Use this tag when you want to determine the thinking that is needed to solve a certain type of problem, as opposed to looking for a specific answer to a question.

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1answer
18 views

Train distances leaving at certain times

A train leaves Boston to Fort Lauderdale traveling at $125$ mph. An hour later, another train leaves Fort Lauderdale traveling to Boston at a rate of $140$ mph. When the two trains meet each other, ...
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1answer
28 views

Number of Chess Moves that a piece is lost

Assuming you have a board, and you attempt to play with your opponent such as that you try to avoid taking each other's pieces. Is there going to be a limit in the number of moves after which you ...
4
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2answers
118 views

finding the difference of perfect squares

Find the difference between the smallest perfect square larger than one million and the largest perfect square smaller than one million. I did not want to use a calculator for this question. I ...
0
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0answers
18 views

Criticise work with simple graphs & problem solving

So I'm studying graph theory at the moment and would like some constructive criticism or thoughts on my method. The problem can be formulated as follows. I'm looking for someone to verify my answer as ...
3
votes
1answer
49 views

Application of the Green-Tao theorem

I am currently trying to find some good exercises in analytic number theory, suitable for undergraduates. I have mentioned the Green-Tao theorem for arithmetic progressions of primes but I am ...
1
vote
1answer
28 views

Derivative Functions [on hold]

Consider $f(x)= ax^2 + bx$ where $a$ and $b$ are real numbers. If $f(1)=-1$ and $f'(-1)=-7$, find the values of $a$ and $b$? I genuinely do not understand how to do it! Please help
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1answer
22 views

Distinct elements in the Union and Intersection of A and B

Take a set $x$ with $10$ distinct elements. Rule: Everytime you have two subsets, $A$ and $B,$ you also have $A\cup B$ and $A \cap B.$ What is the maximum number of subsets you can have such ...
3
votes
1answer
55 views

How do I solve $x=\log^e{(x+1)}$ analytically?

How do I solve the following, analytically? $$x=\log^e{(x+1)}$$ It looks like it should be simple, but whether I take the $e$th root of each side or take the $\log$ of each side (ending up with a ...
0
votes
0answers
25 views

How to solve this Ricatti-like ODE

I have been trying to solve the following ODE \begin{equation*} \dfrac{d\pi}{dx}x=c_1+\pi(x) c_2 + \pi(x)^2(c_3-x), \end{equation*} where, for every $i=1,2,3$, $c_i$ is a constant real value. ...
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votes
2answers
22 views

Lottery problem - Chance of 4 out of 5 balls matching?

In a lottery, an urn contains 40 balls that are numbered 1, 2, ..., 40. Each week, 5 balls are drawn from the urn without replacement. To enter, one chooses 5 numbers. Anyone who correctly predicts ...
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votes
0answers
16 views

How to figure out the math logic for Tournament involving Double Elimination [on hold]

Double elimination operates like two single eliminations. There is a Winners Upper Bracket and a Losers Lower Bracket. The winners bracket moves just like a single elimination with players n players ...
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0answers
28 views

Setting up an integral for a physics question.

The problem begins like this: a charge distribution is given by $\rho(r,\theta,\phi)=\gamma r^3cos\theta,a<r<b,0\le\theta<\pi/2$ and is zero everywhere else. The distance from the origin is ...
1
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2answers
73 views

Solving equation involving binomial function

Solve for $x$ in terms of $i$ and $j$: $$ \binom{x}{i} = j $$ where $x$ is Real; $i$ and $j$ are Integers: $x \geqslant i$, $i \geqslant1$, $j \geqslant 0$. I came across this problem while trying ...
1
vote
1answer
40 views

What to do when a probability problem becomes unwieldy to check via simulation?

I am assuming that some probability problems cannot be solved easily since there may be a lot of cases to handle and it would make miscounting likely. However, some problems do not simulate well on a ...
1
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2answers
25 views

Curiosity - maximising a product with a constraint

I have integers greater than 4, for instance $i_1$, $i_2$, $i_3$, ..., $i_n$. We have to change the greatest of these integers (for instance $i_1$ if they are ranked by descending order) by adding to ...
-1
votes
0answers
38 views

How do i solve this Excel optimization problem? [closed]

Below is the picture of my mathematic problem. I tried to use excel but couldnt get any results
0
votes
1answer
18 views

Calculating accumulated energy production from 5 min interval readings [closed]

I have a nice graph that shows energy production over time from some solar panels. The readings are in MW and come in every 5 minutes. Now if I want to have a bar graph that shows the total energy ...
2
votes
1answer
49 views

Integral of $\frac1{\cos^n x}$

Hi guys I have already proven for an assignment that: $$\int\cos(x)^n dx=\frac{1}{n}\cos(x)^{n−1}\sin(x) + \frac{n-1}{n}\int\cos(x)^{n−2}dx$$ Now we have been asked to calculate ...
1
vote
1answer
58 views

Finding limits of two functions of two variables

Show using the definition of limit that $$\lim _{(x,y)\to(0,1)}\frac{x^2-y^2}{x^2+y^2} = -1$$ and $$\lim_{ (x,y)\to(0,0)}\frac{ (1-\cos(xy))\sin y}{(x^2+y^2) }= 0$$ Definition of limit: ...
1
vote
1answer
17 views

How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?

What I tried was: (9P4)/3!*2! This gave me a wrong answer (since the answer is 626). I'm unable to make use of the hint provided in my book: "make cases". Any help would be appreciated. :)
1
vote
1answer
27 views

how to write a differential equation for a problem like this

I've got a problem and i should solve it using differential equation.I don't know how to write the equation and start. A person is trying to fill a bathtub with water. Water is flowing into the ...
0
votes
2answers
28 views

replacing numbers to get final anser

I found this question in a random problem solving book that I was reading and wanted to know how you would solve it. I am not sure as how to go about this. Take any positive integer $n$ with fewer ...
3
votes
1answer
111 views

Limit of the sum of $\gamma_k(x)=xf((k+1)x)-\int_{(k+1)x}^{(k+2)x}f(t)\mathrm{d}t$

Let $f$ be a continuous, decreasing function, with $\displaystyle\lim_{x\rightarrow\infty}f(x)=0$. Let $\gamma_k(x)=xf((k+1)x)-\int_{(k+1)x}^{(k+2)x}f(t)\mathrm{d}t,\displaystyle x>0$. Let ...
0
votes
1answer
55 views

What is the probability the best case occurs? (Comp Sci Type Question)

I'm having trouble figuring out what's the probability the best case occurs? It's my first time bringing together probabilistic knowledge into computer science. The question goes as such. Consider ...
1
vote
1answer
28 views

raBinomial distribution with dependent trials?

I need your help with following problem: String with n characters is given. For each character in string there is probability p that it is wrong. Now you take a sliding window of length k, k<= n, ...
1
vote
2answers
44 views

Problem Solving Question (Riddle)

this is my first time asking a question here, so sorry in advance if there's anything wrong with the format or place this is posted in. The problem I need to solve is written as the following: "Four ...
0
votes
0answers
20 views

Polynomial systems - conditions for real solution

I was working on the computation of equilibrium points for dynamical systems and arrived in the following system of $n$ polynomials in the variables $(x_1,\ldots,x_n)$ \begin{equation*} ...
3
votes
0answers
25 views

Iterations $n, n^n, (n^n)^{(n^n)},…$

(Note: I'm reposting this, as I posted the original too late in the evening to gain anyone's notice.) A contest problem (#2 on the 2010 Virginia Tech Math Competition) proffers the solver the ...
2
votes
1answer
43 views

Coin-tossing games

Suppose that you start off with $100$ dollars. You toss a coin $10$ times and guess it right $5$ times and lose $5$ times (the order of the outcomes is not known). It is known that every time you ...
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votes
3answers
21 views

Finding dimensions using quadratic formula

A 52 m long fence is constructed on three sides of a housing block with area 240 m^2. The fourth side facing the road is left open. Find the dimensions of the block. Also here's another question I ...
0
votes
1answer
22 views

Solving for x in equation for chem

In the answers to a chem problem is just gives this equation: (34.969) (x) + (36.966) (1 - x) = 35.453, and says solve for x. But I have no clue how to solve for x....
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3answers
18 views

Problem Solving quadratics

A rectangular paddock has perimeter of 600 m and area 21 600 m^2. Find the dimensions of the paddock. So far, I've figured out the formula is x(300-x)=21600 and rearranged to 300x-x^2=21600. I'm not ...
1
vote
1answer
19 views

First-Order ODE Problem

I'm currently taking an ODE course at my school and one of the problems given follows: Suppose that a trajectory of $$(3x^2 - y)dx + (3y^2 - x)dy = 0$$ contains the point $(1,1)$. Show that it also ...
3
votes
1answer
66 views

If $I + A + \cdots + A^{n-1} = O$, $A$ a square integer matrix, $n$ odd, for what $k$ does $\det(\sum_{i = k}^{n-1} A^i) = \pm 1$?

This question is, in a sense, homework. I'm taking a problem-solving seminar which uses questions like these, the first question on the 2010 Virginia Tech Regional Math Competition, as fodder. The ...
0
votes
1answer
38 views

Finding x using the pythagoras theorem

$$x^2 = (x+1)^2 + (x-7)^2$$ can someone please find $x$? Also this is a quadratic equation problem solving question.
2
votes
1answer
48 views

Prove that $\sqrt{a_n b_n}$ and $\frac{1}{2}(a_n+b_n)$ have the same limit

I'm trying to solve the following problem prove $\sqrt{a_n b_n}$ and $\frac{1}{2}(a_n+b_n)$ have same limit. In this post http://math.stackexchange.com/a/267499, I do not understand the following ...
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vote
2answers
38 views

Showing the summation of numbers

Using each of the digits 1 through 9 once, form numbers whose sum is 100. If you think it can't be done, then prove it. My attempt: I say it can't be done because the sum of all numbers $1-9$ is ...
1
vote
1answer
26 views

How many integer solutions are there

How many integer solutions for $a$ and $b$ in $(ab)/(a+b)=3600$? My attempt: $(ab)/(a+b)=3600$ = $ab=3600(a+b)$ where $a+b\not=0$ = $ab=3600a+3600b$ =$ab-3600a-3600b$ =$(a-b)3600$ ...
0
votes
1answer
33 views

Integer solutions of an equation that is set to a number

How many integer solutions for $a$ and $b$ in $(ab)/(a+b)=3600$? My attempt: $(ab)/(a+b)=3600$ = $ab=3600(a+b)$ = $ab=3600a+3600b$ =$ab=3600a=3600b$ Dividing $3600b$ on both sides ...
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votes
2answers
40 views

Writing forms of an equation

Let $x>1/2$. What is the simplest form of the expression $(1+\sqrt{2x-1})/(\sqrt{x+\sqrt{2x-1}})$ Let $a=\sqrt{2x-1}$ $(1+a)/(\sqrt{x+a})$ =$(1+a)/(x+a)^{1/2}$ =$(1+a)(\sqrt{x+a})$ ...
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votes
0answers
50 views

How can we find $\frac{2^m}{e^n}$ with an accuracy of $10$ decimal digits?

If $n$ and $m$ extremely large (1000 digits) and $1 <\frac{2^m}{e^n} < e$, how can we create an effective algorithm to find $\frac{2^m}{e^n}$ with an accuracy of $10$ decimal digits (10 digits ...
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0answers
39 views

Using jugs filled with water problem

Given jugs $m$ and $n$ liters (WLOG $m<n$) is it always possible to get all $i$, $0 \leq i \leq n ?$ If so, prove it. If not, explain which $i$ you can get. Is there also a minimum number ...
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2answers
34 views

Quarters and dimes word problem [closed]

Word problem: if you have three more quarters than dimes, and together they add up to $3.55, how many dimes do you have?
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2answers
47 views

Solving an algebraic equation for x

$(($ 3^$2\sqrt{3x})$/4$)$ $+3=$ 3^$\sqrt{3x}$ = $($ (3^${2}*{3x^{1/2}}$)/4$)$ $+3=$ 3^${3x^{1/2}}$ After simplifying: = ($3^{6x^2}$ $+ 3$)/4 $= 3^{3x}$ = $3^{6x} + 3 = 12^{3x}$ I tried ...
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votes
4answers
69 views

Chance of playing a game

You are offered a chance to play a game. the rules are simple. there are $100$ cards face down. Of these, $55$ say win and $45$ say lose. You begin with $10000$ dollars. You must bet $1/2$ of your ...
2
votes
1answer
23 views

Shared groceries expenses between roommates to be divided as per specific consumption ratio and attendance

My apologies if this question is in the wrong section. Couple of my roommates & I (total 5 people) share the groceries expenses. We record the purchases in an Excel sheet, and also have the ratio ...
2
votes
0answers
36 views

Trying to make a formula to find maximum driving time.

I am trying to figure out how to make a formula (that will eventually be used in excel.) to figure out, how much driving time could be done in a block of time. In this case, 24 hours. And theses are ...
0
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3answers
32 views

If I end up with $10,000 because I lost 20% in 2 years…

If I end up with 10,000 after losing 20% in two years...How much did I have in the first place?
10
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8answers
245 views

Evaluate $ \int_{0}^{1} \ln(x)\ln(1-x)\,dx $

Evaluate the integral, $$ \int_{0}^{1} \ln(x)\ln(1-x)\,dx$$ I solved this problem, by writing power series and then calculating the series and found the answer to be $ 2 -\zeta(2) $, but I don't ...
0
votes
1answer
42 views

To Find the height of the building

A building casts a shadow 50 feet long. A rod 4 feet tall placed near the building casts a shadow 3 inches long. Find the height of the building.