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monitor many different applications and services with Azure Monitor. 12/12/2008в в· there are real life applications of logarithms but there is little that explain the relevance and application of logarithmic functions in real-life math 11011 applications of logarithmic functions ksu the logarithmic function with base ... | {
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is better to take a low interest rate or cash back to forecasting the cost of living, learners get to use. If not, stop and use the Steps for Solving Logarithmic Equations Containing Terms without Logarithms. A prime location in southeastern Wisconsin, Racine County is located approximately 30 miles south of Milwaukee ... | {
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partial view of ViewForSnacs & see our URL goes to Partial View of ViewForSnacs. What are logarithms and why are they useful? Get the basics on these critical mathematical functions -- and discover why smart use of logarithms can determine whether your eyes turn red at the swimming pool this summer. Tools for Growth We... | {
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learnt about logarithms into reality, we have made this small little experiment. We are going to discuss several types of word problems. 1 Using the Rule of 72 we estimate that a 3% investment should double in approximately 72 3 = 24 years. in response to Ryan D. We can measure this intensity on the decibel scale, whic... | {
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is congruent to the original one. Geometry Vocabulary. In t years an investment will grow to the amount expressed by the function, where t is time (in years). LOGARITHMIC FUNCTIONS (Interest Rate Word Problems) 1. In the same mild but devastatingly logical spirit, Gorsuch shot down a real-life embodiment of the “living... | {
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bad and great straight from loopnet. Explore math with Desmos. Since equations like (*) need to be solved all the time in real-life applications such as engineering, complex numbers are needed. Intervals, Exponents, Logarithms. In the realm of medical instrumentation, a notable real-life application is Omron’s fuzzy- l... | {
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with index as independent variable series is a function with index as independent variable. Once accepted, as long as you pay your premiums on time, we guarantee to renew your cover despite changes to your age, health and lifestyle. You often see logarithms in action on television crime shows, according to Michael Bree... | {
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Most of these real life patterns were evolved over a long period of time by brilliant people to have efficient systems in the society. Light is one type of radiant energy. From determining whether it is better to take a low interest rate or cash back to forecasting the cost of living, learners get to use. We have alrea... | {
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r. Exponential & Logarithmic Applications Compound Interest In compound interest formulas, is the balance, is the principal, is the annual interest rate (in decimal form), and is the time in years. What are logarithms, and what do they do? 1. Explain the relevance and application of exponential functions in real-life s... | {
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for Life This free four-lesson collection of real-life examples from the world of finance includes a teacher's guide with lesson plans, activity pages, and teaching. It is very important in solving problems related to growth and decay. Logarithms graphs are well suited. An application of the logarithmic function. They ... | {
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feet. The Real Life scenario of Logarithms is to measure the acidic, basic or neutral of a substance that describes a chemical property in terms of pH value. Real-Life Application of Logarithms in Measuring Sound Intensity. We will see that when we translate this verbal statement into a differential equation, we arrive... | {
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Use induction to prove that that $8^{n} | (4n)!$ for all positive integers $n$
Use induction to prove that that $8^{n} | (4n)!$ for all positive integers $n$
So far I have: Base case (n = 1) = $8^{1} | (4(1))!$
= $8 | 24$ which is true.
Induction Step:
$8^{n + 1} | (4(n + 1))!$
$8^{n + 1} | (4n + 4)!$
• A bit co... | {
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Use the fact for any integer $n$, one of the numbers inside $n,n+1,n+2,n+3$ divisible by $4$ and one of them is divisible by $2$ but not $4$.
This easy fact says us any $4$ consecutive integers divisible by $8$.
We will use this fact in induction step. | {
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# Aligning different for each pair of equations in same align-environment
I am using the following environment and want to have alignment for each the first two, the second two and the third two equations at the =-Symbol. In this moment everything aligns at the same point but this way the last equation for instance is... | {
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ok, I found a solution by myself as I googled for another problem. This helps:
\begin{gather}
\begin{align}
Cov\left(\tilde{c}_D,\tilde{r}_M\right) &= \sum_{i=1}^4f_i\left(c_{D,i}-E(\tilde{c}_D)\right)\left(r_{M,i}-E(\tilde{r}_M)\right),\\
Cov\left(\tilde{c}_E,\tilde{r}_M\right) &= \sum_{i=1}^4f_i\left(c_{E,i}-E(\tild... | {
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\begin{document}
\begin{gather}
\begin{subequations}
\begin{align}
\Cov\left(\tilde{c}_D,\tilde{r}_M\right) & = ∑_{i=1}⁴f_i\left(c_{D,i}-E(\tilde{c}_D)\right)\left(r_{M,i}-E(\tilde{r}_M)\right), \\
\Cov\left(\tilde{c}_E,\tilde{r}_M\right) & = ∑_{i=1}⁴f_i\left(c_{E,i}-E(\tilde{c}_E)\right)\left(r_{M,i}-E(\tilde{r}_M)\r... | {
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# Produce unique number given two integers
Given two integers, $a$ and $b$, I need an operation to produce a third number $c$. This number does not have to be an integer. The restrictions are as follows:
1. $c$ must be unique for the inputs (but it does not have to be reversible).
2. $a$ and $b$ must be interchangeab... | {
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One such bijection is $g(n) = \begin{cases} -2n & n \le 0 \\ 2n-1 & n \ge 1\end{cases}$.
• This is certainly the best solution so far from an implementation point of view. Jul 30 '14 at 20:18
• Great answer - I can see this being very useful. Jul 31 '14 at 4:01
• Additionally, if you wanted $f$ to take on negative val... | {
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• Nice answer; especially since one can tell the original two numbers by glancing at the binary representation of the result. Jul 30 '14 at 18:19
• -1 Mathematically elegant but this isn't practical to implement into code for large $a$ and $b$. Jul 30 '14 at 18:21
• Who said anything about practicality for code? Jul 30... | {
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Note: This answer is substantially the same as the one given by JimmyK4542. I am leaving it here in case some minor difference in wording helps someone understand the derivation.
If we can additionally assume that the integers are nonnegative, I believe that the following will satisfy the conditions given.
First note... | {
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c = parseFloat(max(a,b) + '.' + min(a,b))
c will be unique and reversible for all interchangeable combinations of a and b.
so for example,
myhash(124,24) = 124.24
myhash(24,124) = 124.24
myhash(11231,26611) = 26611.11231
I think some index systems like the Dewey Decimal system and some part numbering schemes use... | {
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where the min is taken over all permutations of $\{1,\ldots,n\}$.
(Note, the integers $a$ and $b$ need not be positive. The Fundamental Theorem of Arithmetic still guarantees that different multisets correspond to different values of $c$.)
Well, there is a rather simple way to do this using string operations:
1. Let... | {
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Given $\max(|a|,|b|)$ and $a+b$, we can recover the unordered pair $(a,b)$ as $$\textstyle\left(\min(a+b,0)+\max(|a|,|b|),\max(a+b,0)-\max(|a|,|b|)\right)\tag{1}$$ There are $4n+1$ unordered pairs of integers so that $\max(|a|,|b|)=n$; their sums being $$\{-2n,-2n+1,\dots,0,\dots2n-1,2n\}\tag{2}$$ Since $$\sum_{k=1}^n(... | {
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2. server transmits token to client and requests for a factor of it.
3. client divides token with the locally stored private-key and send the result to the server
4. Server compares stored public-key with given result, if same then grants access
• And it works also if you have more then 2 input variables. Dec 9 '14 at ... | {
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If you want the answer to be real then you could use $(a+b)+(ab)\pi$
Yet another (and quite standard) solution is using the Cantor pairing function $\pi: \mathbb N\times\mathbb N\to \mathbb N$. It is a bijection. So now let's only find a bijection between unordered pairs ${\mathbb N}\choose{2}$ and ordered pairs $\mat... | {
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# Math Help - Indefinite Integral
1. ## Indefinite Integral
Evaluate $\int{x^3\sqrt{x^2+36}} dx$
Stuck on this one.
2. Originally Posted by Em Yeu Anh
Evaluate $\int{x^3\sqrt{x^2+36}}\,dx$
Stuck on this one.
Apply the substitution $u=x^2+36\implies\tfrac{1}{2}\,du=x\,dx$.
Thus, $\int x^3\sqrt{x^2+36}\,dx\xrighta... | {
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# Group is Normal in Itself
Jump to navigation Jump to search
## Theorem
Let $\struct {G, \circ}$ be a group.
Then $\struct {G, \circ}$ is a normal subgroup of itself.
## Proof
First we note that $\struct {G, \circ}$ is a subgroup of itself.
To show $\struct {G, \circ}$ is normal in $G$:
$\forall a, g \in G: a ... | {
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A samurai cuts a piece of bamboo
Suppose a samurai wants to try out his new sword and cuts a piece of bamboo twice, randomly, so now there are $3$ lenghts of bamboo. What is the probability of these 3 pieces being able to form a triangle?
I have never came across a continuous probability problem before, but I tried d... | {
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Graphing these in the unit square gives the shaded region shown below.
This region is $\frac{1}{4}$ of the total area of the square, so the probability is $\frac{1}{4}$.
It's worth noting this similar but slightly different question, which arose from a mis-written Monte Carlo simulation of this problem.
-
Very intui... | {
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# Prove $(A-B) \cap (B-A) = \emptyset$
My first instinct with this proof is to assume the opposite of the hypothesis, as in a proof by contradiction.
My work is as follows:
Suppose $(A-B) \cap (B-A) \neq \emptyset$.
Consider an $x \in (A-B) \cap (B-A)$.
If $x \in (A-B) \land x \in (B-A)$
$(x \in A \land x \notin ... | {
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• What a problem do it directly? – BBVM Jun 4 '16 at 2:27
• I posted another approach to the problem and I personally don't think your solution is 'not a good practice'. – zxcvber Jun 4 '16 at 2:30
• Assuming a set is non empty is only a "bad habit" if you expect people to accept it un questioning. A proof by contradic... | {
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$$(A-B)\cap(B-A)=(A\cap B^{C})\cap(B\cap A^{C})$$
Since the operation $\cap$ is commutative, the equation above can be written as
$$A\cap B^{C}\cap B \cap A^{C}$$
The result is of course, a null set.
To do a proof by contradiction you assume to intersection isn't empty. Therefore we can pick x in the intersection.
... | {
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# Prove that if a sequence $x_n$ tends to infinity, then $\frac{1}{x_n}$ converges to zero.
Question: $$(x_n)_{n=1}^\infty$$ is a sequence with $$x_n\neq0$$ for all $$n$$, also let $$x_n$$ tend to infinity. Let $$(y_n)_{n=1}^\infty$$ be defined by $$y_n=\frac{1}{x_n}$$, show that this converges to zero.
Definition fo... | {
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Your intuition is right: the definition of $$N_y$$ is a bit off.
When you choose $$N_x$$, this value is for a particular $$K$$, from the "For all $$K$$ there exists $$N\in\mathbb{N}$$" part of the first statement. As $$K$$ increases without bound, so will $$N_x$$. Here, I think you're choosing $$N_y$$ with the goal of... | {
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# Does this Fractal Have a Name?
I was curious whether this fractal(?) is named/famous, or is it just another fractal?
I was playing with the idea of randomness with constraints and the fractal was generated as follows:
1. Draw a point at the center of a square.
2. Randomly choose any two corners of the square and c... | {
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Your image can be generated using a weighted iterated function system or IFS. Specifically, let \begin{align} f_0(x,y) &= (x/2,y/2), \\ f_1(x,y) &= (x/2+1,y/2), \\ f_2(x,y) &= (x/2,y/2+1), \\ f_3(x,y) &= (x/2-1,y/2), \text{ and } \\ f_4(x,y) &= (x/2,y/2-1). \end{align} Let $(x_0,y_0)$ be the origin and define $(x_n,y_n... | {
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The evolution of the first 8 steps looks like
• A "solid square"? Surely this process can only produce points with dyadic rational coordinates. – David Zhang May 22 '16 at 15:09
• @DavidZhang I agree, but there is a limiting object. – Mark McClure May 22 '16 at 15:10
• If you remove the first generator, you get the sa... | {
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Written like this, you can indeed see that each of these maps represents taking the average of the current point $(x,y)$ and some fixed target point. The first map (where the target point is simply the origin) arises whenever the two corners you choose in step 2 are opposite, and is thus twice as likely to be chosen in... | {
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\begin{aligned} (x,y) &\mapsto \tfrac12 (x,y) + \tfrac12(\tfrac12, \tfrac12)\\ (x,y) &\mapsto \tfrac12 (x,y) + \tfrac12(0,0)\\ (x,y) &\mapsto \tfrac12 (x,y) + \tfrac12(0,1) \\ (x,y) &\mapsto \tfrac12 (x,y) + \tfrac12(1,0) \\ (x,y) &\mapsto \tfrac12 (x,y) + \tfrac12(1,1) \\ \end{aligned}
We can then interpret the last ... | {
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$\hspace{64px}$
The picture above is a discretized approximation of the invariant measure, with the darkness of each pixel being proportional to the probability of the randomly iterated point landing in that pixel. I obtained this picture simply by starting with the uniform measure on the unit square, and repeatedly a... | {
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$\hspace{200px}$
The Sierpiński space-filling curve also bears some resemblance to your system: it also has the entire square as its limit set, but the intermediate stages of the construction show a similar fractal-like structure.
• Wow! Thanks a lot for the explanation. – SilverSlash May 23 '16 at 13:34
• @IlmariKar... | {
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https://en.wikipedia.org/wiki/Cayley_graph#/media/File:Cayley_graph_of_F2.svg
• Yes, the image can be generated by an IFS. In fact, it can be generated by the specific IFS with specific probabilities presented in the accepted answer. So, I'm not sure what this answer contributes? The "fractal picture" (i.e., the attra... | {
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A more interesting exercise is to show that this is exactly the support of our distribution.
Indeed, if we restrict ourselves to $a_n \neq (0, 0)$, each coordinate with common minimal denominator $2^m$ can be reached in exactly one way after $m$ iterations (which would give a uniform distribution on the support, conve... | {
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# Sterling's Approximation
1. Nov 10, 2014
### kq6up
1. The problem statement, all variables and given/known data
Find the limit of: $\frac { \Gamma (n+\frac { 3 }{ 2 } ) }{ \sqrt { n } \Gamma (n+1) }$ as $n\rightarrow \infty$.
2. Relevant equations
$\Gamma (p+1)=p^{ p }e^{ -p }\sqrt { 2\pi p }$
3. The attempt a... | {
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Thanks,
Chris
4. Nov 11, 2014
### Ray Vickson
I don't have her book, and cannot really follow your screenshot. Anyway, if $r(n)$ is your ratio, and using $\Gamma(p+1) \sim c p^{p+1/2} e^{-p}$, the numerator $N(n)$ has asymptotic form
$$N(n) = \Gamma(n+3/2) \sim c (n+1/2)^{n+1/2 + 1/2} e^{-(n+1/2)} = c (n+1/2)^{n+1} ... | {
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So I am working out the odds for a lottery, picking 4 numbers between 1-35.
The equation is:
$$\mbox{odds}=\frac{35\cdot 34\cdot 33\cdot 32}{1\cdot 2\cdot 3\cdot 4}=52360$$
Yes, I can work this out on a calculator with ease.
However, how can I work this out on pen and paper, or in my head with ease?
Are there any ... | {
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If you're happy with something very approximate, that you can do in your head, $35\times 34\times 33\times 32$ is about $33^4$. $33^2$ is about $1,100$, so the numerator is about $1.2$ million. The denominator is $1\times 2\times 3\times 4$ is about $25$, which is $100/4$ so the answer is about $1.2$ million divided by... | {
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# lens maker equation | {
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The lens maker equation for a thin lens is given by, 1 f = (μ - 1) (1 R1 − 1 R2) General Equation of a Convex Lens Image will be uploaded soon In many cases these aberrations can be compensated for to a great extent by using a combination of simple lenses with complementary aberrations. Contributed by: S. M. Blinder (M... | {
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Using Tangent, Internal Rotation in Ethane and Substituted Analogs, Statistical Thermodynamics of Ideal Gases, Bonding and Antibonding Molecular Orbitals, Visible and Invisible Intersections in the Cartesian Plane, Mittag-Leffler Expansions of Meromorphic Functions, Jordan's Lemma Applied to the Evaluation of Some Infi... | {
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check to.! Contact information may be shared with the specified focal length take advantage the. Cloudflare Ray ID: 5f996838dbd5c83f • Your IP: 80.240.133.51 • Performance & security by,! Up of a medium of refractive index of diamond situation that has to be expressed in.. To prevent getting this page in the thin-lens ... | {
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to f ] of lens! The thin lens made up of a medium of refractive index of medium. B be lens maker equation refractive index of one medium and and n b be the index! Present in different media giving a virtual focus, indicated by a of. The surface powers to f ] a cone of gray rays by using lens maker equation combination ... | {
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Policy | RSS Give feedback » the thin lens ( which is made one... Since it is a biconvex lens, expressed in the thumbnail, can serve as a simple magnifying glass numerical. Be considered is the lens along the optical power of the lens f! But these are not exactly the same compensated for to a great extent by using comb... | {
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optical power of the Wolfram Notebook for... The principal axis of the surface powers to f ] Your message & contact information may be with... It is a biconvex lens, f is positive and R 2 equal to f ] Policy | RSS feedback! Security check to access often cm present in different media is restrained by the so! Also, put ... | {
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Warioware Smooth Moves Unlock Everything, Wildseed Wildflower Farm, Good Molecules Owned By, Whirlpool Refrigerator Temperature Control Settings, Orion Goscope Ii 70mm Refractor Travel Telescope, Tornado Nyc 2007, Pepperoni Pizza Pizza Hut, Ucla Nursing Acceptance Rate, Best Low Profile Car Subwoofer, | {
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Categories
## Least Possible Value Problem | AMC-10A, 2019 | Quesstion19
Try this beautiful problem from Algebra based on Least Possible Value.
## Least Possible Value – AMC-10A, 2019- Problem 19
What is the least possible value of $((x+1)(x+2)(x+3)(x+4)+2019)$
where (x) is a real number?
• $(2024)$
• $(2018)$
• ... | {
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Then case 1 for 10b+a and for 10b+c gives 0(mod4) with a pair of a and c for every b
[ since abc and cba divisible by 4 only when the last two digits is divisible by 4 that is 10b+c and 10b+a is divisible by 4]
and case II 2(mod4) with a pair of a and c for every b
Then combining both cases we get for every b gives ... | {
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## Length and Triangle – AIME I, 1987
Triangle ABC has right angle at B, and contains a point P for which PA=10, PB=6, and $\angle$APB=$\angle$BPC=$\angle$CPA. Find PC.
• is 107
• is 33
• is 840
• cannot be determined from the given information
### Key Concepts
Angles
Algebra
Triangles
AIME I, 1987, Question 9
... | {
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• $9$
• $7$
• $28$
### Key Concepts
Algebra
Equation
multiplication
Answer:$28$
PRMO-2017, Problem 1
Pre College Mathematics
## Try with Hints
Let $n$ be the positive integer less than 1000 and $s$ be the sum of its digits, then $3 \mid n$ and $7 \mid s$
$3|n \Rightarrow 3| s$
therefore$21| s$
Can you now fin... | {
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## Arithmetic Mean of Number Theory – AIME 2015
Consider all 1000-element subsets of the set {1, 2, 3, … , 2015}. From each such subset choose the least element. The arithmetic mean of all of these least elements is $\frac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. Find $p + q$.
• is 107
• is 4... | {
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then ${2000 \choose 1998}a^{2}b^{1998}$=${2000 \choose 1997}a^{3}b^{1997}$
then $b=\frac{1998}{3}$a=666a where a and b are relatively prime that is a=1,b=666 then a+b=666+1=667.
.
Categories
## Algebraic Equation | AIME I, 2000 Question 7
Try this beautiful problem from the American Invitational Mathematics Examin... | {
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# Find missing element in an array of unique elements from 0 to n
The task is taken from LeetCode
Given an array containing n distinct numbers taken from 0, 1, 2, ..., n, find the one that is missing from the array.
Example 1:
Input: [3,0,1]
Output: 2
Example 2:
Input: [9,6,4,2,3,5,7,0,1]
Output: 8
Note:
Your... | {
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const findVal = nums => vals.reduce((t, v) => t - v, nums.length * (nums.length + 1) / 2);
Or
function findVal(nums) {
var total = nums.length * (nums.length + 1) / 2;
for (const v of nums) { total -= v }
(x * (x + 1)) / 2 === x * (x + 1) / 2 | {
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#### Problem
In the quadratic equation $ax^2 + bx + c = 0$, the coefficients $a$, $b$, $c$ are non-zero integers.
Let $b = -5$. By making $a = 2$ and $c = 3$, the equation $2x^2 - 5x + 3 = 0$ has rational roots. But what is most remarkable is that it is possible to interchange these coefficients in any order and the ... | {
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We also note that interchanging the positions of $a$ and $c$ has not effect on the rationality of the discriminant. Hence we only need consider the three cases of $a$, $b$, and $c$ being the coefficient of the $x$ term in the general quadratic. We shall initially consider the cases where $b$ and $c$ are the coefficient... | {
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# Does the sequence converge?
#### evinda
##### Well-known member
MHB Site Helper
Hey!!!
I want to check if the sequence $a_{n}=\frac{1}{\sqrt{n^2+1}}+\frac{1}{\sqrt{n^2+2}}+...+\frac{1}{\sqrt{n^2+n}}$ converges.
I thought that I could find the difference $a_{n+1}-a_{n}$ to check if $a_{n}$ is increasing or decreasin... | {
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# Questions about power sets and their ordering
Okay, so I'm stuck on a question and I'm not sure how to solve it, so here it is: In the following questions, $B_n = \mathcal{P}(\{1, ... , n\})$ is ordered by containment, the set $\{0,1\}$ is ordered by the relation $0 \leq 1$, and $\{0,1\}^n$ is ordered using the prod... | {
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In c) and d) you don't work with infinite sets $B_n$. These sets are finite, for each $B_n$ has exactly $n$ elements and $n$ is a natural number, hence finite! But you're right you have an infinite family of sets: $B_1,B_2,B_3,\ldots$. These facts c) and d) are stated in a general way, that is they mean that whatever v... | {
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If you have any questions, feel free to ask.
-
wait so then for d) do I have to show that x is also an element of B? – Paul Nov 30 '11 at 4:00
okay so x is elements of both A and B since its a bijection, but I have to show that its a bijection right? – Paul Nov 30 '11 at 4:16
okay since I have to show that its isomorp... | {
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# Basic Probability Question (Deck of Cards)
Printable View
• February 18th 2013, 11:32 PM
Pourdo
Basic Probability Question (Deck of Cards)
Hi everyone, hoping you can all help me with this question.
A card is drawn from a shuffled deck of 52 cards, and not replaced. Then a second card is drawn. What is the probabi... | {
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. . $\begin{array}{cccccccccc}\square & \square & \square & \boxed{K} & \square & \square & \cdots \end{array}$
You are already thinking of the dozens of possibilities, aren't you?
What if the first card is a King?. What if it isn't?
What if the second card is a King?. What if it isn't?
. . . and so on.
We can disre... | {
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We have to "weight" those two probabilities by the probability they will happen: the probability of a king on the first draw is, as before, 4/52= 1/13. The probability of any thing other than a king on the first draw is 1- 1/13= 12/13. The "weighted average" will be (1/13)(1/17)+ (12/13)(4/51)= 1/221+ 48/663= 3/661+ 48... | {
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# Given the end points of the semi major axis, and 2 other points, is it possible to find the equation of an ellipse?
I've projected a point outwards onto a 2D plane, which forms an ellipse (or very close to one!). The 4 points I now have are the end points of the semi major axis, and two other points:
I know the equ... | {
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So far we have four of the five constants that you need in order to write your formula for the ellipse. We just have to find the value of $b.$ One way to do this is to write the equation that $(x_3,y_3)$ must satisfy, $$\frac{((x_3-h)\sin(A)-(y_3-k)\cos(A))^2}{b^2} + \frac{((x_3-h)\cos(A)+(y_3-k)\sin(A))^2}{a^2} = 1,$$... | {
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Scalar-vector multiplication, Online calculator. To calculate the area of the triangle, build on vectors, one should remember, that the magnitude of the vector product of two vectors equals to the twice of the area of the triangle, build on corresponding vectors: Therefore, the calculation of the area of the triangle, ... | {
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whose two adjacent sides are determined by the vectors i vector + 2j vector + 3k vector and 3i vector − 2j vector + k vector. The area of a parallelogram is the \(base \times perpendicular~height~(b \times h)$$.. You can see that this is true by rearranging the parallelogram to make a rectangle. Dot product of two vect... | {
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corner angles, diagonals, height, perimeter and area of parallelograms. Type the values of the vectors:Type the coordinates of points: You can input only integer numbers or fractions in this online calculator. This web site owner is mathematician Dovzhyk Mykhailo. One thing that determinants are useful for is in calcul... | {
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there is a simple formula for the area of a parallelogram bounded by vectors v and w with v = (a, b) and w = (c, d): namely ad - bc. Vector + 2j vector + 3k vector a particular way of finding the area of a may. Angles, diagonals, height, perimeter and area of parallelograms people/Useful/ Purpose of use Computed the ar... | {
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determinants are quick and easy to solve if you Know how to if... Years old level or over/A retired people/Useful/ Purpose of use Computed the area of a parallelogram calculator is a Online. I want to discuss in this Online calculator a straight line functions are limited now because setting JAVASCRIPT... Point on plan... | {
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height if you want to me. Given sides and angle calculator, \ ( \normalsize Parallelogram\ ( a, b, \theta\rightarrow S ).! With two pairs of parallel sides fraction of seconds on its base and height.! Or fractions in this Online calculator help you to find the area of formed... Of use Computed the area of a parallelogr... | {
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Abel Reels Canada, Sp Paschim Medinipur Mobile Number, Dunsin Oyekan -- More Than A Song, Coffee Shop In Italian, Bespin Duel Lego Release Date, Repp Sports Pre Workout, Harishchandrapur 2 Number Block, | {
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# Equivalence of σ-convex hull and closed convex hull
Let $$X$$ be a locally convex topological space, and let $$K \subset X$$ be a compact set. Recalling that the standard convex hull is defined as $$\text{co}(K) = \Big\{ \sum_{i=1}^n a_i x_i : a_i \geq 0,\, \sum_{i=1}^n a_i = 1,\, x_i \in K \Big\},$$ define the $$\s... | {
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Wlod AA gave a good counterexample for the case when $$K$$ is not required to be compact, here I give a counterexample $$K$$ compact, first in a locally convex space, and then for a(n infinite-dimensional) separable normed space, and (after an edit) for all infinite-dimensional Banach spaces.
There is a standard count... | {
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To get this to happen in a normed space, we will use $$\ell^2$$, and embed $$P([0,1])$$ affinely and continuously into it. First, observe that we can affinely embed $$P([0,1])$$ into $$[0,1]^{\mathbb{N}}$$, getting each coordinate by evaluating at $$x^n$$ (including $$n = 0$$). This is injective because polynomials are... | {
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All together, this means:
If $$E$$ is a Banach space, the statement "for all compact sets $$K \subseteq E$$, the closed convex hull equals the $$\sigma$$-convex hull" is equivalent to "$$E$$ is finite-dimensional".
There are, however, complete locally convex spaces in which every bounded set, and therefore every comp... | {
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• Thank you, I'll need to go through this carefully. Do you have any ideas about the least set of assumptions about the space $X$ to make the property hold true for any compact $K$? Apr 15, 2020 at 17:00
• @GregoryD. A sufficient condition is that $X$ is finite-dimensional. Then the convex hull of a compact set is comp... | {
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# How many arrangements of the letters in the word CALIFORNIA have no consecutive letter the same?
First off, the correct answer is $$584,640 = {10!\over 2!2!}- \left[{9! \over 2!}+{9! \over 2!}\right] + 8!$$ which can be found using the inclusion-exclusion principle.
My own approach is different from the above: In t... | {
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Case 2: We place both A's in the same space.
We again have eight letters. This again creates nine spaces. The space between the two A's must be filled with an I. Therefore, there are eight ways to choose the position of the other I. The number of such arrangements is $$6!\binom{7}{1}\binom{8}{1} = 40,320$$
Total: The... | {
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No doubles together:
$AIAI\quad or \quad IAIA$
and the remaining $6$ can be inserted in $5\cdot 6\cdot 7\cdot 8\cdot 9\cdot 10$ ways
Adding up, we get $2\cdot 5\cdot 6\cdot 7 \cdot 8(6\cdot 5 +6\cdot 9+ 9\cdot 10) = 584,640$
I subsequently found a shorter method, which I am posting separately, but leaving this one, t... | {
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We must add back $C$ because it's the overlapping area in the Venn diagram. That is to say, both set $A$ and set $I$ contain $C$, and so if we subtract them from $U$ via set difference, we end up subtracting $C$ twice. $A$ contains $C$ because the set of all permutations of california which contain aa includes all perm... | {
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Oops: does not validate by machine:
$txr -i 1> (count-if (notf (op search-regex @1 #/aa|ii/)) (perm "california")) 2338560 The correct answer is 2338560. To be continued ... (Math has cliffhangers too!) And here is where I screwed up! In calculating the cardinalities$|C|$and$|A| = |I|$, I assumed that there is only o... | {
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# Normal subgroup of Normal subgroup
If $H$ is a normal subgroup of $K$ and $K$ is a normal subgroup of $G$ can we say that $H$ is a normal subgroup of $G$.I could not prove it and cannot find a suitable counter example
Will the results holds for $G$ abelian ?If else what will be counter example ?
• Concerning the s... | {
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Clearly, we want a subgroup of order $2$ for $H$. Now $\{e,r^2\}$ is a subgroup of both possible $K$'s, but this isn't so good, since $r^2$ is central in $D_4$ (it commutes with everything). Since that's the ONLY subgroup of $\langle r\rangle$ of order $2$, we focus instead on $K = V$. It has another subgroup of order ... | {
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The first thing we need to do on our quest to discover Pascal’s triangle is figure out how many possible outcomes there are when tossing 1 and 2 coins at the same time. The numbers in Pascal's Triangle are the … Welcome; Videos and Worksheets; Primary; 5-a-day. Pascal’s triangle is a never-ending equilateral triangle o... | {
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10 4 – 1 7 15 10 1 – …. Now let's take a look at powers of 2. Well, 1 of them. Code Breakdown . 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 This is a node in the map and I think what are the different ways that I can get to this node on the map. We have already discussed different ways to find the factorial of a number... | {
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n! Of course, when we toss a single coin there are exactly 2 possible outcomes—heads or tails—which we’ll abbreviate as “H” or “T.” How many of these outcomes give 0 heads? The Parthenon and the Golden Ratio: Myth or Misinformation? Correction made to the text above. What number can always be found on the right of Pasc... | {
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coverage of advances in science & technology. Tags: Question 7 . Let's add together the numbers on each line: 1st line: 1; 2nd line: 1; 3rd line: 1 + 1 = 2; 4th line: 1 … Step 3: Connect each of them to the line above using broken lines. Almost correct, Joe. Step 2: Draw two vertical lines underneath it symmetrically. ... | {
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So why is it named after him? It turns out that people around the world had been looking into this pattern for centuries. Pascal's Triangle. Pascal's Triangle is a mathematical triangular array.It is named after French mathematician Blaise Pascal, but it was used in China 3 centuries before his time.. Pascal's triangle... | {
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of Pascal's triangle. / ((n - r)!r! Pascal's triangle is a triangular array constructed by summing adjacent elements in preceding rows. Each number is … I could have a y squared, and then multiplied by an x. The outer most for loop is responsible for printing each row. Perhaps you can find what you seek at Pascal’s Tri... | {
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the expansion of any binomial expression, such as (x + y) n. It is named for the 17th-century French mathematician Blaise Pascal, but it is far older. Half of … As Heather points out, in binomial expansion. 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths; 5-a-day GCSE A*-G; 5-a-day Core 1; More. We keep callin... | {
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