All Questions
Tagged with algebra-precalculus arithmetic
795
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Shouldn’t $0$ to any power be undefined?
So one of my younger cousins asked me this today. This is the summed up version of what they said.
We know that for all real numbers $x^{n-1} = \dfrac{x^n}{x}$, because $x^{n+1} = x^n \cdot x$.
So let'...
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0
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1
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Commutative Property with More than Two Terms
Suppose I have the expression:
a+b+c+d+e
If I wanted to change the positions of a and e, is this one application of the commutative property of addition, where I can swap these terms directly, or ...
- 29
1
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1
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64
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Formula for Sum of Numbers with Consecutive Digits [closed]
Let's say we have a number $n$ that consists of $b$ digits, all of which are the same digit $x$.
Then we have another number $m$ that has $b - 1$ digits, also all the same digit $x$.
How would you ...
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1
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Why can't fractions be simplified separately within an expression [closed]
Here is a simple example:
$\frac{-x}{2}$ + $\frac{6}{2}$
Why can't I simplify $\frac{6}{2}$ here which would give me 3 for an answer.
The actual equation was y= $\frac{-x}{2}$ + $\frac{6}{2}$
I had to ...
1
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4
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123
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Ambiguity textbook exercise involving $\sqrt{-144}$
Consider the following questions, the whole exercise is dedicated to determining the square root of negative numbers, after introducing the complex numbers. Eg.
$$\sqrt{-144}$$
Solutions for the whole ...
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0
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1
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32
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Need hints (advice) to prove $(\forall a,b,c,d \in \mathbb{R}) (a < b \wedge c<d) \Rightarrow ad+bc < ac +bd$
I'm trying to prove this ( source : my uni's textbook says that it's trivial).
$$(\forall a,b,c,d \in \mathbb{R}) (a < b \wedge c<d) \Rightarrow ad+bc < ac +bd$$
So far, I've managed to get ...
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1
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Are there any cases in which: $x \neq (x)$? [duplicate]
My question: is this true?
$x\over y$= $(x) \over y$
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0
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How do you find the total amount of a group when the given are percentages and an absolute count of a portion of the group?
Let's say you an unknown number of members of a group, and they split up to go to the following locations:
Park: 35% of the members
School: 20% of the members
Post office: 15% of the members
Library: ...
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1
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3
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82
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What is statistically more accurate - the average of a dataset of calculated concentrations or the sum of the total mass divided by the total volume? [closed]
Hopefully an easy question to answer.
But if I have a series of five water samples, each sample is a different volume with a different number of plastic particles contained within. I can calculate the ...
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The 1st, 2nd, and 10th terms of an arithmetic series are equal to 1st, 4th, 17th terms of a geometric series respectively. [closed]
For the arithmetic series, the 1st number is a, the common difference is d.
For the geometric series, the common ratio is r.
How to figure out the value of r?
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1
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123
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Assuming all the terms of A.P. $[a_{n}]$ are integers with $a_{1}=2019$. Find number of such sequence satisfying given condition
Assuming all the terms of A.P. $[a_{n}]$ are integers with $a_{1}=2019$ and for $n\in I^+$ there always exsits positive integer $m$ such that $a_{1}+a_{2}+.....+a_{n}=a_{m}$, then find number of such ...
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2
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Evaluating $x^3-18x^2+90x$, where $x= 6 + 6^{2/3}+ 6^{1/3}$ [duplicate]
If $x= 6 + 6^{2/3}+ 6^{1/3}$,
then find the value of $x^3-18x^2+90x$
My try:
I tried like directly substituting the value but it proved to be quite tedious and then I tried to take $6^{\frac{1}{3}}$ ...
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0
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38
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If there are 29 vehicles per one square kilometers, how many square kilometers per 100 vehicles are there?
29 vehicles/$km^2$ means (1/29) $km^2$/(1 vehicle)
Per 100 vehicles there are 1/2900 $km^2$.
Whatever you sq kilometers are you have to divide by 100 moto vehicles
100/29 $km^2$/100 vehicles
(100/29)/...
user1218223
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Is the fractional part of a real number has to be greater than or equal to 0 but less than 1?
https://en.wikipedia.org/wiki/Fractional_part
I was reading the definition of fractional part, but I have not understood something and I want to make sure.
Is the fractional part of a real number has ...
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2
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Are the operators of the four basic operations of arithmetic binary operators? [closed]
Supposing I have a subtraction (multiplication and division) of 3 or more numbers, e.g., 20 - 3 - 2 - 3 - 1, will the subtraction end up being done in pairs, i.e., the - operator is ...
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