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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A caterpillar eating leaves

I'm no maths genius, by any means... I just thought of this, I think it's math related, and I know that SO is a good place to ask about it... So here goes: A caterpillar can eat half it's body weight per day in leaves. It is on a bush with 12…
Hungry Little Caterpillar
  • 43
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Is $\lfloor x\rfloor$ defined in terms of $|x|$ and branch selection?

Is $\lfloor x\rfloor$ defined in terms of repeated square root branch selection: $$\lfloor x\rfloor = \frac{1}{2}\left(\sum_{n=-\infty}^\infty\frac{+\sqrt{(x-n)^2}}{x-n} \right) - \frac1{2}$$ Or the arctangent's logarithmic branch…
jnm2
  • 3,170
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Ratio + Quantity

I am trying to create a metric which would tell us how good or bad a client is. Right now I am using a simple ratio: $$ \frac{\text{number of bills paid on time}}{\text{number of bills}}. $$ This give me a percentage and it essentially tell us if…
Martin
  • 195
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Can this be solved algebraically? $2^x (6 - x) = 8x$

I've been working on this problem for a few days, but I haven't been able to find $x$ algebraically. (Maybe I'm missing something obvious?) $2^x (6 - x) = 8x$ Using a MATLAB program, I found the solutions $ x = 2, 3, 4 $. I tried using…
Kevin Chen
  • 147
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Solve math equation mentally with algebra shortcut

I'm looking to solve this equation mentally, with the following numbers, using an algebra shortcut. $$a = bc + \frac{1}{2} dc^2$$ with $$ \begin{eqnarray*} c &=& 10.204, \\ d &=& -9.8, \\ b &=& 100. \end{eqnarray*} $$ Can anyone think of a…
xaav
  • 187
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Calculation of $\lambda$, If $x^2+2(a+b+c)\cdot x+3\lambda \cdot (ab+bc+ca) = 0$ has real roots

Let $a,b,c$ be the sides of a $\triangle$ where $a\neq b\neq c$ and $\lambda\in \mathbb{R}$. If the roots of the equation $$x^2+2(a+b+c)\cdot x+3\lambda \cdot (ab+bc+ca) = 0$$ are real , Then which one is Right. $\bf{Options}::$ $\displaystyle…
juantheron
  • 53,015
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Real roots of the equation $1+\sum_{r=1}^{7}\frac{x^{r}}{r} = 0$

The number of real roots of the equation $\displaystyle 1+\frac{x}{1}+\frac{x^2}{2}+\frac{x^3}{3}+\frac{x^4}{4}+\frac{x^5}{5}+\frac{x^6}{6}+\frac{x^7}{7} = 0$ $\bf{My\; Try}::$ Let $\displaystyle f(x) =…
juantheron
  • 53,015
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positive integer ordered pairs $(x,y,z)$ in $\frac{1}{x}+\frac{1}{y}+\frac{1}{z} = 1$

Total no. of positive integer ordered pairs of $(x,y,z)$ that satisfy the equation $\displaystyle \frac{1}{x}+\frac{1}{y}+\frac{1}{z} = 1$ $\bf{My\ Try:}$ Using Simple Guess $x=2\;,y=3\,z=6.$ satisfy $\displaystyle…
juantheron
  • 53,015
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Solution of the equation $\left(x+\frac{1}{x}\right)^{\frac{1}{x}}=A$

Is it possible to solve analytically the following equation? $$\left(x+\frac{1}{x}\right)^{\frac{1}{x}}=A$$ with $A\gt 1$? I tried to transform it in the following: $\frac{1}{x}\ln\left(x+\frac{1}{x}\right)=B$ with $B=\ln(A)$, but it seems to be…
Riccardo.Alestra
  • 10,546
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proving $ \frac{a^2}{c-1}+\frac{b^2}{d-1}+\frac{c^2}{e-1}+\frac{d^2}{a-1}+\frac{e^2}{b-1}\geq 20$

If $a,b,c,d,e>1$, Then prove that $\displaystyle \frac{a^2}{c-1}+\frac{b^2}{d-1}+\frac{c^2}{e-1}+\frac{d^2}{a-1}+\frac{e^2}{b-1}\geq 20$ $\bf{My\; Try}::$ Using Cauchy- Schtwartz Inequality $\displaystyle…
juantheron
  • 53,015
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Find $x$ for $\left(\frac1{1\times101} + \frac1{2\times102} + \dots +\frac1{10\times110}\right)x = \frac1{1\times11} + \frac1{2\times12}...$

$$\left(\frac1{1\times101} + \frac1{2\times102} + \dots +\frac1{10\times110}\right)x = \frac1{1\times11} + \frac1{2\times12} + \dots +\frac1{100\times110}$$ Find x My younger sister in grade 5 had this question in a test. But I, a college student,…
LamNS
  • 41
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Math of Human Pyramids

I was writing a blog post today, and I ended up asking the question of how many layers tall a human pyramid would be if it contained all of the people who use Facebook, approximately 750 million. First I had to define how the pyramid would work.…
Peter
  • 1,021
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Writing $\frac{(\sqrt{2}+1)^{2n+1}+(\sqrt{2}-1)^{2n+1}}{2\sqrt{2}}, n\geq2$ as sum of two perfect squares

I tried to show that $$ {\left(\sqrt{2\,} + 1\right)^{2n+1} + \left(\sqrt{2\,} - 1\right)^{2n+1} \over 2\,\sqrt{2\,}}\,,\qquad n\geq2 $$ is written as the sum of two perfect squares. We used Newton's binomial formula and we did. Is there another…
medicu
  • 4,482
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solving $0<1-(3x/4)<1$ for $x$

My professor wrote this: $$0<1-\frac{3x}{4}<1$$ $$-1<-\frac{3x}{4}<0$$ $$4>3x>0$$ $$\frac{4}{3}>x>0$$ Is that correct?
user2982390
  • 117
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How prove this $\frac{a}{(bc-a^2)^2}+\frac{b}{(ca-b^2)^2}+\frac{c}{(ab-c^2)^2}=0$

let $a,b,c\in \mathbb{R}$, if such $$\dfrac{1}{bc-a^2}+\dfrac{1}{ca-b^2}+\dfrac{1}{ab-c^2}=0$$ show that $$\dfrac{a}{(bc-a^2)^2}+\dfrac{b}{(ca-b^2)^2}+\dfrac{c}{(ab-c^2)^2}=0$$ Does this problem has nice methods? My…
user94270
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