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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18580 | # A problem about the expectation of maximum rise up for a random walk.
Give such a random walk moving on the x-axis:
1. Start from $x_0=0$;
2. After the $i^{th}$ step, the location is $x_i$.
3. The length for the $i^{th}$ step $x_i-x_{i-1}$ is a uniformly generated real number in $[-1,1]$. Negative length means to m... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18581 | # How do you solve ln y = 2t - 3?
Jan 28, 2016
$y = {e}^{2 t - 3} , t = \frac{\ln y + 3}{2}$
#### Explanation:
Solving for $m a t h b f y$:
To undo the natural logarithm that $y$ is attached to, exponentiate both sides with base $e$. Since exponentiation and logarithms are inverse functions, and $\ln$ is equivalen... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18582 | Definition 4.32.1. Let $\mathcal{C}$ be a category. Let $p : \mathcal{S} \to \mathcal{C}$ be a category over $\mathcal{C}$. A strongly cartesian morphism, or more precisely a strongly $\mathcal{C}$-cartesian morphism is a morphism $\varphi : y \to x$ of $\mathcal{S}$ such that for every $z \in \mathop{\mathrm{Ob}}\noli... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18583 | # Properties
Label 3200.2.d.e.1601.1 Level $3200$ Weight $2$ Character 3200.1601 Analytic conductor $25.552$ Analytic rank $0$ Dimension $2$ CM discriminant -4 Inner twists $4$
# Related objects
## Newspace parameters
Level: $$N$$ $$=$$ $$3200 = 2^{7} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\c... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18584 | ## introduction
Added later: there is an Edit near the very end; I removed some silly text.
In this post I want to “finish off” syllogisms. No, this is certainly not the last word on syllogisms, and is almost certainly not my last word on them… but when I pick them up next, it will probably be to look at them using B... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18585 | # MATSUI Tetsushi
Last updated: May 14, 2012 at 17:10
Name MATSUI Tetsushi tetsushinii.ac.jp
## Published Papers
Tetsushi Matsui, Akihiro Higashitani, Yuuki Nagazawa, Hidefumi Ohsugi and Takayuki Hibi
Journal of Algebraic Combinatorics 34(4) 721-749 Dec 2011 [Refereed]
Satoru Tanaka, Naoki Ogura, Ken Nakamula... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18586 | ## week 6 – precalc 11
This week we started a new unit of solving quadratic equations. last week was mostly a review for the harder lessons we had this week. in lesson 3.2 we started by solving quadratic equations by using the zero product law.
$x^2-6x+5=0$
$(x-1)(x-5)$
$x= 1, 5$
Verify :
$5^2-6(5)+5=0$
In les... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18587 | # Square Calculator
Calculate the various properties of square like area, perimeter and diagonal for given values.
Area of square: [ (side)² ]
Enter the length = Area of Square =
Perimeter of square: [ 4(side) ]
Enter the length = Perimeter of Square =
Diagonal of square: [ (side)(sqrt(2)) ]
Enter the length = D... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18588 | # How do you factor y= 3x^5 -6x^2 -27x-18 ?
Mar 11, 2016
$3 {x}^{5} - 6 {x}^{2} - 27 x - 18$
$= 3 \left(x + 1\right) \left(x + 1\right) \left(x - 2\right) \left({x}^{2} + 3\right)$
$= 3 \left(x + 1\right) \left(x + 1\right) \left(x - 2\right) \left(x - \sqrt{3} i\right) \left(x + \sqrt{3} i\right)$
#### Explanatio... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18589 | New Titles | FAQ | Keep Informed | Review Cart | Contact Us Quick Search (Advanced Search ) Browse by Subject General Interest Logic & Foundations Number Theory Algebra & Algebraic Geometry Discrete Math & Combinatorics Analysis Differential Equations Geometry & Topology Probability & Statistics Applications Ma... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18590 | # Total Distance Travelled by a Ball Dropped Comes to Rest
A ball is dropped from a height of $16$ metres onto a timber floor and bounces. After each bounce, the maximum height reached by the ball is $80 \%$ of the previous maximum height. Thus, after it first hits the floor, it reaches a height of $12.8$ metres befor... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18591 | # What does variety language mean?
In Zilber's paper entitled 'a theory of generic function with derivations', he works in the variety language for fields? What does this mean? If I want to define the variety language what can I say?
-
Let $V$ be a varity (can be any definable set actually) in an algebraically close... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22896 | # Math Help - Observed frequencies of transitions in a Markov Chain
1. ## Observed frequencies of transitions in a Markov Chain
Dear Forum,
I came across the following remark in P. Billingsley, "Statistical Inference for Markov Processes", and I wonder whether someone can point me to further information:
"It is pos... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22897 | Browse Questions
# Find $\mu$ variance for the following distribution :
X 0 1 2 3 P(X) 1/8 3/8 3/8 1/8 |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22898 | It is currently 20 Oct 2017, 11:25
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
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we will pick new questions that match your level based on your Ti... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22899 | # Stratified groups
A Lie group $\mathbb{G}=(\mathbb{R}^n, \circ)$ is called a stratified group (or homogeneous Carnot group) if it satisfies the following two conditions:
(1) For some natural numbers $N_1+...+N_r=n$ the decomposition $\mathbb{R}^n = \mathbb{R}^{N_1} \times ... \times \mathbb{R}^{N_r}$ is valid, and... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22900 | College Algebra 7th Edition
$\sum_{k=1}^{100}(-1)^{k+1}* k* x^{k-1}$
We write the sum in sigma notation: (We notice that the terms have the form $(integer)x^{integer-1}$ with consecutive integers and alternating signs.) $1-2x+3x^{2}-4x^{3}+5x^{4}+ \cdots-100x^{99}=\sum_{k=1}^{100}(-1)^{k+1}* k* x^{k-1}$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22901 | # Chapter 10 Quantum algorithms
About quantum interference in disguise: Hadamard, function evaluation, Hadamard. Also about the early quantum algorithms and how they deal with querying oracles, searching for a needle in a haystack, and estimating periodicity of certain functions.
Classical computers essentially evalu... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22902 | # Simple Parallel Plate Capacitor Question
1. Jan 4, 2010
### MassimoHeitor
Assuming a Parallel Plate Capacitor of area A, separation distance d, plate charges $$\pm Q$$: and plate charge densities $$\pm\sigma$$:
In my textbook and in Wikipedia,
Electric Field of a charged plane with large or infinite area: $$\fra... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22903 | # Why distance is area under velocity-time line
## Video transcript
Let's say I have something moving with a constant velocity of five meters per second. And we're just assuming it's moving to the right, just to give us a direction, because this is a vector quantity, so it's moving in that direction right over there.... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22904 | ## On $$S$$-integral solutions of the equation $$y^ m=f(x)$$.(English)Zbl 0552.10009
Let $$K$$ be an algebraic number field with ring of integers $${\mathcal O}_ K$$, let $$f(x)\in {\mathcal O}_ K[X]$$ and suppose $$f(x)=a_ 0\prod^{n}_{i=1}(x-\alpha_ i)^{r_ i}$$ with $$a_ 0\neq 0$$, $$\alpha_ i\neq \alpha_ j$$ for $$i... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22905 | # Product of Complex Numbers in Polar Form/Examples/3 cis 40 x 4 cis 80
## Example of Use of Product of Complex Numbers in Polar Form
$3 \cis 40 \degrees \times 4 \cis 80 \degrees = -6 + 6 \sqrt 3 i$
## Proof
$\ds 3 \cis 40 \degrees \times 4 \cis 80 \degrees$ $=$ $\ds \paren {3 \times 4} \map \cis {40 \degrees + 8... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22906 | ## anonymous one year ago Find the volume of a rectangular prism if the length is x, the width is x*2, and the height is 5x*2 + 4x + 1. Use the formula V = l ⋅ w ⋅ h, where l is length, w is width, and h is height, to find the volume.
1. phi
by x*2 do you mean x^2 (i.e. $$x^2$$ ) ?
2. phi
if so, they want you to mu... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22907 | Q&A
De-mystifying tricks – If $\{x_n\}$ converges, then Cesaro Mean converges.
+0
−2
Exercise 2.3.11 (Cesaro Means). (a) Show if ${x_n}$ is a convergent sequence, then the sequences given by the averages ${\dfrac{x_1 + x_2 + ... + x_n}{n}}$ converges to the same limit.
I rewrote and colored the official solution.
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22908 | For what value of k does the line y = x + k touches the ellipse $$9x^2 + 16y^2$$ = 144.
Solution :
$$\because$$ Equation of ellipse is $$9x^2 + 16y^2$$ = 144 or $$x^2\over 16$$ + $${(y-3)}^2\over 9$$ = 1
comparing this with $$x^2\over a^2$$ + $$y^2\over b^2$$ = 1 then we get $$a^2$$ = 16 and $$b^2$$ = 9
and compari... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22909 | # A doubt in the proof of Frucht's theorem
I am trying to understand the proof of Frucht's theorem which is:
Every finite group is isomorphic to the automorphism group of some simple graph.
The proof (which I am reading from this book) begins as follows: Let $\Gamma=\{g_1,\cdots, g_n\}$ be a group. Consider a direct... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22910 | # Kerodon
$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
Remark 3.3.8.2. We refer the reader to [KLV] for a proof of Theorem 3.3.8.1 which is slightly different from the proof given below (it avoids the use of Kan's $\operatorname{Ex}^{\infty }$-functor by appealing instead to the theory of minimal K... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22911 | # Distance between closed and compact sets.
This question is (1-21)(b) from M. Spivak's Calculus on Manifolds.
Question: If $A$ is closed, $B$ is compact, and $A \cap B = \emptyset$, prove that there is $d > 0$ such that $||y - x|| \geq d$ for all $y \in A$ and $x \in B$.
Now, I interpret this as an instruction to f... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18592 | At a given instant, the positions of a plane at A and a train at B are measured relative to a radar antenna at O. Determine the distance d between A and B at this instant. To solve the problem, formulate a position vector, directed from A to B, and then determine its magnitude..
### Get this answer with Chegg Study
P... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18593 | Courses
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# The slant height of the frustum of a cone is 4cm and the perimeter of its circular ends are 18cm and 6 cm. Find the area of its whole surface and volume.
Last updated date: 20th Mar 2023
Total views: 312k
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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18594 | # How do you find the slope and intercept of 4x = 3y + 6?
Feb 7, 2016
Slope: $\frac{4}{3}$
y-intercept: : $\left(- 2\right)$
x-intercept: $\frac{3}{2}$
#### Explanation:
A linear equation in standard form: $A x + B y = C$
has a slope of $\left(- \frac{A}{B}\right)$
Re-writing $4 x = 3 y + 6$ into standard form:
$\... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18595 | # Talk:Beat (acoustics)
WikiProject Physics / Acoustics (Rated B-class, Mid-importance)
This article is within the scope of WikiProject Physics, a collaborative effort to improve the coverage of Physics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion an... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18596 | # Finding the Normal Equations
A normal curve is a straight line passing through the point where the tangent touches the curve and is perpendicular (at right angles) to the tangent at that point.
The gradient of the tangent to a curve is $m$, then the gradient of the normal is $\displaystyle -\dfrac{1}{m}$, as the pr... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18597 | # July, 2019
## A folding puzzle
Here’s a tweet from @colinthemathmo: Here's another one. Take a square, crease in the halfway mark, fold up a corner - where does the corner go to? What are its coordinates? pic.twitter.com/Bfr0X8ACur — Colin Wright (@ColinTheMathmo) February 12, 2018 I’m not big on origami, but if Co... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18598 | # How to count solutions to a linear Diophantine equation?
I have the following linear Diophantine equation.
$a+5b+20c+50d+100e+200f=300$
I wish to know the number of solutions to this equation with the constraint that $a,b,c,d,e,f \ge 0$.
What algorithms or techniques may I apply to find the number of solutions?
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18599 | If the sum of first two terms of an infinite GP is 1 every term is twice the sum of all the successive terms,
Question:
If the sum of first two terms of an infinite GP is 1 every term is twice the sum of all the successive terms, then its first term is
(a) 1/3
(b) 2/3
(c) 1/4
(d) 3/4
Solution:
(d) $3 / 4$
Let ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18600 | Richardson's iteration introduce a scalar $$\alpha$$ to the update formula:
$$\textbf{x}^{(k+1)} = \textbf{x}^{(k)} + \alpha \textbf{r}^{(k)}$$
And compute $$\alpha$$ by minimizing the spectral radius:
$$min_{\omega}\{\rho(B)\} = min_{\omega}\{\rho(I-\omega A)\}$$
As I,A do not change over the iterations, it might seem... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18601 | # Normal distribution question
1. May 15, 2009
### Gregg
1. The problem statement, all variables and given/known data
3 (a) A sample of 50 washed baking potatoes was selected at random from a large batch.
The weights of the 50 potatoes were found to have a mean of 234 grams and a standard
deviation of 25.1 grams.
C... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18602 | # Doubts about 0.999 being equal to 1
1. Oct 24, 2006
### Dragonfall
If anyone has any further doubts about 0.999... being equal to 1, please direct your attention to today's http://en.wikipedia.org/wiki/0.999..." [Broken].
Last edited by a moderator: May 2, 2017
2. Oct 25, 2006
### Stevedye56
3. Oct 25, 2006
##... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18603 | Debug
# How to find the Area of a Triangle
To find the area of a triangle, use the following formula
The area of a triangle is always half the product of the height and base.
$Area = \frac{1}{2} (base \cdot height)$
#### So which side is the base?
Any side of the triangle can be a base. All that matters is that t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18604 | # Differential equation
1. Nov 1, 2012
### fxo
1. The problem statement, all variables and given/known data
Use L'Hospitals rule to show that $lim x->0 x^a ln(x) = 0$
I don't know how to solve this. I guess the first thing to do is to transform it in some way so that one can use L'Hospitals rule, but I don't know ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18605 | # Simplify -2 1/6. - (-7 1/3 )a) -5 1/6b) -9 3/6c) 9 3/6d) 5 1/6
###### Question:
Simplify -2 1/6. - (-7 1/3 )
a) -5 1/6
b) -9 3/6
c) 9 3/6
d) 5 1/6
### Why does the signal of pain move slower than other signals in the body? why does the nervous system
Why does the signal of pain move slower than other signals in... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18606 | Solving equations involving powers
I have been solving an OS problem in which I came across this equation where I have to find the value of H as in % but I'm not able to solve it fully. This is not a homework, I'm stuck in between and been left maths from quite some time.
3*10^-8/0.8 = H(2*10^-8 + 10^-8) + (1-H) (10^... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18607 | # A A problem in a paper related to Møller energy distribution
#### wLw
https://arxiv.org/abs/gr-qc/0306101
I am now reading this attached paper. But i can not get energy result(2.8), and I calculated it and found it is zero. here is my process: firstly, i use Gauss law and rewrite the (2.6): $E=\frac{1}{8 \pi} \iint... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18736 | # classification of isometries of Euclidean space
any isometry of Euclidean vector space $$\mathbb{R}^3$$ has the form
$$\mathbb{R}^3\ni x\mapsto A\cdot x + b\in\mathbb{R}^3,$$
where $$A\in O(3)$$ is an orthonormal matrix, and $$b\in\mathbb{R}^3$$. However, geometrically there are only a few types of isometries, nam... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18737 | GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 21 Apr 2019, 11:17
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customize... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18738 | # Proportion Testing, which formula o use on TI-84
#### AUcs13
##### New Member
A researcher wishes to estimate the number of households with 2 computers. How large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 2%? A previous study ind... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18739 | # Representation of the symmetric groups
A linear representation of the group $S _ {m}$ over a field $K$. If $\mathop{\rm char} K = 0$, then all finite-dimensional representations of the symmetric groups are completely reducible (cf. Reducible representation) and defined over $\mathbf Q$( in other words, irreducible f... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18740 | ## Convex functionals and partial regularity.(English)Zbl 0658.49005
The authors study the regularity properties of local minimizers u: $${\mathbb{R}}^ n\supset \Omega \to {\mathbb{R}}^ N$$ of the functional $F(u,\Omega):=\int_{\Omega}f(\cdot,u,Du)dx$ with integrand f(x,y,P) convex in P and of growth order $$m\geq 1$$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18741 | # Exercise E9.3 Areas of Parallelograms and Triangles NCERT Solutions Class 9
Go back to 'Areas of Parallelograms and Triangles'
## Question 1
In the given figure, $$E$$ is any point on median $$AD$$ of a $$\Delta ABC$$. Show that ar ($$ABE=$$) ar ($$ACE$$)
### Solution
What is known?
$$E$$ is any point on media... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18742 | # Homework Help: Sufficient Estimator for a Geometric Distribution
1. Jan 12, 2010
### cse63146
1. The problem statement, all variables and given/known data
Let X1,..,Xn be a random sample of size n from a geometric distribution with pmf $$P(x; \theta) = (1-\theta)^x\theta$$. Show that $$Y = \prod X_i$$ is a suffic... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18743 | # NCERT Solutions for Class 12 Maths Chapter 13 Probability Ex 13.3
In this chapter, we provide NCERT Solutions for Class 12 Maths Chapter 13 Probability Ex 13.3 for English medium students, Which will very helpful for every student in their exams. Students can download the latest NCERT Solutions for Class 12 Maths Ch... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18744 | # mole fraction formula
Mole Fraction. Mole fraction = moles of a constituent/sum of moles of all constituents (mass of the mixture) Or. A solution is prepared by mixing 100.0 g of water, H2O, and 100.0 g of ethanol, C2H5OH. To calculate mole fraction of solute you first calculate the moles of the solute and then you ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18745 | Nature of SXDF 850.6
# Unveiling the Nature of Submillimeter Galaxy SXDF 850.6
B. Hatsukade11affiliation: Institute of Astronomy, the University of Tokyo, 2-21-1 Osawa, Mitaka, Tokyo 181-0015, Japan , D. Iono22affiliation: Nobeyama Radio Observatory, Minamimaki, Minamisaku, Nagano 384-1805, Japan , T. Yoshikawa33affi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18746 | Lesson Objectives
• Demonstrate an understanding of Algebraic Expressions
• Demonstrate an understanding of the Multiplicative Inverse Property
• Demonstrate an understanding of the Multiplicative Identity Property
• Learn about the Multiplication Property of Equality
• Learn how to solve an equation using Multiplicati... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18747 | Rating changes for the last round are temporarily rolled back. They will be returned soon. ×
F. Card Game
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
Digital collectible card games have become very popular recently. So Vova decided to try one of these.... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18748 | # How do you write a quadratic function in standard form whose graph passes through points (1,0), (2,4), (0,2)?
Aug 29, 2017
$3 {x}^{2} - 5 x + 2.$
#### Explanation:
Suppose that, the reqd. quadr. fun. is,
$y = f \left(x\right) = a {x}^{2} + b x + c , \left(x \in R\right) \left(a , b , c \in \mathbb{R} , a \ne 0\r... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18749 | ### Calculate change of variance of a set multiplication followed by addition of two different constants
Question Sample Titled 'Calculate change of variance of a set multiplication followed by addition of two different constants'
The variance of a set of numbers is ${49}$. Each number of the set is multiplied by ${1... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18750 | # Tagged: PID
## Problem 724
Let $R$ be a principal ideal domain. Let $a\in R$ be a nonzero, non-unit element. Show that the following are equivalent.
(1) The ideal $(a)$ generated by $a$ is maximal.
(2) The ideal $(a)$ is prime.
(3) The element $a$ is irreducible.
## Problem 535
(a) Prove that every prime ideal o... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18751 | # Mental Math: Finding Square Roots to 1 Decimal Point
I have 2 questions here.
• What is the most effective and easy way of calculating square roots in your head to an accuracy of 1 decimal point? This would need to work with at least two digit, non-perfect squares and would have to be doable mentally.
• How would ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13104 | # Incline plane, two masses, a pulley
1. Sep 10, 2009
### jimz
1. The problem statement, all variables and given/known data
A string through an ideal pulley connects two blocks, one (mass=2m) is on an inclined plane with angle theta to horizontal and coefficient of kinetic friction mu. The other block (mass=m) hangs... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13105 | # Question 7
Algebra Level 5
let $$f:R\rightarrow R$$ be a bijective function and $f'(x)=\dfrac {x^{100}+1}{x^{100}+2}$. If $$f(1)=\alpha$$, then $$(f^{-1})' (\alpha) =?$$
$$\bullet$$ This question is part of the set For the JEE-nius;P
×
Problem Loading...
Note Loading...
Set Loading... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13106 | ## Algebra & Number Theory
### Modular abelian varieties of odd modular degree
Soroosh Yazdani
#### Abstract
We study modular abelian varieties with odd congruence number by examining the cuspidal subgroup of $J0(N)$. We show that the conductor of such abelian varieties must be of a special type. For example, if $N... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13107 | # Building an algorithm to build a satisfiable formula from a valid existential statement
Question:
Given the following signature - $\Sigma := \lbrace R^2, P^2, c\rbrace$ (2 relations and a constant), prove/disprove: There exists an algorithm that given an existential statement $\phi$ builds a formula $\psi$ with no ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13108 | # The Stacks Project
## Tag 01JO
### 25.17. Fibre products of schemes
Here is a review of the general definition, even though we have already shown that fibre products of schemes exist.
Definition 25.17.1. Given morphisms of schemes $f : X \to S$ and $g : Y \to S$ the fibre product is a scheme $X \times_S Y$ togeth... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13109 | # How gradient of a function be perpendicular to the surface?
Suppose we have $$\phi (x,y,z) = c$$ here c is a constant and $$\phi (x,y,z)$$ is a surface . Now we take differential of both sides and say $$d\phi = \nabla \phi . dr$$ =0. Now i say how can i prove this that $$\nabla \phi$$ is perpendicular to dr or the u... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13110 | # How To Explain Expanded Form?
## How To Explain Expanded Form?
Expanded form is a way to write a number by adding the value of its digits. We can use a place value chart to think of the value of a number’s digits.
## How do you explain expanded form to students?
Expanded form is an alternate way for students to w... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13111 | # generalized way of finding minimum value of a function?
$f(x)=\frac{x^{2}-1}{x^{2}+1}$ for every real number for $x$, the minimum value of $f$ is what?
How can I find the minimum value of this function.I only know trial and error method, but it's not a generalized way.
Please tell me a generic way to solve this typ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13112 | An ultranet $x_\lambda$ is frequentely in $Y$ if and only if it is residually too.
Definition
If $$x_\lambda$$ is a net from a directed set $$\Lambda$$ into $$X$$ and if $$Y$$ is a subset of $$X$$ then we say that $$x_\lambda$$ is redisually in $$Y$$ if there exsit $$\lambda_0\in\Lambda$$ such that $$X_\lambda\in Y$$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13113 | Proof of a series $\sum_{n=0}^{\infty} x_n$ is absolutely convergent. [duplicate]
Let $\{x_n\}$ be a given series such that it satisfies the following conditions for all sequence $\{y_n\}$ in real numbers converging to $0$. It is given that the sequence $\{y_n\}$ converges to $0$ and the series $\sum_{n=0}^{\infty} x_... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13114 | # Proving compactness of a set and perfect functions.
Let $X$ and $Y$ Hausdorff spaces and $f:X\rightarrow Y$ a function. Prove that the next sentences are equivalent.
1) $f$ is a perfect function
2) For all $y\in Y$, the set $f^{-1}[\{y\}]$ is closed in $X$ and for all $\mathcal{U}$ open cover of $X$, closed under ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13115 | # 3. Fill in the blanks. (a) (– 8) + _____ = 0 (b) 13 + _____ = 0 (c) 12 + (– 12) = ____ (d) (– 4) + ____ = – 12 (e) ____ – 15 = – 10
a) (– 8) + _____ = 0
Since we know that, $-a +a =0$. Therefore, the blank space should be + 8.
(b) 13 + _____ = 0
The sum is zero. Therefore it should be additive inverse of 13. ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13116 | ## 109.2 An empty limit
This example is due to Waterhouse, see . Let $S$ be an uncountable set. For every finite subset $T \subset S$ consider the set $M_ T$ of injective maps $T \to \mathbf{N}$. For $T \subset T' \subset S$ finite the restriction $M_{T'} \to M_ T$ is surjective. Thus we have an inverse system over th... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13117 | 1. ## proving √q is irrational by contradiction
Let q≥2 be a positive integer. If for all integers a and b, whenever q|ab, q|a or q|b, then √q is irrational.
I know I should do a proof by contradiction so i should assume √q is rational, and that for all integers a and b if q|ab then q|a or q|b.
So since √q is ration... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13118 | ## Mathjax
---
title:
date:
description:
...
libraries:
- mathjax
---
When $a \ne 0$, there are two solutions to $$ax^2 + bx + c = 0$$ and they are
$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13119 | Sparse Recovery Beyond Compressed Sensing: Separable Nonlinear Inverse Problems
Extracting information from nonlinear measurements is a fundamental challenge in data analysis. In this work, we consider separable inverse problems, where the data are modeled as a linear combination of functions that depend nonlinearly o... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4704 | ## Calculus (3rd Edition)
$g$ is discontinuous at $x=1$; it is left-continuous there. $g$ is discontinuous at $x=3 ;$ it is neither left-continuous, nor right-continuous there. $g$ is discontinuous at $x=5$; it is right-continuous there. We have a removable discontinuity at $x=3$.
From the given figure, we have $$\lim... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4705 | # Number theory
1. Euler: For any positive integer $$n$$, $$8n+3$$ can be represented as a sum $8n+3=(2k-1)^2+2p,$where $$k$$ is a positive integer, and $$p$$ is a prime.
This site uses Akismet to reduce spam. Learn how your comment data is processed. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4706 | # How do you simplify 3^(1/2) * 9^(1/3) / 27^(1/4)?
The answer is $\textcolor{red}{{3}^{\frac{5}{12}}}$.
${3}^{\frac{1}{2}} \cdot {9}^{\frac{1}{3}} / {27}^{\frac{1}{4}}$
=${3}^{\frac{1}{2}} \cdot {3}^{\frac{2}{3}} / {3}^{\frac{3}{4}}$
=${3}^{\left(\frac{1}{2} + \frac{2}{3} - \frac{3}{4}\right)}$
=${3}^{\frac{5}{12}}$(... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4707 | # How much old water do I have?
Assume I fill up a 1-liter bottle of water to the brim.
The next day, I empty $\frac 34$th of the bottle, and fill with fresh water until the bottle is full. I shake the bottle thoroughly to mix the water.
The next day, I again empty $\frac 34$th of the bottle and refill with fresh wa... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4708 | American Institute of Mathematical Sciences
November 2020, 25(11): 4189-4210. doi: 10.3934/dcdsb.2020093
Dynamics of a diffusive Leslie-Gower predator-prey model in spatially heterogeneous environment
1 School of Information and statistics, Guangxi University of Finance and Economics, Nanning, Guangxi 530003, Chin... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4709 | • 0 Vote(s) - 0 Average
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Pictures of the Chi-Star JmsNxn Long Time Fellow Posts: 507 Threads: 89 Joined: Dec 2010 05/28/2017, 08:46 PM (This post was last modified: 05/28/2017, 09:38 PM by JmsNxn.) Very pretty pictures. I thought I might add an interesting quip about how to calculate this complex su... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4710 | Wat is the rule?
1. Apr 9, 2010
sulemanasif
wat is the rule?????????????
if all the signs r present in a calculations then which sign we will operate first???? e.g.
5+7-11/22+5-55
2. Apr 9, 2010
Staff: Mentor
Re: wat is the rule?????????????
For the arithmetic operations (+, -, *, /), do them in this order:
1. ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4711 | # Set of All Mappings of Cartesian Product
## Theorem
Let $R$, $S$, and $T$ be sets.
Then:
$R^{S \times T} \sim \paren {R^S}^T$
## Proof
Define the mapping $F: \paren {R^S}^T \to R^{S \times T}$ as follows:
$\map {\map F f} {x, y} = \map {\paren {\map f x} } y$ for all $x \in S , y \in T$.
Suppose $\map F {f_1}... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4712 | # What is the slope of the line shown in the graph?
· 14.10.2021 16:09
29.06.2019 07:30
step-by-step explanation:
since, in the linear regression formula, the slope is the a in the equation y = b + ax ( by comparing it with the general equation of line y = mx + c )
where, $$a = \frac{\sum y \sum x^2 - \sum x\sum ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4713 | # Wikipedia:Reference desk/Mathematics
Welcome to the mathematics reference desk.
Main page: Help searching Wikipedia
How can I get my question answered?
• Provide a short header that gives the general topic of the question.
• Type '~~~~' (that is, four tilde characters) at the end – this signs and dates your contr... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4714 | +0
# Inequality
0
97
1
What interval consists of all u such that neither 2u nor 2u is in the interval (-1,1)?
May 13, 2022
#1
+9461
0
Neither 2u nor 2u doesn't make much sense to me. Please check if that is a typo.
Anyways, if u is a number such that 2u is not in the interval (-1, 1), that means $$2u \leq -1\tex... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4715 | Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
Share
# Mark the Correct Alternative in the Following Question:Suppose a Random Variable X Follows the Binomial Distribution with Parameters N And P, Where 0 < P < 1. - Mathematics
#### Question
Mark the correct alternative in the follow... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4716 | # Talk:Equivalence of Definitions of Riemann Zeta Function
The proof that is currently up, the equivalency of the sum of reciprocal powers and product of reciprocal 1 - prime reciprocal powers definitions of the zeta function, is not just applicable to the function $f(p) = p^{-z} \$, but to any completely multiplicati... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4717 | Question
# Below is given distribution of profit (in Rs.) per day of a shop in a certain town.Calculate median profit of shops.Profit (in Rs.)500 - 10001000 - 15001500 - 20002000 - 25002500 - 30003000 - 35003500 - 4000No. of shops818272120188
A
Rs. 1867
B
Rs. 1967
C
Rs.2167
D
Rs.2567
Solution
## The correct option ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4718 | Published $\text {\text {c.$600$}}$.
Contents
A useful approximate formula for the sine of an acute angle, for which he credited Aryabhata the Elder.
Also known as
The title can be rendered Maha Bhaskariya |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4719 | # parasys.net
Home > Error Propagation > Error Propagation Formula
# Error Propagation Formula
## Contents
If we now have to measure the length of the track, we have a function with two variables. This leads to useful rules for error propagation. When two quantities are multiplied, their relative determinate errors... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_21920 | • Create Account
# Utilizing vectors to move entities in 3D space
Old topic!
Guest, the last post of this topic is over 60 days old and at this point you may not reply in this topic. If you wish to continue this conversation start a new topic.
3 replies to this topic
### #1Henri Korpela Members - Reputation: 1... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_21921 | # Adjoint of a linear operator
1. Dec 11, 2007
### kingwinner
Q) Let V be an inner product space and T:V->V a linear operator. Prove that if T is normal, then T and T* have the same image. (i.e. imT=imT*)
My Attempt:
<T(v),T(v)>
=<T*T(v),v>
=<TT*(v),v>
=<T*(v),T*(v)>
=>||T(v)|| = || T*(v)||
But this doesn't seem ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_21922 | ## Friday, January 29, 2010
### A gift of the heavens.
Aloha kakou,
Sorry for the long delay between posting. I have been quite busy with homework recently, and when done, I don't really feel like doing anything (actually, being truly 'done' is unlikely to happen till Spring Break, at least).
There has been one inte... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_21923 | # Math Help - proving √n is irration (n=square free + integer)
1. ## proving √n is irration (n=square free + integer)
Hi all!
I have to show that √n is irrational, where n is "any square free positive integer". Ive never worked with "Square free" numbers, but I understand the term (no divisor can be a square).
So I ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_21924 | Articles with primary mathematical subject classification: 11B25
Extremal results for random discrete structures
Pages 333-365 by Mathias Schacht | From volume 184-2
On large subsets of $\mathbb{F}_q^n$ with no three-term arithmetic progression
Pages 339-343 by Jordan S. Ellenberg, Dion Gijswijt | From volume 185-1... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_21925 | # Wrong answer on Linear Algebra and Its Applications 4th Ed.
Tags:
1. Aug 20, 2016
### mafagafo
1. The problem statement, all variables and given/known data
3. The attempt at a solution
$$\left[ \begin{array}{cccc} 1 & 0 & 5 & 2 \\ -2 & 1 & -6 & -1 \\ 0 & 2 & 8 & 6 \end{array} \right] \sim \left[ \begin{array}{cc... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_21926 | # Thread: inequality problem and inequalities Help Please!
1. ## inequality problem and inequalities Help Please!
Hello to all friends of the mathhelpforum I'm new in this community. Thank you!
I would like to help me with this exercise, I have to deliver today :
The temperatures in a 24 hour period between -4 ° F ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_21927 | # Thread: Math is a language, if I may, how do you math experts say, I love you, in math?
1. ## Math is a language, if I may, how do you math experts say, I love you, in math?
I have read nth times that math is a language.
Please forgive me, dear math experts here, but how do you say in math:
I love you?
2. ## Re:... |
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