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 do I start from a 10% discount and find the original price?

I have a database of prices that already have a 10% discount. For example a product could be $100 after a 10% discount. Is there a reusable formula I can use to determine what the original price was of all the 10% discounted prices in the…
Eric
  • 153
5
votes
3 answers

Prove using mathematical induction: $1 \cdot 2 \cdot 3 + \ldots + n \cdot (n+1) \cdot (n+2) = \frac{n(n+1)(n+2)(n+3)}{4}$

So I have the easy stuff done. However, I'm not sure how to go about doing the inductive step with such an awkward proof. :/ Statement: $$ 1 \cdot 2 \cdot 3 + … + n \cdot (n+1) \cdot (n+ 2) = \frac{n \cdot (n + 1) \cdot (n + 2) \cdot (n +3)}{4}…
oorosco
  • 105
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3 answers

Parametric to cartesian conversion

$x= t^2-t, y=t^3-2t^2+t $ $x= 1-\sin t, y=\cos t(1-\sin t)$ Find cartesian equations. For 1, I have $x=t(t-1), y=t(t-1)^2$, then $y/x= t-1$ and $t=(y/x)+1$. $x=(y^2+xy)/x^2$, then $x=(y^2+xy)^{1/3}$. Is there an explicit solution? For 2, I have…
J.c
  • 81
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5 answers

What is completing the square?

Why is it called, completing the square? Is square metaphorical in this sense? How do you complete the square and what is it used for? Thank you, regards.
Janni
  • 79
5
votes
3 answers

System of $\sqrt{7x+y}+\sqrt{x+y}=6$ and $\sqrt{x+y}-y+x=2$

$$\begin{align*}\sqrt{7x+y}+\sqrt{x+y}=6\\\sqrt{x+y}-y+x=2\end{align*}$$ I have tried various things squaring, summing but nothing really helped, got some weird intermediate results which are probably useless such…
Templar
  • 1,743
5
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2 answers

Continuation from here...

p.s I have no idea how to type math on this program so I just copied and pasted from a document. p.p.s I also tried doing it with log base a and that was a travesty. This was my best attempt because it was the nicest looking
jd123
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3 answers

if range of $f(x) = \frac{x^2+ax+b}{x^2+2x+3}$ is $[-5,4]$. Then $a$ and $b$ are

If Range of $\displaystyle f(x) = \frac{x^2+ax+b}{x^2+2x+3}$ is $\left[-5,4\; \right]$ for all $\bf{x\in \mathbb{R}}$. Then values of $a$ and $b$. $\bf{My\; Try}::$ Let $\displaystyle y=f(x) = \frac{x^2+ax+b}{x^2+2x+3} = k$,where $k\in…
juantheron
  • 53,015
5
votes
2 answers

Expressing sums of products in terms of sums of powers

I'm working on building some software that does machine learning. One of the problems I've come up against is that, I have an array of numbers: $[{a, b, c, d}]$ And I want to compute the following efficiently: $ab + ac + ad + bc + bd + cd$ Or: $abc…
dan_waterworth
  • 153
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votes
2 answers

How to find the greatest number among 3 integer numbers?

Can anyone explain to me where & how can I use this equation. I was told to make a program that reads 3 integer numbers and prints the greatest one using the following formula. But how? $$\operatorname{Major} AB = \frac{a+b+abs(a-b)}{2}$$
Fazla Rabbi Mashrur
  • 1,563
5
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4 answers

How to justify what solving method to use

How do you determine what solving method to use, for example what is the reason you solve by the quadratic formula, or by factoring, or by completing the square, or by taking a square root.
user116761
  • 51
5
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1 answer

Uniqueness of a solution of a system of equations

While studying quantummechanics, I encountered following algebraic problem: We know that if $l$ is a non-negative integer: $$2l+1 = \sum_{-l}^l{c_m(-1)^m}$$ $$2l+1 = \sum_{-l}^l{\vert c_m\vert^2}$$ Where $c_m$ are coefficients, that may be complex.…
yarnamc
  • 709
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votes
2 answers

How find this equation

solve this equation $$\sqrt{\sqrt{3}-\sqrt{\sqrt{3}+x}}=x$$ My try: since $$\sqrt{3}-x^2=\sqrt{\sqrt{3}+x}$$ then $$(x^2-\sqrt{3})^2=x+\sqrt{3}$$
math110
  • 93,304
5
votes
3 answers

Is $(0,0)$ a solution to $x^y-y^x=0$?

I am trying to determine if $(0,0)$ a solution to $x^y-y^x=0$. My hunch is that it is undefined since $0^0$ is an indeterminate form. To attempt to prove this, I have tried the usual "different paths give different limits" trick…
NoClue
  • 145
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votes
1 answer

Even, Odd, or Neither

I would like someone to verify my solutions to the problems above? 9a. even 9b. odd 10. neither
user123940
  • 183
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votes
2 answers

solving system of 2 equations

Are there any nice/elegant ways to solve this system of equations? $\left\{\begin{matrix} 2x^2+xy+y^2=28 & \\ x^2-xy+2y^2=32 & \end{matrix}\right.$ I can solve it by isolating one of the variables but it's too messy. Thanks!
gazok
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