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.

learn more… | top users | synonyms (2)

0
votes
1answer
20 views

Why $\tan x>\sin x$ in this question?

The question asks me to prove the identity $\tan ^2x-\sin ^2x=\tan^2 x \sin^2 x$ and use this result to explain why $\tan x>\sin x$ for $0<x<90$ I've proved the identity and I can't explain ...
1
vote
1answer
24 views

How do you factor $3x^{3/2} -9x^{1/2}+6x^{-1/2}$?

How do you factor $3x^{3/2} -9x^{1/2}+6x^{-1/2}$ ? I factored out a 3 to get: $3(x^{3/2} -3x^{1/2}+2x^{-1/2})$, but it seems this can be factored further.
0
votes
2answers
17 views

Domain and range of $f(x,y)=\sqrt{1+x-y^2}$

I need to find the domain and range of $f(x,y)=\sqrt{1+x-y^2}$. Can someone walk me through the proper reasonings in solving this problem? My attempt Domain From looking at the function I get: ...
1
vote
1answer
22 views

How do you factor $x^3-3x^2-4x+12$

How do you factor $x^3-3x^2-4x+12$ ? I tried to factor $x(x^2-3x-4) + 12$ instead and I got $x(x-4)(x+1)+12$ but apparently this can be factored further.
0
votes
0answers
11 views

Throwing a ball off a cliff (simplifying)

I'm looking at the problem from http://www.ib.cnea.gov.ar/~marquezj/Biblioteca/harvard/ch2.pdf on page 31 number 12 "Throwing a ball from a cliff" It says that the solution is obtained from $$ ...
2
votes
1answer
20 views

Largest Triangular Number less than a Given Natural Number

I want to determine the closest Triangular number a particular natural number is. For example, the first 10 triangular numbers are $1,3,6,10,15,21,28,36,45,55$ and thus, the number $57$ can be ...
-5
votes
2answers
21 views

Modifying a recipe, changing it from 8 to 10 servings.

A recipe that makes 8 servings calls for 3/5 cup flour. Jeff modifies the recipe so that it can serve 10. How many cups of flour does he need?
2
votes
4answers
60 views

Why doesn't quadratic formula lead to a the correct factored form of the original equation?

Applying the quadratic formula to $2x^2-3x+1$ we have \begin{eqnarray*} a&=&2 \\ b&=&-3 \\ c&=&1 \end{eqnarray*} which gives me two roots: \begin{eqnarray*} x_1&=&1 ...
2
votes
3answers
57 views

Why does the a*c cheat work when factoring trinomials?

When factoring a trinomial, in the form $ax^2 + bx + c$, I am told that one can multiply $a$ and $c$ which gives a product whose factors add to $b$. So if I have $2x^2 + 5x -3$ that gives me $-6$. ...
-2
votes
1answer
28 views

Solve the quadratic equation $(2-y)^4=3(2-y)^2+1$

Solve $$(2-y)^4=3(2-y)^2+1$$ The answer is supposed to be $y=4\pm \sqrt{6+\frac{13}2}$. I have tried to work this problem out but I cannot get the answer that is in the book.
-1
votes
1answer
17 views

Adding two variables with subscripts

What is the explanation to why $x_{3k} + x_{3k+1}$, is equal to $x_{3k+2}$. Isn't that incorrect because there is no value 1 in the subscript $x_{3k}$? I saw this in a prove in ...
0
votes
1answer
24 views

Two variables in one equation

I am currently having some trouble getting through the following exercise: "There are $25$ apples in a basket in which teacher eats an $X$ amount of them and gives the remaining apples to Y amount of ...
21
votes
1answer
420 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
77 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
15 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
643 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 ...
-3
votes
1answer
28 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
17 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
27 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
44 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
51 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
39 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 ...
-3
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
96 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
71 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
24 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
68 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 ...
2
votes
1answer
55 views

How to solve these equations?

How to solve these equations for a, b, c and x? I have the following: $ 2a+b+c = 1$ $a = (a+b)x + 0.25(a+c) $ $a=(a+c)(1-x)$ $b=a(1-x)+c(x-0.25)$ $c=b(1-x)+a(x-0.25)$ I tried, but ended ...
6
votes
2answers
553 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
27 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
26 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
32 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
18 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
38 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
78 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
58 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
104 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
64 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
71 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
38 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 ...