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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0
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0answers
5 views

State the domain and range of the following graphs.

State the domain and range of the following graphs. Express each domain using interval notation and express each range using set-builder notation. I think I'm beginning to understand using interval ...
0
votes
1answer
15 views

Solve the algebraic expression for a, b, and c of the function x

I am trying to solve for $a$, $b$, and $c$ in the expression below, but I have found that the way I tried to solve it is convoluted and did not work out. I believed that by solving for x, I would be ...
0
votes
0answers
9 views

Algebraically solve a component in a partial sum

I would like to solve this equation for y: T = -a + Σ (x/n - y/n) / (1+b)^n The partial sum (Σ) is from 1 to n. I use the ^ symbol for an exponent. For my purposes all the terms are known except y. ...
1
vote
1answer
39 views

Unclear why the highest argument value for cosine function $\cos(x+\frac{\pi}{4})$ is $\frac{\pi}{2}$

The problem to solve is to find the values of $x$ with which the function $\sin(x)+\cos(x)$ will compute to its highest value. I checked the textbook's answers section: it has the function transformed ...
4
votes
5answers
137 views

$A+B+C=2149$, Find $A$

In the following form of odd numbers If the numbers taken from the form where $A+B+C=2149$ Find $A$ any help will be appreciate it, thanks.
-3
votes
2answers
84 views

How many grandparents do I have? [on hold]

Suppose each of us had two parents, four grandparents, eight great grandparents,...and so on. If there were twenty five years between each generation, how many great-great-great...-great grandparents ...
0
votes
2answers
20 views

Decimal Number Representation As Fraction

Represent the following decimal number in a fractions of integers: $38.07818181...$ $x=0.07818181...$ $10000x=781.8181...$ So $9999x=781\rightarrow x=\frac{781}{9999}$ $38*9999=379962$ ...
-4
votes
1answer
47 views

Difficult product problem $\prod \limits^{2014}_{k=1}\left( 1-\frac{1}{k^{2}} \right)$ [duplicate]

Evaluate the product $$\prod \limits^{2014}_{k=1}\left( 1-\frac{1}{k^{2}} \right)$$ Any help will appreciated!
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2answers
26 views

Finding a point using complex geometry

In the Cartesian plane let $A = (1,0)$ and $B = \left( 2, 2\sqrt{3} \right)$. Equilateral triangle $ABC$ is constructed so that $C$ lies in the first quadrant. Let $P=(x,y)$ be the center of ...
4
votes
3answers
49 views

Do 4 points in ${\mathbb R}^2$ in convex position define a unique elliplse that passes through those 4 points?

So it takes 3 distinct points in the plane, that are not collinear, to define a unique circle that passes through the points. So what about ellipses? Arguing naively in terms of degrees of freedom ...
2
votes
2answers
19 views

Expression for change in 2 dependent variables

Deformation $ \delta $ and stress $ \sigma$ depend on parameters $r$ and $t$ varying inversely as $ r^3 \, t $ and $ r \, t $ respectively. Find the expression how $(r,t)$ depend on $ \delta $ ...
1
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1answer
17 views

changes in 2 dependent variables

Deformation $ \delta $ and stress $ \sigma$ depend on parameters $r$ and $t$, varyjng inversely as $ r^3 \, t $ and $ r \, t $ respectively. In order to reduce $ \delta $ from 6 to 4 and also $ ...
0
votes
1answer
11 views

On determining a function given a certain parametrization of a point

Imagine we have a parametrization of a particle in 2D space like this http://i.minus.com/iXL64EfdJe6w5.gif How do we go about finding an explicit way to express these functions ($f(x)$ and $g(x)$) ...
3
votes
3answers
44 views

Solve the trigonometric equation $\csc^2 \theta= 5 \cot \theta + 7$

Solve the given equation. Let k be any integer. $$\csc^2 θ = 5 \cot θ + 7$$ I just need the first step or two please. I tried converting it: $$\frac{1}{\sin^2 θ} = \frac {5\cosθ}{\sinθ} + 7$$ ...
0
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0answers
40 views

Help with rearranging a large polynomial

I have an expression $$\frac{(-ab)x^2+(a^2+b^2)xy+(-ab)y^2}{2(a-b)^2(0.5(a+b))^2}$$ (a and b are constants) and I need to rearrange it so that it is in the form f(x)*f(y). I am totally lost, and ...
3
votes
2answers
90 views

First 10 digits after decimal point in the number $(1+\sqrt{3})^{2015}$

The question is how to find first 10 digits after decimal point in the number $(1+\sqrt{3})^{2015}$. I keep running into this kind of problems in a context of symmetric polynomials.
1
vote
1answer
39 views

are there closed form solution to $n \cdot y + \log(y) = x$?

I am trying to find a closed-form solution to $n \cdot y + \log(y) = x$ How do we deal with the fact that there aren't, if there aren't? Is it possible to rewrite this in a better way as a ...
0
votes
4answers
116 views

Which number is bigger? [duplicate]

Which number is bigger? $1.01^{101}$ or $2$? and how about $e^{\pi}$ or $\pi^e$? Tried some algebraic manipulations to no end, so would love some suggestions or some different ways to approach those ...
-1
votes
3answers
54 views

Trigonometric double identities [on hold]

Prove the following trigonometric identity: $$(\sec (x) - 1)(\sec (x) + 1)=\frac{\sin^2(x)}{\cos^2 (x)}$$
0
votes
1answer
14 views

convert price per PU in price per ton

Quite basic calculation, but my client insist on telling I am calculating wrong while I am quite sure that my calculation is correct. Given the following variables: weight in kg per packing unit ...
-7
votes
1answer
35 views

I am at lost… please help [on hold]

A boy skis 4 miles down a mountain slope in 10 minutes. What is his average speed, in miles per hour (mph), over that time interval?
0
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6answers
68 views

The sum of two positive integers is 35 and their product is 304. What is the lesser number? [on hold]

The sum of two positive integers is 35 and their product is 304. What is the lesser number? Can anyone show me a step by step tutorial on this?
-3
votes
1answer
21 views

Short structured question [on hold]

After Gary donated 1/3 of his pocket money and Terry donated 1/2 of his pocket money, Gary has \$29 more than Terry. The amount donated by Gary is \$8 more than that donated by Terry. How much ...
2
votes
2answers
40 views

simplifying complex fractions

I have this expression ${2 \over x^2 - 4}$ + ${1 \over x + 2}$ So I would take the LCM to ${x^2 - 4}$ or using the difference of 2 squares to be ${(x + 2)(x - 2)}$ So I would simplify this to: ${2 ...
1
vote
1answer
30 views

How to factor a third degree polynomial? [on hold]

How do I factor $2x^3-6x$? I've looked it up, but I haven't seen advice that helps with my exact problem.
2
votes
5answers
32 views

Is it possible to factor a quadratic equation when $a$, $b$, and $c$ are all equal?

I have the equation $4x^2+4x+4$ to factor. I know that need to start with $$(2x \quad )(2x \quad )$$ to make $4^2$, but I can't seem to factor the rest of the way. What should I do?
0
votes
1answer
26 views

Solving function notations. [on hold]

A gas station attracts customers by offering coupons worth a 0.05 discount for every $1.00 spent on gasoline. a. Complete the table. The equation that represents the relation, using the ...
-1
votes
0answers
46 views

A book on functions! [on hold]

I am looking for a good book on algebra which covers functions very comprehensively. It should cover functions of the type: linear: $f(x) = ax + b$ quadratic: $f(x) = ax^2 + bx + c$ cubic: $f(x) = ...
-2
votes
1answer
46 views

Solve the equation below [on hold]

Solve the equation $$\tan(\cos^{-1}\sqrt{x})=2^{\log_{4}x}.$$ I have no idea where I have to start; it's a little hard for me. So any help?
-2
votes
1answer
28 views

A basic factorial question type [on hold]

Hello could you show me a way that how to solve this kind of questions? a and b are natural numbers $60! = a6^b$ What is the biggest value of b?
0
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0answers
17 views

Exchange Rate scenario. Which is the better option?

You are travelling overseas. If you use your ATM or Credit Card, you will be assessed a 3% surcharge on all transactions. So, you decide to withdraw Euros at your local bank branch to see if you ...
3
votes
3answers
104 views

what is wrong with this natural log conversion

why can't we convert this: $$4e^{1+3x}-9e^{5-2x}$$ to this: $$(1+3x)\ln(4)-(5-2x)\ln(9)$$ or this: $$(1+3x)\ln(4)+(5-2x)\ln(-9)$$ this comes from the q, solve: $$4e^{1+3x}-9e^{5-2x}=0$$ do the above ...
1
vote
2answers
47 views

Seating people in a circular table

It has always been an interesting question. If we have $10$ chairs and a round table, how many ways are there of seating $10$ people? I would say there are $10!$ ways to seat the people due to ...
-1
votes
2answers
30 views

Does the order in a circular arrangement matter?

I posted a question a while ago: Ten chairs are arranged in a circle. Find the number of subsets of this set of chairs that contain at least three adjacent chairs. My question here is: imagine a ...
1
vote
2answers
45 views

( Logarithmic Equation ) Solve for x.

$(x+1)^{log(x+1)} = 100(x+1)$ Attempt at solution : $$ (x+1)^{log(x+1)} = 100(x+1)$$ $$= x^{log(x+1)} + 1 = 100x +1$$ $$=(x+1)+1=100x+1$$ $$=−98=99x$$ $$x=−98/99$$ But the answer given in the ...
2
votes
2answers
380 views

Stars and Bars vs PIE

I randomly made up this question so I could check: There are $3$ kids and $6$ gifts, how many ways to distribute so that each kid has at least one gift. Obviously, $**|**|**$ there are ...
7
votes
6answers
1k views

How to solve this exponential equation?

I'm given this equation and i have to solve for the x. $$ e^{2x} -(e^5 + e^2)e^x + e^7 = 0 $$ The results should be $x =2$ and $x = 5$. At first i thought it would be an easy task, ...
0
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0answers
27 views

Stock Dividends

I just do not get it, and the teacher is teaching a class in the other room. Here is the question: Danielle owned 100 shares of FPIC stock. She purchased 100 shares of FPIC on November 14, 2011, ...
1
vote
1answer
18 views

Logarithmically bounded function fulfills $f(n) \le \lceil m \cdot \log_b r \rceil$ for certain numbers $n,m,r$

Let $f : \mathbb N \to \mathbb N$ be a function such that $f(n) \le 1 + \log_b n$ for some base $b$ and all $n$. Now let $n \in \mathbb N$ have the property that $$ \frac{r^m - 1}{r-1} \le n < ...
0
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0answers
16 views

What would be the equation for “3% in 100 Hz range, 0.5% in the 2000 Hz range”

The smallest distinguishable pitch/frequency by a human ear is something like this: Pitch is our perceptual interpretation of frequency. As mentioned, ideal human hearing ranges from 20 to 20,000 ...
-1
votes
0answers
36 views

polar coordinate transformation

If we have an equation $\mathcal{L_I}=\prod \mathrm{exp}\bigg(-\lambda_j \displaystyle\sum\limits_{m=1}^{\Psi_{j}}\binom{\Psi_j}{m} ...
-1
votes
1answer
47 views

Modulus Problem [on hold]

I do not understand how to solve such a question: $$|x+1| - |x| + 3|x-1| -2|x-2| = x+2.$$ How would you go about all the possibilities with which sign the modulus could take? Appreciate any help!
1
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1answer
64 views

How does one use the complex plane to solve this problem?

Given: $$a^2 + ab + b^2 = 1 + i$$ $$b^2 + bc + c^2 = -2$$ $$c^2 + ca + a^2 = 1$$ Find $$(ab + bc + ca)^2.$$ The solution says to use the complex plane. Can somebody explain to me (an average ...
-3
votes
4answers
179 views

Find the value of the question below [on hold]

If $x^{3}+\frac{1}{x^{3}}=14$ Find the value of $$x^{6}+\frac{1}{x^{6}}$$ Original Question: If $x^{2}+\frac{1}{x^{2}}=14$ Find the value of $$x^{5}+\frac{1}{x^{5}}$$
-1
votes
2answers
75 views

Evaluate the infinite radical expression $2\sqrt{2\sqrt[3]{2\sqrt[4]{2\sqrt[5]{2 \cdots}}}}$ [on hold]

Find the value of $$2\sqrt{2\sqrt[3]{2\sqrt[4]{2\sqrt[5]{2 \cdots}}}} .$$ I really don't know where I start, so any help will be appreciated.
3
votes
3answers
785 views

How can I try myself to solve exponential equations easily?

I spent hours trying to solve: $$4^x + 1 = 2^{x+1}$$ Can you guide me on how to solve this? How can I train myself to always find the right "trick" to solve such equations? Rather than just ...
3
votes
1answer
68 views

How to find unkown height of triangle without hyptenuse

I been trying to solve this question and have tried to solve it for many days, but do not know how, any help would be much oblidged. A cable company owns the roads marked with the dotted lines in ...
0
votes
0answers
38 views

Puzzle on multiplying by fixed values to reach a target number.

So, this one's tricky. There's a keycode combination, and there are six buttons. Each button multiplies the base number of 1 by their respective multipliers (see below). Once the result number gets ...
2
votes
3answers
69 views

Why would the cubic have $5$ roots?

The polynomial $P(x)$ is cubic. What is the largest value of $k$ for which the polynomials $Q_{1}(x) = x^{2}+(k-29)x-k$ and $Q_{2}(x) = 2x^{2}+(2k-43)x+k$ are both factors of $P(x)$? $P(x) = ...
6
votes
1answer
132 views

Find the sum of the series below

Find the sum $$(1\cdot2)+(1\cdot3)+(1\cdot4)+\cdots+(1\cdot2015)+(2\cdot3)+(2\cdot4)+\cdots+(2\cdot2015)+\cdots+(2014\cdot2015)$$ What I have tried... We are looking for ...