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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How to reach $k\cdot 2^{k+2}$ from $(2k)\cdot 2^{k+1}$?

I was trying to figure out the step between these two equal expression: $$(2k)\cdot 2^{k+1} = k\cdot 2^{k+2}$$
malhobayyeb
  • 421
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Roots of polynomial with natural coefficients

A polynomial equation with natural coefficients can have natural roots ?
F. Wolfango Macedo
  • 41
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Intuition: inverse function

Disclaimer: I'm a beginner with inverse functions. Can anyone explain what I'm doing wrong here? I'd like to avoid using "y" -- that is, I want to show everything in terms of x and f(x). Thanks!
mellow-yellow
  • 509
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Relationship between ratios and averages of ratios?

My colleague and I were wondering: For a weighted average of ratios - what weight would need to be assigned to each term in the expression such that the result of the weighted average was the same as the sum of the numerators in the ratios divided…
Steve
  • 177
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Intersection of semicircle and parabola (Omar Khayyam)

(Source: The History of Mathematics 7th Edition, David Burton) I can't even get through question a.. Could someone give a hint? The only thing I can think of is the Pythagorean Theorem, but it turns out that that is not going to help me..
Dr. Heinz Doofenshmirtz
  • 2,360
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Inequalities and rearrangements

Some children are arranged in two rows, so that each child in the front row is taller than the child behind him in the back row. The children are now rearranged in increasing order in each row. Show that in the new arrangement each child in the…
orangeskid
  • 53,909
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6 answers

Proof of the power rule for logarithms

What is the proof for the power rule for logarithms? And are there different ways to prove it?
The Puppet Master
  • 125
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The number of non-negative real roots of $2^{x}-x-1$ are

The number of non-negative real roots of $2^{x}-x-1$ are $ a.)\ 0\\ b.) \ 1 \\ c.)\ 2 \\ d.)\ 3 \\$ I don't have any clue. I have only learned to solve quadratics and cubic equations , i haven't been taught to solve such type of equations…
R K
  • 2,635
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Applying difference of cubes to cube roots

I am stumped as to why this application of the difference of cubes is valid... I am rationalizing the denominator. I don't understand the reasoning of why the difference of cubes formula is applicable to cubed roots, removing the root one gets an…
Kurt
  • 613
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Why cannot $(2x^2 + x)^2$ be simplified to $2x^4 + x^2$?

So, I want to simplify an equation : $(2x^2 + x)^2$. I thought this would simplify to $2x^4 + x^2$ But, if you input a value for $x$, the answers do not equal. For example, if you input $x = 3$, then: $$(2x^2+x)^2 = 21^2 = 441$$ AND: $$2x^4 + x^2 =…
Jordan Ruetz
  • 61
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Where's my mistake?

This is partially an electrical engineering problem, but the actual issue apparently lays in my maths. I have the equation $\frac{V_T}{I_0} \cdot e^{-V_D\div V_T} = 100$ $V_T$ an $I_0$ are given and I am solving for $V_D$. These are my steps: Divide…
Kian
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Find the range of a $4$th-degree function

For the function $y=(x-1)(x-2)(x-3)(x-4)$, I see graphically that the range is $\ge-1$. But I cannot find a way to determine the range algebraically?
Bob Simons
  • 71
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20 years since I was in high school. How do I break this down?

$-5 = 2x + 5$ I want to "re-start" my mathematical education. I am needing it more and more at work. A co-worker asked me to break that down (he couldn't remember either). Where should I start? What books? Thanks!
cbmeeks
  • 143
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Why does my solutions manual take away or add 180 when finding $\theta$?

These are the provided notes: These are the provided questions: I do not understand when I should subtract, add or leave the answer as is (The notes do not make sense to me very much). I do not, clearly, have an intuitive understanding of…
math_enthusiast_but_is_Bad
  • 41
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Solve the equation $x^3-x+\frac16\sqrt3=0$

8 (i) By first expanding $\sin(2\theta+\theta)$, show that $$\sin3\theta=3\sin\theta-4\sin^3\theta\tag4$$   (ii) Show that, after making the substitution $x=\frac{2\sin\theta}{\sqrt3}$, the equation $x^3-x+\frac16\sqrt3=0$          can be written…
Irtiza
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