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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When are the Laws of Exponents correct?

The rules of powers are in highschool books often briefly stated in the following way: $\displaystyle a^n \cdot a^m = a^{n+m}$ $\displaystyle \frac{a^n}{a^m} = a^{n-m}$ $\displaystyle \left (a\cdot b\right )^n = a^n \cdot b^n $ $\displaystyle…
Kasper
  • 13,528
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Difficulty understanding division sign in expression

I have difficulty understanding following expression: $$(64x^3÷27a^{-3})^\frac{-2}{3}$$ Should I interpret the division sign as follows: $$\left(\frac{64x^3}{27a^{-3}}\right)^\frac{-2}{3}$$ Or as I originally interpreted…
user3051847
  • 159
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Every year, there is a contest...

Every year, there is a contest to see who has the heaviest pumpkins for that year. Last year, a farmer brought 5 pumpkins to the contest. Instead of weighing them one at a time, he informed the judges, "When I weighed two at a time, I got the…
Sentient
  • 675
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2 answers

A highschool factoring problem

$x+y+z=0$ $x^3+y^3+z^3=9$ $x^5+y^5+z^5=30$ $xy+yz+zx=?$ I solved this problem by setting $xy+yz+zx=k$ and using the cubic equation with roots $x,y,z$. But is there any other methods?
Gobi
  • 7,458
13
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3 answers

Solve $x^y \, = \, y^x$

Possible Duplicate: $x^y = y^x$ for integers $x$ and $y$ I obtained a question asking for how to solve $\large x^y = y^x$. The given restraints was that $x$ and $y$ were both positive integers. By a bit of error an trial we quickly see that $x=2$…
N3buchadnezzar
  • 10,896
12
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3 answers

Is it possible to solve this equation by hand?

I am working on a physics task, and reduced it to the following equation for $y$: $$\frac{1}{4y^3}-\frac{2}{(y^2+b^2)^{\frac{3}{2}}}=0$$ I handed it to Mathematica, and it gave me two real solutions, $$y_{1,2} = \pm\frac{b}{\sqrt{3}},$$ along with…
Pascal Engeler
  • 711
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Is there a name for the point of a exponential curve where the y axis significantly increases?

It's been hard to come up with a question title that makes sense so please bear with me. On an exponential curve there's a point on the x axis where the y axis starts increasing significantly. The exact location/ calculation of the point isn't…
BaronGrivet
  • 245
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3 answers

Is there any good reason not to define $0^0=1$ , such as contradictions in algebra or arithmetic?

Math people: The title is the question: Is there any good reason not to define $0^0=1$ , such as contradictions in algebra or arithmetic? I searched for similar questions before I posted this question, and couldn't find any. After I posted it, I…
Stefan Smith
  • 8,192
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Complex slope of line $a\bar{z}+\bar{a}z+b = 0$

How can we prove......... [1] The Complex slope of the line $a\bar{z}+\bar{a}z+b = 0$ is $\displaystyle \omega = -\frac{a}{\bar{a}}$ [2] Complex slope of line joining the points $z_{1}$ and $z_{2}$ is $\displaystyle \omega =…
juantheron
  • 53,015
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Is solving an equation the same as finding the roots?

For example, would solving for $x$ in $x^2=8x+7$ be the same as finding the roots of the equation? Also, would finding the roots of this be the same as finding the zeros?
Neal
  • 121
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3 answers

Finding :$x_1^8+x_2^8+\cdots+x_8^8$

If $x_1,x_2,\ldots,x_8$ are roots for the equation : $$x^8-13x^2+7x-6=0$$ then how to find $$x_1^8+x_2^8+\cdots+x_8^8$$
user64688
  • 123
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Prove $\sqrt[n]{m}\leq\sqrt[3]{3}\lor\sqrt[m]{n}\leq\sqrt[3]{3}$ for $n,m\in\mathbb{N}>1$.

Prove that for any integers $m$ and $n$ greater than $1$, at least one of the numbers $\sqrt[n]{m}$ or $\sqrt[m]{n}$ is not greater than $\sqrt[3]{3}$. My attempt goes something along the lines of stating that for…
Lazar Ljubenović
  • 2,896
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1 answer

A simple mathematics riddle that has me batty.

I'm looking to confirm an answer I came up with. I'm pretty sure this is going to seem really silly to many of you because it's probably very easy for you to understand, but I can't wrap my head around it. Problem: You have 23 lights, each with its…
Charles Ar
  • 129
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8 answers

What is really the purpose of $i$?

We started talking about imaginary numbers again this year and asked this question in class, but nobody could really give a straight answer. So if anyone could tell me the real reason we have imaginary numbers that would be great! :)
Angelina Wallis
  • 129
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5 answers

How to show this fraction is equal to 1/2?

I have the fraction: $$\frac{\left(2 \left(\frac {a}{\sqrt{2}}\right) + a \right) a} {2(1 + \sqrt{2})a^2}$$ Using Mathematica, I've found that this simplifies to $\frac{1}{2}$, but how did it achieve the result? How can I simplify that fraction to…
user305676
  • 159
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