Linear, exponential, logarithmic, polynomial, rational, and trigonometric functions, conic sections, binomial, surds, graphs and transformations of graphs, equation- and system-solving, and other symbolic-manipulation topics.

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-4
votes
2answers
75 views

Finding $f(m-1)$ where $f(x) = x^2 + 2x+2$

If $f(x) = x^2 + 2x + 2$, find $f(m - 1)$. Can someone please solve this for me, with the steps.
2
votes
2answers
172 views

Multiply: $(4 + x)(x^2 + 2x +3)$

How would I solve this: Multiply: $(4 + x)(x^2 + 2x +3)$
-3
votes
4answers
178 views

Finding Consecutive Integers

Find four consecutive odd integers such that 5 times the sum of the first and the third is 15 more than 5 times the fourth.
2
votes
4answers
514 views

Elementary Algebra Problem About Nickels and Pennies

The question is: When the piggy bank was opened, it yielded $5.22 in nickels and pennies. If there were 162 nickels and pennies altogether, how many of each were in the bank?
0
votes
2answers
426 views

Questions on perfect squares and perfect cubes

Which of the following are true? 1:for every positive integer m, there is a positive integer n such that m+n+1 is a perfect square. 2:for every positive integer m, there is a positive integer n such ...
4
votes
3answers
807 views

Implies sign in math

I get myself confused sometimes when to use => or = = x + y = x + 5 = x = -5 or ...
27
votes
7answers
3k views

Do odd imaginary numbers exist?

Is the concept of an odd imaginary number defined/well-defined/used in mathematics? I searched around but couldn't find anything. Thanks!
2
votes
3answers
379 views

How is $Ax + By = C$ the equation of a straight line?

I know the equation, $y = mx + b$ where $m$ is slope and $b$ is $y$-intercept, is a straight line. But I know also that $Ax + By = C$ is a straight line equation, but how does it represent a straight ...
1
vote
2answers
229 views

An arithmetic sequence of positive logarithms

Suppose $a$, $b$, $c$, and $d$ are positive numbers and each is not equal to $1$. If $\log_a(d)$, $\log_b(d)$, and $\log_c(d)$ are an arithmetic progression in this order, then what is ...
3
votes
4answers
173 views

Factorization of sum of two square

The difference is $a^2 - b^2 = (a - b).(a + b)$ But what about when I have $a^{25} + 1$ ? According to wolfram alpha, the alternate form is: $(a+1) (a^4 -a^3 + a^2 -a + 1)( a^{20} - a^{15} + a^{10} ...
6
votes
3answers
752 views

Solve $\sin(5A) + \cos(5A)\sin(A) - \cos(3A) = 0$

How do you solve this equation for A: $~~\sin(5A) + \cos(5A)\sin(A) - \cos(3A) = 0$ I've tried expanding it many times, but I can't seem to be able to reduce it to a format I can work with. Is there ...
0
votes
1answer
86 views

Intuition for a simple conversion

I was working on a scheme in cryptography and came up with the following scenario. To put it in proper words. We have an element $\frac{1}{x+m}$. The 2 elements $x$ and $x_1$ are known. We ...
5
votes
1answer
417 views

How can I re-arrange this equation?

I haven't used my algebra skills much for years and they seem to have atrophied significantly! I'm having real trouble working out how to re-arrange a formula I've come across to get $x$ by itself on ...
2
votes
1answer
6k views

Solving inequality with two absolute values

Hey, ! In my pre-calculus class the teacher showed the solution of the following example: \begin{align} \vert x-3 \vert \lt \vert x - 4 \vert + x \end{align} He started by stated the domains ...
46
votes
10answers
3k views

Division by $0$

I thought it was elementary to me, but I started to do some exercises and came up some definitions I have sort of difficulty to distinguish. In parentheses are my questions. $\dfrac {x}{0}$ is ...
8
votes
3answers
458 views

Partial fraction of $\frac{x^n}{(1-x)(1-2x)(1-3x)\ldots(1-nx)}$

How should you break $\displaystyle \frac{x^n}{(1-x)(1-2x)(1-3x)\ldots(1-nx)}$ into partial fractions?
5
votes
3answers
169 views

trigonometric inequality

please help me establish(etablir): $\forall n\in \mathbb{N}-\left\{ 0,\left. 1 \right\} \right.$ , $x\in \mathbb{R}-\left\{ \pi \mathbb{Z} \right\}$ , $\left| \sin \left( nx \right) ...
3
votes
2answers
290 views

Induction problem: log of product equals sum of logs

Please help me prove by induction that $\displaystyle\forall n\in {{\mathbb{N}}^{*}}$, $\displaystyle\forall {{a}_{1}},\ldots ,{{a}_{n}}\in {\mathbb{R}}^{*}_{+}$, $\displaystyle \ln \left( ...
3
votes
3answers
357 views

Proof by induction: $\sum\limits_{i=0}^n i \cdot i! = (n+1)!-1$

Let n be a positive natural number , $n\ge 0$, then. $\displaystyle\sum_{i=0}^n i \cdot i!= (n+1)!-1$ Here is my attempt.I'm not going to write the base case because I understand that part. ...
14
votes
6answers
3k views

No radical in the denominator — why?

Why do all school algebra texts define simplest form for expressions with radicals to not allow a radical in the denominator. For the classic example, $1/\sqrt{3}$ needs to be "simplified" to ...
1
vote
1answer
72 views

Calculating gradient of a line: how do you know which way to order the points?

Very simple question but I keep getting this wrong! If you have two points e.g. A$(13, 6$) & B$(11, 12)$, Using the gradient formula $m = (y_2 - y_1)/(x_2 - x_1)$ how do you know which of A or B ...
2
votes
1answer
610 views

Stretch Logistic Function

Follow up from: http://stackoverflow.com/questions/5225061/exponential-decay-surrounding-bounding-box How can I manipulate a simple logistic function like this one: So that the lower bound is at ...
1
vote
2answers
89 views

Help Me Figure Out What R Is

find the value of R so that the line through (3, 13) and (R, -5) has a slope of 8
0
votes
2answers
746 views

Find intersection of linear and logarithmic lines

I have equations for two lines, one of which is linear and the other is logarithmic, ie: $$y = m_1 x + c_1$$ $$y = m_2 \cdot \ln(x) + c_2$$ ..and I need to find out where (if at all) these lines ...
2
votes
3answers
655 views

Squaring across an inequality with an unknown number

This should be something relatively simple. I know there's a trick to this, I just can't remember it. I have an equation $$\frac{3x}{x-3}\geq 4.$$ I remember being shown at some point in my life that ...
1
vote
1answer
266 views

Percentages don't add up

Why is my overall delta percentage of 0.9% (bottom right) less than all 5 of the values that make it up (1.7%, 3.2%, ...)? I know with the difference in magnitude of each row and column that it could ...
1
vote
2answers
126 views

Is it possible to reduce this algebraic expression $\frac{(2x+y)(x-y) }{ (2x-y)(x+y)}$?

Is it possible to reduce this expression further? $$ \frac{(2x+y)(x-y) }{ (2x-y)(x+y) } .$$
0
votes
1answer
2k views

Computing the break-even point

Problem The Lake Shore Inn is trying to determine its break-even point. The inn has 50 rooms that are rented at $60 per night. Operating costs are as follows, in dollars ...
5
votes
4answers
2k views

Why do rhombus diagonals intersect at right angles?

I've looked all over and I can't find a good proof of why the diagonals of a rhombus should intersect at right angles. I can intuitively see its true, just by drawing rhombuses, but I'm trying to ...
2
votes
3answers
165 views

How can I prove the formula for calculating successive entries in a given row of Pascal's triangle?

I've found in Wikipedia the formula for calculating an individual row in Pascal's Triangle: $$v_c = v_{c-1}\left(\frac{r-c}{c}\right).$$ where $r = \mathrm{row}+1$, $c$ is the column starting from $0$ ...
3
votes
1answer
628 views

How may I solve this Cubic Equation?

How can I solve this cubic equation? $$H^{3} − 3\left[(1 + A\cos(T) )^{2} + \frac{2r \cdot A \sin(T)}{B}\right]H + 2(1 + A \cos(T))^{3} = 0$$ Solution in terms of H. Edited in order to give more ...
2
votes
1answer
385 views

How to find basic algebra conversion formula?

I'm doing some programming for a video game in which the player characters and monster enemies can move at different speeds on 2-dimensional, cell-based tile map. Examples of these speeds are as ...
1
vote
1answer
64 views

Solve for A (Exponents)

Question: The area covered by a newly-introduced species of invasive weed doubles every 4 years. Suppose the weed currently covers 23 km^2. a) Write an equation that gives the area, A, covered by the ...
2
votes
1answer
404 views

Use of algebra and factorials for a question related to proof by induction

$$ \begin{align*} &= (n+1)! − 1 + ( (n+1) · (n+1)! )\\ &= (n+1)! (1+n+1) − 1\\ &= (n+1)! (n+2) − 1\\ &= (n+2)! − 1\\ \end{align*} $$ I'm confused at how the first ...
0
votes
1answer
450 views

Determining a closed-form solution for the following sum

I have the following summation: $$\sum_{i=0}^n\left(6in + n(8n+2)\right).$$ Evaluating I get \begin{align*} 6n\left(\frac{n(n+1)}{2}\right) + n(8n+2) = 3n(n(n+1)) + n(8n+2)\\ &=3n^2(n+1) + ...
1
vote
2answers
73 views

How to evaluate an expresssion

$$\frac{(z x^{-1} y)^5 y^5}{x^{-4} z^{-4}}$$ How would I evaluate this if $x = 10$, $y = -3$ and $z = 3$ ? I would like a step-by-step solution to help me fully understand it.
4
votes
3answers
193 views

Why does the sum of a division applied to individual items not equal the division applied to the sum of those items?

I hope the simplicity of this problem doesn't offend anyone's intelligence, however i'm unsure where else I should post this, and fairly certain its due to some kind of math rule (or just my stupid ...
1
vote
2answers
71 views

Trying to find a point X

(sorry, low level so I can't attach the image in the post) a is given. b is given. c is given. For X, I don't have a clue where he is. I was thinking about rect / vector instersection, ...
2
votes
3answers
162 views

How to signal to the reader the difference between a function and a multiplication?

The following is alpha of t times x: $$\alpha(t)x$$ The following is alpha times t times x: $$\alpha(t)x$$ My instructor had one interpretation, I used the other. ;) Is there an easy or standard ...
18
votes
1answer
576 views

Is this algebraic identity obvious?

If $\lambda_1,\dots,\lambda_n$ are distinct positive real numbers, then $$\sum_{i=1}^n \prod_{j\neq i} {\lambda_j\over \lambda_j-\lambda_i}=1.$$ This identity follows from a probability calculation ...
4
votes
4answers
489 views

Factoring $a^{10}+a^5+1$

I'm very interested to know how I can factorise $a^{10} +a^5 +1$ in two factors with integer coefficients. I've tried a lot but I don't have any idea how do that.
3
votes
1answer
306 views

Compute base price of each item in a list of items given the total sales tax

I'm having a disagreement with a client that I think is relatively simple mathematics, but I'd like a third party to confirm or dispute my assertions. Here's the situation: We have a list of N final ...
1
vote
1answer
379 views

Related Rates Problem With Ladder

A 30-foot ladder rests vertically against a wall. A bug starts at the bottom of the ladder and climbs up at a rate of 3.5 feet per minute. At the same time, the foot of the ladder is being pulled ...
1
vote
2answers
1k views

Converting polar equation to cartesian coordinate polar equation and back again?

OK, so I have the following polar equation: $r = Θ/20$ And I would like to translate this a little to the right, and down from the polar origin. Now, I figure since I know cartesian coordinate ...
1
vote
2answers
211 views

Problems with the number $0$

Here is the original formula: $$\frac{256}{2^x}=y$$ In order to solve for $x$, I've done this: $$\log_{2}\left(\frac{256}{y}\right)=x$$ The problem is that $y$ can be zero. What should I do to solve ...
13
votes
5answers
6k views

Good book for high school algebra

I'm gonna take a Calculus course next year, my professor suggest me to review high school algebra. I want to know, which book is good for refresh knowledge on high school algebra?
1
vote
3answers
452 views

Missing exponent?

$\frac{256}{2^S}=64$ How would you solve for S?
0
votes
3answers
107 views

How do I solve for $V$ in this equation?

$$\frac{\ln(T+1)-\ln(V-S+1)}{\ln(V-S+1)}=\frac{1}{K}-1$$ What are the steps if I want to solve for $V$?
3
votes
2answers
156 views

How to solve 700 = 7x + 6y for a range of values?

Last time I did any maths was A-Level (some time ago!). This is a programming/layout problem where I need to display 7 items across a page, with 6 gaps between them. I have a fixed width, but need to ...
5
votes
2answers
116 views

Rewrite equation to solve for x, not y

I am doing calculus integration, and need to show my work for Horizontal slicing (even though Vertical slicing is far easier). The equation is y= x/$\sqrt{2x^2+1}$ I need to rewrite the equation so ...