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

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0answers
18 views

Given bond duration, price, interest rate, what happens to bond? [on hold]

suppose a bond has a duration of 8 years and is selling in the market for R1085 currently market interest rates are 6% and is expected to rise by 1.5%.what should happen to this bond?
0
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2answers
24 views

multiply fraction with what number to get a whole number?

I'm solving some programming puzzle and it has come down to this: I've a fraction, say 12/13, and I need to multiply it with a smallest possible natural number (say x) to get a whole number. How do I ...
3
votes
2answers
29 views

Number of $1$s in the binary representation of $n$

Trying to define the function $b(n)$ which counts the number of $1$s in the binary representation of $n$ arithmetically I came up with the following definition: $$b(n)=m :\equiv (\exists k_1\dots ...
1
vote
1answer
26 views

Fractions and stretch your thinking. [on hold]

Carol's book shelf has 4 shelves with 6 books on each shelf. Her brother Robert has 3 shelves and 7 books on each. They want to combine their books. They put 9 books on a shelf; how many shelves will ...
2
votes
3answers
88 views

A hard square root question

This is my first question on StackExchange. So my question is: If $$x = \frac{\sqrt{\sqrt5 +2}+\sqrt{\sqrt5-2}}{\sqrt{\sqrt5 + 1}} + \frac{\sqrt{\sqrt5 +2}+\sqrt{\sqrt5-2}}{2\sqrt{\sqrt5 + 1}} - ...
6
votes
3answers
98 views

Confused about the $\pm$ sign?

I have multiple questions about the $\pm$ sign, since it seems to confuse me in general... Question 1: Say I have $15=\pm(a+x)$, Can I use the distributive property so it becomes $15=\pm a \pm x$? ...
0
votes
1answer
30 views

Quadratics help please [on hold]

Does it matter when you are solving quadratics and you get an or would it matter if you said does x always go first $x<9$ or is it the same as $9<x$?
0
votes
0answers
20 views

How to reduce the complexity? [on hold]

Given an array of size n. There are k operations to be made. In each operation the maximum value of the array is reduced by one and minimum value of the array is increased by one. Find the difference ...
1
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2answers
25 views

Compensation Question

I want to create a compensation system which takes into account two variables. Lets say I have $1M to distribute among ten employees who produce widgets. I want to compensate each employee by two ...
1
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2answers
52 views

Prove an addition property of Natural numbers

Prove: For any $x,y \in \mathbb{N}, y \neq x+y$. I'm only suppose to use the Peano axioms as defined here http://aleph0.clarku.edu/~djoyce/numbers/peano.pdf and the properties of addition in ...
2
votes
6answers
76 views

Why is the result of $-2^2 = -4$ but $(-2)^2 =4$?

I am really new into math, why is $-2^2 = -4 $ and $(-2)^2 = 4 $?
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votes
1answer
19 views

How can we generate a $2$-digit number $XY$ on base $B$, such that $BX+Y=Y^X$?

For example, $25$ on base $10$ is equal to $5^2$. This should be pretty easy to solve using fairly simple arithmetic. But I'm finding it hard to generate any other solutions besides the one ...
5
votes
5answers
183 views

The number $(3+\sqrt{5})^n+(3-\sqrt{5})^n$ is an integer

Prove by induction that this number is an integer: $$u_n=(3+\sqrt{5})^n+(3-\sqrt{5})^n$$ Progress I assumed that it holds for $n$ and I tried to do it for $n+1$ but the algebra gets quite messy and ...
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votes
0answers
23 views

the sum of trigonometric functions and harmonic numbers [closed]

The first equation in a) gives a sum of 1 and the second equation starts with a sum equal to $\pi$. By removing $\sqrt x$ in b) the value of y is still almost the same.What is the exact value of y ...
0
votes
3answers
29 views

How to solve for x in this eq

I'm doing a physics E&M problem, but I'm stuck on a math part. I can't remember how to solve for x in this instance. ${x\over 2} = {0.04-x\over 5}$
0
votes
1answer
20 views

How to break changes in ratios into two changes?

I am running into a real world problem. But I think this is more like a math problem. So here it is. Suppose I have $$A = B + C.$$ The $A, B, C$ in this period are called $A_{1}, B_{1}, C_{1}$. ...
2
votes
3answers
55 views

Ambigous question regarding how to view surds with numbers infront

Say I want to multiply 2 by 5$\sqrt3$ . Do I firstly do 2 * 5, then 2 * 3? I'm not sure about the order of operations here. Such a dumb question, I know. Edit - can someone show me the systematic ...
0
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0answers
31 views

Extensions by recursive definitions

In the Wikipedia entry on Extension by definitions I learn that an explicit definition in the language of a theory $T$ yields a conservative extension $T'$ of $T$. I wonder if this eventually does ...
-1
votes
2answers
51 views

Squared binomial paradox?

When you square this $$(5-2)^2$$ you will get 49 $$ 5^2 - 2 * 5 * (-2) + (-2)^2$$ $$25 + 20 + 4 = 49$$ but if you do it like this (5-2) * (5-2) you will get 9 $$ 5(5-2) - 2(5-2)$$ $$25-10-10+4$$ ...
0
votes
2answers
23 views

Looking for a Formula to apply to a set of numbers (input) that will output a certain result.

Sorry for the crude title: I'm looking for a formula to apply to each element of an "input set" of numbers that will output elements in another "output set" with the following characteristics: The ...
3
votes
2answers
47 views

Automorphisms of $\langle \mathbb{N}, \cdot \rangle$

It is an elementary fact that multiplication in $\mathbb{N}$ is commutative: $$(\forall n,m)\ n \cdot m = m \cdot n$$ This - among other things - implies that the representation of an $n \in ...
9
votes
4answers
420 views

Expression with last digits different

Given the expression: $$1234567893 \times 1234567894 - 1234567895 \times1234567892$$ Is it correct to say that the answer is $ (3 \times 4) - (5 \times 2) $? If so, why?
5
votes
5answers
113 views

How $\sqrt{2}=1+\frac{1}{\sqrt{2}+1}$?

I have found it in the chapter about chain fractionals. I am unable to transform it to such state. $$\sqrt{2}=1+\sqrt{2}-1=?=1+\frac{1}{\sqrt{2}+1}$$
1
vote
1answer
39 views

Recursive definitions of $n<m$, $n\mid m$, and $n \bmod m$

Without referring to the apparatus of (primitive) recursive functions one can introduce addition into the language of successor arithmetic by two additional axioms which naturally reflect the essence ...
0
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1answer
40 views

Why is every number which ends in 5 divisible by 5?

Is there more of an answer to this which is more than just 'it does'?
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3answers
52 views

Derivation of the “Combined Work Formula”

Before I get to my question, some background: Person $A$ can paint a fence at the rate $9 \frac{hour}{fence}$ (or equivalently $\frac{1}{9} \frac{fence}{hour}$) Person $B$ can paint a fence at the ...
2
votes
2answers
147 views

Why we can't define $\frac{1}{0}$ to be $1$ (or anything else), but we can define $1^0$ to be $1$?

We know that we can't define division by zero "in any mathematical system that obeys the axioms of a field", because it would be inconsistent with such axioms. (1) Why can we define $a^0$ ($a\neq 0$) ...
0
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0answers
20 views

Adding a fixed quantity of something to two different sized containers yields a different result

For example: An object has 29,880 health. It starts out at 10% of that, and in order to get it to full health you need to add 30 health packs to it. So we can calculate that each health will add 897, ...
0
votes
1answer
32 views

Finding distance using rates of change — best approach?

The question: A man drives from state $A$ to state $B$ going $60 \frac{miles}{hour}$. Then he returns from state $B$ to state $A$, driving $45 \frac{miles}{hour}$. His total driving time is $2.5 ...
1
vote
2answers
33 views

Overall difference in percent

I want to calculate the total difference in % between two investments {A,B} in the following scenario: In year t=0 revenue A is 70 % smaller than revenue B. Every year the revenue from A further ...
0
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1answer
80 views

Is this real number an integer?

Is this real number : $$\Big(2+\frac{10}{9}\sqrt{3}\Big)^{1/3}+\Big(2-\frac{10}{9}\sqrt{3}\Big)^{1/3}$$ an integer ? I've tried different factorization, but nothing seems to work.
2
votes
2answers
69 views

Proving that a number is non-negative?

The numbers $a$,$b$ and $c$ are real. Prove that at least one of the three numbers $$(a+b+c)^2 -9bc \hspace{1cm} (a+b+c)^2 -9ca \hspace{1cm} (a+b+c)^2-9ab$$ is non-negative. Any hints would be ...
1
vote
0answers
33 views

Find out the no of digits in product between some prime.

How many digits are there in? $2^{17}*3^{2}*5^{14}*7$. help me.
1
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1answer
17 views

Arithmetic regarding area under curve

I am looking at a textbook example but I am not able to go from where I have set the question mark and to the where the arrow is pointing. Could someone please explain where the x's are coming from ...
0
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2answers
42 views

Different arithmetics

The original Peano axioms were based on a single unary operator $\operatorname{succ}$ and one second-order induction axiom: $\lbrace \operatorname{succ} \rbrace + \operatorname{IND}_2$ Peano ...
0
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2answers
25 views

Arithmetic simplification

I am asked to find $\frac{d^2y}{dx^2}$, and prove that $\frac{d^2x^2+y^2=a^2}{dx^2}$=$-\frac{a^2}{y^3}$, This is how I have proceeded: $2 y \frac{dy}{dx}+2 x=2 a \frac{da}{dx}$ => ...
0
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1answer
34 views

Simplifying an equation step by step

I am not able to go from the left hand side to the right hand side. Could someone take me through the steps, I tried using common denominator (y^2-x)^2, but was not able to get the result on the right ...
3
votes
5answers
59 views

Determine variables that fit this criterion…

There is a unique triplet of positive integers $(a, b, c)$ such that $a ≤ b ≤ c$. $$ \frac{25}{84} = \frac{1}{a} + \frac{1}{ab} + \frac{1}{abc} $$ Just having trouble with this Canadian Math ...
1
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0answers
44 views

Inverse element of “-”

What is meant by the inverse element of "-"? There is a statement in my book that says there exists an inverse element of "-" in $\mathbb{R}$ and I have to mark it true or false. I know that the ...
0
votes
0answers
36 views

Find the ratio of sides in a triangle, if they form an arithmetic progression and the largest angle is 90 degrees more than the smallest [duplicate]

The three sides of a triangle form an arithmetic progression. Given that the largest angle is 90 degrees more than the smallest angle, show that the sides are in the following ratio $$\sqrt{7}\, -1 : ...
0
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0answers
30 views

Comparing Fractional Numbers

Does a formula exist for comparing two fractional numbers, without resolving to using anything other than integers and fractions? (Thus not real numbers). In other words: given $\dfrac{a}{b}$ and ...
0
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5answers
59 views

Arithmetic Progression.

Q. The ratio between the sum of $n$ terms of two A.P's is $3n+8:7n+15$. Find the ratio between their $12$th term. My method: Given: $\frac{S_n}{s_n}=\frac{3n+8}{7n+15}$ ...
25
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14answers
5k views

Logic behind dividing negative numbers

I've learnt in school that a positive number, when divided by a negative number, and vice-versa, will give us a negative number as a result.On the other hand, a negative number divided by a negative ...
3
votes
2answers
145 views

Simple subtraction that I can't figure out. [duplicate]

A bat and a ball cost £1.10 in total. The bat costs £1 more than the ball. How much does the ball cost? The answer to this question is somehow 5p. How?!! Should it not be 10p?
0
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1answer
31 views

Having problem with 10's complement subtraction

From what I've found, to find A - B using 10's complement; where A and B are decimals Let A = 215 , B = 155 Find 10's complement of B = (1000 - 155) = 845 Add 10’s complement of B to A If it ...
13
votes
3answers
231 views

How to prove: $\left(\frac{2}{\sqrt{4-3\sqrt[4]{5}+2\sqrt[4]{25}-\sqrt[4]{125}}}-1\right)^{4}=5$?

Question: show that: the beautiful ${\tt sqrt}$-identity: $$ \left({2 \over \sqrt{\vphantom{\Large A}\, 4\ -\ 3\,\sqrt[4]{\,5\,}\ +\ 2\,\sqrt[4]{\,25\,}\ - \,\sqrt[4]{\,125\,}\,}\,}\ -\ ...
0
votes
2answers
27 views

Common divisor of the form d = ax+by

There is a theorem that says that every pair of integers $a$ and $b$ has a common divisor $d$ of the form $d = ax+by$ where $x$ and $y$ are integers. Is it true that $d$ is also definitely the ...
-1
votes
1answer
44 views

counting the number of code words from a computer programme with some restriction [closed]

A computer program is devised to generate all $3-$letter code words that can be formed by using the letters A, B, C, M,N,P, W,X, Y, Z only. Repetition is allowed. When we sort the resulting words in ...
1
vote
4answers
55 views

Explaining multiplication of fractions

The best way I've been able to describe multiplication is as $$ a\times b = \sum^a_{i=1} b$$ But my definition does not account for things such as $2.99792458\times8.987551787$ and ...
0
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1answer
30 views

Vector Image Representation on 640X480 Screen

Im trying to learn Computer Graphics. I have the following statement For the representation of vector images, we assume that a typical image consists of 500 lines [BHS91]. Each line is defined by its ...