Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [algebra-precalculus]

For questions about algebra and precalculus topics, which include linear, exponential, logarithmic, polynomial, rational, and trigonometric functions; conic sections, binomial, surds, graphs and transformations of graphs, solving equations and systems of equations; and other symbolic manipulation topics.

This tag is for questions typically taught in precalculus, as well as elementary algebra.

These topics include linear, exponential, logarithmic, polynomial, rational, and trigonometric functions; conic sections, binomials, surds, graphs and transformations of graphs, solving equations and systems of equations; and other symbolic manipulation topics.

47234 questions
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Find the value of $\frac{a^2}{a^4+a^2+1}$ if $\frac{a}{a^2+a+1}=\frac{1}{6}$

Is there an easy to solve the problem? The way I did it is to find the value of $a$ from the second expression and then use it to find the value of the first expression. I believe there must be an simple and elegant approach to tackle the problem.…
learning
  • 1,749
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Looking for a trick to solve $2\sqrt {2x}+\sqrt {2x+3}=\sqrt {3x+2}+\sqrt {6x+20}$

Consider the equation: $$2\sqrt {2x}+\sqrt {2x+3}=\sqrt {3x+2}+\sqrt {6x+20}.$$ Find a trick ( if exists ) which allows to solve it elegantly i.e. with avoiding the systematic squaring. (The systematic squaring inevitably leads to a fourth-degree…
Maria Mikolayevskaya
  • 81
8
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9 answers

Cutting cake into 5 equal pieces

If a cake is cut into $5$ equal pieces, each piece would be $80$ grams heavier than when the cake is cut into $7$ equal pieces. How heavy is the cake? How would I solve this problem? Do I have to try to find an algebraic expression for this?…
Steven
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8
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6 answers

What's the midpoint of $[a,b)$?

While the midpoint of either $[a,b]$ or $(a,b)$ is $\dfrac{a+b}{2}$, what's the midpoint of $[a,b)$ if it has been defined at all?
user231343
8
votes
1 answer

Four $2$'s to make $7$

So I'm trying to use four $2$'s to make the number $7$. I can use parenthesis, addition, subtraction, indicies, addition, division, multiplication edit: also have the same problem with $9$ but I'll try that myself if someone could help with $7$
iphone7
  • 91
8
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7 answers

How to convert a decimal to a fraction easily?

Given a decimal like $1.5$, I want to find an easy way to write it as $3/2$ in this case is easy but given a decimal such as $0.3760683761$, how could I figure out it can be written as $572/1521$? Thx. Edit In case anyone is interested in more about…
NoChance
  • 6,427
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4 answers

How to expand $(x_1 + x_2 + x_3 + x_4 + x_5 +\cdots+x_n)^{2}$

How to expand $(x_1 + x_2 + x_3 + x_4 + x_5 +\cdots+x_n)^{2}$. Is their any general formula for this? Thanks
Taylor Ted
  • 3,408
8
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6 answers

How to solve this exponential equation?

I'm given this equation and i have to solve for the x. $$ e^{2x} -(e^5 + e^2)e^x + e^7 = 0 $$ The results should be $x =2$ and $x = 5$. At first i thought it would be an easy task, substituting $e^x$ with $y$, but I can't get rid of the…
user258607
  • 475
8
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2 answers

How do I solve for $P$ in $ A=\frac{\left \lfloor (n+1)^{P} \right \rfloor}{\left \lfloor n^{P} \right \rfloor} $

I have the following equation: $$ A=\frac{\left \lfloor (n+1)^{P} \right \rfloor}{\left \lfloor n^{P} \right \rfloor} $$ How to solve for $P$ using $A$ and $n$, where $n \in \Bbb N \setminus \{ 0 \}$ and $A, P \in \Bbb R$?
japseow
  • 311
8
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4 answers

An elementary doubt on Inequalities

Given the following expression: $$(7y-1)(y-7) \le 0$$ To me this inequality implies $y \le 7$ and $y \le \frac{1}{7}$ but the correct expression (from my module) happens to be $\frac{1}{7} \le y \le 7$ Where exactly I am wrong?
Quixotic
  • 22,431
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3 answers

e and its applications

In math when people want to model population growth or radioactive decay we use exponential functions. In many cases, we use base $e$. My question is, what is the purpose of using base $e$ rather than some other base?
user250837
  • 89
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5 answers

Proving that the number $\sqrt[3]{7 + \sqrt{50}} + \sqrt[3]{7 - 5\sqrt{2}}$ is rational

I've been struggling to show that the number $\sqrt[3]{7 + \sqrt{50}} + \sqrt[3]{7 - 5\sqrt{2}}$ is rational. I would like to restructure it to prove it, but I can't find anything besides $\sqrt{50} =5 \sqrt{2}$. Could anybody give me some hints?…
geomquestion
  • 403
8
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2 answers

Equation with absolute values and parameters

In my textbook there is a statement that for a fixed positive integer $a$, there is at most one positive integer $b$ such that: $|b-1|+|b-2|+\cdots+|b-2001|=a(a+1)$. They claim that it's obvious but to me it is not obvious. Can anyone explain why…
chen h.
  • 723
7
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5 answers

What is $(-8)^\frac{2}{3}$?

I am comfuse about something. I want to compute $(-8)^\frac{2}{3}$ Is it $(-2^3)^\frac{2}{3}$=$(-2)^{3\cdot\frac{2}{3}}$=$(-2)^2=4$ ? Is there any problem here because the base is negative? Thanks.
ruth
  • 73
7
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2 answers

Reverse the equation to solve for y

I'm trying to solve for $Y$ in this equation: $\frac {(X-Y)}{Y} = Z.$ I tried applying some of the answers from other questions but I'm having special trouble with figuring out how to get the $Y$ out of the parenthesis. Thanks!
Mishka1
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