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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2answers
166 views

What does $y_i=f(\sum_j w_{ij}y_j)$ mean (in an artificial neuron model)?

While trying to understand artificial neural networks, I came upon an equation for finding the net input of an artificial neuron. Can someone explain this to me and what it means? Here is the original ...
0
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2answers
163 views

The Polynomial concept needs to include both variables and contants?

As in Wikipedia: In mathematics, a polynomial is an expression of finite length constructed from variables (also known as indeterminates) and constants. So, it's only considered a polynomial if ...
2
votes
3answers
321 views

Can my proof be simplified and is it valid? $n(n+2) = (n+1)^2 - 1$ for all integers

I've decided to learn the basics of proofs and here is my first attempt. Could I improve or simplify my proof in any way? Is my formal language correct? Thanks! Let $n$ be any integer. $$n(n+2) = ...
1
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1answer
215 views

Finding the minimum value of a quadratic within a range

Given any quadratic equation of the form $y=ax^2+bx+c$, I want to find the minimum value for a specific range of $x$. My programmer brain can do it in a branchy, algorithmic way as follows, but is ...
1
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1answer
131 views

Finding X to minimise summed integral of two equations

I have two equations. In this example I'll make them linear, and later see if the solution generalises to different forms of equation: $$y_1=-0.1x + 0.65$$ $$y_2=0.15x - 0.825$$ I'm interesting in ...
6
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5answers
983 views

If $\sin x + \cos x = \frac{\sqrt{3} + 1}{2}$ then $\tan x + \cot x=?$

Hello :) I hit a problem. If $\sin x + \cos x = \frac{\sqrt{3} + 1}{2}$, then how much is $\tan x + \cot x$?
0
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1answer
124 views

How did they simplify this function

I'm currently practicing differentiation. The exercise I currently have is the following Find the derivative of: $(x + 6)^3 (9 x^3 - 2)^5$ Okay, well I can do that now. When I do this I uses the ...
11
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4answers
1k views

Algebraic Proof that $\sum\limits_{i=0}^n \binom{n}{i}=2^n$

I'm well aware of the combinatorial variant of the proof, i.e. noting that each formula is a different representation for the number of subsets of a set of $n$ elements. I'm curious if there's a ...
2
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2answers
605 views

How can I solve for a single variable which occurs in multiple trigonometric functions in an equation?

This is a pretty dumb question, but it's been a while since I had to do math like this and it's escaping me at the moment (actually, I'm not sure I ever knew how to do this. I remember the basic ...
4
votes
1answer
225 views

How to solve for x when it is in the exponent of 2 variables

I'm actually a programmer so I'm sorry if this is a stupid question. I am trying to solve for $x$, but I got stuck at this step: $$e^{\frac{q1 + x}{b}} = e^{\frac{p - x\cdot o}{mb}} - ...
1
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3answers
131 views

Simplifying this expression

How to simplify this? $\displaystyle\frac{n^{\log m}}{m^{\log n}}$
1
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5answers
261 views

General term of $1,2,3,10,11,12,13, \dots$

what is the 444th term of the series $1,2,3,10,11,12,13,20,21,22,23,30,31, \dots$
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2answers
317 views

Number of zeros not possible in $n!$ [duplicate]

Possible Duplicate: How come the number $N!$ can terminate in exactly $1,2,3,4,$ or $6$ zeroes but never $5$ zeroes? The number of zeros which are not possible at the end of the $n!$ is: ...
1
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6answers
3k views

Word problem: Monkey climbing up a pole

Problem edited since i missed a line from the problem, A monkey wants to climb up a pole of 50 metre height. he first climbs up 1 m but he falls back by same height. Again he climbs up 2 m but he ...
2
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2answers
3k views

8th Grade Algebra Problem I Can't Solve

I have no idea how to solve this. Could anyone give a hand? Thanks! $$2x^{5a} + 6x^{3a} - x^{2a} - 3 = 0$$ PS: I'm guessing this doesn't make sense unless it's also "solve for x" and the equation is ...
0
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2answers
203 views

Two inequalities

In course of a particular research I ran into these two inequalities which I would like to have some help with. $r,R>0$ for both the questions. Is there a function $M(r)$ for which this ...
0
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1answer
88 views

4 machines producing 100mg, one of them is making 90mg, once chance to weigh 2 machines versus each other

You have 4 machines that are supposed to create 100mg chocolate bars. One of the four machines is not working correctly and is making 90mg chocolate bars. You only have 1 chance to weigh the chocolate ...
2
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2answers
448 views

Algebra word problem (Red and Yellow Jelly Beans)

A jar contains some red and some yellow jelly beans. If a child ate 1 red jelly bean, 1/7 of the remaining candies would be red. If instead the child ate 5 yellow jelly beans, 1/6 of the remaining ...
4
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6answers
401 views

Prove that $(n-m) \mid (n^r - m^r)$

In respect to a larger proof I need to prove that $(n-m) \mid (n^r - m^r) $ (where $\mid$ means divides, i.e., $a \mid b$ means that $b$ modulus $a$ = $0$). I have played around with this for a while ...
0
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3answers
139 views

Proofs for polynomial divisons

I've got a couple of theorems that I must prove, but I'm completely stumped. Could someone help me out? Prove: If P(x) can be divided by Q(x), then it can be divided by cQ(x), where c - any non zero ...
4
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1answer
262 views

Inequalities: $y \leq 3y+2 \le 8 + 2y$

I have some maths homework due in on monday, therefore I can't ask my teacher for help and the three equations I have are a bit more advanced than what sir taught us. Here is the question I'm stuck ...
3
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1answer
147 views

How many possible solutions for 6 wires?

Imagine 2 sets of 6 wires. How would I find how many possible connections there are? Every wire must be used to be considered a connection. ...
2
votes
2answers
264 views

How quickly with better tool

If: I can make two tools which would serve the same purpose and: I need 10 times less time to make first tool but work with this tool is a half time slower than work with the second tool, after what ...
1
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5answers
1k views

How can I find inverse of function?

My question is ; How can I solve the following inverse of function question? $y=x^2-6x+4$ Thanks in advance,
1
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1answer
5k views

How to derive Gordon growth model

The formula for the Gordon growth model is: $\hspace{1in}P= \sum_{t=1}^{\infty} D\times\frac{(1+g)^t}{(1+k)^t}$ So summing the infinite series we get: $\hspace{1in}P=\frac{D(1+g)}{k-g} ...
0
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1answer
83 views

Determine concentration

How would I go about solving a problem that goes roughly as such? Solution A: .1% Solution B: .15% ...
2
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3answers
180 views

If $4^x + 4^{-x} = 34$, then $2^x + 2^{-x}$ is equal to…?

I am having trouble with this: If $4^x + 4^{-x} = 34$, then what is $2^x + 2^{-x}$ equal to? I managed to find $4^x$ and it is: $$4^x = 17 \pm 12\sqrt{2}$$ so that means that $2^x$ is: $$2^x = ...
2
votes
3answers
196 views

can x / (1/y) be expressed more simply

If you divide an number by another numbers reciprocal i.e x / (1 / y) Can this be expressed in another way is dividing by the reciprocal equivelant to another operation?
0
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1answer
837 views

Relative error reduction

Please forgive me a really simple question: Am I calculating the relative error reduction correctly? Example: Model 1 gets 80/100 examples wrong, model 2 gets only 20/100 examples wrong, so the 80 ...
1
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3answers
304 views

Finding positive solutions to two equations

After solving a system of equations I get this: x + 0.03125z = 0.242813 y + 0.40625z = 0.456563 How can I filter solutions that are only positive for x y and z ...
0
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2answers
478 views

Three linear equations in four integer variables

Hi I have these equations that I wish to know how to reach the variables for example A=6 D=A-C ...
2
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5answers
801 views

AGM Inequality Proof

I have been stuck on this one for hours. Let $x$, $y$, $z$ be non-negative real numbers. Also we know $x + z \leq 2$. Prove the following: $(x - 2y + z)^2 \geq 4xz - 8y$. Apparently this can ...
0
votes
2answers
483 views

How to divide it: $\frac{cx+d}{ax+b}$?

Somebody divided $\frac{cx+d}{ax+b}$ into $$ \frac{c}{a} + \frac{d- \frac{bc}{a}}{ax+b} .$$ For use for integrals. Does anybody knows how was it done? Could you show me how to do something like ...
1
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2answers
115 views

What is a good way to pick points for polar equations?

If I want to plot $r = 4\sin3\theta$ what is a good way to pick points? The period is $2\pi/3$ so it will repeat after that, but how do I pick points so that I get a good range of values so that I ...
0
votes
3answers
163 views

How $44:9.3 = 5.5:1.16 $?

This is actually mentioned in my module,I am not sure how they have got this result but I think this may not be correct,I tried using wolfarm alpha which gives false or am I missing something? I ...
1
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1answer
623 views

what is “average increase percentage” and how to calculate it?

What exactly it is meant by "average increase in percentage"? I stumble upon this term in while solving this problem: The average monthly income and expenditure of a person in the year $1995$ is $ \$ ...
3
votes
2answers
86 views

What is this question asking for?

I have a question that is: Find a degree 3 polynomial with real coefficients whose leading coefficient is 5 that has -2, 1, and 4 as zeros? I do not want the question answered for me what I want it ...
7
votes
6answers
1k views

Do values attached to integers have implicit parentheses?

Given $5x/30x^2$ I was wondering which is the correct equivalent form. According to BEDMAS this expression is equivalent to $5*\cfrac{x}{30}*x^2$ but, intuitively, I believe that it could also look ...
2
votes
4answers
146 views

Why both of the conditions are necessary?

If $a^2 = b^2 $ and $a,b \gt 0$ then we can answer "Is $a > b$?" I know that $a^2 = b^2 \Rightarrow |a| = |b|$ but still I don't understand why the second condition is absolutely necessary.
8
votes
3answers
1k views

How to check if a quadratic surd is a perfect cube?

While trying to answer this question, I got stuck showing that $$\sqrt[3]{26+15\sqrt{3}}=2+\sqrt{3}$$ The identity is easy to show if you already know the $2+\sqrt{3}$ part; just cube the thing. If ...
3
votes
3answers
336 views

Need help with a power equation

If $x^3 + \frac{1}{x^3} = 52$, then what is $x^2 + \frac{1}{x^2}$? I'm not sure which formulae or methods should I used to solve this problem, so could somebody show me a way? what should I be ...
0
votes
2answers
175 views

Algebra Problem

The expression $x^2-4x+5$ is a factor of $ax^3+bx^2+25$. Express the sum a+b as an integer. Please give an explanation of how the answer
2
votes
2answers
269 views

Find the values of $m$ in the 2nd degree equation $mx^2-2(m-1)x-m-1=0$ so that it has one root between $-1$ and $2$

Find the values of $m$ in the 2nd degree equation $mx^2-2(m-1)x-m-1=0$ so that it has only one root between $-1$ and $2$. Like in this almost identical question there are two ways to solve this, one ...
1
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3answers
888 views

Problem on working together (Time and Work)

If $A$ can complete a job in $6$ days. $B$ can complete it in $10$ days.If they work on alternate days, in how many days the job would be completed ? Does it depend on who ($A$ or $B$) starts the job? ...
0
votes
1answer
528 views

Suggest quicker method for finding rate percent per annum

$1$.The compound interest on certain sum for $2$ years is $\$410$ and simple interest is $\$400$. Find the rate of interest per-year. $2$.A sum of money invested at compound interest amounts in 3 ...
0
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2answers
116 views

On profit loss (II)

It seems like I am having troubles while dealing with dishonest merchants! Here is another problem: A cloth merchant says that due to slump in the market, he sells the cloth at $10\%$ loss but he ...
-1
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2answers
141 views

Solving $x$, $y$ and $z$

If I have $22x = 23y = 24z$ and $x+y+z = 3865$ how to obtain the values of $x$,$y$ and $z$ ?
2
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1answer
271 views

On Profit and loss

A dishonest dealer marks his goods $20\%$ above the cost price. He gives a discount of $10\%$ to the customer on the marked price and makes a profit by using a false weight of $900$ gms in place of ...
1
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2answers
176 views

Rewriting an equation in percentage terms

This equation: $\hspace{1in}X=S\times(P_{FC}/P_{DC})$ Can be rewritten in terms of percentage change over a time period as follows: $\hspace{1in}x=s+I_{FC}-I_{DC}=s-(I_{DC}-I_{FC})$ How can I ...
3
votes
2answers
356 views

Square for $x^2$, Cube for $x^3$, Quartic for $x^4$, and what's for $x^1$?

What's the general form for $x^y$? What's the specialized form for $x^1$ and $x^0$?