; ℓ 1 ) spaces
The noncommutative $$H^{(r,s)}_{p}({\mathcal A};\ell _{\infty })$$ H p ( r , s ) ( A ;... In this paper we introduce the noncommutative $$H^{(r,s)}_{p}({\mathcal A... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9776 | # Chapter 9 – Limiting Properties of Samples
9.1 The Law of Large Numbers
The Law of Large Numbers establishes a linkage between the observable properties of random samples and the properties of underlying populations from which such samples are drawn. The next few sections provide a proportionalist interpretation o... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9777 | # Tag Info
3
Using the Segre embedding $\mathbb P^1 \times \mathbb P^1 \hookrightarrow \mathbb P^3$ given by $(x_0:x_1)x(y_0:y_1) \mapsto (x_0y_0,x_0y_1,x_1y_0,x_1y_1)$, we can rewrite the curve as an intersection of two hypersurfaces in $\mathbb P^3$. Explicitly, these hypersurfaces will be $xw=yz$ and $x^2+y^2+z^2+... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9778 | birth-and-death process is a special kind of continuous-time Markov chain that has applications in queuing. If we assume that arrivals to a queuing system follow a Poisson process and that service times are exponentially distributed, then the resulting queuing system is a birth-and-death process. In this post we’ll d... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9779 | Share
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# Find:30.94 Division of a Decimal Number 0.7 - CBSE Class 7 - Mathematics
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ConceptDivision of Decimal Numbers Division of a Decimal Number by Another Decimal Number
#### Question
Find: 30.94 ÷ 0.7
#### Solution
30.94 ÷ 0.7 = ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9781 | ## Chemistry: Molecular Approach (4th Edition)
We have,$P_{1} V_{1} = P_{2} V_{2}$ (combined gas equation) We are required to find: $P_{2}$ (final pressure) Therefore, (13.9) (1.22) = (10.3) $P_{2}$ $P_{2}$ = $\frac{(13.9)(1.22)}{(10.3)}$ $P_{2}$ = 1.65 atm |
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