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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Determine the number of terms in simplified expression

I've just started teaching myself algebra from a high school text-book and I stumbled upon this problem : How many terms does the simplified form of $(a+b+c)^{2006}+(a-b-c)^{2006}$ have ? I found something on Wikipedia that appeared to be useful,…
jake
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If $f(x) = \sin^4 x+\cos^2 x\;\forall x\; \in \mathbb{R}\;,$ Then $\bf{Max.}$ and $\bf{Min.}$ value of $f(x)$

If $f(x) = \sin^4 x+\cos^2 x\;\forall x\; \in \mathbb{R}\;,$ Then $\bf{Max.}$ and $\bf{Min.}$ value of $f(x).$ My Solution:: Let $$\displaystyle y = \sin^4 x+\cos^2 x \leq \sin^2 x+\cos^2 x=1$$ And for Minimum, We take $$\displaystyle y = \sin^4…
juantheron
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$a^2b + abc + a^2c + ac^2 + b^2a + b^2c + abc +bc^2$ factorisation

I came across this from a university mathematics resource page but they do not provide answer to this. What I did was this: $(a^2+b^2+c^2)(a+b+c) - (a^3 + b^3 + c^3) + 2abc$ But I don't think this is the correct solution. How should I spot how to…
zcahfg2
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Find the value of $(-1)^{1/3}$.

Evaluate $(-1)^{\frac{1}{3}}$. I've tried to answer it by letting it be $x$ so that $x^3+1=0$. But by this way, I'll get $3$ roots, how do I get the actual answer of $(-1)^{\frac{1}{3}}$??
JSCB
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Why does cubic equation have 3 roots but not 9?

In here: http://en.wikipedia.org/wiki/Cubic_function#Cardano.27s_method Cardano's method says that for $ax^3+bx^2+cx+d=0$, $x=y-\dfrac{b}{3a}$, and $y=u+v$. We have found the values of $u^3$ and $v^3$, but both $u^3$ and $v^3$ should have $3$ roots…
JSCB
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Can $y=\frac{e^\frac{t^4}{12}}{e^{\frac{t^3}{3}}}$ be simplified?

Can $y=\frac{e^\frac{t^4}{12}}{e^{\frac{t^3}{3}}}$ be simplified? So, I'm working on a problem and I encounter this problem instead. For some reason, the way it looks is intimidating. So this is how I'm tackling it: I multiply the bottom denominator…
Justin
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Why/How does this sqrt term work? The inverse of a fraction in a sqrt

Why does this term work? $$ \frac{1}{\sqrt{\frac{g}{l}}} = \sqrt{\frac{l}{g}} $$
ColdStormy
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Easy calculation for room mates

I have a very simple question which is bugging me. We are 3 roommates and our total electricity bill is $61 this month, I was home for the whole month, Friend X was home for 15 days, Friend Y was home for 20 days now the easy question, how much…
ufucuk
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Why is the graph of $x=y^2$ and $y=\sqrt{x}$ not the same?

So if you take $x=y^2$ and get the sqrt of both sides you get $y=\sqrt{x}$ so they are the same right? But when you graph them, $y=\sqrt{x}$ only shows the positive $y$ values because you can't sqrt a negative number because no 2 same numbers…
gopro_2027
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Simplify arithmetic equation

I have to solve the system : $$\begin{align*} a+b &= S\\ a\times b&= P\\ \end{align*}$$ Someone told me it was equivalent to solve the equation $x^2-S.x+P=0$. I think it's linked with the formula of sum and product of the roots of a second-degree…
Cydonia7
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Reducibility of a fraction

I encountered this problem in "Elementary Mathematics" by Dorofeev. For what natural numbers n is the fraction $\frac{2n+3}{5n+7}$ reducible to lower terms? So this means that $2n + 3$ and $5n + 7$ must share a common divisor $D$ for it to be…
geomquestion
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One clock gains, another clock loses time. When will both clocks next show the same time?

Problem: A wall clock gains $2$ minutes in $12$ hours while a table clock loses $2$ minutes every $36$ hours. Both are set correctly at $12$ noon on Tuesday. When will both clocks next show the same time? Choices: $\text{a.)}\quad 12:30\quad …
R K
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Prove $\frac{a}c = \frac{a-b}{b-c}$

Suppose $\frac{1}a,\frac{1}b,\frac{1}c$ are three consecutive terms in an arithmetic sequence. Show that: $$\frac{a}c = \frac{a-b}{b-c} $$ and that: $$\frac{2ac}{a+c} = b$$ How would I prove this?
user1843145
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Writing an expression of the form $X^2 − A^2$

"Write the following expressions in the form $X^2 − A^2$ using the method of completing the square." "1) $x^2 + 8x + 9$" I don't understand how that can be, but I did try to do it, with no obvious next steps. My solution:- $x^2 + 8x + 16 -16 +…
w4j3d
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3 points lie in the same straight line. Then why is this formula valid?

I am given that the points $(0,1)$, $(x,y)$ and $(\phi(x,y),0)$ are all lying in the same straight line from the north pole of the circle $S^1=\{ (x,y)\in \mathbb{R}: x^2+y^2=1 \}$ to the point $(\phi(x,y),0)$ which is a point on the $y=0$ axis. The…
Marion
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