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Questions tagged [arithmetic]

Questions on basic arithmetic involving numerical quantities only. Questions involving variable values (other than the result of the operation) should be placed under the (algebra-precalculus) tag.

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1answer
26 views

How can I properly force this “object” to follow the indicated path

I'm working with drones and I want them to follow a path. This is the current behavior (black is the path, red is the drone): As you can see, it goes to the destination point (C), but it doesn't ...
2
votes
2answers
74 views

Plurality of arithmetics? Or absoluteness of arithmetical truths? (i. e. Are all mathematical truths actually conditional?)

The following assertion is attributed to Russell ( as a quote from Mysticism and logic) : Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is ...
1
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2answers
34 views

How to calculate the complex fractional values with sum of numbers and letters in an equation

Below is the equation. Not sure if I am doing the right thing but i can't seems to get the right value. $$ \mathbf{1.6\over 121.8} = \frac { \mathbf{15\over M}} {\frac{15} M + {250\over 78} } $$ ...
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1answer
18 views

How to calculate overall ratings

I have three values total ratings so far for example(4/5) total trips so far rating for this trip and now I have to mingle 2 value to the 1 value , and output of the values should be x/5
1
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1answer
19 views

How to transform a fraction into the integer that is in the denominator?

Suppose I have a function that has transformed a sequence of integers like so: $$ f(n) = \log_{10}\frac{1}{n} $$ I then want to convert those numbers back to $n$. I understand that I first must take ...
3
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2answers
38 views

Countability of a subset of sequences

Let $\mathcal{A} = \{a \in \{1,2,3,4,5\}^\Bbb N : |a_i- a_{i+1}| = 1 \; \forall i\}.$ Is the set $\mathcal{A}$ countable? I tried an argument like Cantor's diagonalization process but without success....
0
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1answer
26 views

information theory find g(12)

i want to know how can i find g(12), is there a way beside trial and error way ? i know i can find g(n) that differ 1 bit from 1110 since it satisfy d(g(n), g(n+1))=1 such as 1010,1111,0110,1100 ...
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0answers
31 views

A prime $p$ doesn't divide $\dbinom{p^am}{p^a}$ [duplicate]

Let $p$ be a prime, and $(a,m)\in{\Bbb{N}^2}$ with $\gcd(p,m)=1$. Then $p$ doesn't divide $\dbinom{p^am}{p^a}$. I need this to prove the existence Sylow theorem. I don't really know how to proceed.
1
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1answer
19 views

Prove that all terms in an arithmetical equations are equals with border conditions

Would it be possible to prove that there is an equation that includes a number N of unknown numbers that are all equal, between 0 and 1 and whose sum is equal to 1 ? And to find this equation ? I ...
1
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1answer
49 views

Pigeonhole principle, $20$ translators and $18$ languages.

I stuck with the following problem, which I think is relevant with pigeonhole principle. Problem. There are $20$ translators and $18$ languages. It is known that for every given language there ...
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0answers
28 views

Confusion in cost-benefit analysis in research paper

I am quoting a research paper, “...in control ex ante analyses, the impacts of air pollution are based on hypothetical future clean air, the benefits consist of the value of potential ...
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1answer
33 views

Simple cost-benefit analysis

I am stuck at a very simple problem: Suppose, I am running out of insurance, and as a result, I am incurring a the cost of A with event 1 + the cost of B with event 2. Now, I go ahead and buy an ...
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1answer
72 views

What is 4 divided by 6? [closed]

I had some difficulty , with this problem in class yesterday. I don't know where to begin with. Thanks
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1answer
31 views

Need help with a GMAT applied arithmetic question - please explain

I just don't understand the following question nor the answer. Can someone help me make sense as to what it's actually asking? Many thanks in advance. GMAT Princeton Review 2019 Edition Drill 8 (...
2
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1answer
62 views

How to find the value of x?

I was trying to find the value of X for an hour now but don't know how to start and I don't know why A= 42.9cm2. I mean wasn't A supposed to be 16.5cm2. Thank you in advance.
2
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2answers
36 views

Simplifying fractional surds

I have this fractional surd: $$\frac{5\sqrt{7}+4\sqrt{2}}{3\sqrt{7}+5\sqrt{2}}$$ I can calculate this with a calculator fairly easily obviously but what is the best tactic without one? Thank you!
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1answer
25 views

Proof of $LCM(a,b)=\prod_{i=1}^{\infty}p_i^{\max(\alpha_i,\beta_i)}$

For $a,b\in\mathbb{N}$ with prime factorization $a=\prod_{i=1}^{\infty}p_i^{\alpha_i}, b=\prod_{i=1}^{\infty}p_i^{\beta_i}$ with $\alpha_i,\beta_i\in\mathbb{N}_0$ prove: $$LCM(a,b)=\prod_{i=1}^{\infty}...
1
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3answers
75 views

What is the meaning of multiplying on both sides? [duplicate]

If $5 \not= 6 \implies (5×2) \not = (6×2)$ This is true. But, $(5×0) \not = (6×0)$ which is false. How this contradiction arises? What basic operation we ...
1
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4answers
59 views

How to prove this basic fact : $(a) (-1) = -a$ . How to prove that an additive inverse can be expressed multiplicatively?

As an exercise I try to prove this inequality principle : the sense of an inequality is reversed if each side is multiplied by the same negative number. In steps $(2)$ and $(4)$ of the proof ( below)...
2
votes
1answer
27 views

How to find position of two endpoints given a distance to travel?

Let's say I walking on the number line starting from 0 to 5. When I reach 5, If there still distance I need to travel, I go the reverse direction, walking from 5 to 0. Examples: Given 3 units of ...
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1answer
29 views

What percentage should be removed? [closed]

The price in the shop is $ 20 by how much % you how to reduce the price to get 15 So 20= to 100%. if you take away 20 from 15 you get 5 So if you take 100-5 =95 So is it 95% if it is wrong explain ...
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0answers
52 views

Problem with taking the xth root of both sides.

An equation like $x^x = 2$, I can see why it's tempting to take the xth root of both sides. But isn't there a major problem with that? You are supposed to take the +/- root if the root is an even ...
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4answers
38 views

Sum of “intertwine” of Arithmetic & Geometric Series (to infinity)

I am just wondering is there any method to evaluate the following: $$ 2\cdot (1/2) + 3\cdot (1/4) + 4\cdot (1/8) + 5\cdot (1/16) + \ldots =\sum_{n=2}^\infty \frac{n}{2^{n-1}} $$ Frankly, I have no ...
1
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1answer
29 views

What is the process/algorithm for extracting the nth root of x (x and n are integers)?

What is the process for determining $\sqrt[n]{x}$, where n and x are both positive integers? I have seen algorithms for specific cases. n = 2, there is an extraction method where you group the digits ...
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1answer
45 views

help on an arithmetic exercise [closed]

Let $p$ a prime number of the form $p = 4k + 1$ for $k \in \mathbb{N}$ and let $a \in \mathbb{N}$ be such that $a^2 + 1$ is a multiple of $p$. We denote $r$ the integer part of the number $\sqrt{...
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1answer
38 views

An intermediate Arithmetic exercise [closed]

Deduce that if $p$ is a prime number of the form $(4k + 1)$ for $(k ∈N),$ then there exists $a ∈ N$ such that $(a² + 1)$ is a multiple of $p$.
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0answers
18 views

Maximize quasi - dot product

I have to lists of e.g. $10$ integers from certain range let's say $[0,50]$, I want to maximize a value of a sum of multiplication of pairs of values from those lists. I am allowed to multiply two ...
0
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2answers
58 views

$10x+7\equiv 2$ mod 25

$10x+7\equiv 2$ mod 25 Solve for x, Correct answer is 2,7,12,17,22 What method can we use to solve this problem? I tried and got this far: $10x+7\equiv 2$ mod 25 $10 x + 7 = 2 + 25n$ $10x + 5 ...
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1answer
16 views

Proving inequality equivalence using propositional logic: stuck with redundancy at the end of the proof + circularity problem

I would like to prove formally that : ~ ( a is less than b or equal to b) is equivalent to ( a is strictly greater than b ). But I cannot get rid of a redundant conjoint at the end of the proof. ...
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4answers
26 views

Why does this log simplify to this?

I was answering a question on integrating a log, but I don't understand one part: Why does $e^{1-ln4}$ simplify to $e^1/e^{ln4}$?
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2answers
28 views

Cumulative Percentage Loss

I wondered if anybody knew how to calculate a percentage loss/gain of a process over time? Suppose for example Factory A conducted activity over 6 periods. In t-5, utilisation of resources was: 80% ...
1
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3answers
67 views

How to get an accurate result in the following problem?

I just wanted to know simple how many percent 1.7 is smaller than 1.9 (and vice versa). What I did is: $\frac{1.7\cdot100}{1.9}= 89.4736842105$.. It means that 1.7 is smaller than 1.9 in 10.5263157895%...
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0answers
13 views

Hilbert Symbol, JP Serre

There is one minor part of Theorem 4, page 24 of Serre's A Course in Arithmetic that I don't understand. I linked screenshots of the definition of Hilbert symbol, the statement, proof and lemma's ...
2
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0answers
63 views

Can iterated arithmetical operators break closure over $\mathbb C$? [duplicate]

Multiplication is iterated addition; exponentiation is iterated multiplication, tetration is iterated exponentiation, call all of those as different grades of iterated arithmetical operators. Is ...
3
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2answers
48 views

Are numbers independent of the basis we use?

So I have recently read about Kaprekar's Constant (https://en.wikipedia.org/wiki/6174_(number)) and It made me wonder If this number is really "special"? It seems to me that the notion 6174 (and the ...
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0answers
35 views

How can I show this simple inequality?

Let us consider $\mathbb{R}^n$ and $\lambda_1$, $\lambda_2 \in \mathbb{Z}^n$. For any $x\in 2^j \lambda_1 + [0,2^j)^n$ and $y\in 2^j \lambda_2 + [0,2^j)^n$, how can I show the following inequality, $$ ...
0
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1answer
35 views

This problem has been giving me headache for past couple of days. Please, Solve it for me.. [closed]

Ram completed a piece of work in 10 days. When the work was extended by 75%, Ram reduced his speed to (1/ A) times for the extended work. For the same extended work only, Ravi took (3.2B) days. If ...
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0answers
43 views

Reference Request: Had this line of solution about division by zero been investigated before?

If we add a single transfinite cardinal number $\aleph$ to the non negative reals, weaken the arithmetical operators to be ternary relations instead of functions, and define subtraction and division ...
2
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2answers
73 views

DIvisibility Error in the TI-84

I am trying to factorize a large number, $$600851475143$$ So I just started trying primes and in my TI-84, I got that $$600851475143=61\cdot 9850024183$$ so then I got $$9850024183=7\cdot ...
1
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1answer
44 views

Would exponentiation by non rational algebraic numbers also result in a non-algebraic number?

Exponentiation break closures. For example with the integers, exponentiation of an integer (other than $0$) to a negative integer can be a rational number that is not equal to any integer. With the ...
3
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1answer
48 views

Can origami math solve polynomial equations of degree greater than 3?

I heard that straight edge + compass can solve up to quadratic equations. I've also heard the Origami/Paper-folding can solve cubic equations. But can it solve higher-degree polynomial equations (e.g. ...
6
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3answers
108 views

Is equality of two fractions ( like $2/10$ and $1/5$) really equality or equivalence?

In propositional logic, one could not correctly say that : $(A \& B) = (B \& A)$. The reason is syntactic: the first conjunct of $(A \& B)$ is $A$, while the first conjunct of $(B \& ...
2
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6answers
264 views

A coin is thrown until it comes up tails. What is the probability of making at most $3$ throws?

A coin is thrown until it comes up tails. What is the probability of making at most $3$ throws? The answer is :$\frac{7}{8}$. I don't understand why. What are the possible cases and what are the ...
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2answers
46 views

Question of the test of the Brazilian naval college [closed]

Determine the number of digits required for the even numbers from 6 to 281 inclusive a) 356 b)830 c)546 d)637 e)365 I'm improving my English yet ...
1
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1answer
36 views

First-order Peano arithmetic and (the lack of) implicit definition of addition

I'm trying to show, through the existence of non-standard models of arithmetic, that the first-order Peano axioms (without those of multiplication) don't implicitly define addition in the sense of ...
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2answers
50 views

Of 100 questions about numerals and numerical bases, these I could not solve. I need help! [closed]

1) What change has the number 6783, when inserting a zero between the numbers 7 and 8?
1
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1answer
45 views

Prove that if $a$ and $b$ are coprime then so are $a^n$ and $b^m$

I have to prove that if a and b are relatively prime then so are $a^n$ and $b^m$ by contrapositive I'm asking for help please because i really don't know how to proceed and this assignment is due ...
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2answers
46 views

A number when divided by 899 gives a remainder 63. The remainder when this number is divided by 29 is? [closed]

Am I supposed to try division algorithm . I don't know what to do at all . Plz help
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1answer
24 views

A problem with an infinite multitude of numbers that follow some rules

We call the number n a "special number" if there are three distinct natural numbers divisors (of n) so that the sum of their squares is equal to n. We know that n is a natural number and n is diffrent ...
6
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2answers
77 views

Can roots be thought of as a repeated arithmetic operation?

Multiplication can be thought of as repeated addition, where we add something up a certain number of times. Division can be thought of as repeated subtraction, where we subtract something from the ...