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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2
votes
1answer
47 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
50 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
22 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
36 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
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 $a=\sqrt{2x-1}$ $(1+a)/(\sqrt{x+a})$ =$(1+a)/(x+a)^{1/2}$ =$(1+a)(\sqrt{x+a})$ ...
0
votes
0answers
15 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
2answers
25 views

Problem Solving with Quadratics [on hold]

Two numbers have a sum of 4, and the sum of their reciprocal is 8. Find the numbers.
3
votes
1answer
58 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 ...
3
votes
0answers
21 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
29 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 ...
-2
votes
0answers
39 views

Using quadratic equations for problem solving [on hold]

The numerator of a fraction is 3 less than the denominator. If the numerator is increased by 6 and the denominator is increased by 5, the fraction is doubled in value. Find the original fraction. At ...
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 ...
0
votes
3answers
18 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
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 ...
0
votes
1answer
20 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....
-2
votes
2answers
22 views

Problem Solving Quadratic Equation [on hold]

A right angled triangle has sides which are 2cm and 7cm than its hypotenuse. Find the length of the hypotenuse: a) exactly b) to the nearest millimetre
1
vote
1answer
18 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 ...
0
votes
4answers
72 views

Given circle and point, where does the tangential line through the point touch the circle?

Given a circle with known center $c$, known radius $r$ and perimeter point $p$: $$ (x - c_x)^2 + (y - c_y)^2 = r^2 $$ with a tangent line that also goes through a point $pp$ lying outside the circle. ...
3
votes
2answers
568 views

Proving Holder's inequality using Jensen's inequality

Let $p$ and $q$ be positive reals such that $\frac{1}{p}+\frac{1}{q} = 1$, so that $p,q$ in $(1,\infty)$. For $\vec a$ and $\vec b \in \mathbb{R}^2$ prove that $|\vec a \cdot \vec b | \leq ||\vec ...
0
votes
1answer
34 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.
1
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 ...
2
votes
1answer
44 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 ...
1
vote
1answer
25 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
30 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 ...
0
votes
1answer
304 views

Distributions of $X^2$ and $X-1$ when $X$ is geometric

Let$ X$ be a discrete random variable with the probability mass function given by $p_x(x)= 2^{-x}$ for $x=1,2,3,\ldots$ and $0$ otherwise. a) Let $Y=X^2$, find the probability mass function of ...
1
vote
0answers
44 views

What to do with hints? [closed]

Many problems in math textbooks come with hints. Almost invariably, hints annoy me very much. I don't know what to do with them. Usually, in the end I simply ignore them and go on to find my own ...
0
votes
0answers
46 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 ...
-2
votes
2answers
25 views

Word problem - finding the equation [closed]

Find two numbers with sum of 28 and half their difference 2. Whats the equation?
0
votes
0answers
36 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 ...
0
votes
2answers
26 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?
-1
votes
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 ...
0
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 ...
8
votes
7answers
209 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 ...
1
vote
1answer
25 views

What would the answer be using Linear Equation

How many ways to arrange HATE...............................................
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 ...
12
votes
5answers
1k views

Proving identities like $\sum_{k=1}^nk{n\choose k}^2=n{2n-1\choose n}$ combinatorially

I have to give a combinatorial proof of $$\sum_{k=1}^nk{n\choose k}^2=n{2n-1\choose n}.$$ I find it difficult to solve such problems. I'm not a brilliant person and never will be so I need to have ...
0
votes
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?
2
votes
1answer
59 views

Set of numbers that add up 1 to n

I am currently trying to solve the following problem: Given a number $n \in \mathbb{N}$, find the size of a set $S$ of positive numbers $s_1, \ldots, s_k\in \mathbb{N}$, such that $\sum_{i=1}^kS_i ...
0
votes
1answer
40 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.
2
votes
3answers
99 views

Is this Chinese card game solved?

There is a card game here in China, use a standard 52 card deck of cards. Draw four cards and use any elementary operators $(+,-,\times, \div)$, and only use each card value once to get a result of ...
0
votes
0answers
30 views

Conditional Probability - Order is important!

Probability that Mark wins a tennis match he plays is 0.8. A knockout tournament requires players to win 5 matches to win the tournament. What is the probability that Mark wins the tournament? ...
12
votes
3answers
314 views

Calculate $\frac{1}{5^1}+\frac{3}{5^3}+\frac{5}{5^5}+\frac{7}{5^7}+\frac{9}{5^9}+\cdots$

I'm an eight-grader and I need help to answer this math problem. Problem: Calculate $$\frac{1}{5^1}+\frac{3}{5^3}+\frac{5}{5^5}+\frac{7}{5^7}+\frac{9}{5^9}+\cdots$$ This one is very hard for me. It ...
2
votes
3answers
1k views

Crossword puzzle- Crossnumber puzzle

The puzzle below is a cross number puzzle, similar to a crossword puzzle except that the entries are numbers. Enter one digit per square. The thick heavy line is a separator. ACROSS: a. A prime ...
0
votes
1answer
53 views

How to solve this age problem?

I am solving the following question. Please guide me!! The ages of A and B are in the ratio of 5:7 and C and D are in the ratio of 5:7.Let sum of their ages is 150, what is the difference between the ...
1
vote
2answers
50 views

simple math question from civil service exam

The weight per foot of a length of square bar 4" x 4" in cross section as compared with one 2" x 2" in cross section, is ______ as much. A. Twice B. 2 1/2 times C. 3 times D. 4 times This question ...
1
vote
2answers
360 views

Problem Solving ( Sequences and series)

After injection of a dose $D$ of insulin, the concentration of insulin in a patient's system decays exponentially and so it can be written as $D\exp^{-at}$ where $t$ represents time in hours and $a$ ...
2
votes
1answer
58 views

Stair flight problem

A stair flight has 10 steps. A kid can move in jumps of 1, 2 or 3 steps. Assume the kid starts on the floor (step 0), and always has to end in step 10 because there is a door that needs to be open. In ...
6
votes
2answers
448 views

Find the probability of winning at this lottery.

So, the problem I found goes like this: You have $n$ different numbers, numbered from $ 1 $ to $n$. You can randomly choose $m$ (different) of them. The computer also randomly selects $m$ ...
0
votes
1answer
18 views

Solving an equation

I have the following equation: $x_1^3 = \hat{x}_1^3 + e_1\delta(x_1,e_1)$ I have to find the function $\delta(\cdot)$ for which this equation holds. By definition: $e_1 = \hat{x}_1 - x_1$ So I am ...