Questions on basic arithmetic, e.g. addition, subtraction, multiplication, division, powers, radicals, etc.

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2
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How to set up these ratios?

Here's a question while reading my textbook: For about 10 years after the French Revolution, the French government attempted to base measures of time on multiples of ten: One week consisted of ...
19
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6answers
416 views

$\lim_{n\to\infty}\sqrt{6}^{\ n}\underbrace{\sqrt{3-\sqrt{6+\sqrt{6+\dotsb+\sqrt{6}}}}}_{n\text{ square root signs}}$

We have the following representation of pi: $$\pi=\lim_{n\to\infty}2^n \underbrace{\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\dotsb+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}}}}}}}_{n\text{ square root ...
6
votes
2answers
196 views

Number of sudokus with no consecutive arithmetic progression of length 3 in any row or column.

How many such Sudokus are there? Any reference to papers, books, articles or any insight into the problem will be greatly appreciated. I've tried several search engines, scholarly and not, with no ...
0
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3answers
159 views

How to find the total amount from given percentage

I am trying to answer this question from internet for my mathematics practice. ...
5
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2answers
65 views

Intuition behind sum of multiplication arithmetic sequence

Maybe this is a stupid question but please guide and enlighten me patiently. I have just known something fact that quite shocking me. Let start from this simple fact $$\sum_{k=1}^n ...
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0answers
32 views

Number Pyramid Help

I was searching around the internet to try to find the name to the following pyramid: ...
0
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0answers
13 views

understand problem for limiting sum of a geometric progression

a more mathematically enlightened philanthropist endows a bursary that is to pay 100 000 to a student each year beginning now. The philanthropist is able to invest funds for the endowment at 10% p.a. ...
17
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2answers
637 views

How to define addition through multiplication?

One might define multiplication $\bullet$ on $\mathbb Z$ as follows: $\bullet: \mathbb Z\times \mathbb N\ni (a,b) \mapsto a+\cdots+a\in \mathbb Z$ where we add $b$ times. But suppose we are in a ...
6
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0answers
107 views

Mersenne primes

A Mersenne prime is a prime number of the form $2^p-1$ where $p$ has to be a prime number. Now, let $p_0$ be a prime number, and let us define the sequence $p_n = 2^{p_{n-1}}-1$. Is there a $p_0$ such ...
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5answers
88 views
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2answers
27 views

Help me evaluate this equation in Scientific Notation

How do i solve this using Scientific Notation? $$ \frac{3\times 10^8}{4\times 10^{-5}} $$ I have been trying for hours now! Help please
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1answer
28 views

Unique Number Calculations

What do you call numbers you can add together that will always be unique. a = 1, b = 2, c = 4 Any combination of the above will always result in a unique number. eg: 7 = abc, 6 = bc, 3 = ab Sorry if ...
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1answer
35 views

How can the two basic binary operations (addition and subtraction) be defined in set-theoretical terms?

I recently stumbled upon this interesting definition of mathematics: Math is the study of things that can be described as sets I am aware that the integers and the real numbers can be defined in ...
3
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3answers
852 views

Missing dollar problem

This sounds silly but I saw this and I couldn't figure it out so I thought you could help. The below is what I saw. You see a top you want to buy for $\$97$, but you don't have any money so you ...
1
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1answer
34 views

Even powers and perfect squares

Does $2^{2k}$ (where $k$ is a natural number) always result in perfect squares?If so, why?I just tried it with a few values and it appears to be true. I need the result for this to simplify a ...
4
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0answers
53 views

Prove $\forall n\in\mathbb{N}, \exists m\in\mathbb{N}; n=\pm1^2\pm2^2\pm\cdots\pm m^2.$

And we choose the positive and negative signs in a way that the equation becomes true. I think it can be proved with mathematical induction. So here's how I begin: For $n=1$, $1=+1^2$ which is true. ...
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2answers
36 views

Parallel line with a known point

Line m goes through a point D(2, -4). Line m is parallel to line l: $5x+3y=-17$. Describe line m with an equation of type $ax+by=c$. The solution should be $c=5*2+3*-4=-2$ so $\text{m: }5x+3y=-2$ ...
1
vote
1answer
42 views

Decide whether the following number is rational

Working needs to be shown $\sqrt{\sqrt{5}+3}+\sqrt{\sqrt{5}-2}$ My guess is to multiply by $\sqrt{\sqrt{5}+3}-\sqrt{\sqrt{5}-2}$ then we have a rational number but is it enough to prove the ...
0
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1answer
37 views

Irrationality proof

Prove that $\sqrt{7-\sqrt{2}} $ is irrational My idea is the following $\sqrt{7-\sqrt{2}} \in\mathbb{Q}$ $w^2=7+\sqrt{2}$ $w^2-7=\sqrt{2}$ thus w cannot be rational is this correct? edit: or ...
0
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2answers
28 views

What is the difference between a quadratic equation and a quadratic function?

I cannot dicepher the difference between a quadratic equation and a quadratic function. I read the following "A quadratic equation can tell us a lot about the graph of a quadratic function." I see the ...
0
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0answers
23 views

An example for Liouville's theorem (1844)?

This Liouville's theorem (the most unknown of his work) : "If $n \in \mathbb{N^{*}}$ and $p>5$ a prime number, then the equation $(p-1)! + 1 = p^{n}$ has no solution." The standard proof is clear. ...
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1answer
18 views

basic proportions, why the results are inconsistent?

Simple 3rd grade problem: A friend got a 10% raise to its salary. He got angry and asked for more. After much Negotiation he got another 10% raise on top of the first one. He asked me to check how ...
2
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4answers
133 views

Why does dividing by zero give us no answer whatsoever?

I've heard about this and I know that division can be used in one way like this: For example, if I want to do $30$ divided by $3$, how many times can I subtract $3$ from $30$ to get to $0$? Well, I ...
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2answers
41 views

Is there an operator for adding the numerator and denominator of a fraction separately?

Numbers in the Farey sequence are expressed as fractions e.g $F_5$: $0\over1$ $1\over5$ $1\over4$ $1\over3$ $2\over5$ $1\over2$ $3\over5$ $2\over3$ $3\over4$ $4\over5$ $1\over1$ All of the $n\over5$ ...
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7answers
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Why do we stop at exponentiation stage in arithmetic of natural numbers?

In natural numbers the unary successor operator $S$ is the most natural function which maps each number to the next one. Furthermore we may consider the binary relation $+$ as an iteration of $S$. ...
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0answers
35 views

Some geometric equations

Correct me if I'm wrong by saying that the circumference of the circle equals to $180\times 1 $ rad where 180 and 1 are constants and the volume of the sphere equals to $30\times 1$ rad$\times 1^3$ ...
3
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1answer
66 views

Why does $(n+1)^n\lt n^{n+1} \implies \left(1+\frac{1}{n}\right)^n\lt n$?

During an example done in lecture, I encountered an inequality by the form of $$(n+1)^n\lt n^{n+1}$$ My professor immediately simplified it to $$\left(1+\frac{1}{n}\right)^n\lt n$$ I have attempted to ...
5
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1answer
23 views

Elementary operations

There are four elementary arithmetic operators. Are all operations in mathematics derived from the four elementary arithmetic operators? I'm studying linear algebra and noticed that some exercises ...
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3answers
160 views

How are the elementary arithmetics defined?

In the book Principles of Mathematical Analysis by Rudin, I read that "a < b" is defined this way: if b - a is positive, then a < b or b > a. Then some questions arose to me: we know that ...
0
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1answer
21 views

Chopping arithmetic

I would like to use chopping arithmetic for 3 digit chopping for the following: $a)\pi$ and $b) 456788.1234567$ My guess is that it is $3.141$ and $456788.123$, but my book says the pi after ...
2
votes
2answers
20 views

if $Re(z\overline w)=|z||w|$ then $w=tz$ where $t\in \mathbb R$

I was given the following exercise in complex numbers: Assume that for some $z,w \in \mathbb C$: $Re(z\overline w)=|z||w|$ Show that this implies $w=tz$ where $t$ is some positive real. What I ...
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0answers
30 views

Finding V and W for complex equation

I'm currently writing a physics engine for a game. However, I need to evaluate this problem somehow into a function of V and W. Help? ...
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1answer
18 views

Difficulty understanding the solution to a problem.

I am studying a book right now, and I'm having a difficulty understanding a (solved) problem regarding congruent modulo. Below I will list the problem and what I have understood of the problem, along ...
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2answers
141 views

How can you prove that a value raised to $\frac{1}{n}$ is the n'th root of $x$?

I know that if you raise a value to $\frac{1}{2}$ for example, you take the square root, but that is not what I am asking, what I am asking is; what are you actually doing when raising a value to ...
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3answers
91 views

Why is $2x-1=7$ not $x=-4 \text{ or } x=4$

How would you explain why $3(2x-1)^2=147$, is $2x-1=7 \text{ or } 2x-1=-7$. But not $2x=8 \text{ so } x=4 \text{ or } x=-4$?
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0answers
24 views

Arithmetic expression that evaluates to 21 only using numbers 1,5,6,7

I need to come up with arithmetic expression that evaluates to 21 and only uses the numbers 1,5,6,7. each number used only once.
1
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1answer
77 views

Proofs involving Fermat's Little Theorem

Let $p$ be a prime and $a$ be an integer such that $p$ does not divide $a$. Suppose $d$ is the smallest positive integer such that $a^d ≡ 1 \ ($mod$ \ p)$. Prove that $d|(p−1)$. So far I've ...
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0answers
16 views

Calculate relative rate of percentage change

This question could probably just as easily go on quant.SE, but the problem I am having is mathematical in nature, so the domain hopefully shouldn't matter. The problem: Say you have two moving ...
3
votes
2answers
116 views

Why is $x(x+2)(x-3)$ not $x^2+2x(x-3)$?

How would you explain the principle why $x(x+2)(x-3)$ is not $x^2+2x(x-3)$ but $(x^2+2x)(x-3)$? This may involve the fundamentals of eliminating parenthesis.
6
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0answers
43 views

Is there a numeral system that makes both addition and multiplication easy?

Decimal positional notation, the system for writing numbers we all use every single day, makes addition very easy by transforming it from a computation to a repeated operation on individual digits ...
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2answers
40 views

Get values of multiple variables from simple additions

What is the process to get the values of each variable when I only have these calculations to go on? These are the sums: ...
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1answer
25 views

Solving a non-linear congruence

How would I go about solving the following: $$x^2+1\equiv2\pmod8$$ I know I can subtract, and I get: $$x^2\equiv1\pmod8$$ I'm not sure if I am allowed to square root both sides, or if I should ...
2
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2answers
95 views

Origin or author of 'Japanese Multiplication Method'

What is the origin or author of the method 1 shown in the following image? Notes Also known as Japanese Multiplication Method for Kids.
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2answers
36 views

$\sqrt{1\pm10\varepsilon+\varepsilon^2}=1\pm P(\varepsilon)$. Is there a better way than mine to find $P(\varepsilon)$?

Some days ago we did a classwork, and there was this exercise: Using the limit definition, verify $$\displaystyle \lim_{x\to0} \frac{3x^2-1}{x+1}=-1.$$ From $\displaystyle ...
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1answer
10 views

Quick question about functions distributing over addition, multiplication, minimum and injection.

So consider for example I have the function $$F(x) = -3\cdot x$$ I have to prove that either true or false and then prove my answer if false with a counter example and justify fully a true answer. ...
0
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1answer
63 views

Expressing a number as a finite sum of terms $a_k/k!$

The original problem is as - Suppose $a_2,a_3,a_4, \cdots a_7$ are integers such that $$\frac{5}{7}=\sum_{k=2}^7 \frac{a_k}{k!}$$ where $0 \le a_j < j$ for $j=2,3,4,5,6,7$ Then find $a_2+a_3+ ...
0
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2answers
26 views

linear equation for vertical line

If we want to graph a horizontal line, we will do the following: y = 0x + 3 No matter the domain for x, the range for y will always be 3. Therefore, we have a ...
70
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5answers
2k views

Root Calculation by Hand

Is it possible to calculate and find the solution of $ \; \large{105^{1/5}} \; $ without using a calculator? Could someone show me how to do that, please? Well, when I use a Casio scientific ...
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1answer
44 views

How am I supposed to convert between a teaspoon and a tablespoon?

I've sometimes been having trouble figuring out the conversion between a teaspoon (tsp.) and a tablespoon (tbsp.). How will I know when to multiply or divide by three to do these conversions? I ...