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
0
votes
1answer
39 views
Finding a function which fits this data?
I need to find a polynomial (or other continuous elementary function) on the interval [70, 180] such that it passes through the points (70, 0) (this is a relative min), (105, 17) (this is a relative ...
0
votes
3answers
27 views
steps for finding inverse tangent
My textbook gives me this:
Can someone please walk me through the steps to get -pi/3 from the inverse tangent?
1
vote
1answer
42 views
Adding integer multiples of pi
I have an angle with a given radian measurement and need to express it differently by adding integer multiples of pi. Is it accurate to say that I can simply add 4 to the coefficient of pi? It seems ...
0
votes
0answers
126 views
Power of compounding daily
Suppose that a vegetable vendor pays 7% interest daily on a \$10 loan. Then, suppose that this individual was able to save \$0.50 per day by drinking less tea. Calculate the number of days it would ...
3
votes
2answers
110 views
Irrational equation, How to solve it?
The equation
$$\sqrt[3]{x^2-1} + x = \sqrt{x^3-2}$$ has a solution $x = 3.$ How to solve this eqution?
0
votes
1answer
24 views
Uniqueness of nonterminating decimal expansion…
Prove that decimal representation is unique iff the number has no terminating expansion. Prove also that any terminating expansion also has a nonterminating expansion. How are these nonterminating ...
1
vote
1answer
37 views
How to determine a function that satisfies the following:
This question is to determine a function which will later help me answer this question:
Given this set of points, how do I determine an equation which satisfies them:
n ...
2
votes
1answer
35 views
Number of positive integer solutions to an equation
How many positive integers $(a, b, c)$ are there such that $c(a+b)^2 = a(b+c) + b(c+a)$?
I tried to play with this equation, and what I got is $c(a+b)(a+b-1)= 2ab$. However $a,b,c$ need not be primes ...
0
votes
1answer
59 views
Local expansion of a polynomial
I've been staring at this local expansion, from a paper, of a multivariate polynomial but I can't quite understand it. It goes as follows:
$\mathcal{C}$: Field of Complex numbers
Let $x=(x_1, ...
7
votes
7answers
165 views
Derivation of the general forms of partial fractions
I'm learning about partial fractions, and I've been told of 3 types or "forms" that they can take
(1) If the denominator of the fraction has linear factors:
$${5 \over {(x - 2)(x + 3)}} \equiv {A ...
0
votes
1answer
32 views
confusing part to basic accounting question
Directions: Given the information find the weekly and monthly taxable wages (4.3 weeks per month).
This is for federal income taxes.
Weekly Taxable Wages: $\$21.40$ per hour, $40$ hours a week, $47$ ...
0
votes
1answer
48 views
Ratio and Percentage
What ratio should be used to prepare a mixture of 100% (absolute) alcohol with 20% chlorhexidine solution and water to end up with a mixture of 70% alcohol and 2% chlorhexidine (considering the 80% of ...
2
votes
3answers
43 views
A question on a proof of $y(y+1) \le (x+1)^2 \implies y(y-1) \le x^2$
I was reading the question posted here:Does $y(y+1) \leq (x+1)^2$ imply $y(y-1) \leq x^2$?. The solution posted was:
"Given $y^2+y≤x^2+2x+1$, if possible, let $x2<y(y−1)$. Clearly $y>1.$
...
0
votes
1answer
38 views
Algorithm for root function $[2^{n-1}]$
I am attempting to convert this function $[2^{n-1}]$ into a root function to return original value. Thus far all my attempts have ended in abject failure.
Base : 1 2 3 4 5 6 7 8 9
Result : ...
0
votes
0answers
30 views
System of equations and Abel theorem
Consider this system of 3 equations to be solved in x,y and z:
$a x^m=(y+z)^n$
$by^m=(x+z)^n$
$cz^m=(x+y)^n$
The parameters $(a,b,c)$ and the unknown $(x,y,z)$ are all in $ℝ₊$. Also, m and n are ...
0
votes
0answers
22 views
How to find more precise estimation for fraction: $\frac{q^2 c1}{1+0.5q^2(1+c2)}$
I have a sum of fractions:
$$\sum\limits_{i=1}^n \frac{t^2\sigma_i^{2}(1-a^{\delta'})}{1+t^2\sigma_i^2(1+2a^{\delta'}(\frac{\cosh{\mu} - 0.5\mu^2 - 1}{\mu^2}))}$$
where $ \delta' = \{1,2\}$, $1 ...
0
votes
2answers
64 views
Statement, equivalent to fundamental theorem of algebra
In the article THE CLASSIFICATION OF REAL DIVISION ALGEBRAS (written by R. S. PALAIS) it is said that if D is finite dimensional division algebra over $\mathbb{R}$, then:
"One way of stating the ...
2
votes
4answers
55 views
How can I prove this inequality about square roots and absolute value?
How can I prove that $$\left|x^{1/2}-y^{1/2}\right|\leq\left|x-y\right|^{1/2}$$ for all $x,y \geq 0$
3
votes
4answers
93 views
How to find $x$ of this equation?
I'm doing some equations and I'm not sure how to find $x$. Any idea? Step by step answers please, it's like my first time.
$$2(3x^2+x-5)(2x^2-7x+3)=0.$$
1
vote
1answer
27 views
Properties of Exponentiation
I am a Computer Programmer and this Question might be too trivial to true practitioners of pure Mathematics.
I recently came across a programming puzzle (Project Euler #29). I have to find out the ...
0
votes
2answers
30 views
Investigate monotony, bound and convergence
I'm doing an exercise in the college, and I ran into a doubt: a friend says me that I've made a mistake, but I can't find it.
The exercise asks: "Investigate if the sequence $2^n\over{(n+1)!}$ is ...
1
vote
3answers
32 views
I need help with this word problem.
A pet store owner wants to mix together an high quality dry cat food costing 1.10
per pound with a lower quality dry cat food costing 0.85 per pound. How many
pounds of each should be mixed together ...
1
vote
1answer
120 views
Is there an identity for $\sum\limits_{n=1}^\infty \frac{1}{k^n}$?
What is an identity for
$$\sum_{n=1}^\infty \frac{1}{k^n}\quad ?$$ I found numerous identities for $\sum_{n=1}^\infty ak^n$, all of which extremely complex, but are there any simpler identities?
2
votes
1answer
43 views
How to write a function which depends on another function which in turn depends on the first function…
Here’s something I can’t figure out, and I need some insight—let me know what you think.
Two boxers are in a ring.
Boxer A can deliver 20 hits each round.
Boxer B can deliver 15 hits each round.
...
-4
votes
0answers
95 views
New Research in Math [closed]
I did a new research in math especially (algebra).What I did discover is a new way to find the cubic roots of the complex numbers exactly without de Moivre's formula and without using calculator, and ...
5
votes
1answer
88 views
Expressing a number in $\sqrt a/b$ form
Express the number $\sqrt3 \sin(10^\circ) +\dfrac38\tan(10^\circ)$ in the form $\dfrac{\sqrt a} b$, where $a$ and $b$ are integers.
I am sure that trigonometric formulas must be used here, but I ...
3
votes
5answers
165 views
With the binomial expansion of $ (3+x)^4$ express $(3 - \sqrt 2)^4$ in the form of $p+q\sqrt 2$
I know how to expand the binomial expansion but I have no idea how to do this second part.
Hence Express $$(3 - \sqrt 2)^4$$ in the form of $$P+Q\sqrt 2$$
Where P and Q are integers, and then how to ...
0
votes
0answers
55 views
What is newton's raphson method? [closed]
I have a question,
"obtain newton's raphson formula for solving the equation $x^3-1=x$ although i just cannot really get a idea of what it is/ what i need to do
0
votes
1answer
20 views
Integrating with the substitution $u = N^{-v}$
Integrate
$$\frac{dN}{dt} = rN(1 - K^{-v}N^v)$$
where $r,v,K$ are positive constants (and so I think $N$ is a function of $t$), using the substitution $u =N^{-v}$, given that $N$ has an ...
1
vote
1answer
19 views
Formula for Damage Calculation Based on Distance
I am working on programming a game, and I want the damage that a player takes to be based off of the distance they are from the explosive. Consider it like a grenade. Right on the blast radius ...
2
votes
4answers
59 views
How to factor $a^2+10ab+25b^2-9c^2$
This is what I got so far $a^2+10ab+(5b)^2-(3c)^2$. I think I can group $a^2+10ab$ but not sure about $(5b)^2-(3c)^2$. Can someone explain this?
1
vote
4answers
63 views
How to factor $a^2-4b^2+4ac-8bc$
I am not sure how I would factor this. Can someone explain how I would factor this?
1
vote
5answers
99 views
How to factor $x^4-7x^2-18$
I am not sure how I would factor this. The $x^4$ and $x^2$ are really throwing me off. Can someone explain how I would factor this?
0
votes
1answer
35 views
State the domain of each composite function?
So we started a new section in precal today and I'm still trying to get the hang of it. I have a problem asking for:
For the given functions $f$ and $g$ find:
(a) $f\circ{g}$
(b) ...
7
votes
2answers
166 views
Calculate the number of real roots of $x^8-x^5+x^2-x+1 = 0$
Calculate the number of real roots of $x^8-x^5+x^2-x+1 = 0$
My try: $$\left(x^4-\frac{x}{2}\right)^2+\frac{3}{4}x^2-x+1 = ...
2
votes
2answers
67 views
How do you factor $2ab-6ac-15c^2+5bc$
$$2ab-6ac-15c^2+5bc$$
Here is what I have done:
$$(2ab-6ac)-(15c^2+5bc)$$
$$2a(b-3c)-5c(3c+b)$$
$$2a(b-3c)+5c(-3c-b)$$
$$2a(b-3c)+5c(-b-3c)$$
$$(b-3c)(2a-5c)$$
I know this isn't the correct answer ...
1
vote
1answer
29 views
simple logarithms with exponents
Note: I am using log base 10 and I am trying to rewrite the equation using exponents instead of logs.
Here is what I have and I am wondering if I did it correctly (if not how am I suspose to solve ...
0
votes
2answers
69 views
Check my answers to these problems on rationalizing denominators? [closed]
I just need to check my answers for these problems. I did the work already on paper. I'm not trying to get free answers because I know that would hurt me in the long run. So here's the questions:
...
0
votes
1answer
54 views
Two step equations $-1=5+x/6$
I need help turning $x$ into a negative number to solve
$$-1=5+x/6$$
The problem looks easy, but I'm missing something and I can't figure it out
-2
votes
0answers
71 views
How to justify these steps in a proof of $\frac{a}{b}\times\frac{c}{d}=\frac{ac}{bd}$?
Need help....
$$\begin{align*}
\frac{a}{b}\times \frac{c}{d} & =\left(a\times\frac{1}{b}\right)\times\left(c\times\frac{1}{d}\right) & &\text{Def 6.2 - def of fractions}\\
&=(a\times ...
0
votes
1answer
53 views
Solving a 'two step equation' $-6+x/4=-5$
I need help with the break down of this problem. I need to know exactly what I need to do to solve this problem. Please help!
5
votes
4answers
240 views
What is a simple example of a limit in the real world?
This morning, I read Wikipedia's informal definition of a limit:
Informally, a function f assigns an output f(x) to every input x. The
function has a limit L at an input p if f(x) is "close" to ...
0
votes
2answers
37 views
find the number b where a = b + 19% of b
Find which number plus its 19% gives for example 200, 233 ..
Story short:
for example I have the number 0.30 now I need to know with formula how can I get which ...
0
votes
2answers
46 views
Calculating page numbers to link to
I'm trying to jog my memory of calculus from 10 years ago and it's proving a bit difficult. I'm hoping someone can give me a push in the right direction here. I've found a number of good resources ...
0
votes
1answer
15 views
Lopsided percentages
I'm trying to make a table in Excel where I have two different sets of data totaling different amounts representing market share in two different markets (totals=550,000 tons and 700,000 tons) and I ...
1
vote
3answers
38 views
Question about simplifying absolute value/exponents
Does $|x^n|^{\frac{1}{n}} = |x|$? Also n is a natural number. Sorry that this is such a stupid question, I'm just simplifying something and trying to make sure I'm doing it right.
2
votes
1answer
41 views
Find or estimate constant in inequality
For given $0<\alpha<1$ I want to find a constant $C(\alpha)>0$ (minimal as possible) such that for any positive numbers $x_1,\ldots,x_n >0$ the equality holds
$$
...
0
votes
0answers
24 views
expression that constrain the range of x to a positive interval
For any $x \in R$, I used the exponential $f(x)=e^x$ to constrain the value of $f$ to a positive interval. While serving this purpose, it happens that I cannot use the exponential for some other ...
1
vote
1answer
44 views
Solving basic exponential equation with logs
I am having trouble with this grade 12 pre-calc question that I am sure will be elementary to most of you. I understand most of it but I do not understand one of the steps.
These are the steps in my ...
0
votes
0answers
34 views
Using Law of Sines instead of Law of Cosines…?
This is the question:
A ship travels 60 mi due east, then adjusts its course 15 degrees northward. After traveling 80 mi in that direction, how far is the ship from its point of departure?
Now, I ...
