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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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3 Ants going at different speeds, when they will be at the same place Motion Problem

The circumference of a circle has length 90 centimeters, Three points on the circle divide the circle into three equal lengths. Three ants A, B, and C start to crawl clockwise on the circle, with starting from one of the three points. Initially A is…
suomynonA
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Intersection of a circumference with a the curve: $y=ax^k$

Given the circunference centered in the origin of a cartesian reference frame, its equation is: $x^2+y^2=r^2$, Assuming $r=1$, we have: $x^2+y^2=1$. The intersections of this curve with the curve described by the equation: $y=ax^k$ with…
Riccardo.Alestra
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If the numerator of a fraction is increased by $2$ and the denominator by $1$, it becomes $5/8$....

If the numerator of a fraction is increased by $2$ and the denominator by $1$, it becomes $\displaystyle \frac{5}{8}$ and if the numerator and the denominator of the same fraction are each increased by $1$, the fraction becomes equal to…
Abhishekstudent
  • 1,211
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3 answers

Cannot follow the algebra

The following equality is stated in my text book and I cannot follow the algebra that makes it true. Please help me step through this to show how $$\frac{4^x}{3^{x-1}} = 4 \left(\frac{4}{3}\right)^{x-1}$$
Jessie
  • 63
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If $y^y=x$, can $y$ be expressed as a function of $x$?

If $y^y=x$, can y be expressed as a function of x? Specifically, I am finding the solution to a PDE where the most general solution is $u=t^{-\frac{1}{2}} f(x,t)$ and $$\LARGE f^f=Ce^{\frac{-x}{2\sqrt{t}}} $$ Any help will be appreciated!
atomteori
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4 answers

An Inequality about power numbers

Which number is larger? $4^{25}$ or $9^{15}$. Why? I know that it used powers of 2 and 3 but how?
bigli
  • 161
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3 answers

Simplify expression $(x\sqrt{y}- y\sqrt{x})/(x\sqrt{y} + y\sqrt{x})$

I'm stuck at the expression: $\displaystyle \frac{x\sqrt{y} -y\sqrt{x}}{x\sqrt{y} + y\sqrt{x}}$. I need to simplify the expression (by making the denominators rational) and this is what I did: $$(x\sqrt{y} - y\sqrt{x}) \times (x\sqrt{y} - y\sqrt{x})…
user160137
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Solve $\dfrac{x}{x-2}>2$ by first rewriting it in the form $\dfrac{P(x)}{Q(x)}>0$

Edit: So then is this the correct final solution? $x<4,(\infty,4), x\ne2$ I am asked to do this: Solve $\dfrac{x}{x-2}>2$ by first rewriting it in the form…
nitrous2
  • 2,451
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How to solve: $\frac{2^{n+1}}{n+1}=\frac{4+2^n}{3}$

$n$ is an integer variable satisfying $$\frac{2^{n+1}}{n+1}=\frac{4+2^n}{3}$$ How can I find $n$?
Purushothaman
  • 497
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1 answer

$a^b=b$; $a \ne b$ Find a rational solution.

I am a high school teacher and last week we were given some example problems for the new End of Course Exam for Algebra 1. One such is "$a^b=b$; $a \ne b$ Find a rational solution." I know I can take $a=b^{\frac{1}{b}}$ and use any value of…
John Tompson
  • 43
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Why this recursively defined sequence of real numbers converges to -Pi?

Remy J. Cano in his private email described the sequence of real numbers, recursively defined as $$a(n) = a(n-1)+\frac{2 \cdot \cos(\frac{a(n-1)}{2})}{2 \cdot \sin(\frac{a(n-1)}{2})-1},a(0)=0$$ This sequence converges to $-\pi$ that is for $n…
Alex
  • 56
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How do you prove the domain of a function?

Edit: Man, I actually had a bachelor's completed when I asked this dumb question, like even more than the terry tao dumb thing. Don't judge me! But to be fair even when I was in calculus we're always asked to 'find the domain' of single variable…
BCLC
  • 13,459
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3 answers

What is the inverse of $f(x) = \sqrt{x} + 2$?

I got $$f^{-1}(x) = (x-2)^2$$ Is this answer right?
Prologue
  • 235
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2 answers

Solving for $x$ when $x$ is the denominator

How do you solve for $x$ when $x$ is in the denominator? E.g. $$10 = \frac{g-1}{x}$$
methuselah
  • 283
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How to solve this equation for $x$?

How do I solve for $x$ from this equation? $$ -\frac{1}{x^2} + \frac{9}{(4-x-y)^2} = 0.$$ I need to get this into $x=$"blah"?
PhilCK
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