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
25 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
21 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
20 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
69 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
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1answer
52 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
67 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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2answers
42 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
27 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
35 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
44 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
54 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
52 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
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2answers
38 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
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2answers
48 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
70 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
26 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
40 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
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8answers
274 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
68 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
61 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
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0answers
38 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? ...
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1answer
26 views

What would the answer be using Linear Equation

How many ways to arrange HATE...............................................
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4answers
79 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 $x$: $$ (x - c_x)^2 + (y - c_y)^2 = r^2 $$ with a tangent line that also goes through a point $p$ lying outside the circle. ...
0
votes
1answer
59 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
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2answers
118 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
71 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 ...
7
votes
2answers
573 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
21 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
32 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
44 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
358 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 ...
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0answers
18 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 ...
1
vote
2answers
55 views

Problem solving: Counting and probability

i am a little bad at probability, i'm studying to overcome this lack. Since i'm not with a tutor i need some help on the correct way to approach a basic probability problem. I would appreciate your ...
1
vote
1answer
48 views

How do i solve this to find PMT?

I know this may seem like a stupid question but i've been up late working on this math assignment and this question just isn't working when i transpose it. So this is the formula to find Present ...
0
votes
1answer
43 views

Problem Solving - Project Crashing Time

My working out: (EST,EFT) times for the activities: A: (0,0) B: (0,8) C: (3,3) D: (10,38) E: (10,18) F: (18,18) G: (25,33) H: (58,58) I: (25,33) J: (45,53) K: (118,118) Finish: (133,133) ...
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0answers
24 views

The use of Weighted arithmetic mean to determine the extent to which the data correspond

I don't know when I can ask such question, because it is not a completely mathematic question. I have a text and a topic (single word). I want to check how much this text corresponds to the topic. ...
3
votes
1answer
60 views

How to solve $\int \frac{\tan^{-1}x}{(1+x)^2}dx$?

I know how to solve the following integral $$\int \frac{\tan^{-1}x}{(1+x^2)}dx$$ . We have to substitute $\tan^{-1}x$ as $t$ and we will be done. After this one, I tried to find out $$\int ...
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2answers
50 views

Solving for $\theta$ in a circle

Let's say you have a pendulum hanging straight down and touching the ground at the lowest point. The pendulum has length $l$. If you pull the pendulum back so that the end is height $h$ above the ...
0
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0answers
34 views

Series representation for $L=\frac{3}{2} \sqrt{4 \pi ^2 A^2+W^2}-\frac{\sqrt{5 W \sqrt{4 \pi ^2 A^2+W^2}+6 \pi ^2 A^2+3 W^2}}{\sqrt{2}}$

My question is, is there a series representation or other function of $L$ and $A$ I can use when I solve the following equation for $W$? $L=\frac{3}{2} \sqrt{4 \pi ^2 A^2+W^2}-\frac{\sqrt{5 W \sqrt{4 ...
3
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2answers
38 views

first order linear PDE solving

$$\dfrac{\partial{\phi}}{\partial{i}}=0$$ $$\dfrac{\partial{\phi}}{\partial{v}}=E-v-i R_0$$ Where E,$R_0$ are constants. How do I solve these kind of PDE's.
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3answers
89 views

Derivation of the “Combined Work Formula”

Before I get to my question, some background: Person $A$ can paint a fence at the rate $9 \frac{hour}{fence}$ (or equivalently $\frac{1}{9} \frac{fence}{hour}$) Person $B$ can paint a fence at the ...
0
votes
1answer
64 views

Finding distance using rates of change — best approach?

The question: A man drives from state $A$ to state $B$ going $60 \frac{miles}{hour}$. Then he returns from state $B$ to state $A$, driving $45 \frac{miles}{hour}$. His total driving time is $2.5 ...
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9answers
2k views

Problems that become easier in a more general form.

When solving a problem, we often look at some special cases first, then try to work our way up to the general case. It would be interesting to see some counterexamples to this mental process, i.e. ...
1
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3answers
45 views

Consider the following system of linear equations..

Story cut short, I have an exam in a weeks time and this is a question off a previous exam paper - I'm unsure as to how I should go about it as there are 4 variables with only three linear equations.. ...
7
votes
3answers
411 views

How to find natural solutions of an equation?

When I'm solving problems, I'm often confronted to solving equations, and when I'm solving equations, I'm often confronted to find the natural solutions of these equations. My actual personal ...
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0answers
36 views

Slicing through a cuboid containing spheres, how many are exposed to the surface and what is their combined volume

So I place spheres of radius chosen at random from a normal distribution of known mean and standard deviation in a cub or cuboid at random (not overlapping) until a known density of the entire cube is ...
3
votes
1answer
92 views

Russian Old Merchant Problems

Anybody know where I can find more of these old merchant problems: Lui: Please tell us a little bit about your early education. Were you already interested in math- ematics as a child? ...
1
vote
1answer
21 views

Problem involving pseudomonotone mappings on Banach space

I have the following question regarding mappings on a Banach space $X$. If anyone has an idea or hint as to how to resolve this question it would appreciated. Let $X$ be a Banach space, $X^{*}$ its ...
0
votes
2answers
27 views

Die Probability Question + Basics of Conditional Probability

A die is rolled twice. What is the probability of observing: a) a four and a three P (obtaining a four and a three) or P(obtaining a three and a four) therefore P(obtaining a four)* P(obtaining a ...