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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9
votes
1answer
921 views

What is the standard interpretation of order of operations for the basic arithmetic operations?

What is the standard interpretation of the order of operations for an expression involving some combination of grouping symbols, exponentiation, radicals, multiplication, division, addition, and ...
1
vote
1answer
126 views

Solving inequalities comparing $f(x)$ to $0$ where $f$ is an elementary function

Any inequality comparing elementary functions can be rearranged to compare some elementary function $f$ to $0$. What is the best way to approach, in general, solving such inequalities at the ...
0
votes
3answers
116 views

How would I express $f(x)=2x^3-5x^2+3$ in the form $f(x)=(x-c)q(x)+r$ for $c = -2$?

How would I express $f(x)=2x^3-5x^2+3$ in the form $f(x)=(x-c)q(x)+r$ for $c = -2$? I have no idea where to even start. Could anyone help me out?
-3
votes
1answer
495 views

A simple but ambiguous expression [duplicate]

Possible Duplicates: Implicit multiplication order of operation What is 48÷2(9+3)? i am so confused after knowing different answer of this ques 48/2(9+3) though google cal comes up ...
1
vote
2answers
121 views

-$\frac{2\sqrt{2}-6}{7}$ = $\frac{6-2\sqrt{2}}{7}$ correct?

When asked to rationalize the denominator for $\frac{2}{\sqrt{2}+3}$, I came up with $\frac{6-2\sqrt{2}}{7}$ but my algebra book gives -$\frac{2\sqrt{2}-6}{7}$ as the answer. I think we're both ...
0
votes
2answers
1k views

Simplifying as an exact value (Simplest Radical Form)

Hey, I have a problem: solve for exact value (simplest radical form) $-3\sqrt{27}$ , the result is $-9 \sqrt3$ . I'm in 8th grade studying for a Math placement test to take trigonometry as a freshman ...
0
votes
1answer
229 views

How could I model this with a polynomial?

An engineer is designing a storage compartment in a spacecraft. The compartment must be 2 meters longer than it is wide and its depth must be 1 meter less than its width. The volume of the compartment ...
4
votes
3answers
176 views

Simplifying simple radicals $\sqrt{\frac{1}{a}}$

I'm having a problems simplifying this apparently simple radical: $\sqrt{\frac{1}{a}}$ The book I'm working through gives the answer as: $\frac{1}{a}\sqrt{a}$ Could someone break down the steps ...
2
votes
1answer
69 views

Ratio Language Help

I'm having a little trouble interpreting the following: The Ratio between the wage a worker could receive if they worked and the benefit they actually receive if they don't work So lets say the ...
0
votes
1answer
131 views

Trigonometry. Sec

$\sec(\theta)=x/5$. What does $\sin(\theta)$ equal? What does $\tan(\theta)$ equal?
2
votes
2answers
264 views

How to solve this basic math problem?

I'm having this problem on some game I'm coding which I think it's just math and has nothing to do with coding, that's why I'm posting it here and I'm going to simplify the problem without describing ...
-4
votes
1answer
71 views

By how many meters can A beat C in the race

A beats B by 200 m in arace of 800 m.B beats C by 100 m in a 1000 m race. 1)Approximately by how many meters can A beat C in a race of 560m? 2)Approximately by how many meters can A beat ...
3
votes
1answer
62 views

Curves simplify to lines?

I have what is supposed to be a curve: $$25x^2 - 4y^2 = 100$$ When simplify this to be: $$y = 2.5x - 5$$ it is a line. But isn't it supposed to be the same?
0
votes
1answer
292 views

Elements of Algebra (Euler) in comparison to similar texts

I have no problem with Elements of Algebra simply because of its age; in fact, I strongly agree with Abel's famous assertion regarding the proper place to look for knowledge. What do you guys think ...
4
votes
1answer
434 views

Find the minimum for a trigonometric function

Find the local minimum of the following function: $$\tan\left(x+\frac{2\pi}{3}\right)-\tan\left(x+\frac{\pi}{6}\right)+\cos\left(x+\frac{\pi}{6}\right)$$ I am wondering how can I simply this ...
0
votes
1answer
83 views

Standard form numbers and algebra

I have a situation like this: $3\times 10^n$ and $4\times 10^m$ and $a\times 10^p$ are all in standard form. $$\frac{3\times 10^n}{4\times 10^m} = a\times 10^p.$$ Is it possible to calculate the ...
1
vote
0answers
133 views

most comprehensive coverage of arithemetic and elementary algebra?

To put it shortly, I never learned mathematics. I never learned the algorithms for multiplication and division, &c. (I had always just mentally scaled by powers of 10, making it unnecessary for me ...
3
votes
1answer
139 views

Simplification of a sum

Any ideas on how to approximate and/or simplify this crazy-looking sum will be massively appreciated) $$\frac{1}{\mu}\sum_{j=0}^{\frac{\lambda}{2}} ...
1
vote
1answer
75 views

Checking the digits in an integer

This question is a bit basic, but how do I check the number of digits in an integer? I need to check if an integer P is between ...
0
votes
3answers
4k views

Why do you multiply a complex number by its complex conjugate to get rid of it in a fraction?

For example, in $\displaystyle{\frac{a+bi}{n+zi}}$, you would multiply both by the complex conjugate of the denominator, $n-zi$, to get rid of the complex number in the denominator. Wouldn't ...
0
votes
2answers
219 views

What is wrong with this simple equation?

Consider the following equation: $$\Bigl(\bigl((100 + 5 - 2) * 1.15 + 6\bigr) * (1.07) - 3\Bigr) = 130.1615.$$ I want to take the above and add 3% non-compounded, meaning I want to take 3% of 100 and ...
5
votes
5answers
268 views

Calculate $x$, if $y = a \cdot \sin{[b(x-c)]}+d$

I am not an expert when it comes to trigonometric functions. I need to calculate value of $x$ for a program. If $y = a \cdot \sin{[b(x-c)]}+d$ then what will be the formula to calculate $x$? Please ...
0
votes
1answer
139 views

perpendicular distance to center of square from line in terms of slope

I am trying to find the relationship between the vertical distance (V) from the center of the square to the line to the perpendicular distance (P) from the center of the square to the line in terms of ...
3
votes
3answers
6k views

Compound interest formula with regular deposits, solve for time

I cant seem solve the following problem due to my bad memory of logarithms if someone opens an account with initial balance of $B$ interest rate of $R$ and does a constant monthly deposit of $D$ ...
7
votes
0answers
396 views

Why is $\sum\limits_{i=1}^n i = \frac{n(n+1)}{2}$? [duplicate]

Possible Duplicate: Proof for formula for sum of sequence $1+2+3+\ldots+n$? I was just messing around in Haskell: ...
3
votes
2answers
180 views

Calculating a total based on a percentage

I have an event that I am running and I need to figure out what to charge participants so that I break even. I know the formula for doing this: ...
6
votes
3answers
311 views

How to find the minimum value of this expression?

Given that $b_1+b_2+\dots+b_n = 1$, how do I find the minimum value of $$\frac{x_1+x_2+\dots+x_n}{x_1^{b_1}x_2^{b_2}\dots x_n^{b_n}}?$$ For $n=2$ I used calculus and found the answer to be ...
5
votes
1answer
871 views

Algorithm for computing square root of a perfect square integer?

My question is the following: Is there a polytime non-numerical algorithm for computing square root of perfect square integers? The more elementary the algorithm is, the better! EDIT: ...
3
votes
2answers
261 views

Integrating $\int_0^\infty \frac{1}{x^2 + 2x + 2} \mathrm{d} x$

I've been trying to integrate this: $$\int_0^\infty \frac{1}{x^2 + 2x + 2} \mathrm{d} x .$$ Unfortunately I haven't found a way so far. I've been trying to factor the denominator in order to end up ...
0
votes
1answer
551 views

recurrence relation on bank interest

Invest 1000 dollars at bank at 3 percent interest compound annually. Every year the bank deducts 15 dollars in charges. If $A_n$ is the value of the investment at the end of $n$ years write down a ...
1
vote
1answer
1k views

how to solve a quadratic equation in three unknowns

Is there any elegant way of solving this system of equations? \begin{gather*} a_1 x^2+a_2 x+ a_3 y^2+a_4 y+a_5 z^2+a_6 z+a_7=0 \\ b_1 x^2+b_2 x+b_3 y^2+b_4 y+b_5 z^2+b_6 z+b_7=0\\ c_1 x^2+c_2 x+c_3 ...
4
votes
1answer
119 views

How do I factor this polynomial?

How do I factor the followinig polynomial? $$x^6-14x^4+49x^2$$ I can't find a way to get this to work. The previous problems were all over either a difference of squares or sum/difference of cubes, ...
1
vote
2answers
120 views

Arithmetic error when calculating inverse of the logistic?

I would like to rearrange the logistic function: $$y=\frac1{1+\exp(-a+bx)}$$ To calculate $x=f(y)$ So I did the following: $$\frac1{y}=1+\exp(-a+bx)$$ $$\ln\left(\frac1{y}-1\right)=-a+bx$$ ...
0
votes
1answer
257 views

Simplifying $(\sqrt{7x} - \sqrt{2y})^2$

how do i solve this? how can i simplify it? $(\sqrt{7x} - \sqrt{2y})^2$
1
vote
1answer
715 views

Trajectory of a projectile meets a moving object (2D)

First of all, I asked this question on Stackoverflow, but I realize this is a better place to ask the question. So i moved it here. I've looked for quite some time now to find a nice math solution ...
0
votes
1answer
99 views

Is there a way in the following scenario get back my original value by going in the same order I used to get to the calculated value?

I have a base value of 100 and I apply a +10% and a + 7% increase to it. To get the calculated value, I do: 100 * 1.1 = 110 110 * 1.07 = 107 100 + 10 + 7 = 117 Now, to get back to 117, I was ...
11
votes
1answer
1k views

Is solving an equation the same as finding the roots?

For example, would solving for $x$ in $x^2=8x+7$ be the same as finding the roots of the equation? Also, would finding the roots of this be the same as finding the zeros?
6
votes
2answers
97 views

3 variable systems

$$\begin{align*} x + 2y - z &= -3\\ 2x - 4y + z &= -7\\ -2x + 2y - 3z &= 4 \end{align*}$$ I multiply (1) by $-2$ and get $-2x-4y+2z=6$ and then add it to (2) which gives me $-8y+3z = ...
2
votes
3answers
142 views

Order of precedence: in $ab^{c}$, which operation goes first?

If you have $$x^3(x^2 + 1)^{-\frac{1}{2}},$$ os the power or the product calculated first? I'm assuming the power comes first but I don't like to just assume.
3
votes
1answer
100 views

Trigonometric re-write I don't understand

$$\int \sin^3{x}\,\cos^5{x}\,dx = \int \sin{x}\,(\cos^5{x}-\cos^7{x})\,dx$$ My ignorance amuses me hehe. Even if I multiply it out I still don't get it.
2
votes
1answer
111 views

problem solving using quadratics

Ralph is mowing a yard 16 m long and 12 m wide. He mows continuously around the yard working towards the centre. He wonders how wide a strip must be cut before he is half done.
6
votes
5answers
38k views

How to calculate percentile? Is it possible to get 100 percentile?

How do we calculate percentile? I think it should be calculated as: P = Total number of candidates L = Number of candidates whose marks are below yours ...
1
vote
1answer
119 views

Simple algebra question

You drive $600$ miles in $2$ days. You drive $120$ miles less than you did on day one than on day $2$. How many miles did you drive both days separately? Solve algebraically. $$d_1+d_2=600$$ ...
1
vote
1answer
81 views

3 variable systems

1) $x+y-z = 6$ 2) $x+3y-2z = 14$ 3) $3x - 2y + z = -5$ I multiply 1 by -1 and add to 2, I multiply 2 by -3 and add to 3. I do not get anyone close to a proper answer.
3
votes
4answers
170 views

Solution of a system with 3 variables

$$\begin{array}{rcrcrcr} x & - & 2y & + & 3z & = & 7 \\\ 2x & + & y & + & z & = & 4 \\\ -3 x & + & 2y &- &2z & = & -10 ...
3
votes
0answers
143 views

Algorithm/Formula to compute adding and/or removing compound and/or non-compound percentages from a value?

I will first start with a scenario, I have to apply some adjustments to a particular value. These adjustments are either compound or non-compounded and they can either be added or subtracted to the ...
3
votes
1answer
290 views

What is the formula for add/removing compound and non-compound tax from a value?

I had posted this question on stack overflow because I am trying to implement a method that will loop through a set of percentages and add or remove them to a value based on some properties that are ...
2
votes
2answers
74 views

What will the value of following log expression

What will be the value of the expression $$\log_x \frac{x}{y} + \log_y \frac{y}{x}?$$ I tried: $$\log_x x - \log_x y + \log_y y - \log_y x = 1 - \log_x y + 1 - \log_y x = 2 - \log_x y - \log_y ...
0
votes
2answers
170 views

Solve two equations

I've tried unsuccessfully to solve these two problems. I'd grateful for any help here. What is the biggest real number $z$ that obeys these two conditions: $$x + y + z=5 \quad\text{and}\quad ...
4
votes
1answer
411 views

Finding the first term of a geometric series by the sum and $n$

I have the following exponential series: $$S = ar^0 + ar^1 + ar^2 + \cdots + ar^n$$ I know $S$, $r$ and $n$. How do I find $a$? I actually need this done by a script so all "crazy" methods like ...