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
2answers
108 views

$1^\infty=1$ or is indeterminate?

$$\underbrace{1\cdot1\cdot1\cdot1\cdot1\cdot1\cdot1\cdots1\cdot1}_{\infty}=1$$ because of $1^\infty$ is indeterminate?$$$$ And $$\lim_{x\to\infty}1^x=\lim_{x\to\infty}1=1?$$
0
votes
1answer
26 views

delivery performance

I need to calculate average speed of a driver as a performance indicator. I have the total miles driven and the total hours they took. Simple division of mi/hr is the speed. But I want to factor in ...
0
votes
1answer
74 views

Solving $Ae^{Bx}+Cx+D=0$

Is it possible in general to solve equations of the form $Ae^{Bx}+Cx+D=0$? The most I have been able to do is rearrange the equation as ...
4
votes
1answer
449 views

What is a logical solution to this problem?

Monkey beans. An urn contains 23 white beans and 34 black beans. A monkey takes out two beans; if they are the same, he puts a black bean into the urn, and if they are different, he puts in a white ...
1
vote
1answer
650 views

Proving the transitivity of a relation

I want to prove that the relation $\sim$ on fractions given by $\frac{a}{b} \sim \frac{c}{d}$ if $ad = cb$, where $a, c \in \mathbb Z$ and $b, d \in \mathbb Z_{> 0}$, is transitive. (My last ...
2
votes
3answers
104 views

Given $x \wedge y=\mathbf{F}$, how to simplify $x \wedge \lnot y$?

Given that the boolean expression $x \wedge y=\mathbf{F}$, how to simplify $x \wedge \lnot y$? Is the above question equivalent to the following question? Find z so that $\lnot(x \wedge ...
0
votes
1answer
28 views

Equation matching after inserting a value.

A little confusion I have got, In this question (in the middle), $$\chi''(r) + \frac{d - 1 + 2\beta}{r}\chi'(r) + \left(k^2 + \frac{\beta(\beta + d - 2)}{r^2}\right)\chi(r) = 0.$$ Form this line he ...
14
votes
3answers
505 views

Decipher the greeting card $( X^2 +Y^2 -1 ) ^3 - X^2 Y^3 = 0$

A friend of mine just got a rather weird congratulations card through the door They have zero idea what it means, I have tried graphing it and nothing spectacular comes out. Is there a standard ...
2
votes
1answer
47 views

Probability problem without replacement and series

I have a probability problem but I am unsure about the result. I would like to confirm my guesses. During an exam, 10 students are drawing one by one a question (among 12 questions) without putting ...
0
votes
1answer
34 views

Same attribution depending on salary

there's a house hold that consists of a husband and a wife, the husband earns $1500$ and the wife earns $2000$ and their rent is $2000$, what's the calculation to determine what percentage of their ...
4
votes
1answer
113 views

Is there a better way to solve this problem in Linear Algebra?

Well I have the following problem: Let $\alpha = \{v_1,v_2,v_3\}$ and $\beta=\{u_1,u_2,u_3\}$ be two bases of $\mathbb{R}^3$ such that $v_1=(1,0,1)$, $v_2=(1,1,0)$ and $v_3=(0,1,1)$. It's known that ...
1
vote
1answer
72 views

Need help with boundary conditions of a differential equation.

QUESTION: A particle $A$ is moving along the $X$ axis at a constant horizontal velocity $u\hat{i}$. Another particle $B$ is moving such that its velocity vector always points towards the particle ...
5
votes
1answer
142 views

What are the positive rational solutions of $x^{(x+y)} = (x+y)^y$?

I saw this problem in the Problem-Solving through Problems book by Larson (# 3.3.25b). I got to here: $$x \log(x) = y\log\left(1+ \frac yx\right)$$ But I can't seem to find a way to reduce this ...
2
votes
3answers
116 views

Finding roots of $-3x^{1.25}-3x+10$

I'm in a math workshop, where one of the problems given was $y=–3x^{1.25} –3x+10$. Much to my frustration, the only stated way to find roots was finding x by trial and error. Is there any way to ...
0
votes
1answer
57 views

Scaling something back to 1

I'm currently working in an modeling program and scaled something down to 85%. I would like to use another scale to transform it to back to its original size, however is proving more difficult than I ...
1
vote
1answer
66 views

Optimisation Problem about convex curve

A smooth closed curve C is said to be convex if it lies wholly to one side of each tangent . Show that for the triangle of minimum area circumscribed about C that each side is tangent to C at its ...
1
vote
0answers
110 views

What is a good source of problem-solving type problems?

I am not looking for contest problems where there is a clever trick or a standard approach, I am looking for more creative and open-ended problems such as this , and I am not looking for questions ...
1
vote
2answers
90 views

Exercise 1(d) from Courant

I'm having trouble understanding this "hint" in the back of (the first volume of) Courant's Differential and Integral Calculus text, which I'm just starting: One of the "challenging" Chapter 1 ...
1
vote
1answer
80 views

What is the relative strength of each of the players in this game?

This is a real life problem. A group of people meet once a week to play a game between two teams. Each round 2 people are randomly appointed captains. Each captain takes turns picking people to be on ...
-1
votes
1answer
350 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
2answers
111 views

Problem of Ages (Problema das Idades)

English: Somebody help me with this challenge? It's very confusing: Today, both me and my younger brother are between $10$ and $20$ years old. Also, our ages are expressed by prime numbers and the ...
1
vote
1answer
51 views

Divergenceless proving

We can define a topological current, \begin{equation} J_{top}^u = \frac{1}{2v} \epsilon^{\mu \nu} \partial_\nu \phi \end{equation} How to prove it divergenceless? where the the condition is ...
2
votes
1answer
85 views

Linear Algebra; computational problems

I dug this problem up from an old exam. I am not asking how to solve them, but I want to get a "feel" for the problem. I could technically solve this brutally,I just want to develop some problem ...
0
votes
2answers
110 views

Find n term of sequence

A sequence is given: $$1,10,11,100,101,110,111,1000,\dots,a_n,\dots$$ The question is: what is the value of $a_n$ for a given $n$? I have tried a lot of patterns but was not able to meet the ...
2
votes
1answer
435 views

What is another, perhaps quicker and nicer way of solving this question?

In a calculus book, a question reads: A car is traveling at night along a highway shaped like a parabola with its vertex at the origin. The car starts at a point 100 m west and 100 m north of the ...
6
votes
3answers
920 views

Calculating Non-Integer Exponent

I just wanted to directly calculate the value of the number $2^{3.1}$ as I was wondering how a computer would do it. I've done some higher mathematics, but I'm very unsure of what I would do to solve ...
1
vote
1answer
102 views

Calculate the exact weekday of a given date.

I've seen questions about calculating the exact weekdays on a given day, such as the AMC few years ago asking for the weekday that Charles Dicken's birth. For example, yesterday's Sunday, August 4, ...
4
votes
4answers
4k views

Using + - * / operators and 4 4 4 4 digits find all formulas that would resolve to 1 2 3 4 5 6 7 8 9 10

I had a conversation with a colleague of mine and he brought up an interesting problem. Using the + - * / operators and four 4 4 4 4 digits, create an algorithm that will output all the formulas that ...
0
votes
4answers
272 views

How many positive and even factors does $2013!$ have?

How many positive and even factors does $2013!$ have? So I know that $2013 = 2\times1006 + 1$ So, does that mean $2013!$ has $1006$ even factors?
14
votes
4answers
465 views

Find the value of $3^9\cdot 3^3\cdot 3\cdot 3^{1/3}\cdot\cdots$

Find the value of $3^9\cdot 3^3\cdot 3\cdot 3^{1/3}\cdot\cdots$ Doesn't this thing approaches 0 at the end? why does it approaches 1?
3
votes
2answers
302 views

Find the number of digits of $2013^{2013}$?

Is is possible to find the number of digits of $2013^{2013}$ without a calculator?
10
votes
2answers
439 views

The $2013$th digit of $1234567891011213141516\ldots$

How do I find the $2013$th digit of the string $12345678910111213141516\ldots$ I still don't get it, how are you suppose to find the exact digit. How did you hint help at all?
1
vote
1answer
56 views

Days that cashier will work [duplicate]

A cashier wants to work five days a week, but he wants to have at least one of Saturday and Sunday off. How many ways can he choose the days he will work?
-1
votes
2answers
149 views

Sophomore + Junior + Senior

A class is attended by $n$ sophomores, $n$ juniors and $n$ seniors. In how many ways can these students form $n$ groups of three people each if each group is to contain a sophomore, a junior, and a ...
2
votes
1answer
652 views

Ways to place n non-attacking rooks on an $n^2$ square board.

How many ways are there that we can place n number of non-attacking rooks on an $n \times n$ chess board?
3
votes
1answer
1k views

Time between 3 and 4 that the hour and minute hands overlap each other?

This problem is on the practice problems for my math club, but I'm not sure how to solve it. What's the exact time that the hour and minute hands overlap each other between 3 and 4 o clock on an ...
5
votes
2answers
198 views

Combinatorial Proof of ${n\choose{m}}=\frac{n}{m}{{n-1}\choose{m-1}}$

How do prove the following identity combinatorially? $${n\choose{m}}=\frac{n}{m}{{n-1}\choose{m-1}}$$ Any help or hints would be great!
1
vote
1answer
132 views

find the value of 1/(2+1/(4+1/(4+1/(…))))

the question is to find the value of this ugly non-stopping fraction $$\frac{1}{2+\frac{1}{4+\frac{1}{4+\frac{1}{\ldots}}}}$$. I have totally no clue; thanks for the help! How am I suppose to solve ...
1
vote
2answers
362 views

$\frac1a+\frac1b+\frac1c=0 \implies a^2+b^2+c^2=(a+b+c)^2$? [closed]

How to prove that $a^2+b^2+c^2=(a+b+c)^2$ given that $\frac1a+\frac1b+\frac1c=0$?
2
votes
3answers
122 views

How many isosceles triangles with total side length $100$ are there?

Let the sum of the three sides of a triangle be $100,$ and all the sides are positive integers length, how many possible isosceles triangles are there?
0
votes
1answer
69 views

Find the value of $\sqrt{(b-a-4)^2}- \sqrt{(a-b+1)^2}$ if a>0 and b<0

Find the value of $\sqrt{(b-a-4)^2}- \sqrt{(a-b+1)^2}$ if $a>0$ and $b<0$. How do i find the value? This doesn't make any sense.
3
votes
3answers
564 views

Fractions in Ancient Egypt

In ancient Egypt, fractions were written as sums of fractions with numerator 1. For instance,$ \frac{3}{5}=\frac{1}{2}+\frac{1}{10}$. Consider the following algorithm for writing a fraction ...
1
vote
2answers
251 views

Graphing - Absolute Value and Circle

The diagram Shows The Graphs of $y = |x + 2|$ and $y = \sqrt{4 - x^2}$ Write down the solution for $\sqrt{4 - x^2}$ is equal to or less than $y = |x + 2|$.
0
votes
2answers
45 views

Solve for c , $y = x + c \big( \frac{mx}{c} + s \big)^a$

I get this equation $y = x + c \big( \frac{mx}{c} + s \big)^a$ how can I get the $c$ or $m$ ? I try with $\ln$ $\ln\big(\frac{y-x}{c}\big) = a \ln \big( \frac{mx}{c} + s\big)$ and now ?
4
votes
2answers
209 views

A challenge geometrical

Let $ABC$ a right isosceles triangle and $M$ the middle point at the hypotenuse $AC$. Inside the triangle, draw a circle that is tangent to $AB$ at $P$ and to $BC$ at $Q$.The line $MQ$ cuts newly to ...
9
votes
3answers
204 views

The Keys problem

Another challenge: A calculator has two special keys: A key transforms a number x in the number 2x. B key transforms a number x in the number 2x - 1. Is it true that if you start with any positive ...
1
vote
2answers
75 views

Does the Pigeonhole principle apply in this problem?

I came accross this problem a while ago at school during a math contest. I dont remember the exact instruction (word for word) but it went something like : Randomed A and B, 2 natural integer $\in ...
3
votes
1answer
184 views

A simple elementary school math/physics problem - but where's the mistake?

I've come across this problem and managed to get the right answer, but there remains a mystery that I wasn't quite able to solve: the minus sign (or a lack thereof)! Here's the problem and my ...
-1
votes
1answer
117 views

linear velocity conversion problem

A ford F-$150$ comes standard with tires that have a diameter of $25.7$ inches. If the owner decided to upgrade to tires with a diameter of $28.2$ inches without having onboard computer updated, how ...
2
votes
5answers
1k views

Can you hand calculate an unknown exponent above 0 and below 1 easily?

Can you hand calculate an unknown exponent? I was recently calculating something and entered $\log 6.7$ in my calculator only to quickly feel frustrated that I did not even know how to begin to ...