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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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Maximum of Sums of Product Pairs

Given two ascending distinct integer sets, $A = A(0), A(1), \dots, A(n)$, and $B = B(0), B(1), \dots, B(n)$, I'm looking for the maximum sum, where elements from $B$ are multiplied by elements from $A$, for example: $$\begin{align} \max \{ &…
גלעד ברקן
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Simple, find-intersection task by calculation. How do I know only one is valid?

Possible Duplicate: Is there a name for this strange solution to a quadratic equation involving a square root? As you can see, they only cross once. By setting $3-x=\sqrt{15-x}$ I manage somehow to find two possible values for…
Algific
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How to solve $y=-x^3/(x^2-9)$ for $x$

This is not a homework question. I am doing a independent study refresher on precalc prior to taking calculus. Wolfram gives an unbelievably long series of steps with techniques I have not even heard of. Yet this is a problem out of a precalc book.…
wkyniston
  • 33
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Express in terms of $x$ and $y$ when the values of $x$ and $y$ are given.

Given, $x=1+3a+6a^2+10a^3+\ldots$ $y=1+4b+10b^2+20b^3+\ldots$ $s=1+3ab+5(ab)^2+7(ab)^3+\ldots$ Express $s$ in terms of $x$ and $y$. My work: I could see how the first sequence works, but could not find how the second sequence works, until I wrote…
Hawk
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Please explain where the $2x$ came from in this cubic identity:

The question is to factorize the difference of cube identity $(x + 1)^3 - y^3$ I obviously want to put it in the form of $(a - b)(a^2 + ab + b^2)$ My working out: $(a - b) = (x + 1) - (y) = (x + 1 - y)$ $(a^2 + ab + b^2) = (x^2 + 1) + (x + 1)(y) +…
Hypertrophy
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Solving $[x]=ax+1$

Given the equation $[x]=ax+1$, where $a \in \mathbb{R}$ and $[x]$ is the whole part of $x$, how do I solve for $x$?
user130556
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Simple equation, but I don't get it

I don't know how to do this simple equation, could you help me? thanks! 6x + 4 = 4 [ 2x -5 ( x -2 ) ] 6x +4 = 4 [ 2x -5x +10 ] 6x +4 = 8x -20x +40 +6x -8x +20x = -4 +40 18x = 36 36:18 = 2 Thank you all!
mesacuadrada
  • 53
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What ever happened to convex functions? – or, Since when is a function “concave up”?

Possible Duplicate: Why does “convex function” mean “concave up”? Forty years ago I recall seeing the definition of a convex function (ie, that the points on the line segment joining two points on its graph are above its graph), with the…
Mike Jones
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How do I algebraically manipulate this?

From a paper that I have been reading, I have: $n \pi = +\sqrt{(+k_2+\sqrt{k_2^2-4k_3k_1}) \times \dfrac{1}{2k_1}}$; where $k_1 = (1-\dfrac{\alpha^2 \lambda^2}{\zeta^2})$; $k_2= \lambda^2[\Omega + \dfrac{1-\Omega \alpha^2…
Train Heartnet
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Adding fractions is not at all obvious

Why does $\frac{5}{4} + \frac{2}{3}$ need to be rewritten as $\frac{15}{12} + \frac{8}{12}$ to be added? It's not obvious. I'm looking towards the fact that any integer can be rewritten as $x=qy$ but these work for rational numbers as well. Can…
user3200098
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An inequality question

The question says that $x > 0$ and then we have to prove that $(x + 1)^{1/2} < 1 + (1/2)x$. I tried this question and proved that $(x + 1) < (1 + (1/2)x)^2$ but after this I am not able to proceed because I can't do square root in both sides …
Achal Kumar
  • 503
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Find an equation of the line cut off by the axes such that the midpoint is (2,6)

I'm currently taking precalc level math and I was given a question, which I solved, I was just wondering about an alternate way to do it. "Find an equation of the line that passes through the point (2, 6) in such a way that the line cut off between…
Howcan
  • 395
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Why is $p^2-q^2 = p-q$ when $p+q = 1$?

I'm having trouble to see why it is that: $p^2-q^2 = p-q$ when $p+q = 1$ If I take a number for which $p+q \not= 1$, this doesn't hold. What's so special about the former case? Can someone take me through this, algebraically?
BigSmoke
  • 155
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Max. and Min. value of $f(x,y) = \frac{x-y}{x^4+y^4+6}$

[1] Calculation of Max. and Min. value of $\displaystyle f(x) = \sqrt{x^3-6x^2+21x+18}$, where $\displaystyle -\frac{1}{2}\leq x\leq 1$ [2] Calculation of Max. and Min. value of $\displaystyle f(x,y) = \frac{x-y}{x^4+y^4+6}\;,$ where $x,y\in…
juantheron
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How do I find the relationships between two variables in a formula that are on the same side of the equals sign?

When I've been asked to find the relationship between two variables in a formula (assuming the other variables are constant), it's generally been things like find the relationship between $F$ and $R$ in $F=\frac{kQq}{R^2}$, where the relationship is…
Threethumb
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