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

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Properties of exponentiation proof

I'm trying to prove the following: "Let $x, y$ be non-zero rational numbers, and let $n,m$ be integers. Then we have $x^n x^m = x^{n+m}$." I've managed to prove by induction the case $n,m \geq 0$ ...
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2answers
34 views

Rounding to nearest 100 mm. [on hold]

Suppose x = 4.567 m. If I want to round this to the nearest 100 mm, is the answer 4.6m or 4.57m? My thoughts are round down to 4.6m as it is the nearest 100th milimeter. Please explain your answer.
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0answers
7 views

Moving average where periods have unequal # of samples

I'm trying to compare a simple moving average approach to one that normalizes by the number of samples in a period to determine which is "more correct." Here's a representative piece of the data: ...
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1answer
38 views

is the sum of all the odd numbers the same as all the even numbers to infinity? [on hold]

Is the sum of all the odd numbers to infinity equal to the sum of all the even numbers to infinity. For very small numbers the difference is quite large... 1+3+5+7+9=25 0+2+4+6+8=20
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0answers
13 views

new profit / old profit ratio of a merchant [on hold]

A merchant was selling his goods at 20% profit. When he allowed a discount of 5p per rupee on sale, his sale improved in the ratio 8:5. What is the new profit/old profit ratio? 1 Rupee= 100p
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2answers
63 views

Mathematical induction problem. Let $S_{n}=\left (3+\sqrt{5}\right)^{n}+\left(3-\sqrt{5}\right)^{n}$ [on hold]

Let $S_{n}=\left (3+\sqrt{5}\right)^{n}+\left(3-\sqrt{5}\right)^{n}$then, by mathematical induction, show that $S_{n}$ is an integer. Also, prove that the next integer greater than ...
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1answer
41 views

Add or subtracts 1 to 9 numbers and get the answer 100 [on hold]

so the question is that we have add or subtract numbers from 1 to 9 and the answer should be 100. (Note: The numbers shouldn't repeat). so what is the solution to this problem? Please answer this ...
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3answers
439 views

Unusual result to the addition

Question: Prove that (666... to n digits)^2 + (888... to n digits)=(444... to 2n digits) My way: I just proved the given equation for three values of n and written at the bottom. "Since the ...
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3answers
33 views

Finding the remainder while dividing negative numbers? [closed]

What is the remainder when dividing $-29$ by $8$?
4
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4answers
86 views

$(x+y+z)^3-(y+z-x)^3-(z+x-y)^3-(x+y-z)^3=24xyz$?

The question given is Show that $(x+y+z)^3-(y+z-x)^3-(z+x-y)^3-(x+y-z)^3=24xyz$. What I tried is suppose $a=(y+z-x),\ b=(z+x-y)$ and $c=(x+y-z)$ and then noted that $a+b+c=x+y+z$. So the ...
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2answers
81 views

How to show this fraction is not an integer

Suppose $k\geq 2$ is an integer. I want to show $$\frac{1+k+k(k-2)}{1+\frac{k-1}{k}+\frac{(-1-\sqrt{k-1} )^2}{k(k-2)}}$$ is not an integer. It is equal to $$\frac{(k-2) k (k^2-k+1)}{2 (k^2-2 ...
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5answers
141 views

If $a+b+c+d=1$ then why is the maximum value of $(a+1)(b+1)(c+1)(d+1)$ is ${\left(\frac{5}{4}\right)}^4$?

What I know is that for equations of type $x+y=8$, $xy$ attains its maximum value when $x=y$ and this can be proved by either solving the quadratic equation with completing the squares or finding the ...
4
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1answer
120 views

How do I find two integers - $x$ and $y$ - whose values satisfy the expression $x^2 + y^2 = z$, where $z$ is a perfect square?

I watched a YouTube video of an episode of Who Wants To Be A Millionaire?, in which a contestant was presented with a list of perfect squares. He was asked to choose the number that was also the sum ...
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2answers
78 views

If $\frac{(b−c)}{a} + \frac{(a+c)}{b} + \frac{(a−b)}{c}=1$ and $a-b+c \neq 0 $, then prove that $\frac 1a = \frac 1b + \frac 1c$

The question given is If $\dfrac{(b−c)}{a} + \dfrac{(a+c)}{b} + \dfrac{(a−b)}{c}=1$ and $a-b+c \neq 0 $ then prove that $\dfrac 1a = \dfrac 1b + \dfrac 1c$ I tried to take $abc$ on the right ...
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1answer
43 views

Area of shadow and an object [closed]

A $12 m \times 4 m$ rectangular roof is resting on four $4 m$ tall thin poles. Sunlight falls on the roof at an angle $45^\circ$ from the east, creating a shadow on the ground. What will be the area ...
1
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1answer
41 views

(Visual) Intuition: Division and complex fractions

When treating division as "groups of the numerator" (sorry, I don't know the technical term -- see image), why does a complex fraction in the denominator get added together to produce a 1 (number of ...
1
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2answers
31 views

Significant figures reduction of solution

I have a problem which has to be answered using two significant figures from the solution value. My solution value is x = 303.385789245434541 What should my answer be? Thanks
0
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1answer
17 views

Summing Bases and Comparing

Let $b$ be an integer greater than 2, and let $N_b = 1_b + 2_b + \cdots + 100_b$ (the sum contains all valid base $b$ numbers up to $100_b$). Compute the number of values of $b$ for which the sum of ...
2
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0answers
22 views

Determine if the members of a set can be made to equal a given number

Is there an easy way to determine if some combination of addition, subtraction, multiplication, and division will enable the numbers in a set to equal a given number? For example, if I have the ...
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1answer
64 views

Is multiplication commutative?

Say you have 3 apples and 2 oranges, and you want to multiply these two groups of fruits together to obtain a desired result, for instance: A. You want 3 apples for each orange, so you have 6 apples ...
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0answers
32 views

Starting to proof… Fundamental Theorem of Arithmetic [duplicate]

I have the following: $$ m^2 = 3 n^2 \quad\text{where } m, n \in\mathbb{Z} \text{ and } n \neq 0 $$ I know how the Fundamental Theorem of Arithmetic works, every number is a unique product of ...
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1answer
43 views

Euler and probability - a $\zeta$-distributed random variable

Let's consider a random variable $X$ on $\mathbb{N}^*$ such as $\mathbb{P}[X=n]=n^{-s}\zeta(s)$. Thanks to that random variable we can prove that $\zeta(s)= ...
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1answer
73 views

Adding $inches^2 + inches$?

At our school we have a "summer packet" we have to complete. In this packet was the following problem: At first the "sum" part puzzled me. I had no idea why they would quiz us on basic arithmetic ...
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1answer
56 views

What are examples of cases where floating-point $aaaa\ne(aa)(aa)$?

As explained in answers to this question on SO, due to non-associativity of floating-point arithmetic repeated multiplication like $aaaa$ can't be optimized to $(aa)(aa)$. Of course, aside from just ...
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2answers
44 views

Do negative signs count as subtraction or multiplication?

Would $-x$ count as $0 - x$ or $(-1)\times x$?
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0answers
48 views

Primitive recursion and $\Delta^0_0$

Until recently I assumed that primitive recursive relations are exactly $\Delta^0_0$ (i.e. bounded) ones, but I learned they're different (the former is a proper superclass of the latter). I have ...
0
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1answer
20 views

Permutation of numbers that there are all modulo M .

Let's say I have $M-1$ integers, all of them different from each other, and all of them smaller than integer M: $$1,2,3...M-1$$ I multiply each of them by another integer S, and write the result ...
2
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1answer
35 views

Saving should start early

This is a very interesting word problem that I came across in an old textbook of mine. So I know its got something to do with compound interest, but other than that, the textbook gave no hints really ...
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1answer
77 views

How do you make the number 43 using all of these numbers:7,7,6,5 [closed]

How do you make the number 43 using all of these numbers:7,7,6,5
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0answers
39 views

Calculate the loss

If a man walks in to a shop and steals £50 then the next day goes back to the shop and spends £40 but gets £10 change.How much does the shop keeper loose?
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3answers
45 views

Why are there opposite rules for dividing positive numbers and negative numbers?

I'm in confusion from some time about division of negative numbers. When we divide a positive number with a positive number, for example $$5/3 = 1.66 $$ we see what is biggest multiple of 3 which is ...
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0answers
27 views

Addition set confusion [duplicate]

Prove that for any two sets we have the following: ∣A∪B∣=∣A∣+∣B∣−∣A∩B∣. Not sure what the + means here.
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1answer
47 views

Set Addition proof

Prove that for any two sets we have the following: A∪B=A+B−A∩B Not sure what the + means here. Do i just add the two sets together including the duplicated elements? Yes sorry it should be ...
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0answers
31 views

Is this an improper method of averaging grades? If so, what is a simple mathematical way of explaining it?

I have a professor who employs a unique method of averaging grades. On each assessment, the professor assigns a raw numerical score to each student based on performance. He then converts particular ...
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1answer
32 views

What is the remainder of an n-th root called?

I feel like there should be a better word than remainder, but I don't know it. What do you call the thing that's left over when performing an $n$-th root? For example, $\sqrt[3]{29}$ is $3$ with 2 ...
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1answer
13 views

Proof of Specific Distribute Property for Vectors

Wasn't really able to find something here or on Google which answers my question. I am asked to prove the distributive property of vectors such that $$(r + s) * \vec{a} = r * \vec{a} + s * \vec{a}$$ ...
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1answer
37 views

Is there an example of nonassociative arithmetic addition?

Are there any clear, accepted examples of operations that are appropriately defined as "addition" but are not associative? Although I can find references to abstract discussions of arithmetic systems ...
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1answer
40 views

A strain of bacteria doubles every 14 h. If there are 100 bacteria cells to start with in a colony, how many will there be in 7 days?

A strain of bacteria doubles every $14$ h. If there are $100$ bacteria cells to start with in a colony, how many will there be in $7$ days? This is a sequence question. My answer: We start with ...
6
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1answer
72 views

Why is multiplication treated differently to addition?

I am a grade 11 student in South Africa. Just so you know, this is my first time posting here. My understanding is that multiplication is simply a shorter way of writing addition problems. E.g. ...
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2answers
39 views

How do we find out angle from x & y coordinates?

I found the following sentence. To find the angle you use the arctangent function like this, angle $=\tan^{-1}\left(\frac{y}{x}\right)$. But I am curious, is this the only way to know the angle? ...
6
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2answers
172 views

How to find out the greater number from $15^{1/20}$ and $20^{1/15}$?

I have two numbers $15^{\frac{1}{20}}$ & $20^{\frac{1}{15}}$. How to find out the greater number out of above two? I am in 12th grade. Thanks for help!
0
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2answers
56 views

Paradox - minus one equals one using square roots [duplicate]

I was looking on Howard Eves's book "An Introduction to the History of Mathematics" and I stumbled upon a demonstration on how $-1 = 1$. The demonstration follows: $$ \sqrt{-1} = \sqrt{-1} $$ $$ ...
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3answers
19 views

Regarding the simplest multiplying methods

I got something method like the simplest multiplying methods when I googling. If you had a number, like 123.456 and you wanted to multiply by 100 you'd just ... Move the decimal point to the ...
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0answers
26 views

Modulus to a range -x to x

I'm trying to solve positions of the planets as described in this paper. Step 3 of the computation starts with "Modulus the mean anomaly so that $-180^o \lt M \lt +180^o$." I understand what that ...
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4answers
105 views

How does one explain addition?

What is $1 + 2$? The question may seem dumb but how can one prove the answer? I heard there is a proof but don't know where to find it so please help. Thanks in advance.
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1answer
19 views

Multiplication and binary xor

I have to prove one thing that combines logical xor and arithmetical sum of binary representation of some numbers. Could you direct me what can I read on this topic? Specifically, I need to prove ...
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4answers
110 views

Why is $3 \times 0 = 0$? [closed]

Can someone explain? $3$ is $3$. It has a value. $0$ is $0$. It is nothing. Then why is $3 \times 0 = 0$?
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2answers
36 views

Why negative times negative is positive? [duplicate]

I know that many people would say I don't even know this. But I know it very well that negative × neagtive = positive. But I don't know Why? So kindly give a logical answers.
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0answers
18 views

Question about the sums of the entries in an infinite array

Imagine you have an infinite array of numbers. You can divide this array in columns with labels of opposite signs that go to infinity and negative infinity starting from the center of the array. Each ...
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1answer
67 views

How can one make sense out of a negative number?

We know that if you have 3 apples and somebody gives you 4 apples, you then have 7 apples but then if we deal with negative numbers and we have -3 apples and somebody gives us -4 apples, things can ...