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
9 views

Convert from base 10 to base 5

I understand the integer part, keep dividing by 5 and I get 112, but for the fraction part I need a help. The number is: $$ (32.\bar 5)_{10} = (112, ??)_{5} $$ $$ 0,5 * 5 = 2,5\\ 0,5 * 5 = 2,5\\ ...
1
vote
0answers
28 views

Algebric equation problems

Find $a, b, c \in \Bbb Q$ such that: $\sqrt[3] a + \sqrt[3] b + \sqrt[3] c = \sqrt[3]{\sqrt[3] 2 - 1}$.
-1
votes
1answer
29 views

Problem of Mathematical Induction [on hold]

Show that $n!\leq 2^{-n}(n+1)^n$ for all $n\in\mathbb{N}$ and equality holds if and only if $n=1$.
-4
votes
2answers
66 views

Solve equation $x^3 - 3x = \sqrt{x + 2}$ [on hold]

Solve :  $$x^3-3x=\sqrt{x+2}$$ For any real number x.
0
votes
0answers
14 views

Additive exponential function

I am trying to solve the following for $x$: $$ ax = b(P-P^x)$$ where $a$, $b$ are positive constants, and $P \in (0, 1)$. I already know that the left hand side is linear and the right hand side ...
-3
votes
1answer
14 views

ATV business and percentages [on hold]

I have 12 ATVs. My friend owns 2 of them. Through rental, we make $2,020$ \$. What percent of that amount is of my friend? How much is it?
0
votes
1answer
9 views

Modulus of Z (Normal distribution)

The random variable $Z$ is distributed such that $Z \sim N(0,1)$ find the probability of $P(\left|Z\right| >2.4)$. How to solve this modulus type of question ?
2
votes
2answers
14 views

Finding $P$ knowing $\overrightarrow{PQ}×\overrightarrow{b}$, $\overrightarrow{PQ}⋅\overrightarrow{c}$, $\overrightarrow{b}$, and $\overrightarrow{c}$

Let $Q$ be the point $(1,2,3)$, let $\overrightarrow{b} = \langle -1, 0, 1\rangle$, and let $\overrightarrow{c} = \langle 2, 1, 5\rangle$. It is known that $\overrightarrow{PQ} \times ...
1
vote
2answers
39 views

Equality in AM GM Inequality

In AM GM inequality for nonnegative real numbers $a_1,a_2,\ldots,a_n$, How to show that if equality holds then $a_1=a_2=\ldots=a_n,$ using method of induction?
0
votes
0answers
9 views

Why is Distribution Prioritized Over Combining?

In every algebra (or basic analysis) book that I've seen, three properties of real numbers are taken as axiomatic: commutativity, association, and distribution of multiplication over addition [a(b + ...
0
votes
0answers
11 views

What are the loci of points z which satisfy the following relations?

a) |Z-Z1|=|Z-Z2| b) 0< Re(iZ)<1 c) |z|=ReZ+1 d) Im((Z-Z1)/(Z-Z2))=0 The professor did not explain loci in class and the text does not have any examples, so I am completely lost.
0
votes
2answers
19 views

How do I complete composite functions that use cos(x) and a polynomial? [on hold]

Let $f(x)= \cos(x)$ and $g(x)= 3x^3+4x^2-7$. Find $g(f(x))$ and $f(g(x))$
-1
votes
0answers
15 views

simplifying distance equation

The optimal angle for throwing a ball from a cliff is $$\sin \theta = \frac{1}{(2+ \beta)^{1/2}}$$ the original distance equation is $$ x = \cos \theta (\sin \theta + (\sin^{2} \theta + ...
2
votes
4answers
37 views

Solving for b for equation $3a−5=−4b+1$ [on hold]

I have a math problem, and I'm trying to solve for 'b'. The problem answer shows that the first step is going from Step 1 to Step 2. I don't understand how they are doing this. How does the $-4b$ ...
3
votes
2answers
57 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
2answers
44 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
31 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: ...
2
votes
1answer
27 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.
3
votes
1answer
30 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
22 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
78 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
4answers
65 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
33 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
23 views

Adding two variables with subscripts [on hold]

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
26 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
437 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
78 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
20 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
661 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
29 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
20 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
28 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
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
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
98 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
73 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
70 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
2answers
70 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
558 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
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
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 ...