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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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Traffic Homework Help

At 5am, a pedestrian starts walking from $A$ to $B$, a distance of $30$ km. At $7$ am a bicyclist whose speed is $2$ times the pedestrian's speed, started riding from $A$ to $B$, too. After some time, the bicyclist met and passed the pedestrian.…
Alon Gubkin
  • 634
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Coefficients of $1,x,x^2$ in $((\cdots (x-2)^2-2)^2-2)^2\cdots )-2)^2$

Finding coefficients of $x^0,x^1,x^2$ in $((\cdots (x-2)^2-2)^2-2)^2\cdots )-2)^2$ where there are $k$ parenthesis in the left side Try: Let $P(x)=((\cdots (x-2)^2-2)^2-2)^2\cdots )-2)^2$ Let we…
DXT
  • 11,241
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Small question on Pythagoras theorem

The projections-of-the-legs over the hypotenuse should add up to the hypotenuse $c$. Is there any alternative way to prove below? $$a\cos \alpha + b\sin \alpha = \sqrt{a^2+b^2}$$
AgentS
  • 12,195
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Finding the coefficient

How to find the coefficient of $a^3b^4c^5$ in the expansion of $(ab+bc+ca)^6$
user62581
  • 51
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Simple algebra question (find the LCM of the polynomials by factoring)

First of all, I am so embarrassed by this. I am tutoring this kid in math and this question came up: Find the LCM of $y^2 - 81$ and $9 - y$, which factor into $(y + 9)(y - 9)$ and $-(y - 9)$ My answer: $-(y+9)(y-9)$ Her book's answer:…
Ninosław Brzostowiecki
  • 1,411
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Stuck on $6y-3-(2y-1)=12$

Solve for y: $$6y-3-(2y-1)=12\tag1$$ $$6y-3-2y-1=12\tag2$$ $$4y-4=12\tag3$$ $$4y=12+4\tag4$$ $$y=4\tag5$$ But when I plugged into $(1)$ it is wrong, $y=4$ $$6y-3-(2y-1)=12\tag1$$ $$24-3-(8-1)=12\tag a$$ $$24-3-(7)=12\tag b$$ $$14=12\tag c$$ Where…
Endgame
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Formula for calculating transaction fees

Let's say a credit card processor wants to charge $(3\% + \text{US}\$ 2)$ for all transaction. What formula do I use to make sure that after the charges are deducted, I get the figure I want. Example: If my product is $\text{US}\$ 100$ How much do…
Lasker
  • 53
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Find out when $(x + y)^5 = x^5 + y^5$ (Spivak's Calculus Book)

I know that I can see that this match with $y = 0$, $x = 0$ and $y = -x$. But, the author of the book says: "Hint: From the assumption $(x + y)^5 = x^5 + y^5$ you should be able to derive the equation $x^3 + 2x^2y + 2xy^2 + y^3 = 0$ if $xy \neq 0$.…
Jonatan Garcia
  • 415
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Expanding $(1-a^k-a^{-k})^m$, where $m$ is a positive integer

How can I find the expansion of $$(1-a^k-a^{-k})^m$$ where $m$ is a positive integer? I know that I can split the sum and use the binomial theorem but this seems really ugly. Does anybody recognize instantly what will this be, or, even better, can…
Zugzwang14
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Three men travelling

Three men want to travel from town $P$ to town $Q$ (distance between towns: $a$). They have a motorbike (vehicle speed: $b$), but only two of them can be on the motorbike at the same time. Their walking speed is $c$ ($b$ > $c$). How much time do…
Rakaho
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AIME 1997, problem 12

Please have a look : Problem The function $f$ defined by $f(x)= \frac{ax+b}{cx+d}$, where $a$,$b$,$c$ and $d$ are nonzero real numbers, has the properties $f(19)=19$, $f(97)=97$ and $f(f(x))=x$ for all values except $\frac{-d}{c}$. Find the unique…
adnan2nd
  • 162
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I need to know the formula to compute time to reach a star

I am working on a sci-fy short story and I need to use a somewhat realistic value for the time in transit for going to a star. Assume that energy on the space ship is not a problem. The space ship accelerates at some amount of G-force until…
Kent Byerley
  • 151
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How to solve $\left(\frac3{p-3}-1\right)\left(2+\frac4{p-2}\right)=0$?

I'm currently preparing myself for uni and thus learning on my own. This equation is killing me as the book doesn't explain how to solve it. $$\left(\frac3{p-3}-1\right)\left(2+\frac4{p-2}\right)=0$$
B.Cakir
  • 71
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How is $\sqrt{n^2+2n}-\lfloor\sqrt{n^2+2n}\rfloor=\frac{2}{\sqrt{1+\frac{2}{n}}+1}$.

I have trouble seeing how $$\sqrt{n^2+2n}-\lfloor\sqrt{n^2+2n}\rfloor=\frac{2}{\sqrt{1+\frac{2}{n}}+1}.$$ I can't see where to start even.
Krau
  • 53
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Integral part of sum of huge powers

Question: What is the integral part of the following expression?$$(a+\sqrt{b})^{2n}+(a-\sqrt{b})^{2n}$$ The question has specific values of $a=2,b=5$ and $2n=2016$. I was able to simplify (or complexify) it…
Anvit
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