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
41 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
36 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
15 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
24 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 ...
-2
votes
0answers
23 views

Probability of no person being present on a website [on hold]

Given that an average of 2 people are present on a website X at any given minute. What is the probability that no person is present on the website X in a 5 minute interval window (they need to take ...
-2
votes
0answers
14 views

What is the solution of the problem below? [on hold]

What is the solution for this problem: A car travels 20 kph faster than a truck. The car covers 350 km in two hours less than the time it takes the truck to travel the same distance. What is the ...
0
votes
2answers
25 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
107 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
54 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
26 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
41 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
17 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 [closed]

Two numbers have a sum of 4, and the sum of their reciprocal is 8. Find the numbers.
3
votes
0answers
23 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
39 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 ...
0
votes
3answers
20 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
21 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....
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 ...
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 ...
3
votes
1answer
65 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
47 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
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
31 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
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
49 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 ...
0
votes
0answers
37 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
30 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 ...
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
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?
10
votes
8answers
241 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
41 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
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
0answers
31 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? ...
1
vote
1answer
25 views

What would the answer be using Linear Equation

How many ways to arrange HATE...............................................
0
votes
4answers
73 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. ...
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
53 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 ...
2
votes
1answer
60 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
450 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 ...
2
votes
1answer
30 views

Find some probabilities given the probability tree

i've been practicing probability since it's not my strength, but i am doing that without a tutor or an official course, just books and videos. I was reading a problem, and i was capable of draw the ...
0
votes
0answers
38 views

Is this polynomial equation solvable? $ \alpha x^{n+2} + \beta x^{n+1} + \gamma x^3 + \delta x^2 + \epsilon x + \zeta = 0 $

I have an equation I wish to solve. I was going to solve it numerically but maybe there is a way to handle it analytically? $ \alpha x^{n+2} + \beta x^{n+1} + \gamma x^3 + \delta x^2 + \epsilon x + ...
2
votes
3answers
92 views

Simplifying nested/complex fractions with variables

I have the equation $$x = \frac{y+y}{\frac{y}{70} + \frac{y}{90}} $$ and I need to solve for x. My calculator has already shown me that it's not necessary to know y to solve this equation, but I ...
0
votes
1answer
76 views

I'm not understanding this puzzle [closed]

At first, I was thinking, mininmum amount of sticks it takes to create the figure, and then how many draw strokes it takes to create the boxes without crossing paths...but I can't figure out what's ...
0
votes
0answers
7 views

Dominance Network Worded Problems

What are some methods to solve this? Normally for dominance I do as such: Write a matrix for one step dominance, then find total dominance by = D+D^2 - then sum each row of the matrix. Using this ...