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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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Converting Single Equation To A System Of Equations

Assuming $f\neq 0$ I'm trying to rewrite $$0 = 2 \cdot g \cdot ((x-a)^2 + 1) - 2 \cdot d \cdot f \cdot (x - a)$$ into a system of equations of the form $a = $(something not containing $d$) $d = $(something with $a$ in it) I'm pretty sure you need…
Jon
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Solving Equation $\lfloor|x|\rfloor+\lfloor |y|\rfloor=3$

How can I solve this equation for $(x,y)$? $$\lfloor|x|\rfloor+\lfloor |y|\rfloor=3$$ Can you help me? Thanks.
user97601
3
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3 answers

Time taken to complete a piece of work

A can complete a piece of work in 80 days. He worked work for 10 days , after that B completed the remaining work in 42 days. If A and B work together how many days will it take them to complete the entire piece of work? a)30 b)25 c)40 d)none of…
Ravi Jain
  • 143
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2 answers

How to properly divide equations and inequalities by a variable?

Let's consider a simple equation: $$3x^2-2x+x=x^2-1$$ or inequality $$3x^2-2x+x < x^2-1$$ or $$3x^2-2x+x > x^2-1$$ How to properly divide by $x^2-1$. In many examples I've seen it is stated that division can be done properly only if $x^2-1$ is…
Misery
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Question which has no answers

Sorry, I don't really know how to improve this question, this quiz has been given me today and I think there is no a true answer, because in the different cases of $a > 0, a < 0, b > 0, b < 0$(and nested cases) you have that every answer can be…
Niccolò Campolungo
  • 131
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2 answers

Find all natural numbers n such that $7n^3 < 5^n$

Find all natural numbers $n$ such that $7n^3 < 5^n$. I drew a graph which showed that $n \geq 4$ wolfram How can I prove that? I guess I need to use induction with the base case $n=4$? But I am stuck because the induction hypothesis uses a $\geq$…
Justin D.
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interpret a sum geometrically

I have this sum: $1+3+5+...+(2n+1)$, where $n$ is a natural number. I have to calculate it and interpret geometrically. Well, it's easy to find out that it equals $(n+1)^2$. But how to interpret it geometrically? I don't think it's about a…
user95553
3
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2 answers

Which steps I have to do to get this equation?

I don't know what to do to derive the right side from the left side: $$\frac{B}{1+r} = B - \frac{r B}{1+r}.$$
Georg
  • 31
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5 answers

Distance between a point and a plane

I was just working on some review textbook problems in James Stewart's Multivariable Calculus when I encountered a problem that looked like the following: Find the distance between the point $(1,2,3)$ and the $xz$-plane. I've seen questions that…
Sujaan Kunalan
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If $\,x-\frac 1 x=k, \, k$ being any integer,then $\,\,x^5-\frac {1}{x^5}=?$

I am stuck with the following problem which one of friends gave me : If $\,x-\frac 1 x=k, \, k$ being any integer,then $\,\,x^5-\frac {1}{x^5}=?$ The options are $\,\,k^5+4k^3+4k, \,k^5+5k^3+6k,\,k^5+5k^3+5k,\,k^5+5k^3+4k $. We see that $x-\frac 1…
learner
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1 answer

$F(\frac{1} {x})=x^3 - 2$; what is $F(\frac{x} {y})$?

$$F\left(\frac{1} {x}\right)=x^3 - 2$$ $$F(x)=\left(\frac{1} {x}\right)^3 - 2$$ $$F\left(\frac{x} {y}\right) = \left(\frac{y} {x}\right)^3 - 2 $$ I don't understand what I'm doing wrong.
Myles
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Stuck on computing the derivative of $f(x)=6x^2-\dfrac{6}{x}$ using the limit definition of the derivative.

First I set up the difference quotient as follows: $$\dfrac{6(x+h)^2-\frac{6}{x+h}-(6x^2-\frac{6}{x})}{h}$$ Then I expand the binomial in the first term, and distribute $6$ and…
xvymnp
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Solve $2x^2-3\sqrt{2x^2-7x+7}=7x-3$

Solve $2x^2-3\sqrt{2x^2-7x+7}=7x-3$ $\Rightarrow (2x^2-7x)-3\sqrt{2x^2-7x+7}=-3$ Let $\sqrt{2x^2-7x+7}=y$ so that $2x^2-7x+7=y^2$, $\Rightarrow (y^2-7)-3y=-3$ or $y^2-3y-4=0$ So $y=4$ or $y=-1$ $\sqrt{2x^2-7x+7}=4$ or…
ronald christenkkson
  • 1,623
3
votes
1 answer

Find the smallest value of n for which the nth term of the series is less than 0.001

Question: The common ratio and the first term of a geometric series are 0.55 and 18 respectively. Find the smallest value of n for which the nth term of the series is less than 0.001 $${\text{My solution:…
Audrey G
  • 51
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3 answers

Calculating Interest

A person deposited $5000\$$ at $10\%$ simple interest for $2$ years. How much more money will she have in her account at the end of two years, if it is compounded semi-annually? $50/40/77.5/85.5$ My attempt: $\dfrac{5000*10*2}{100}=1000,$ so…
aarbee
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