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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Mathematical Invariant

Start with the set {3, 4, 12}. You are allowed to perform a sequence of replacements, each time replacing two numbers a and b from your set with the new pair 0.6 a - 0.8b and 0.8 a + 0.6b. Can you transform the set into {4, 6, 12}? Look for an…
Jebediah
  • 543
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Express in the form (x-a)

How to express $2x-1$ in the form $x-a$ ? Isn't $x-1/2$ wrong? And how to express $2x+3$ in the form x-a? this is for using it in the remainder theorem: when $f(x)$ is divided by $x-a$, the remainder is $f(a)$
gcse
  • 65
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Maximum of the product $P(N)=\prod_{k=1}^N\frac{k^a}{a^k}$

Given the following product: $$\displaystyle P(N)=\prod_{k=1}^N\frac{k^a}{a^k}$$ it can be expressed as: $$P(N)=\Gamma(N+1)^a\frac{1}{a^{\frac{1}{2}(N+1)^2-\frac{1}{2}N-\frac{1}{2}}}$$ I have to find the maximum of $P(N)$ vs. $a$. The derivative of…
Riccardo.Alestra
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Calculate a ratio from part of a range.

I'm building a smartphone javascript application but my question today is really only math related. To give you a quick idea of what I'm doing, my code checks the smartphone's gyroscope to determine how much it is rotated. Based on that rotation,…
kthornbloom
  • 133
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Tax inclusive pricing

I have a system where is user can enter a price (without tax) and a tax rate. I then calculate the total cost of the item. Example: Price:100.00 Tax percent: 10% Final price: 110.00 = (100 + (100* (10/100)) I have got a request to work backwards and…
Chris Muench
  • 151
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Simplifying the sum of a fraction and an integer under a radical sign

I'm trying to help my little bro, a bit rusty here... Wolfram Alpha is telling me that: $$ x\sqrt{1+{\frac{x^2}{16-x^2}}} $$ simplifies to: $$ 4x\sqrt{\frac1{16-x^2}} $$ I can't for the life of me figure out why. I'm thinking there's a simple rule…
Michael Lewis
  • 225
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Vector linear combination problem

Point $A$ and $B$ have position vectors $\vec a$ and $\vec b$ respectively relative to an orgin $O$. The point $D$ is such that $\overrightarrow{OD} = k\overrightarrow{OA}$ and the point $E$ is such that $\overrightarrow{AE} =…
mathguy80
  • 1,321
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Cauchy-Schwarz inequality for i=2 ; the quickest proof possible

I've already found some proofs of this inequality: $$\sum_{i=1}^n a_i b_i \le \sqrt {\biggl(\sum_{i=1}^n a_i^2\biggr)\biggl(\sum_{i=1}^n b_i^2\biggr)}$$ (using dot product) but they were far too long. I need only a proof for i=2, meaning I need to…
somnock
  • 33
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Solving equation with absolute value. Two solutions where only one is right.

I have solved this equation: $$ \sqrt{3x}-\sqrt{4x-5}=0 $$ And I got that the solutions are: $$ x=\frac{5}{7}, x=5 $$ My question is, did I do it right, because $$ x=\frac{5}{7} $$ dont fit in the equation. I mean, if I put 7/5 in equation, I…
depecheSoul
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$a+b+c=0;a^2+b^2+c^2=1$ then $a^4+b^4+c^4$ is equal to what?

$a+b+c=0;a^2+b^2+c^2=1$ then $a^4+b^4+c^4$ is equal to what? I tried to solve this problem, and I get $a^4+b^4+c^4 = 2(a^2b^2 + 1)$ but I'm not sure if it's correct
bububu
  • 55
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how can I solve this kind of equation?

I've got a system of equations which is: $\begin{cases} x=2y+1\\xy=10\end{cases}$ I have gone into this: $x=\dfrac {10}y$. How can I find the $x$ and $y$?
Orel
  • 33
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Calculation of all values of $a$ for which $3x^2+(4-2a)x-8-a^2\leq 0$.

Calculation of all values of $a$ for which $3x^2+(4-2a)x-8-a^2\leq 0$. Given that $x$ lies between $-3$ and $2$. My Try:: Let $x = \alpha,\beta$ be the Roots of Given equation. where $-3<\alpha,\beta<2$ So $\displaystyle \alpha+\beta =…
juantheron
  • 53,015
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If $|z| = 2$. Then Locus of $z$ Representing The Complex no. $-1+5z,$ is

If $|z| = 2$. Then Locus of $z$ Representing The Complex no. $-1+5z,$ is $\underline{\bf{My\;\; Try::}}$ Let $z^{'} = -1+5z$, Where $z^{'} = x^{'}+iy^{'}$. So put $5z = z^{'}+1$ in $|z| = 2\Leftrightarrow |5z| = 10$ $|z^{'}-(-1+0\cdot i)| = 10$,…
juantheron
  • 53,015
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2 answers

Are all values of $\sin(x)$ algebraic.

Can we prove that for all $x$ in $(0,2\pi)$ $\sin(x)$ is an algebraic number? I have seen people express various values of $\sin(x)$ like $\sin(3)$ and $\sin(30)$ using radicals so I suspect that all values of $\sin(x)$ must be algebraic. Is that…
Adam
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The Three-Number Problem

I am currently working on a little extra credit for my 9th grade math class and I am stuck on the one of the problems. The Three-Number Problem I have chosen three numbers. The second is twice the first, and the third is three times the second. The…
Shawn Holman
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