0
votes
3answers
52 views

What is the meaning of $\log^2n$ and how should it be read in word form?

$\log^2n$ is what I need assistance with. How is this read in word form? What exactly does this mean? No matter how much I read about logarithms, they still seem new to me.
0
votes
4answers
66 views

If statements in equations?

When creating an equation is there any way to let someone know that if this number doesn't fit into this then use this other equation? Ex: $x>1$ then use $x+y$, or if $x<1$ then use $x-y$. Or ...
-5
votes
1answer
40 views

function notations

can you explain how you get this answer? and explain the answer? the distance in feet $d(t)$ a dropped object falls in $t$ seconds is given by the function $d(t)=16t^2$. suppose you drop a ball from ...
0
votes
1answer
32 views

Are several equality operators okay to use in mathematics?

For example, is it okay to say: $x=y=z=1$ if $x,y,z$ all equal $1$?
0
votes
1answer
58 views

How to find the domains of functions $f(x) = x-5$, $g(x) = \sqrt{x-5}$, and of their sim?

I've been studying on Study Plan Practice, on MyMathLab for my College Algebra class. We're going over the Algebra of Functions right now and several things don't make much sense. The question is: ...
6
votes
3answers
110 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
44 views

Expressing a solution in interval notation

I am faced with this problem. I am told to express the answer in interval notation. |3x| > 12 I solve like usual, by doing this: ...
5
votes
2answers
78 views

What is this notation for a function? I've never seen it written like this before.

What does this mean? $$ f=\{ (x,y): y= x+2 \}$$ I don't understand what "$(x,y):$" means in regard to the problem. Also why is the $y$ inside of the $f(x)$ function. Isn't it supposed to be outside? ...
0
votes
0answers
24 views

Creating a formula (notation) from series of equations

I need some help with "shrinking" of few equations I have a couple of categories of circles. For each one of these, a certain equation, which represents the circle radii is written: for 1st ...
0
votes
1answer
23 views

Using $\pm$ to express “in the range of” statement.

Does it make sense to write: $x = \left\{A\pm B\right\}$ To mean that $x$ falls in the range of $\left\{A-B,A+B\right\}$? If not, what would be the correct way of expressing this? Many thanks!
3
votes
2answers
75 views

If you were asked to evaluate $x^2$ for $x = -1$

Would you bracket the $x$? I ask this because $-1^2$ is equal to $-1$, but $(-1)^2$ is equal to $1$. Which is valid?
10
votes
5answers
2k views

Why does two terms immediately adjacent “mean” multiply?

I am currently teaching a GED math class. While learning about the order of operations, the students asked why does a number next to a parentheses mean multiplication? I understand the rule that two ...
0
votes
4answers
45 views

Why do you add +- to only one side when you remove square root from both sides?

As the title says, why when you take a square root of both sides of the equation do you add $\pm$ only to the side which is a number, as opposed to an unknown? For example: $$x^2 = 9 \implies x = ...
2
votes
4answers
112 views

Notation: is it correct to state $3a=a3$?

If $a$ is a real constant, do you regard $3a$ and $a3$ as equal or different?
0
votes
3answers
54 views

Question about variable and constant notation in some properties

I am just starting to think about mathematical notation a lot more and some parts of it do not make as much sense to me as I would like. I am operating under the convention that beginning alphabet ...
0
votes
0answers
71 views

Compact notation for expression

Consider the following expression: $$(a^2+b^2)^2 = a^4 + b^4 + 2a^2b^2$$ $$(a^2+b^2+c^2)^2 = a^4 + b^4 + c^4 + 2a^2b^2+2a^2c^2 +2b^2c^2$$ Or this one, in which you cannot group terms: $$(a+b)(a^3+b^3) ...
8
votes
6answers
634 views

What we're never taught explicitly

I would like to make a complaint really. School math(s) can be the most boring way to learn: sitting down and rote learning binomial expansion or the volume of a cylinder is just not interesting. It ...
0
votes
1answer
116 views

Problem with simple Projectile motion formula

I'm really new to all this, so please don't be rude. I have here what appears to be a simple formula. Yet I cant get my head around it: $$\begin{align} y &= y_0 + v_{0y}t + (1/2)a_y t^2 \\ 0 ...
1
vote
2answers
69 views

What does this function mean?

$$f(x) = \frac{x}{e^{x^2}}$$ Differentiate $f(x)$. How should the above function be interpreted? Is the function equivalent to: a)$$f(x) = \frac{x}{e^{x^2}} = \frac{x}{{(e^x)^2}} = ...
4
votes
1answer
53 views

Is there a commonly accepted notation for algebraic numbers?

In this question I needed a way to denote an algebraic number using a polynomial equation it satisfies and its isolating polynomial. Because I am not aware of any commonly accepted notation for this, ...
1
vote
1answer
139 views

Symbol of equivalence for comparing two equations?

If I need to compare two distinct equations, such as $y=\log_a x$ and $x=a^y$, is there any symbol that I can use in order to compare them instead of using words: "[equation 1] is equivalent to ...
2
votes
0answers
192 views

Set Notation with Intercepts

I really love set notation, and I'm finding myself using it more and more. My question is whether this would be a valid symbolic representation of intercepts. For example, take $$y=x^2-10x+16$$ ...
0
votes
1answer
33 views

Value expressions

What is the value of the expression: $\sum_{k=0}^{d}b^{k}\left[\begin{array}{c} d\\ k \end{array}\right]\prod_{i=0}^{k-1}\left(c-b^{i}\right) $ for $ k = 0 $? In particular, what is then the value ...
1
vote
1answer
370 views

Identities for Kronecker delta and alternating unit tensor

How I can prove this equations? Please help me... I can solve it. $$\sum_j\sum_k \varepsilon_{ijk} \varepsilon_{hjk} = 2\delta_{ih}$$ $$\sum_k \varepsilon_{ijk} \varepsilon_{mnk}= \delta_{im} ...
0
votes
1answer
132 views

Function and dependent variable are represented by the same symbol?

Is it wrong to represent a dependent variable and a function using the same symbol? For example, can we write the parametric equations of a curve in xy-plane as $x=x(t)$ , $y=y(t)$ where $t$ is the ...
1
vote
1answer
278 views

using the same symbol for dependent variable and function?

Is it wrong to represent a dependent variable and a function using the same symbol? For example, can we write the parametric equations of a curve in xy-plane as $x=x(t)$, $y=y(t)$ where $t$ is the ...
3
votes
3answers
67 views

unknown equals constant or constant equals unknown?

Frequently, in solving a simple equation involving an unknown such as x + 1 = 2, at the end, we often write the answer as x = 1 instead of writing the answer as 1 = x, that is an unknown equals a ...
1
vote
2answers
107 views

Deriving logarithmic identities

Wikipedia says: The numerical value for logarithm to the base $10$ can be calculated with the following identity: $$\mathrm{log_{10}}(x) = \frac{\mathrm{ln}(x)}{\mathrm{ln}(10)} \\ ...
2
votes
1answer
48 views

The convention regarding the use of the radical sign

It is well known that the expression $\sqrt[n]{z}$ (where $n$ is a natural and $z$ a complex number) is somewhat ambiguous - there are in fact $n$ complex numbers which satisfy $x^n=z$ (if ...
0
votes
1answer
66 views

Intervals and sets

I never took calculus until now, but as a stat major I have sometimes used the notation $x\in [a, b]$ as an alternative way of writing $a\leq x \leq b$. Does it make sense to express it like this, or ...
3
votes
1answer
922 views

What does the notation min max mean?

Min clearly means minimum and max maximum, but I am confused about a question that says "With $x, y, z$ being positive numbers, let $xyz=1$, use the AM-GM inequality to show that min max $[x+y,$ ...
3
votes
1answer
128 views

Notation: What is the scope of a sum?

I would interpret $\sum_{i=1}^2 x_i + y$ as $x_1 + x_2 + y$, but I would interpret $\sum_{i=1}^2 x_i + y_i$ as $x_1 + y_1 + x_2 + y_2$. I realize this is a little inconsistent. Should the latter be ...
0
votes
3answers
101 views

Question about changing a logarithm's base

I've been using the following method to derive/remember the logarithm base conversion formula: If I want to convert $\log_a(x)$ to an expression in base $b$, I say, $$a^{\log_a(x)}=x\\ ...
4
votes
3answers
132 views

Order of calculation in all math equations

I already asked a question (Order of operations in rotation matrix notation.) about the order in which a particular equation is "processed" and now I need to generalise that and learn the rules of ...
2
votes
2answers
97 views

How can we simplify $(a\pm b)(c\pm d)$?

Is there any way to simplify the expression: $$(a\pm b)(c\pm d)\quad ?$$ At first, I tried just distributing the values, and through FOIL I achieved: $$ac \pm ad \pm bc \pm bd$$ This works when the ...
0
votes
6answers
2k views

An easy way to remember PEMDAS

I'm having trouble remembering PEMDAS (in regards to precedence in mathematical equations), ie: Parentheses Exponentiation Multiplication & Division Addition & Subtraction I understand ...
1
vote
3answers
107 views

A question about Algebra

4 years ago I have not been in sight for a math book. Today I had a dumb question. I hope you can understand me. $(\sin(x))^2$ is $\sin(x^2)$ or $\sin^2(x)$ I believe that to learn calculus, the ...
0
votes
3answers
106 views

Dumb percentage question?

Why do we multiply by 100 while calculating percentage ? example : 2/100 * 100 =2%
0
votes
1answer
4k views

How to write such sqrt (sqrt(x)) in equation?

Is it correct to write sqrt(sqrt(x)) as equation/formula ? or root4(x) ? I mean if x = 10000 it will be 10
1
vote
1answer
62 views

Is there a simplified equation for doing something like this:

Is there a simplified equation for doing something like this: $$(1x) + (2x) + (3x) + (4x) + (5x)$$ but the number it goes to (the example goes to 5 ) can be variable?
4
votes
2answers
1k views

What are functions used for?

When I say functions, I don't mean the trigonometric functions like $sin$, $cos$, and $tan$, I mean defined functions like $\large f(x) = 2x + 4$. Why is $\large f(x)$ used and why isn't a single ...
3
votes
1answer
97 views

How do I refer to a certain element in a set?

I have an idea about how to do this. I've seen this before so this is what I think. Is this how you refer to a single element in a set? $$a = \{5, 7, 3, 4\};a_2 = 7$$ Is this correct?
1
vote
1answer
157 views

Solving quartic equation - notation

I am going through Wikipedia's solution of a quartic equation and have got stuck with notation in the solution. The solution is given by this equation: What is confusing me is the significance ...
3
votes
2answers
83 views

Origin of the notation $(x-h)$ and $y-k$ in shifting

Does anyone know the origin of the notation $(x-h)$ and $(y-k)$ when shifting functions in algebra? Why $h$ and $k$?
0
votes
2answers
265 views

distributive law in polish notation

On page 18 "Logic as Algebra" Halmos&Givant wrote the distributive law in Polish notation as $$ = \times a + bc + \times ab \times ac $$ I fail to see anything remarkable here, is there a ...
0
votes
2answers
227 views

How to write a functional fold in mathematics?

Given is a sequence of natural numbers: $1,2,...,n$. I want to choose two elements $a,b$ of this sequence, calculate $c=ab+a+b$ and write $c$ back to the sequence. After $n-1$ iterations, there is ...
2
votes
2answers
99 views

Elementary question on Sums notation

I reading on Sums and I am reading about the difference between using a generalized Sigma notation and the delimited form. Ok, I understand that the generalized form is more expressive. But I ...
17
votes
2answers
12k views

Weird E letter? (sigma) [duplicate]

Possible Duplicate: What does the math notation $\sum$ mean? My school's prescribed book uses the weird letter E character without explaining what it is in the first chapter when it talks ...
3
votes
5answers
1k views

What does the exclamation mark do?

I've seen this but never knew what it does. Can any one let me in on the details? Thanks.
17
votes
3answers
613 views

How to answer a student objection to the use of “of” in pronouncing f(x)?

Once upon a time in elementary school, a student learned how to translate certain English words into math. For example, 'and' usually means 'plus' such as "If John has 3 oranges AND 5 apples, how ...