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

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0
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1answer
65 views

Is it possible to follow another way to perform this calculation steps? [on hold]

So, I have an four numbers. There is they are: Number 1 is 40008260280899465341031700284668165694305281399205262735419849961365494809955 Number 2 is ...
14
votes
3answers
2k views

How to find out which number is larger without a calculator?

So I have a question which is: Which is larger? $$2.2^{3.3} \text{ or } 3.3^{2.2} $$ Now I need to find out with using a calculator but the answer is $3.3^{2.2}$. The only thing I could think of ...
5
votes
2answers
54 views

Riddle : Given an integer power, does any integer to this power start with the power?

I initially found the following riddle somewhere : Is there an integer $n$ such that $n^{2004}$ starts (from the left) by $2004$ ? I was unable to find an answer, but I found the question rather ...
-10
votes
1answer
79 views

Prove or disprove the following statement: [on hold]

For each $a, b∈ℝ$, where $a≠0, b≠0$ and $a≠ -b$, we have $$\frac{1}{a+b} = \frac1a+\frac1b$$
0
votes
0answers
20 views

Currency conversion using available rates

I have the following rates available: USD -> USD = 1 USD -> EUR = 0.887662 USD -> GBP = 0.654514 I want to calculate the following rates ...
5
votes
2answers
39 views

Sequence of equations

The sequence continues infinitely, why do the equations below work? $$1+2=3$$ $$4+5+6=7+8$$ $$9+10+11+12=13+14+15$$ So I've been trying to observe some patterns but none seem to help me. So I ...
0
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0answers
32 views

What is the physical significance of arithmetic operations?

Here is an example of what I mean by physical significance: When we use some geometric or trigonometric identity, let us say Pythagoras' theorem to calculate the length of the diagonal of a field, ...
22
votes
1answer
469 views

Parabolas in sequences of digits from the Fibonacci sequence

In preperation for an exam, I was studying Haskell. Therefore I was solving an old assignment where you had to define the fibonacci series. After solving the task (see 1] for source code) and ...
4
votes
4answers
80 views

Calculate simple expression: $\sqrt[3]{2 + \sqrt{5}} + \sqrt[3]{2 - \sqrt{5}}$

Tell me please, how calculate this expression: $$ \sqrt[3]{2 + \sqrt{5}} + \sqrt[3]{2 - \sqrt{5}} $$ The result should be a number. I try this: $$ \frac{\left(\sqrt[3]{2 + \sqrt{5}} + \sqrt[3]{2 - ...
0
votes
1answer
23 views

Converting a negative decimal with fractions to binary and hex

I am asking the question even though it has been answered before because I am looking at 3 different pages with 3 different answers right now. I am wondering how to convert a negative decimal with a ...
3
votes
0answers
34 views

Is there a name for this property of multiplication (and other functions)?

Suppose $x,y \in \mathbb{R_+}, x<y$, and $ 0 < \varepsilon \leq (y-x)/2$. It seems to me that $xy < (x+\varepsilon)(y-\varepsilon)$ and equivalently that $(x+\varepsilon)(y-\varepsilon)$ is ...
-2
votes
2answers
58 views

If you have only 3 coins and 1 is a penny is it possible for you to have a Dollar? [on hold]

If you have only 3 coins and 1 is a penny is it possible for you to have a Dollar?
-3
votes
0answers
16 views

Calculate the number of spheres [on hold]

Calculate the number of spheres in two cases inside a cube having volume of 1m3 in the most dense packing possible. The diameter of each sphere is 1 micrometer and 1mm for both the cases respectively. ...
0
votes
2answers
23 views

null empty set has 2 subsets?

The question in the book was: How many subsets does $\{\emptyset\}$ have? a) 0, b) 1, c) 2, d) 3. The answer was c. How can an empty set have 2 subsets?
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votes
1answer
24 views

The Sum of the first five terms of an arithmetic sequence is 65/2… [on hold]

The sum of the first five terms of an arithmetic sequence is 65/2. Also, five times the seventh terms is the same as six times the second term. Find the first term and the common difference of the ...
0
votes
3answers
43 views

The result of subtracting the integer part of $x$ from $x$

I want to know what does this formula do with the integer $x$ $$\text{frac}(x) = x - \lfloor {x}\rfloor ,\ x >= 0$$ I've searched and found that this is called finding the fraction part of $x$ ...
0
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0answers
12 views

Solutions for the dependency problem

Currently I read about the dependency problem of interval arithmetic. Mainly it's the problem that in the equation $X-X$ for $X$ being an interval the following is calculated: $$X-X=\{x-y:x\in X, y\in ...
1
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0answers
35 views

Guess the rule of transformation of a natural number

I came across a playful problem. On a sheet of paper it is written the number $\overline{1234xy}$, where \begin{equation}\overline{1234xy}=1*10^5+2*10^4+3*10^3+4*10^2+x*10^1+y\end{equation} Five ...
1
vote
0answers
20 views

What formula can I use to calculate how much protein per 100 calories a given food has?

I have an Excel spreadsheet of 529 items all with calories, carbs, fats, and protein listed. I'd like to add a grams of protein per 100 calories column but my math ability is embarrassingly ...
5
votes
3answers
99 views

Which is more simplified: $a\sqrt{b}$ or $\sqrt{c}$?

Which is considered more simplified (if it matters)? $a \sqrt{b}$ or $\sqrt{c}$ For example: $2 \sqrt{3}$ or $\sqrt{12}$
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votes
1answer
30 views

Distribute coins fairly

$10$ coins weigh $10$ grams each, and another $10$ coins weigh $11$ grams each. So the average weight is: $$\frac{10 \cdot 10 + 10 \cdot 11}{20} = 10.5\text{ grams}.$$ Now I need to distribute coins ...
3
votes
2answers
57 views

What is this method of calculating int number times int number called?

I saw this video on Facebook and I'm curious about this. I have very basic questions on this because I can use it but I can't understand the technique. Link to the video explaining this method on ...
4
votes
2answers
101 views

Consecutive sets of consecutive numbers which add to the same total

I'm looking at examples of numbers that can be written as the sum of integers from $j$ to $k$ and from $k+1$ to $l$. For example $15$ which can be written as $4+5+6$ or $7+8$. Or $27 = 2+3+4+5+6+7 = ...
2
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1answer
28 views

How many unique numbers can be obtained by adding two numbers from two different sequences?

Let the two integer sequences $\{a_m\}$ and $\{b_m\}$, be defined as: $a_n+D_n=a_{n+1}$ and $b_n=a_n-k$, where $D_n$ may be any natural number (and $D_i$ may or may not be equal to $D_j$), $k$ is an ...
6
votes
1answer
58 views

“there exists” and “for some” are the same, right?

I think "there exists" and "for some" are the same, but still want to make sure. Ex: $x > ky$ for some k or there exists a k such that $x > ky$
0
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3answers
34 views

Arithmetic and geometric sequence

Which two numbers should be placed between -5 and 49 so that the first three numbers form an arithmetic sequence, whereas the last three numbers form a geometric sequence?
3
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1answer
17 views

Check algebraic transformation with trial numbers?

I did some algebraic transformations on equations with multiple real variables $x_i$, and I'd like to check whether the transformed equation is still valid. The equations are basically only rational ...
3
votes
2answers
29 views

Order of parsing + and -

This seems like an absurdly simply question, and is possibly below the level of this forum, but it seems the most sensible place. I'm building an arithmetic equation parser, and currently working on ...
10
votes
2answers
129 views

When is $\sqrt{a^2}=\pm a$ and when is $\sqrt{a^2}=a$?

When we derive some formula and have to do huge algebraic expansions that deal with raising powers we use exponent rules mindlessly and we never write down the $\pm$ symbol. Why is this right? My ...
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votes
2answers
67 views

2+2=square root of 16. What's the appropriate answer? [closed]

4? Positive and negative 4? I just got into an argument with a buddy about this. He argues if it's not an i, it's not included as a imaginary number, but only the real positive number.
0
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3answers
52 views

Exponential Function, Help Appreciated :-)

my text book asks me to 'Simplify, and express in terms of positive indices'. But my answer always seems to come up with: $x^{\frac {35} {36}}$. The term is $$\frac{ (x^{-\frac 1 2})^{\frac 2 3} \ ...
6
votes
1answer
64 views

Tzaloa 2015 game problem (piles with $1,2,4 \dots 2^{19}$ coins each)

We have $20$ piles with $1,2,4,8\dots 2^{19}$ coins repectively and two players. In each turn a player must select five piles that have at least one coin and remove exactly one coin from each. Player ...
-6
votes
1answer
77 views

How to make the expression from the left of the equation look like the expression to the right of the equation? [closed]

I cannot see how my teacher rewrites this equation.. : The answer is the expression to the right of the equation. I want to know how my teacher gets this expression from the left of the equation. ...
1
vote
2answers
57 views

Combination of $n$ objects taken $p$ at a time where $n$ contains $r$, $s$, and $t$ identical objects.

I am talking about something like this: $ N = \{2, 3, 3, 3, 5, 5, 7\}$ $ n = 7$ $ s=3 $ $t=2$ In my case specifically, those numbers in $N$ are the prime factors of a number $Z$ repeated the number ...
1
vote
3answers
25 views

average of an inequality

what is the result of $<1 + <1$? ; $<1 + <1 = <2$? or <1 + <1 = <1? Now what is that number divided by 2? Either we have: <2 / 2 = <1 or <1 / 2 = <0.5
3
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0answers
49 views

If $(x^2+y^2+z^2)=2(x+z-1)$, then show that $x^3+y^3+z^3$ is constant and find its numeric value.

I am trying to solve this question, If $(x^2+y^2+z^2)=2(x+z-1)$, then show that $x^3+y^3+z^3$ is constant and find its numeric value. I've tried this, $$x^2-2x + z^2-2z + 2 + y^2 = 0$$ $$ ...
10
votes
2answers
176 views

What would Gauss do in this case: adding $1+\frac12+\frac13+\frac14+ \dots +\frac1{100}$?

We all know the story related to Gauss that Gauss' class was asked to find the sum of the numbers from $1$ to $100$ as a "busy work" problem and and he came up with $5050$ in less than a minute. He ...
2
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0answers
38 views

Solving $-1=e^a-2e^{av}$ as part of a equation system

Problem Given $f_2(x)=e^{ax-b}+c$ with $x \in \left(0,1\right)$, I am trying to calculate the parameters $a,b,c$ in respect to the following constraints: $$ \begin{align} f_2(0) &= 0 \\ ...
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0answers
19 views

Definition arithmetic progressions of any given length.

I have been studying erdős conjecture on arithmetic progressions for some time and have an interesting question for you : How do I strictly define "a set containing arithmetic progressions of any ...
1
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1answer
85 views

Number puzzle : “You can't determine my sum.”

Albert said to Bob, "I have two unequal positive integers; the smaller is at least 2; the larger is at most 25. I will only tell you their product." So he did. Later, Albert has forgotten the numbers ...
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1answer
44 views

Does 0/0 = a new branch of numbers? Have I made a mistake in the equation? [duplicate]

So I thought... 0/0 = x... then 0 = x*0... then 0x = 0... then its technically possible to divide by 0 again 0x/0 = 0/0 ... since 0/0 = x and 0x/0 = 0/0.. then x = 0x/0 ... 0x = 0 ... x = 0/0 ...
3
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0answers
32 views

Comparing Large Exponents with different bases.

How to compare large exponents with different bases? Is there any way to roughly approximate their values? For example, sort the elements of list below based on their magnitude. ...
0
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2answers
36 views

calculating costs of manufacture [closed]

I apologize in advance if I'm asking this question in the wrong forum, but I'm having trouble with the Math, not the spreadsheet here. I'm calculating the cost per round of hand made ammunition, and ...
0
votes
1answer
39 views

Understanding A simple mathematical addition operation

I was just doing a simple maths operation: $s = 158 + 46 \times -1: \Rightarrow s = 112$ and $s = (158 + 46) \times -1:\Rightarrow s = -204$ In the latter case $158 + 48$ gets calculated first ...
4
votes
1answer
86 views

Infinite exponentiation $n^{n^{n^{…^n}}} \equiv m \pmod q$ , find m?

let $(n,q) \in \mathbb N^{*^2}$ I was wondering if it was possible to find a function $f_q$ such that : $f_q(n)=m$ where $m$ is such that $n^{n^{...^n}} \equiv m \mod q$ or at least an easy way to ...
1
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2answers
21 views

division of fraction simplification

The expression is this: ${{y^2 - y} \over 1 {}} \div {{y^2 - 1} \over 3}$ The first step is to swap the second expression round to: ${{y^2 - y} \over 1 {}} \div {3 \over {y^2 - 1}}$ The answer ...
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0answers
8 views

I want to find the % taken from the gross amount to reach the net amount

I know the gross amount and I know the net amount I want to know how to find the % of the gross taken to get the net amount
5
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0answers
60 views

imo question to be explained in a manner so as to a layman

Suppose that you mark a finite collection of points on an infinite plane in such a way that you cannot draw a straight line through any three marked points. We define a windmill to be the following ...
1
vote
2answers
49 views

Proving that an expression returns a real non-integer number (Number 2)

Let $$a=443372888629441 = 17*31*41*43*89*97*167*331$$ $$b=(3+\sqrt{13})/2$$ $$c=(2+\sqrt{8})/2$$ $$d=(1+\sqrt{5})/2$$ How can you prove that the expression ...
1
vote
3answers
55 views

Proof of the division algorithm

I wasn't happy with the proof provided by the book, so I had an attempt at it, but I don't know if it's right. The theorem is: Let $a,b\in\mathbb{Z}$ and $b\neq0$. Then there exist unique ...