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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Proof an equation is wrong?

How can I prove that the equation $r=16^r$ is wrong for any arbitrary value of $r$? I have tried: \begin{align} &r=16^r &&\implies \log_r r = \log_r 16^r \\ &&& \implies 1 = r\log_r 16 \\ &&& \implies 1/r = \log_r 16 \\ &&& \implies r^{1/r} =…
Sharod Saor
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Logarithm Equality.

$$\sqrt {\log_a(ax)^{\frac{1}{4}} + \log_x(ax)^{\frac{1}{4}}} + \sqrt {\log _a{(\frac{x}{a})^{\frac{1}{4}}} + \log_x (\frac{a}{x})^\frac{1}{4}} = a,$$ for $a>0$ and different than 1... I keep getting $a = 1$, but that cannot be. I use log…
Aaron Oberländer
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Help with composite functions?

Suppose that $u$ and $w$ are defined as follows: $u(x) = x^2 + 9$ $w(x) = \sqrt{x + 8}$ What is: $(u \circ w)(8) = $ $(w \circ u)(8) = $ I missed this in math class. Any help?
Spaceman
  • 31
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If $a = \frac{\sqrt{5}+1}{2}$ then $(a+1)^{25} =$?

I have no idea how to do this. If $a = \dfrac{\sqrt{5}+1}{2}$ then $(a+1)^{25} =$? I tried to transform $a$ to polar form but failed, because if it can be in polar form, I could calculate with de Moivre's formulae. Can anyone please explain me…
ABCDEFG user157844
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Why can one take the power of $e$ directly?

The definition of Euler's constant to the power $x$, $e^x$, is $$e^x = \sum_{n=0}^\infty \frac{x^n}{n!} = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + {...}$$ And of course, we have the number $e$ defined as $$e = \sum_{n=0}^\infty…
user158163
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Find the exact value of the trigonometric Function csc(-630 °) Answer is csc( 90°) but why is it positive 1?

I evaluated csc(-630 °) = csc(90°) and understand it is a quadrantal, but I do not understand why it is 1 nor why it is +1 and not -1. Can someone explain?
user137452
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Completing the following equation by the suitable method

i got this linear equation two variable problems for my school. I understand the basics of the normal linear equation but this seems different instead having a pure number after the "=" they got a ration, here is the problem. $$X:2Y = 5:14$$ $$(X+4)…
Scott
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Can someone please check my answer for this exponential question?

Would someone mind helping me by checking my answer that I have worked out? I think I am correct... but I can't seem to find an answer for it anywhere so I want to be sure I am right. Thank you in advance! $$ (x^4 y)^{2/3} (xy^3)^{1/3} \over x^{2/3}…
Dani
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An $n$th root simplification - why is my answer an absolute value?

Ok so I need to simplify this: $$\sqrt[\LARGE 6] {x^{25}y^{10}\over x^7 y^4}$$ I can easily break it down to the answer $x^3 y$ but I have seen that my answer is actually meant to be $|x^3 y|$ Can anyone please explain to me why I must put my…
Dani
  • 171
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$\frac{2t-t^2}{t+2} \cdot (\frac{5t}{t-2} - \frac{2t}{t-2} )$

Simplify: $$\frac{2t-t^2}{t+2} \cdot \left(\frac{5t}{t-2} - \frac{2t}{t-2} \right)$$ I first subtracted the parenthesis because the denominator is equal. I then got: $$\frac{2t-t^2}{t+2} \cdot \frac{3t}{t-2}$$ Then I was lost. I tried multiplying…
user160137
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System of quadratic equations with three variables

The problem is as follows: For $x,y,z \in R$, $$ \left\{ \begin{array}{l} x^{2} -yz-8x+7=0 \\ y^{2}+z^{2}+yz-6x+6=0 \end{array} \right. $$ What is the domain of $x$? One way to solve this is to use another variable. This is shown in this answer.…
mentoR
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How do you prove a function is defined for a a certain set?

Spin-off from here. Context: Highschool textbooks often ask students to find the domain of functions. Let's say $f(x) = x+2$. The domain is $\mathbb{R}$...suppose a student (highschool or o/w) asks why $f(x)$ is defined ∀$\mathbb{R}$...? What about…
BCLC
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Find the roots of $ t^2 + at + bc = 0 $ .

Question: $x^2 + bx + ca = 0 $ and $ x^2 + cx + ab = 0 $ have only one non-zero common root , show that their other roots satisfy $ t^2 + at + bc =0 $ . I have tried to solve it by first finding the common root which is equal to $-(b + c)$ . Then I…
user142971
3
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2 answers

Solve the equations $\tan x=x$ and $\ln x=x$

Is it possible to solve the equations $\tan x=x$ and $\ln x=x$ in their respective domains of definition ?
user20010
3
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3 answers

Use division instead of multiplication

Is there any way to calculate x/y without using division? Like 1/10 = 1 * 0.1 . I'm asking because dividing is slower than multiplying in programming programs.
Cobold
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