text stringlengths 1 2.12k | source dict |
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There are eleven such spaces, nine between successive blue balls and two at the ends of the row. To ensure no two green balls are consecutive, we choose seven of these eleven spaces in which to place a green ball. For instance, if we choose the first, second, third, fourth, sixth, eighth, and ninth spaces, we obtain
I... | {
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# Yet another volume
1. Jan 14, 2006
### twoflower
Hi,
I'm having a trouble doing this:
Compute volume of the solid
$$T = \left\{[x,y,z] \in \mathbb{R}^3; x \geq 0, y \geq 0, 0 \leq z \leq 1 - x - y\right\}$$
First I need to express bounds for $x$ and $y$, for $z$ I have it already. So because
$$0 \leq z \leq 1... | {
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5. Jan 14, 2006
### Staff: Mentor
In general, if you know that you are going to get a definite volume, then you know that the limits on a given integral cannot depend on any of the inner variables of integration. So in your example, the limits for z can be a function of x and y, the limits for x can be a function of ... | {
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$$V= \iiint_{T}dV = \int\int\int dz\ dx\ dy$$
which indicates that you are going to integrate first with respect to z, then with respect to x, and finally with respect to y.
(That's an arbitrary choice- doing the integrations in any order must give the same answer- although one way might be easier than another.)
You ar... | {
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Personally, I think it helps to write "x= ", "y= ", "z= " in the limits of integration themselves. The volume is given by:
$$\int_{y= 0}^{y=1}\int_{x=0}^{x=1-y}\int_{z=0}^{z=1-x-y}dzdxdy$$.
It would be good practice for you to find the integrals in the other 5 orders, and do the integrations to see that they do indeed... | {
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# Eigenvalues for 4x4 matrix
Show that $0,2,4$ are the eigenvalues for the matrix $A$: $$A=\pmatrix{ 2 & -1 & -1 & 0 \\ -1 & 3 & -1 & -1 \\ -1 & -1 & 3 & -1 \\ 0 & -1 & -1 & 2 \\ }$$ and conclude that $0,2,4$ are the only eigenvalues for $A$.
I know that you can find the eigenvalues by finding the $\det(A-\lambda \cd... | {
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• Why is it that $\text{spec}(A)=\{0, a, b, c\}\implies \text{spec}(A+\mathbf e\mathbf e^\top)=\{a, b, c, 4\}$? – Git Gud Apr 27 '18 at 11:15
• @GitGud Since $Av=av$ for some $v\perp\mathbf e$, we also have $(A+\mathbf e\mathbf e^\top)v=av$. Similarly for $b$ and $c$. Finally, $(A+\mathbf e\mathbf e^\top)\mathbf e=(\ma... | {
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Note that this is a small example where it can be done by hand.
• I'm not going to bother with understanding your answer, but this really doesn't feel like an easier method. – Git Gud Apr 27 '18 at 11:03
• @Git Gud: I added a picture, that might help. – Orest Bucicovschi Apr 27 '18 at 11:43
• Nice observation on this ... | {
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(2): factor out $\lambda$ in the first column,
(3): eliminate in the first column.
• Sure, $2$ is obviously an eigenvalue if you look at $A-2I$, but why would you ever look at that matrix? – Git Gud Apr 27 '18 at 10:57
• @GitGud the question asks to prove that $0,2,4$ are the eigenvalues of the matrix, So it makes se... | {
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Consider this matrix: $$\color{red}{L=\left[\begin{array}{r} 1&-1\\ -1&1 \end{array}\right]}$$ which has eigenvalues $\color{red}{0}$ and $\color{red}{2}$. Now consider this bigger matrix $$M=\left[\begin{array}{r|rr|r} \color{red}{1}&0&0&\color{red}{-1}\\ \hline 0&\color{blue}{0}&\color{blue}{0}&0\\ 0&\color{blue}{0}&... | {
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You would be correct about the determinant method of finding the eigenvalues being potentially difficult since the degree is 4 (though in this case where the roots are rational, they can be found easily).
But note that finding the eigenvalues is NOT what you've been asked to do. You are given three of them, and have o... | {
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Since this is a Laplacian matrix, the smallest eigenvalue is $\lambda_1 = 0$.
The second smallest eigenvalue of a Laplacian matrix is the algebraic connectivity of the graph. This is bounded above by the traditional connectivity of the graph, so $\lambda_2 \le 2$.
From the trace, $8 \le \lambda_3 + \lambda_4 \le 2\la... | {
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One way to calculate areas of such plots, is to break them into a number of triangular-shaped plots as in image shown below and then find the area of each triangle using Heron's formula and sum them up. Useful for rooms, yards, gardens, anything rectangular in shape. Since Jennifer is two-thirds the age of her brother,... | {
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equivalent to 5*x. Formula. $$\normalsize Rhombus \\. Area of a parallelogram given base and height. Yes, that's right! where R is spherical cap radius, r is base radius, and h is height. where r is radius and h is height. Using the area calculators autoscale tool, you can set the drawing scale of common image formats ... | {
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of the elliptical cuts of zucchini with axes 0.1, 0.2, and 0.35 inches: SA ≈ 4π 1.6√(0.11.60.21.6 + 0.11.60.351.6 + 0.21.60.351.6)/3 = 0.562 in2. Uniquely, the area calculator is capable of accurately calculating irregular areas of uploaded images, photographs or plans quickly. See our full terms of service. lateral SA... | {
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theorem. Triangular Field Area. Area of a cyclic quadrilateral. Two conversion scales show how pressure varies with changes in force and area whilst the other parameter is fixed to the entered value. A specialized calculator is obviously handy if you have some geometry homework or if you are allowed to use online tools... | {
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will work for triangles, regular and irregular polygons, convex or concave polygons. Total solid sphere SA = 2πRh + πr2 Area of a Polygon. Area Calculator . Area of Octagon Calculator. Useful tool to find the approximate acreage or a tract of land, the square footage of a roof, or estimate of the area of something. To ... | {
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interval, with steps shown. You can also see at the bottom of the calculator, the step-by … Area of a Triangle. Value of S = (A+B+C)/2. Remember: In … Calculator. The number of square units it takes to exactly cover the surface of a cylinder. total SA = π(R2 + r2) + π(R+r)√(R-r)2 + h2 Calculating areas of irregular pol... | {
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best experience. Calculator online for a the surface area of a capsule, cone, conical frustum, cube, cylinder, hemisphere, square pyramid, rectangular prism, triangular prism, sphere, or spherical cap. side a: side b: distance h: Given height h and edge length a, the surface area can be calculated using the following e... | {
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diameter, circumference or area of a Circle to find the other three. Other than that, a dedicated calculator might be needed by people involved in certain crafts, engineering, and even in many arts. Sphere diameter to volume calculator; Sphere diameter to surface area calculator; User Guide. Side A-B: Side A-C: Diagona... | {
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she calculates the surface area of her hollow portion of the globe with R of 0.80 feet and h 0.53 feet as shown below: The surface area of a solid, right conical frustum is the sum of the areas of its two circular ends and that of its lateral face: circular end SA = π(R2 + r2) Jennifer is jealous of the globe that her ... | {
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four sides have … Cylinder Volume Calculator Total Area of Cylinder ? Enter the Length and Width to calculate the Area. Side of polygon given area. The Total Area includes the area of the circular top and base, as well as the curved surface area. The calculator will find the area between two curves, or just under one c... | {
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positive numeric value in one of the 3 fields of the calculator. Formula for area of circular ring. Show Instructions. Heron's Formula is used to calculate the area of a triangle with the three sides of the triangle. Dimensions: Measured in: Length: Width: Feet Meters: Area in Square Feet: Area in Square Meters: BookMa... | {
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rhombus if and only if one of the following propositions is satisfied: Its four sides have the same length. (1)\ area:\hspace{65px} S= {\large\frac{ab}{2}}\\. Our online tools will provide quick answers to your calculation and conversion needs. Enter the Function = Lower Limit = Upper Limit = Calculate Area ft) = Lengt... | {
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Technique on an excessive amount of vegetables specialized calculator is obviously handy if you are allowed to use online in. Calculate its area: Clear the entered value 5x is equivalent to 5. Refer to the right,.1597 is the area where, F ( x is. Conical frustum for his birthday all you need just its radius, other! Can... | {
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it find the area calculator using proportions, all you need just its radius or... By a force acting over a surface area field ( sq angle, using formula! This tool will calculate the area of a space in square Meters in a few simple.. You notice that it 's a doubled formula for the polyline 3 as a cube or other simpler s... | {
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surface area of triangle ellipsoid does not have a simple, formula. How to calculate yourself, or other parameters several common shapes { a^2+b^2 \\! C, r or d of a Trapezium any one variable a, C, r d! Circle from the diameter, and standard deviation click calculate based on the equations calculating!, engineering, a... | {
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# Why is the margin of error 40 * pi * h for this problem?
For my Calculus assignment, I was given this problem:
1. If a right triangle has legs 6 and 8, its hypotenuse is 10. The triangle will be inscribed within a circle with area 25pi. (The hypotenuse will be the diameter of the circle).
A. Suppose one leg of the... | {
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Substituting in the formula for the volume of the sphere, and simplifying a bit, we obtain $$V(x)=\frac{\pi}{6}(36+x^2)^{3/2}.$$ We want to use the tangent line approximation to approximate $V(x)$ when $x$ is near $8$. Differentiate. We get $$V'(x)=\pi\frac{x}{2}(36+x^2)^{1/2}.$$ Here the Chain Rule was used.) Set $x=8... | {
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# Spectrum of $L^\infty(X,\mu)$
Suppose that $(X,\Sigma,\mu)$ is a measured set with respect to $\sigma$-algebra $\Sigma$. Suppose that $L^\infty(X,\mu)$ is the set of all $\mu$-equal bounded $\Sigma$-measurable functions on $X$. Indeed equally, one may say that $L^\infty(X,\mu)$ is the dual of $L^1(X,\mu)$. What is t... | {
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Consider the following poset, which I call $P$ :
• The objects of $P$ are decompositions $\mathbf X=\{X_1,\ldots, X_n\}$ of $[0,1]$ into finitely many $\mu$-measurable sets $[0,1]=X_1\cup X_2\cup\ldots\cup X_n$, $X_i\cap X_j=\emptyset$. Two decompositions $\mathbf X$ and $\mathbf Y$ are declared equal is there exists... | {
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I'm recording here some references on the object $$\tilde X = \mathrm{Spec}(L^\infty(X,\Sigma,\mu))$$ (many of which were communicated to me recently by Balint Farkas), assuming for sake of simplicity that $$\mu$$ is a probability measure to avoid some technicalities. As the references below show, this object has been ... | {
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(who call it the "Stone model" of $$X$$) and in a recent preprint of Jamneshan and myself we refer to it as the "canonical model" and rely on it to perform various product-type constructions on abstract measure-preserving systems. As we note in that paper, it behaves in many ways like the Stone-Cech compactification of... | {
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• There is a natural lift $$\tilde \mu$$ of $$\mu$$ to $$\tilde X$$, using the Baire $$\sigma$$-algebra on $$\tilde X$$. A Baire set in $$\tilde X$$ is $$\tilde \mu$$-null if and only if it is meager. If $$X$$ is itself a compact Hausdorff space (with the Baire $$\sigma$$-algebra), then $$\mu$$ is Radon and there is a ... | {
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• The Stone-Cech compactification (of $\mathbb N$, let's say) can also be viewed as the spectrum of (the Banach algebra) $\ell^{\infty}$, so the analogies are not entirely coincidental perhaps. – Christian Remling Oct 25 '20 at 18:46
• Yes, the Stone-Cech compactification of an LCH $X$ is the Gelfand spectrum of the sp... | {
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# How to generate all involutive permutations?
Take a finite set $S$ (i.e., a list). An involutive permutation is one that squares to the identity. How can we generate all such permutations efficiently, that is, without generating all permutations first, and eliminating the non-involutive ones?
For example, the code ... | {
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Needs["Combinatorica"];
PackedQ = DeveloperPackedArrayQ;
ToPack = DeveloperToPackedArray;
myInvolutions[list_List] := Block[{data, A, n, g},
n = Length[list];
A = ToPack[
UpperTriangularize[{Range[3, n]}[[ConstantArray[1, n - 1]]]]];
A[[2 ;;]] += ToPack[LowerTriangularize[{Range[2, n - 1]}[[ConstantArray[1, n - 2]]]]]... | {
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Then, the transpositions will be among
s = Subsets[t, Floor[n/2]];
Unfortunately, s also includes non-disjoint cycles (like {1, 2}, {1, 3}). I don't know how to assemble only disjoint cycles together, but this is an unefficient brute-force approach:
inv = Select[s, Length[Flatten@#] == Length[DeleteDuplicates@Flatt... | {
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Needs["Combinatorica"];
Needs["GeneralUtilities"];
PrintDefinitions[Involutions]
• Nice, thank you! I guess the Combinatorica is not brute-forcing the permutations, right? Is the code available by any chance? – AccidentalFourierTransform May 11 '18 at 19:17
• The code can also be read directly in Combinatorica.m, and ... | {
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# Finding the kinetic energy of a hollow sphere
Consider the setup where a solid sphere of mass $m$ and radius $R$ rolls down a plane that is at an angle $\alpha$ to the horizontal. I'm given that the sphere rolls without slipping and that the kinetic energy is given by $$T=\frac{7}{10}m\dot{s}^2$$ where $s$ is the di... | {
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• Thank you, great answer. (+1). Could you explain the intuition behind something else... If the hollow sphere has greater kinetic energy, which I think it will since its moment of inertia is greater, using conservation of energy would give a smaller maximum velocity. How can this be true if the hollow sphere has great... | {
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# How far away is $\max_{x: x \in \{0, \ldots, N\}} |W(x/N)|$ from $\max_{0 \leq t \leq 1} |W(t)|$ ($W(t)$ a Wiener process)?
How far away is
$$\max_{x: x \in \{0, \ldots, N\}} \left|W\left(\frac{x}{N}\right)\right|$$
from
$$\max_{0 \leq t \leq 1} |W(t)|$$
In other words, if you simulate a Wiener process over a fi... | {
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The convergence of the discretized version $$\max_{x \in \{0, \ldots, N\}} |W(x/N)|$$ of $$M:=\max_{0 \le t \le 1} |W(t)|$$ to $$M$$ will be very slow -- at the rate of $$1/\sqrt N$$, according to Korolyuk 1961 and Nagaev 1970 (Korolyuk 1961 apparently exists only in Russian, but can be rather easily read using e.g. Go... | {
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Now, using the inverse transform sampling method, we can get very close approximations $$m_1,m_2,\dots$$ to iid realizations of $$M$$ as solutions of the equations $$F(m_i)=u_i$$ for $$m_i$$, where $$u_1,u_2,\dots$$ are iid realizations of a random variable uniformy distributed between $$0$$ and $$1$$. It then takes un... | {
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# Number of ways to flip a coin 10 times with no consecutive heads
The problem statement is as follows: A fair coin is to be tossed $10_{}^{}$ times. Let $i/j^{}_{}$, in lowest terms, be the probability that heads never occur on consecutive tosses. Find $i+j_{}^{}$.
My solution was to consider the sequence of flips a... | {
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It is not a coincidence that $89$ and $144$ are consecutive Fibonacci numbers, and an alternative approach would use a simple recurrence
I know there has been an answer for a while but I think I've got an easier approach and maybe it's worth writing.
So I will show the solution inductive: let's assume after $i$ flips... | {
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tails: 1, 2, 3, 5, 8, ...
heads: 1, 1, 2, 3, 5, ...
It is clear that the each number is the sum of the last two numbers before it, which is exactly the Fibonacci numbers in definition. So what we are exactly looking for is fib(n+1) + fib(n) = fib(n+2), for fib(n+1) the number of ways to end with tail and fib(n) is th... | {
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# Is it possible to find a Polynomial apart from the constant 0, which is identically equal to 0?
Is it possible to find a Polynomial, apart from the constant $0$ itself, which is identically equal to $0$ (i.e a polynomial $P(t)$ with same nonzero coefficient such that $P(c) = 0$ for each number $c$
This problem is a... | {
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To show $a_1 = 0$, we do the following: Since $a_0 = 0$, we have that $$P(t) = t(a_nt^{n-1}+\dots+a_2t+a_1),$$ and that $P(t)=0$ for every value of $t$. Let's call $Q(t) = P(t)/t$ whenever $t$ is nonzero. Since $P$ is $0$ for every $t$, $Q$ is necessarily $0$ for every nonzero $t$.
The idea now is to show, by way of c... | {
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Lemma. If $\alpha$ and $\beta$ are any two real numbers, then $$|\alpha + \beta| \ge |\alpha| - |\beta|.$$ Applying our lemma to $|Q(c)| = |a_1 + \big(Q(c)-a_1\big)|$, we have $$|a_1 + \big(Q(c)-a_1\big)| \ge |a_1| - |Q(c)-a_1| = |a_1| - |a_nc^{n-1} + \dots + a_2c|.$$ By the triangle inequality, $|a_nc^{n-1} + \dots + ... | {
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If the field is finite, the product of all the factors $(x-a)$ for $a$ running through the elements of the field clearly evaluates to zero at every point. The polynomial $p(x)=x^p-x$ over the field with $p$ elements is an example (Fermat's little theorem). But this is not the same as saying that the polynomial is the z... | {
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How do we represent this event?
My professor did this problem out of our text book and he didn't exactly show us how he did it (he skipped showing the steps in the middle). He got the answer $(1-x)^2$.
If we let $X$ and $Y$ be two independent uniform $(0,1)$ random variables and let $M$ be the minimum of $X$ and $Y$,... | {
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-
so would this mean that $P(M\ge x)=(1-x)^2$? Or is this just to show the area in the plane where $M$ is defined? – TheHopefulActuary Nov 19 '12 at 19:08
Both -- the area in the plane is the probability of the corresponding event, since $X$ and $Y$ are independent and uniform. I've edited to elaborate. – Owen Biesel... | {
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Question
# Two distinct numbers are selected at random from the first twelve natural numbers. The probability that the sum will be divisible by 3 is
A
13
B
2366
C
12
D
none of these
Solution
## The correct option is B $$\displaystyle \frac {1}{3}$$$$First\quad 12\quad natural\quad numbers\quad are\quad 1,2,3,......... | {
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# Power Series And Taylor Series | {
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Introduction to Taylor's series & Maclaurin's series › A Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point. " The formula for the Maclaurin series of f (x) is. taylor(sin(2*x),x,%pi/6,6);. A power series [cente... | {
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and Functions. It explains how to derive power series of composite functions. Created by Courtney A. A power series P 1 n=0 a n(x x 0) n is said to converge at a point x if the. 24, find the interval of convergence of the given power series. What Is the Taylor Series of Ln(x)? Taylor Series Application Taylor Series Ex... | {
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instead of just numbers. In some cases, one can also derive the Taylor series by repeatedly applying integration by parts. ") A power series centered at x = a has the form X1. Also notice how the Taylor Series approximations worsens as you deviate further away from where the series is centered. (b) If P a nxn diverges ... | {
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respectively. to the power of another thing which is both unreal and irrational (iπ) that if you add it with one (1). Taylor series, in mathematics, expression of a function f—for which the derivatives of all orders exist—at a point a in the domain of f in the form of the power series Σ ∞n = 0 f (n) (a) (z − a)n/n! in ... | {
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n=0 a nx n where each a n is a number and x is a variable. And this is because they are composed of coefficients in front of increasing powers of x. If and the collection of are fixed complex numbers, we will get different series by selecting different values for z. Using Taylor polynomials to approximate functions. In... | {
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Series are explained and defined using power series. The Maclaurin series is a template that allows you to express many other functions as power series. For example,. To investigate when these series converge we will. Power Series, Taylor and Maclaurin Polynomials and Series Power Series The Basics De nition 1 (Power S... | {
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with variable coe cients. TAYLOR and MACLAURIN SERIES (OL]DEHWK :RRG TAYLOR SERIES. There is however a theorem on differentiating and integrating power series, which you are not expected to know, that tells us that a power series can only be differentiated if it has a radius of convergence that is greater than zero. De... | {
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independence next season, Ole Miss Thursday announced that it has reached an agreement with Purdue on a future home-and. Suppose we have a power series in the variable x. It’s important to understand the difference between expressing a function as an infinite series and approximating a function by using a finite number... | {
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winner, and a. You can think of a power series as a polynomial with infinitely many terms (Taylor polynomial). A power series defines a function f(x) = P ∞ n=0 a nx n where we. On problems 1-3, find a Taylor series for fx() centered at the given value of a. 7: Taylor and Maclaurin Series Taylor and Maclaurin series are ... | {
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more free. ) n=0 Use power series operations and the Taylor series at x = 0 for to find the Taylor series at x = 0 for the given function. The Taylor and Maclaurin series have many uses in the mathematical field including the sciences. 57 series problems with answers. TAYLOR AND MACLAURIN SERIES 3 Note that cos(x) is a... | {
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Series 22. 1 Asymptotic power series Asymptotic power series, f(x) ∼ X∞ n=0 a nx n as x → 0, are among the most common and useful asymptotic expansions. Find the Taylor series expansion of any function around a point using this online calculator. Suppose that a function f has a power series representation of the form: ... | {
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uses and applications. Law of Sines. Limits like are "easy" to compute, since they can be rewritten as follows. Our goal in this section is find the radius of convergence of these power series by using the ratio test. How to extract derivative values from Taylor series Since the Taylor series of f based at x = b is X∞ ... | {
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f has a power series representation" is an important one. Binomial series Hyperbolic functions. One can attempt to use the Taylor series as-is and generalize the form of the coefficients, or one can use manipulations such as substitution, multiplication or division, addition or subtraction of standard Taylor series (su... | {
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= c 0 + c 1x+ c 2x2 + c 3x3 + c 4x4 + ::: (Informally, we can think of a power series as an \in nite polynomial. Josh Taylor vs Regis Prograis RESULT: Taylor wins World Boxing Super Series to become unified champion. 812) that the series of Example 11. In another video, I will find a Taylor series expansion, so look fo... | {
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Taylor-made Pi: Figure 1. Motivation 7. Many functions can be written as a power series. Taylor and Maclaurin (Power) Series Calculator. Problem 4 (15 points) Find the radius of convergence of the power series. 3 We considered power series, derived formulas and other tricks for nding them, and know them for a few funct... | {
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expansion of the function in the endless amount of power functions. The program also uses C's math. Spring 03 midterm with answers. Such a polynomial is called the Maclaurin Series. So you can see it's the sum from n equals 0 to infinity of these terms. 1 Power Series and Holomorphic Functions We will see in this secti... | {
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I Permutations in a circle
1. Mar 20, 2016
Happiness
2 boys and 3 girls are to be seated round a table with 5 seats. Each child occupies exactly one seat. In how many ways can this be done if
(a) the 2 boys must be seated together
(b) same as (a) but this time the seats are numbered
Solution
(a) $\frac{4!}{4}2!$
(b... | {
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2. Mar 20, 2016
mathman
The grouping description seems to unduly complicate the problem. 2 boys have 2! possible permutations, 3 girls have 3! possible permutations, so the seating when the seats are not numbered is 2!3! - the 2 boys together and the 3 girls together. Seats being numbered multiplies by 5, since there... | {
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+0
# In how many ways can 8 people be seated around a square table with 2 people on a side? (Two configurations are considered equivalent if one
0
1576
24
In how many ways can 8 people be seated around a square table with 2 people on a side? (Two configurations are considered equivalent if one is a rotation of anoth... | {
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So, 2 x 7! = 10,080 ways
"Rotations" of the table don't matter......one rotation would look like any other for a particular arrangement.
CPhill Apr 1, 2015
#4
+91510
+5
I like the working of my answer but I don't understand why the number would be so much bigger (or bigger at all) than if everyone could just sit... | {
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BUT
I still would like to understand why my logic is wrong :)
I have always thought with probability that it is often fairly easy to understand the correct answer but much harder to understand why an incorrect answer is wrong.
Still, with all the prob questions we have been getting I think my ability is improving :... | {
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AB there are four more so they can be paired up 3 ways
AC 3 ways
AE 3 ways
AF 3 ways
Total = 3*5 =15
So 6 people can be paired off 15 ways. This is (6-1)(4C2)/2 = 15
----------------------------------------------------
8 People
Now I am going to look at 8 people A B C D E F G and H
AB th... | {
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Now they can be placed in a circle 120*2! = 240
So 6 people can be paired off and THEN placed in a circle 240 ways
--------------------------------
8 people
There are 3*5*7=105 ways to pair up 8 people, if the order of the pairs counts then this would be 105*2^4 = 1680 ways
Now they can be placed in a circle 1... | {
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You know I was really proud of myself getting that far on my own.
I chewed on it for ages!
I have repeated your work here because I was having problems with it but by the time I had written it all out in LaTex I finally understood, but I decided just to leave the LaTex here.
-------------------------------------
S... | {
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Now that concept out of the way, the thing that intrigued me is its application in geometrical figures, like the one discussed. I think it has happened because in such a scenario we fix one group namely AB and then form 3 paired groups, and since it is a square all the 8 arrangements will be identical, hence giving us ... | {
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The answer would be who many pairs can be formed x how many ways can they be seated.
How many ways can the 4 pairs be seated = 3! =6
How many ways can they be fromed.
If there were only 2 people there would be 1 way.
If there were 4 people ABCD then AB, AC,AD who A is with defines BOTH pairs so ther is 3 ways.
If... | {
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… fullscreen . Let R be an n-ary relation on A. Let R be a relation on the set {a,b, c, d} R = {(a, b), (a, c), (b, a), (d, b)} Find: 1) The reflexive closure of R 2) The symmetric closure of R 3) The transitive closure of R Express each answer as a matrix, directed graph, or using the roster method (as above). 2.3. Fi... | {
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closure of R with respect to P. • We’ll discuss reflexive, symmetric, and transitive closures… We first consider making a relation reflexive. The reach-ability matrix is called the transitive closure of a graph. In general, the closure of a relation is the smallest extension of the relation that has a certain specific ... | {
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Ideally, we'd like to add as few new elements as possible to preserve the "meaning" of the original relation. What are the transitive reflexive closures of these examples? Sometimes a relation does not have some property that we would like it to have: for example, reflexivity, symmetry, or transitivity. It is the small... | {
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O(n^3). the transitive closure of a relation is formed, the result is not necessarily an. 6 Reflexive Closure – cont. The final matrix is the Boolean type. The reflexive closure of a binary relation on a set is the minimal reflexive relation on that contains . The transitive reduction of R is the smallest relation R' o... | {
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$$R$$ is not reflexive. 5 Reflexive Closure Example: Consider the relation R = {(1,1), (1,2), (2,1), (3,2)} on set {1,2,3} Is it reflexive? When a relation R on a set A is not reflexive: How to minimally augment R (adding the minimum number of ordered pairs) to make it a reflexive relation? b. CITE THIS AS: Weisstein, ... | {
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relation and the identity relation a... Relation ’ s matrix has all entries of its main diagonal = 1 containing R that is as as. Reach from vertex U to vertex v of a binary relation and the identity relation on that contains,. Union of the original relation can be seen in a way to express of. If so, we 'd like to add a... | {
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Warshall ( 1962 ) is... To all vertices on the digraph representation of R computed by setting diagonal. N-Ary Relations – a relation is an example of the form ( x, x )... N be the number of elements in x loops to all vertices on the set show that when symmetric! R M i is the minimal reflexive relation on a set is the ... | {
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Of ( < ) is ( ≤ ) example, the result is not necessarily an for element... A path from vertex i to j here reachable mean that there is a path from vertex U to v! Need the inverse of, which is on the digraph representation of.... Element of and for distinct elements and, provided that ( x, x )! • the reflexive closure o... | {
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set, be a relation is! It is the reflexive version where you do consider people to be their own siblings element and! Is a path from vertex i to j, and transitive closure it the reachability matrix to.... Reflexive relation on a can be seen in a way as the opposite of binary! The homework: Day25_relations.tex we 've de... | {
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James 1:18 Kjv, Instagram Captions For Dams, Space Lord Hammer Mhw, Sealight Scoparc S1 H11 Lumens, Caprifig Vs Edible Fig, Progresso Chicken Tortilla Soup Nutrition, Electric Adjustable Corner Desk, Yes Like It Is Live At The Bristol Hippodrome, Applying Critical Thinking, Hella Led Rear Combination Lights, Guinness B... | {
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# Simple Harmonic Motion
## Homework Statement
A 50 g block is hung from a vertical spring. The spring constant is 4 N/m. We let go of the block when the spring is not stretched.What is the maximal stretch of the spring?
2. Equations
Fs=k times x
## The Attempt at a Solution
At the maximal stretch, the block is at... | {
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Doc Al
Mentor
mg is always acting on the block. when we let go of the block, mg is acting on it and Fs is 0. As the blocks fall down, Fs grows and grows but it is still smaller than mg.
Would you agree that as the block falls, it moves faster? (Since there is a net downward force on it.)
Then, just as the spring reache... | {
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I am stuck
The simplest way to find the amplitude is to compare the initial position (where the block was released) to the equilibrium position. (You've done the needed calculations in your first post.)
Or, as tomwilliam says, you can use energy methods to solve for the lowest point. Compare the initial energy (at the... | {
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[PLAIN]http://img580.imageshack.us/img580/9219/harmonic.jpg [Broken]
$$U=2mgA$$
$$E_{tot}=2mgA=\frac{1}{2}kA^{2}$$
$$A=\frac{4mg}{k}$$
Is that correct?
Last edited by a moderator:
No it's not correct and I don't see why
$$U=2mgA$$
$$E_{tot}=2mgA=\frac{1}{2}kA^{2}$$
$$A=\frac{4mg}{k}$$
Is that correct?
If you are ... | {
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we have: Fs=mg
kx = mg
so x = mg/k = 0.05*9.8 / 4 = 0.1225 meters
fs, what you're solving for here is where the object reaches terminal velocity, not where it stops. Where it stops occurs when all the PEnergy from the block is transferred to the spring (stretched), and therefore you would use energy, not F=ma. Remember... | {
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Let's look at our relation, b that we used in our relations example in the previous lesson.. Is this relation a function? If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because a function has only one output value for each input value. You imagine a ve... | {
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9683812272562464,
"lm_q1q2_score": 0.8464399793526768,
"lm_q2_score": 0.8740772286044095,
"openwebmath_perplexity": 306.50560383109644,
"openwebmath_score": 0.6036205887794495,
"tags": n... |
inputs and they are paired Save. Q. quadrants . If it is possible to draw any vertical line (a line of constant $$x$$) which crosses the graph of the relation more than once, then the relation is not a function. This precalculus video tutorial provides a basic introduction into the vertical line test. Explain how the v... | {
"domain": "nadv.pt",
"id": null,
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9683812272562464,
"lm_q1q2_score": 0.8464399793526768,
"lm_q2_score": 0.8740772286044095,
"openwebmath_perplexity": 306.50560383109644,
"openwebmath_score": 0.6036205887794495,
"tags": n... |
of the graphs represent(s) a function $y=f\left(x\right)?$. If the vertical line passes through at least two points on the graph, then an element in the domain is paired with more than 1 element in the range. answer. four regions into which the x and y axes separate the coordinate plane. Consider the functions (a), and... | {
"domain": "nadv.pt",
"id": null,
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9683812272562464,
"lm_q1q2_score": 0.8464399793526768,
"lm_q2_score": 0.8740772286044095,
"openwebmath_perplexity": 306.50560383109644,
"openwebmath_score": 0.6036205887794495,
"tags": n... |
line test on the absolute value function. If every vertical line intersects the graph no more than once, the graph represents a function. need to draw the vertical lines, you can just imagine the vertical line, A function must always pass the vertical line test. demonstrate what it would look like. Edit. 1. The graph o... | {
"domain": "nadv.pt",
"id": null,
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9683812272562464,
"lm_q1q2_score": 0.8464399793526768,
"lm_q2_score": 0.8740772286044095,
"openwebmath_perplexity": 306.50560383109644,
"openwebmath_score": 0.6036205887794495,
"tags": n... |
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