Tagged Questions

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

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0
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2answers
49 views

Find the additive and multiplicative inverse of $-36$

Find the additive and multiplicative inverse of $-36$. I don't remember how to do these problems. If you can help that would be great. thanks!
2
votes
3answers
71 views

Finding the remainder when $1.1!+2.2!+3.3!+ … +10.10! +2$ is divided by $11!$

Find the remainder when $1.1!+2.2!+3.3!+ ... +10.10! +2$ is divided by $11!$ An attempt: Rearranging: $$\frac{1}{11!}+\frac{2.2!}{11}+\frac{3.3!}{11} \cdots +\frac{10.10!}{11}+\frac{2}{11!}$$ ...
0
votes
1answer
58 views

Objective questions on complex calculations.

how to solve these type of questions ? i have tried logarithm and inequalities but could not pin point the exact and correct method.
1
vote
2answers
265 views

How can a negative multiplied by a negative give positive? [duplicate]

On first look this can seem weird. But I can explain what I am looking for. We all know from elementary maths that $(-\times-)=+$. Now, lets say there are 3 cows and I say they will become doubled ...
4
votes
1answer
104 views

Sum of difference of numbers in an arrangement of the numbers $0,1,2,\cdots, n$

A seemingly interesting (easy?) problem came to mind and I thought it would be nice to ask your opinion about it. Suppose we are going to arrange numbers $0$ to $n$ in a row in such a way that the ...
2
votes
2answers
211 views

Landau's “Foundations of Analysis” - Addition of natural numbers

At the beginning of his Foundations of Analysis book (translated from German), Landau writes in his Preface for the Teacher : Peano defines $x+y$ for fixed $x$ and all $y$ as follows : $$x+1 = ...
1
vote
0answers
32 views

On the Legitimacy of Grossone [duplicate]

A paper describing grossone used to measure such things as the sierpinski carpet here:http://arxiv.org/abs/1203.3150 I'd like to discuss the legitimacy of grossone. What is the general consensus ...
1
vote
4answers
158 views

Which is larger :: $y!$ or $x^y$, for numbers $x,y$.

This is a generalization of this question :: Which is larger? $20!$ or $2^{40}$?. No explicit general solution was presented there and I'm just curious :D Thank-you. Edit :: I want a most-general ...
1
vote
1answer
40 views

How to calculate the interest amount per day

I need to implement this calculation in my project... Its a simple calculation But I dont know... I googled about that but can't to find the solution.... I have the following values (note:its a ...
0
votes
1answer
24 views

Ratio Questions

this question is stumping me which is a pain because it was found in a basic high school math book. When a car is moving at 108 km/hr, it travels 18km on a litre of petrol. If petrol costs €1,62 ...
3
votes
4answers
157 views

Is $\sqrt{x^2}=|x|$ or $=x$? Isn't $(x^2)^\frac12=x?$ [duplicate]

$|x|=\sqrt{x^2}$ as Wolfram|Alpha shows. But, as $(x^2)^\frac12=x$, I can't understand where am I wrong interpreting Square-root.
0
votes
1answer
47 views

Calculate desired profit given unit price and fee

This seems simple, but I'm struggling to find the answer... How much should I sell my apple for if I want to achieve the desired profit? Cost for me to buy the apple (A) = £10 Desired profit (B) = ...
0
votes
3answers
69 views

A.P problem gaussian sum (average of terms explanation)

The question is "the sum of first n terms of an arithmetic progression,if the last term is given $S_n=\frac{n(a+l)}{2}$; what does "$\frac{a+l}{2}$" represent?
0
votes
0answers
39 views

The order of operations [duplicate]

I've scoured the internet and I have asked many people, but I can't seem to get a finite answer to the multiplication and division step in the order of operation. Does multiplication precede division ...
0
votes
1answer
37 views

Fractional exponentiation in modular arithmetic

Does raising a modular expression to a fraction mean anything? For example, $a\,\,mod \,\,N$ raised to $1/b$ where $b>0$. Does this violate the rules of modularity?
1
vote
2answers
114 views

Convert angles from the sexagecimal system to centesimal one

How do you convert angles from the sexagecimal system to centesimal one? For example 63 degrees 14 minutes 51 seconds reduced to centesimal ?? Here's how it's done but I don't understand the ...
1
vote
0answers
47 views

Is undecidability of arithmetic a corollary of Tarski undefinability theorem?

Arithmetic is undecidable, in other words the set of Godel numbers of theorems of arithmetic is not recursive, and so there is no algorithm/ recursive function to decide if a statement is provable or ...
1
vote
1answer
80 views

Square root notation and lengths of vectors

I'm reading a textbook and it's going over finding the dot product of two vectors: $$u * v = \|u\|*\|v\|*\cos\theta$$ The vectors are: $$u = (0, 0, 1) \\ v = (0, 2, 2)$$ With lengths: $$\|u\| = 1 ...
2
votes
4answers
1k views

Limit of $\sqrt{x^2-6x+7}-x$ as x approaches negative infinity

What is $\lim\limits_{x\to-\infty}(\sqrt{x^2-6x+7}-x)$ ? Don't understand how to approach this question
3
votes
1answer
163 views

Understanding countable ordinals (as trees, step by step)

Even though ordinal numbers – considered as transitive sets – are perfect non-trees, it is worth (and natural) to visualize them as trees, starting from the finite ones which are given as ...
6
votes
1answer
58 views

Defining natural numbers without $0$ or $1$.

Let's define Peano's axioms having $2$ as the first number: $\newcommand\Nt{\mathbb N''}2\in\Nt$. $\newcommand\next{\mathop{\mathrm{next}}}\forall n\in\Nt:\next n\in\Nt$ (or $\next:\Nt\to\Nt$). ...
3
votes
2answers
68 views

Why is the coefficient in front of $\sqrt n$ always 1 in the intermediate terms for finding the continued fraction expansion of $\sqrt n$?

After playing around on paper for a bit, I came up with a short python generator to find the continued fraction expansion of $\sqrt n$. I understand why it gets the right answer when it gets an ...
1
vote
2answers
199 views

why does double rounding 9.46 give 10 but “regular” rounding gives 9?

What's the correct way to round, or estimate, a number to a specified precision? Starting with wikipedia: Rounding a number twice in succession to different precisions, with the latter ...
3
votes
0answers
138 views

Visualizations of ordinal numbers

I find this picture of the ordinal numbers up to $\omega^\omega$ rather hard to grasp: I wonder if the following might be a more compelling way to visualize ordinal numbers up to $\omega^\omega$: ...
0
votes
4answers
101 views

Why does $ \frac {\frac {1}{\sqrt{x}}}{x} = \frac {\sqrt{x}}{x^2} $?

A homework question recently asked for me to simplify: $\frac{1}{\sqrt{7}} \div {7}$ It's easy to see that this becomes $\frac{1}{7\sqrt{7}}$ But according to wolfram alpha this is also equal to ...
0
votes
1answer
136 views

The sum of two numbers equals 318, express the product of the numbers according to the lowest

I didn't understand the question on the title, what am I supposed to do?
2
votes
1answer
91 views

Show that $\frac{\sqrt[n]a}{\sqrt[n]{ab}+\sqrt[n]a+1}+\frac{\sqrt[n]b}{\sqrt[n]{bc}+\sqrt[n]b+1}+\frac{\sqrt[n]c}{\sqrt[n]{ac}+\sqrt[n]c+1}=1$ [closed]

If $$\sqrt[n]{{abc}} = 1,$$ Prove that $$\frac{\sqrt[n]a}{\sqrt[n]{ab}+\sqrt[n]a+1}+\frac{\sqrt[n]b}{\sqrt[n]{bc}+\sqrt[n]b+1}+\frac{\sqrt[n]c}{\sqrt[n]{ac}+\sqrt[n]c+1}=1.$$
1
vote
0answers
331 views

Property of arithmetic means?

$a,b,c,d \geq 0.$ It seems to me that this inequality is true and equality holds when $a=b=c=d$? $$\dfrac{a+b}{2}\dfrac{b+c}{2}\dfrac{c+d}{2}\dfrac{d+a}{2}\leq ...
0
votes
0answers
43 views

LCM of these polynomials

I'm having a hard time wrapping my head around how to get the lcm of these polynomials $$h(x+h+1), x+h+1, h(x+1)$$
0
votes
2answers
39 views

How do you simplify this expression?

$$\lim_{h\to0}(\frac{x}{h(x+h+1)} + \frac{1}{x+h+1} - \frac{x}{h(x+1)})$$ I know the answer is $$\frac{1}{(1+x)^2}$$ But I can't get there
0
votes
2answers
112 views

Combining products of like terms in a division

I was seeing an example on a book which says that: $$\frac{t}{t(x+t+1)} = \frac{1}{x+t+1}$$ The instructions read: "combine products of like terms" What exactly is that? Why does it work and why ...
1
vote
3answers
52 views

I need some basic introduction to limits

So, I know you can obviously cut out a value if it is multiplying and dividing something at the same time, right? Like: $$\frac{4h-2xh-h^2}{h} = \frac{h(4-2x-h)}{h} = 4-2x-h$$ But then I saw this ...
0
votes
0answers
53 views

Basic question about simplifying a square root

I just wanted to know how to get from $\sqrt{12}$ to $2\sqrt{3}$ Because my buddy was teaching me math the other day and gave me a list with some basic exercises to do, one of which is to solve ...
3
votes
2answers
43 views

Question about arc length.

I am having some trouble finishing an arc length problem. Specifically, what is $\int_{0}^{1}|x'(t)| dt=?$ Is it just $\int_{0}^{1} |x(t)| dt=|x(1)-x(0)|$? If so why?
0
votes
0answers
43 views

Proof that $ k^2<2^k$ [duplicate]

I'm struggling with this problem of proof by induction: For any natural number $k\geq 5$, prove that $k^2<2^k$. I assumed that $k^2<2^k$ I want to show that $(k+1)^2<2^{k+1}$ The ...
1
vote
1answer
91 views

Solving $[x]+[x]=[2x]$

Solving the equation $[x]+[x]=[2x]$ Since $[x]$ is the greatest integer function. I tried, $\forall x\in\mathbb{N}$, we have $[x]=x$ and $[2x]=2x$ this implies that $[x]+[x]=[2x]$, but if ...
2
votes
2answers
154 views

Sum of the reciprocals of divisors of a perfect number is $2$?

How do I show that the sum of the reciprocals of divisors of a perfect number is $2$? I tried $d_i\mid n$ with $i\in\mathbb{N},\;d_i\leq n$ then ...
2
votes
6answers
143 views

Proof that $n^3-n$ is a multiple of $3$. [duplicate]

I'm struggling with this problem of proof by induction: For any natural number $n$, prove that $n^3-n$ is a multiple of $3$. I assumed that $k^3-k=3r$ I want to ...
-1
votes
3answers
79 views

How does these square roots work? [closed]

$$\tag{1}2\sqrt{90} - 5\sqrt{160} + 3\sqrt{250} - 2\sqrt{40} = ?$$ $$\tag{2}\sqrt[3]{a\cdot b^2} \cdot \sqrt[4]{a^3 \cdot b \cdot c^2} = ?$$ $$\tag{3}\frac 6{2 \cdot \sqrt{3} - 3} = ?$$ picture
7
votes
4answers
6k views

Factorial, but with addition [duplicate]

Is there a notation for addition form of factorial? $$5! = 5\times4\times3\times2\times1$$ That's pretty obvious. But I'm wondering what I'd need to use to describe $$5+4+3+2+1$$ like the ...
0
votes
0answers
24 views

vector addition, would like to check my answers

If U = ( 1, 2 ) V = ( 3, -4 ) Is the answer to 2u + 1/2v ( 3.5, 2 ) I did the following: ...
5
votes
4answers
3k views

What's the algebraic property where you can flip the fractions in an equation?

Earlier in algebra, we spent over 20 minutes trying to figure out $$ \frac{1}{R_1} + \frac{1}{R_2} = \frac{1}{R_e} \,\,\,\, \text{solve for }R_2 $$ when the teacher said "What you start out with is ...
6
votes
2answers
221 views

struggle simplifying $\sqrt{9+\sqrt{5}}$

I need to simplify $\sqrt{9+\sqrt{5}}$ I already do this (proven it) $\sqrt{9-4\sqrt{5}}=2- \sqrt{5}$ But I couldn't when apply to ...
0
votes
0answers
677 views

Splitting an array into two subarrays with minimal sum

My question is if given an array,we have to split that into two sub-arrays such that the absolute difference between the sum of the two arrays is minimum with a condition that the difference between ...
0
votes
1answer
46 views

How to calculate sum?

As you can see in my screenshot, I take 25% from score and sum the result which come up to 64. My question is that how can I obtain the same 64 from sum of full(175) and score (144)? I have tried ...
0
votes
1answer
894 views

Time and Work in Unitary Method

Let us suppose, A and B can do a given work in 12 and 18 days respectively. They work alternately for equal period of time. And A started the work. Now, what is the time taken by A and B to complete ...
5
votes
1answer
69 views

$x;y;z\in \mathbb{Z}$ such that $(x-y)(y-z)(z-x)=x+y+z$. Prove that : $27\mid x+y+z$

Let $x;y;z\in \mathbb{Z}$ such that $(x-y)(y-z)(z-x)=x+y+z$. Prove that : $27\mid x+y+z$ Thanks :) P/s : I don't have any ideas about this problem..!!
0
votes
3answers
38 views

Adding and subtracting roots

I have to find (a/b), b=(1-(√3/3)), a= (1+ (1/√3)) I know I can just punch this into my calculator. However, my teacher says we need to know how to add these and subtract these but just as said that, ...
2
votes
2answers
60 views

show that $ \forall n \in \mathbb N$, $9\mid\left(10^n + 3\cdot4^{n+2} +5\right)$

Using congruence theory, show that $ \forall n \in \mathbb N$, $9\mid\left(10^n + 3 \cdot 4^{n+2} +5\right)$. The proof is quite simple with induction, but how can it be proved with congruences?
0
votes
3answers
153 views

how to solve factorial involving multiplication

I am trying to solve this question but not able to find any helpful material. It involves factorial with multiplications, $$\frac{8!}{5!}\cdot \frac{7!}{7!10!}$$ I tried crossing 8 and 5 and 7 with ...