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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22
votes
1answer
456 views

Parabolas in sequences of digits from the Fibonacci sequence

In preperation for an exam, I was studying Haskell. Therefore I was solving an old assignment where you had to define the fibonacci series. After solving the task (see 1] for source code) and ...
4
votes
4answers
79 views

Calculate simple expression: $\sqrt[3]{2 + \sqrt{5}} + \sqrt[3]{2 - \sqrt{5}}$

Tell me please, how calculate this expression: $$ \sqrt[3]{2 + \sqrt{5}} + \sqrt[3]{2 - \sqrt{5}} $$ The result should be a number. I try this: $$ \frac{\left(\sqrt[3]{2 + \sqrt{5}} + \sqrt[3]{2 - ...
0
votes
0answers
36 views

For the classical diffusion equation ut = r (5ru) (in 3 space dimensions)

fi nd TWO changes of variables which changes the di ffusion constant from 5 to D = 1 for the new coordinate system?
8
votes
4answers
670 views

Simple Trig Equations - Why is it Wrong to Cancel Trig Terms?

In the following problem, I first did it using a cancellation of $sin^2\theta$, working shown below, which gave the wrong answer. Having looked at the question again, I saw it could be solved by ...
-2
votes
1answer
30 views

How do you find an expression for the sum of the first 35 terms of a logarithmic series? [on hold]

$$\ln(x^2/y^0) + \ln(x^2/y^1) + \ln(x^2/y^2)+ \ln(x^2/y^3)+ \ln(x^2/y^4)+ \cdots$$
0
votes
0answers
22 views

Parametric vector form of cartesian equation

Cartestian equation: $$-2x-y+z=6$$ I know to find the parametric vector form we can find any 3 points P, Q and R which satisfy the cartesian equation. $$ \begin{pmatrix} x_1\\ y_1\\ z_1 ...
-1
votes
0answers
29 views

Please solve this algebra question [on hold]

2(24-____)=____-34 I really don't know who to do this! I really need some help D;!
0
votes
3answers
47 views

prove $x\le y$ when $x<z$ for every $z>y$ [on hold]

Let $x,y$ be real numbers. Prove that if $x\le z$ for every $z>y$, then $x\le y$.
2
votes
2answers
52 views

If $a,b,c,d,e,f$ are non negative real numbers such that $a+b+c+d+e+f=1$, then find maximum value of $ab+bc+cd+de+ef$

$(a+b+c+d+e+f)^2=$ sum of square of each number (X)+ $2($ sum of product of two numbers (Y) $)$ $ab+bc+cd+de+ef \le Y$ since all are positive. Therefore $1\ge X+(ab+bc+cd+de+ef)$ Edit: From AM GM ...
2
votes
2answers
40 views

How does uniqueness of the additive inverse imply that $-(ax) = (-a)x$?

How does uniqueness of the additive inverse imply that $-(ax) = (-a)x$? In my title, I should be clear that the additive inverse should be unique. But how does this help? I dont even get why ...
-2
votes
4answers
41 views

Find two numbers knowing their sum and their difference [on hold]

The sum of two numbers is 15 and their difference is 3. What are the numbers and their product?
-3
votes
0answers
12 views

graph and equation [on hold]

a. How many times as large is the change in the cost of the flight, Δc, (in dollars) than the change in the number of weeks elapsed since January 1, 2015, Δt. Express this relationship by writing a ...
0
votes
0answers
23 views

Finding n for a given P of a Bernoulli trial

I'm randomly sampling $N$ items and I want to find $n$ such that I have a probability $P$ that I'll miss one. Practically, I'd select $P$ to be something like $10^{-12}$ so I'm almost assured to ...
2
votes
7answers
101 views

Proving that $\frac{1}{2}<\frac{2}{3}<\frac{3}{4}<$…$<\frac{n-1}{n}$

In an attempt to find a pattern, I did this: Let a,b,c,d be non-zero consecutive numbers. Then we have: $a=a$ $b=a+1$ $c=a+2$ $d=a+3$ This implies: $\frac{a}{b}=\frac{a}{a+1}$ ...
0
votes
1answer
14 views

What does “Normal” mean in the context of linear equations?

My summer packet has the question: "Write equations of the line through the given point a)parallel and b) normal to the given line: $(−6, 2)$, $5x + 2y = 7$" I had no problem with finding the ...
0
votes
4answers
76 views

How many solutions does this equation have?

The question is: how many solutions does this equation have? $$\frac {2x^3+1.6x}{x^2-1} = 7$$ I don't even have a clue how to approach this...
-1
votes
0answers
25 views

Slope and intercept word problem [on hold]

In my example: $.5$ pounds of apples cost $\$5.00$ and $82$ pounds of apples cost $\$411.00$ How much does it cost for $37$ pounds of apples? I need a simple math formula for a program I am working ...
0
votes
4answers
71 views

Highschool Algebra: $n^2 = 18n$?

I'm beginning to get into maths outside of school and at the moment I'm refreshing myself on the basics which explains why this question appears to be so simple. I formulated this equation to find ...
3
votes
2answers
94 views

How to solve this system of nonlinear equations?

How to solve these equations for $a$, $b$, $c$ and $x$? I have the following: \begin{align} 1 &= 2a+b+c\\ a &= (a+b)x + 0.25(a+c)\\ a&=(a+c)(1-x)\\ b&=a(1-x)+c(x-0.25)\\ ...
6
votes
2answers
559 views

Seemingly Simple Equation Question “Verify my solution please!”

"A container is $1/8$ full of water. After $10$ cups of water are added, the container is $3/4$ full. What is the volume of the container, in cups?" Ok, I wrote out an equation: $\frac{1}{8}V + 10C = ...
1
vote
3answers
35 views

Prove that from the equalities, $\frac{x(y+z-x)}{\log x}=\frac{y(x+z-y)}{\log y}=\frac{z(y+x-z)}{\log z}$ follows $x^yy^x=y^zz^y=z^xx^z$.

Problem : Prove that from the equalities, $$\frac{x(y+z-x)}{\log x}=\frac{y(x+z-y)}{\log y}=\frac{z(y+x-z)}{\log z}$$ follows $$x^yy^x=y^zz^y=z^xx^z$$. My approach : $$\frac{x(y+z-x)}{\log ...
0
votes
1answer
28 views

Can't figure out this basic algebra

Been a while since I did math but I'm trying to understand how they got the final equation in this step: http://i.imgur.com/Y09bqwT.png When I solve for P I get this: $$ P(t) = ...
-4
votes
1answer
27 views

A plant can manufacture 50 golf clubs per day at a total daily cost of $ \$5423$ and $70$ golf clubs per day for a total cost of $ \$6,923$.

Assuming that daily cost and production are linearly related, find the total daily cost, $C$, of producing $X$ gold clubs Interpret the slope and $Y$-intercept of the cost equation. I have no idea ...
2
votes
2answers
33 views

Determine polynomial whose roots are a linear combination of roots of another polynomial

Let $\alpha_1, \alpha_2, \alpha_3$ be the roots of the polynomial $p(x)=x^3+5x^2+7x+11$. Find a polynomial whose roots are $\frac{\alpha_1+\alpha_2}{2}, \frac{\alpha_2+\alpha_3}{2}, ...
0
votes
2answers
19 views

Use the difference quotient to compute a formula in terms of h

Using the difference quotient: $\frac{f(x+h) - f(x)}{h}$, I need to compute a formula in terms of $h$, given $f(x)$ and $x$, ensuring that the $h$ in the denominator gets cancelled out. Given an ...
0
votes
2answers
39 views

Solving an equation with $\sin(x)$ in the exponent: $2^{\sin(x)} \cdot \cos(x) + 1 = 1$

Hi I need help with a trig problem: I have $2^{\sin(x)} \cdot \cos(x) + 1$, and I need this to equal $1$ between $x = -3$ and $3$. I keep going in circles with substitution, etc. Any help would be ...
-3
votes
1answer
24 views

How do you solve these for Intersection Points [on hold]

How do you get the intersection points between these algebraically? $$\sqrt{4-y} = (y-2)^2+2$$
-4
votes
2answers
20 views

math problem two possible values [on hold]

Find the two possible values of x that make the expression true. (2x – 6) (x + 5) = 0
1
vote
3answers
79 views

Showing for any real number $\lfloor a\rfloor+1>a$

This seem a simple proposition For any real number a $\lfloor a\rfloor+1>a$ For any example $\lfloor 2.9\rfloor=2$ $\lfloor 3.1\rfloor=3$ $\lfloor 4\rfloor=4$ I think this is obvious. Because ...
0
votes
2answers
59 views

Function that transforms the interval $[a,b]$ into $[0,1]$ [on hold]

Could someone please give me an example of function that translates the interval $[a,b]$ into $[0,1]$ I tried $\frac{x-a}{p(x)}$ and after that $x(x+b-a-1)+a$.
-3
votes
0answers
33 views

I have 70 gallons of water at 660 ppm. I need to bring the ppms up using 30 gallons of water, what does my ppm for the 30 gallons need to be? [on hold]

I have 70 gallons of water at 660 ppm, I need to use 30 gallons to bring the ppms up, what ppm does my 30 gallons need to be at ? Trying to bring the ppms in the 70 gallons up to 770?
2
votes
3answers
25 views

Considering Units When manipulating system of Equations?

I few days ago I solved a problem on a website called brilliant.org, I can not seem to find the problem there anymore but I still remember it: Q: You go to a candy store to buy m&ms and ...
0
votes
2answers
33 views

Find the solution set of the equation $5.(\frac{1}{25})^{\sin^2x}+4.5^{\cos2x}=25^{\frac{\sin2x}{2}}$

Problem : Find the solution set of the equation $5.(\frac{1}{25})^{\sin^2x}+4.5^{\cos2x}=25^{\frac{\sin2x}{2}}$ where $x \in [0,2\pi]$ My approach : ...
1
vote
0answers
16 views

$n$-tuples of points of $\mathbb{C}$, identification.

Fix $n \in \mathbb{N}$. Forgive me if this is a very silly question, but how can I see that the set of unordered $n$-tuples of points of $\mathbb{C}$ can be naturally identified with $\mathbb{C}^n$?
3
votes
4answers
107 views

Find a Polynomial in $x-\frac1x$

Given that $x^n - (1/x^n)$ is expressible as a polynomial in $x - (1/x)$ with real coefficients only if $n$ is an odd positive integer, find $P(z)$ so that $P(x-(1/x)) = x^5 - (1/x)^5.$ To start, I ...
3
votes
0answers
65 views

Evaluate $\int \dfrac{1}{\sqrt{x-1}+\sqrt{x}+\sqrt{x+1}} \ \mathrm{d}x$ [duplicate]

Evaluate $$\int \dfrac{1}{\sqrt{x-1}+\sqrt{x}+\sqrt{x+1}} \ \mathrm{d}x$$ I tried rationalizing the denominator by twice multiplying, but it didn't do any good. I also tried trig ...
3
votes
1answer
72 views

Prove that $s(n-1)s(n)s(n+1)$ is always an even number

Let $n$ be a natural number, and let $s(n)$ denote the sum of all positive divisors of $n$. Show that for any $n>1$ the product $s(n-1)s(n)s(n+1)$ is always an even number. I calculated the sum of ...
1
vote
1answer
39 views

ASTC: Finding exact values of trigonometric functions

Our teacher showed us this really dodgy way of finding exact values by drawing up the 4 ASTC (all stations to central diagram) quadrants and making a right angle to the x axis. So how would I do a ...
1
vote
1answer
45 views

About a matrix identity.

In a document named as "The Matrix Cook-Book" I saw two expressions of which I do not get any clue how they are derived. For $n = 3:$ $\det(I + A) = 1 + \det(A) + Tr(A) + 1/2\ Tr(A)^2 − 1/2\ ...
-2
votes
3answers
45 views

write an expression [on hold]

A word processor determines the width of the body of text on a page. The page is 11 inches wide and has two equal size margins of x inches on each side of the text. Write a formula that gives the ...
3
votes
3answers
92 views

Why does $e^{-x}$ approach $0$ as $x$ gets large? [on hold]

Why is it that $$\lim_{x \to -\infty} e^x = 0?$$ Context: College has started back up again and I like to understand the reasons why things do the things they do, rather than just memorizing. I'm ...
2
votes
1answer
270 views

Probability or Set

I'm really good at probability, but this time I seems like I'm not. My friends asked me a very tricky question, and I want to see if there's anyone who can find out the answer. Here's the ...
1
vote
6answers
59 views

Limit of $\lim_{x \rightarrow 0} \frac{\sin xy^2}{x}$ [on hold]

Limit of $$\lim_{x \rightarrow 0} \frac{\sin xy^2}{x}$$ I know (thanks to wolfram) it is equal to $y^2$, but i do not know how to show that.
1
vote
2answers
64 views

trying to solve $\sqrt{\cos(x)-2\cos(2x)}+\sqrt{2}\cos(2x)=0$

The equation is $$\sqrt{\cos(x)-2\cos(2x)}+\sqrt{2}\cos(2x)=0$$ The system is $$ \begin{cases} \cos(x)-2\cos(2x)=2\cos^2(2x) \\ -\sqrt{2}\cos(2x)\ge 0 \iff \cos(2x)\le 0 \end{cases} $$ The ...
0
votes
2answers
41 views

Find the limit of $\frac{x+y+\sin xy}{x^2+y^2+\sin^2 (xy)}$

Find the limit of: $$\lim_{(x,y)\rightarrow(+\infty, +\infty)}\frac{x+y+\sin xy}{x^2+y^2+\sin^2 (xy)}$$ I think the solution could be: $$\frac{x+y+\sin xy}{x^2+y^2+\sin^2 (xy)} \le \frac{x+y+\sin ...
1
vote
1answer
49 views

Algebra Problem: Division

Can someone help me with a problem involving the expression $$\frac{(2x^3-3x^2+b)}{(4-x^2)}?$$ The question is to find which values $b$ can be to simplify the expression, but I do not know how to ...
0
votes
8answers
108 views

$x(x^2-2)=0$, The answers are $x = 0, \sqrt{2}$, how do I get there? [on hold]

$$x(x^2-2)=0$$ The answers are $x=\sqrt{2}, 0$ how do I get there?
3
votes
2answers
28 views

Minimum of $f(x)=\sum_{i=1}^n\frac{a_n}{x-b_n}$ occurs at extreme point?

Let $a_1,\ldots,a_n$ be real numbers and $b_1,\ldots,b_n>1$. Define $$f(x)=\sum_{i=1}^n\frac{a_i}{x-b_i}.$$ Is it always true that $f(x)\geq\min\{f(0),f(1)\}$ for all $x\in[0,1]$?
0
votes
2answers
28 views

Changing equation to x equals

Im currently stuck on this equation I need to modify to be in terms of x $$y=-x^2+4$$ I got something like this which looks wrong $$x = -\sqrt{y+4}$$ First you would subtract the 4 from both ...
1
vote
3answers
34 views

Distance/Speed word problem

A train of length 300m can cross a pole in 8 seconds. How long will it take to cross a platform of length 600m. I can't seem to appreciate the very beginning. Crossing the pole implies that the time ...