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 can I prove this equation: $(1+ \frac{1}{n})^n = 1+ \sum\limits_{k=1}^n{\frac{1}{k!}}1(1-\frac{1}{n})\cdot(1-\frac{2}{n})…(1-\frac{k-1}{n})$

Possible Duplicate: Proving sequence equality using the binomial theorem $(1+ \frac{1}{n})^n = 1+ \sum\limits_{k=1}^n{\frac{1}{k!}}\cdot1\cdot(1-\frac{1}{n})\cdot(1-\frac{2}{n})\cdot…\cdot(1-\frac{k-1}{n})$ This is how far I came using the…
Lenar Hoyt
  • 1,062
3
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2 answers

If $A= \left\{1,2,3,4,5,6\right\}$ and $f(x)$ be a onto fn. from $A$ to $B$ such that $f(i) \neq i \;\; \forall \; i\in \{1,2,3,4,5,6\}$.

If $A,B = \left\{1,2,3,4,5,6\right\}$ and $f(x)$ be a onto function which is defined from $A$ to $B$ such that $f(1) = 2$ and $f(i) \neq i \;\; \forall \; i\in \{1,2,3,4,5,6\}$. $\bf{My\; Try::}$ No. of onto function from $A$ to $B$ is equivalent to…
juantheron
  • 53,015
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If $f:\mathbb{R}\rightarrow \mathbb{{R}}$ and $f(x)$ satisfying $f(2x+3)+f(2x+5) = 2$ . The period of $f(x)$

If $f:\mathbb{R}\rightarrow \mathbb{{R}}$ and $f(x)$ be a function satisfying $f(2x+3)+f(2x+5) = 2$. Then period of function $f(x)$ is. $\bf{My\; Solution::}$ Let $(2x+3) = t\;,$ Then equation is $f(t)+f(t+2) = 2$ Now Replace $t\rightarrow…
juantheron
  • 53,015
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3 answers

If $ab=3$ and $\frac1{a^2}+\frac1{b^2}=4,$ then $(a-b)^2=\;$?

If $ab=3$ and $\frac1{a^2}+\frac1{b^2}=4$, what is the value of $(a-b)^2$? I think $a^2+b^2=36$, please confirm and is it possible to to figure out one of the variables?
user154989
  • 195
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Steps to calculate, $(\frac{5}{3})^{-3}$

So first I calculate, $(\frac{5}{3})^{3}$ Which gives me, $(\frac{27}{125})$ But where should I go from there?
user11406
  • 301
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5 answers

How to convert $\sqrt{\frac{5}{3}}$ to $\frac{\sqrt{15}}{3}$?

Disclosure: This is homework, but not part of the homework. This is just something that I do not understand. $$ x = \sqrt{\frac{5}{3}} $$ $$ x = \frac{\sqrt{15}}{3} $$ Could anyone please explain this to me? Thanks in advance.
JFW
  • 243
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Algebra equations - how to solve?

I have two equations that I want to solve but I can solve the first but not the second, here's an example: $$\begin{align*} 100 &= 120 \times x\\ 0.83 &= 123/ x \end{align*}$$ The first one I know how to solve, basically I am doing on…
Hanan
  • 307
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3 answers

Simple question (hopefully) on unitary method

In India we have an exam called NEST. I gave it today, and this was a question I encountered: Lactobacillus sp. and Streptococcus sp. are two bacterial species responsible for curdling milk. One quantum of each of these species was introduced to a…
TKRao
  • 31
3
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1 answer

Multiplying binomial by negative 1 to reverse order of variables

I apologize for asking about an incredibly simple math concept but I'm trying to brush up on my algebra and Googling hasn't helped, I don't know the name of the rule I am looking for. According to a problem I've been walking through step-by-step on…
Irresponsible Newb
  • 1,323
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Simplify expression, skanavi 2.001

How can I simplify this expression? $$ \frac {\sqrt{x}+1}{x\sqrt{x} + x +\sqrt{x}} \colon \frac {1}{x^2 - \sqrt{x}} $$ Solving: $$ a = \sqrt x $$ $$ \frac {a+1}{a^3 + a^2 + a} \colon \frac{1}{a^4-a} = \frac{ a(a + 1)(a-1)(a^2 + a + 1) }{a(a^2 + a +…
ozik.dev
  • 211
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1 answer

Solving three equations by assuming a fourth equation.

Solve the equations:- $\frac{x}{a+l}+\frac{y}{b+l}+\frac{z}{c+l}=1$ $\frac{x}{a+u}+\frac{y}{b+u}+\frac{z}{c+u}=1$ $\frac{x}{a+v}+\frac{y}{b+v}+\frac{z}{c+v}=1$ My friend had asked me this question and then gave me a solution which i dont…
Adesh
  • 87
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0 answers

Is it possible to simplify this equation?

I am wondering if it is possible to simplify the following equation $$ \frac{P}{r-g} \left( 1- \frac{(1+r)^n}{(1+g)^n} \right) = a$$ In order to obtain an expression for $g$ such as: $$ g = \ldots $$ I'm not sure whether there is a closed-form…
Elements
  • 2,638
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1 answer

remainder when $3^{2014}$ is divided by $10,000$.

How can we calculate remainder when $3^{2014}$ is divided by $10,000$? Can we solve it using the binomial theorem? My solution: We can write $3^{2014} = 9^{2007} = -(1-10)^{2007}$. Now, $$(1-10)^{2007} =…
juantheron
  • 53,015
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3 answers

How to show that $x=\ln 3$ solves $x=\ln(10/3 - e^{-x})$

My homework has tasked me with finding $x$ when $\cosh x=5/3$. I know that the solution is $\ln (3)$, but I can't figure out how to solve it myself. The furthest I can simplify it is the following: $$\frac{e^x+e^{-x}}{2} = 5/3$$ $$ e^x+e^{-x} =…
Matt Munson
  • 1,537
3
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5 answers

Can you explain this please $T(n) = (n-1)+(n-2)+…1= \frac{(n-1)n}{2}$

Possible Duplicate: Proof for formula for sum of sequence 1+2+3+…+n? Can you explain this please $$T(n) = (n-1)+(n-2)+…1= \frac{(n-1)n}{2}$$ I am really bad at maths but need to understand this for software engineering.
java
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