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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-5
votes
1answer
33 views

An urn contains 15 balls, 8 of which are red and 7 are blue [on hold]

An urn contains 15 balls, 8 of which are red and 7 are blue. In how many ways can 7 balls be chosen so that at least 5 are red?
2
votes
1answer
38 views

How can I solve an exponential equation of the following type?

I have an equation of the form $$ \frac{a^x}{d_1^x} + \frac{b^{x/2}}{d_2^x} = 1, $$ which I have already rewritten to $$ a^xd_2^x+d_1^xb^{x/2}-d_1^xd_2^x = 0. $$ However, I seem to be stuck here. ...
0
votes
3answers
3k views

How to calculate perimeter using the area and the perimeter of a smaller area

I have having trouble understanding how to break this problem apart. I have an $ L$ shape with a rectangle in it. The smaller rectangle has a side of $5 m$ and a side of $7 m$, the $L$ shape has an ...
0
votes
0answers
10 views

calculate the fortnightly repayment amount

can anyone offer me some help?? I really don't know how to solve it, your help would be grateful, thanks!!! For (a), I don't understand how the $(1+1.005)$ come from, I know we should deduct ...
2
votes
1answer
33 views

How to deal with long and tedious logic problem? [on hold]

I am always pretty bad at logic problems. Because most of the logics used aren't really logical (to me)So, as you might think, a long logic problem only adds to it already boring nature. The ...
0
votes
5answers
37 views

Give the number of solutions of $x+y+z = 30$, for $4 \leq x \leq 14$, $3 \leq y \leq 17$, $10 \leq z \leq 25$.

How would I find the number of solutions with both upper and lower bounds? Can anyone give a step by step way to solve this problem? This is question is in preparation for my discrete math final, so ...
2
votes
0answers
40 views

Shortlist of problems in linear algebra

A while ago I remember seeing a very nice shortlist of problems in linear algebra. It was a list of about 40-50 problems. The idea was that if you solve them, you learn linear algebra very well and ...
46
votes
5answers
2k views

Finding the value of $\sqrt{1+2\sqrt{2+3\sqrt{3+4\sqrt{4+5\sqrt{5+\dots}}}}}$

Is it possible to find the value of $$\sqrt{1+2\sqrt{2+3\sqrt{3+4\sqrt{4+5\sqrt{5+\dots}}}}}$$ Does it help if I set it equal to $x$? Or I mean what can I possibly do? ...
1
vote
0answers
22 views

In spherical co-ordinates, 3 unknowns, possible to solve for 1?

So I am trying to get either $\theta$ or $\phi$ in terms of $\theta_1$ and $\phi_1$, where a,b,d and e are constants but c is unknown too and below is as far as I have gotten, I keep going in circles ...
1
vote
0answers
40 views

Finding the convergent value

The sequence is defined as follows : Start : $(x_0,y_0)$ with $ 0 < x_0 < y_0 $ Step : $x_{n+1} = \frac {x_n+y_n} {2}$ , $y_{n+1}= \sqrt{x_{n+1}y_n} $ Find $\lim_{n\to \infty}(x_n,y_n)$ . ...
41
votes
16answers
13k views

Interview riddle

On the Mathematics chat we were recently talking about the following problem @Chris'ssis had to solve during an interview : $$3\times 4=8$$ $$4\times 5=50$$ $$5\times 6=30$$ $$6\times 7=49$$ ...
4
votes
2answers
66 views

Using Sticks and Stones for Counting number of Ways

From the first twenty positive integers, how many ways can we select 6 integers so that no two integers from the six chosen ones are consecutive? I tried using sticks and stones, but my thought ...
0
votes
1answer
39 views

Use of Delaunay Triangulation and Voronoi Diagram to find alpha shape using Edelsbrunner's algorithm

I am learning how to find the shape of a set of points in 2-D. I understand that Alpha Shape method is a good way to find the shape of a set of points. Alpha Shape was originally introduced by H. ...
3
votes
1answer
49 views

Find all positive solutions of the system of equations

Find all positive solutions of the system of equations $x_1+x_2=(x_3)^2$ , $x_2+x_3=(x_4)^2$ , $x_3+x_4=(x_5)^2$ , $x_4+x_5=(x_1)^2$ , $x_5+x_1=(x_2)^2$ What i have done : ...
0
votes
1answer
31 views

How do you figure out the formula to convert between units?

I know that to, for example, convert from Fahrenheit to Celsius you subtract 32 and then divide by 1.8. I'm interested in how this type of formula can be developed. So, given two different sets of ...
1
vote
0answers
19 views

When setting up a probability problem, when is it appropriate to use conditioning?

I understand the principles of conditioning and its rules, but when do I decide if a problem will be easier using conditioning versus determining through other methods? I'm teaching myself probability ...
0
votes
0answers
19 views

Efficient method to calculate passes (rises and sets) for satellites

There is a function describing the characterisic elevation of ISS seen from an observers horizon. Calculating of an elevation at one time is pretty expensive. So I wanna try to avoid naive iterating ...
21
votes
8answers
386 views

Examples where it is easier to prove more than less

Especially (but not only) in the case of induction proofs, it happens that a stronger claim $B$ is easier to prove than the intended claim $A$ (e.g. since the induction hypothesis gives you more ...
1
vote
0answers
15 views

The Jugs of Water Problem - with constraints

Given three jugs containing any amount of water such that a1 <= a2 <= a3 and each jug is large enough to contain all the water, show that it's possible (or not) to empty one jug. Only ...
3
votes
2answers
377 views

Does an elegant solution exist for this trigonometric equation?

I'm trying to solve this: $\cos ^{-2}x + A\tan{x} = B$ Wolfram alpha spits out an incredibly long and convoluted solution for x. Is there no simple, straightforward analytical way to solve this?
0
votes
2answers
38 views

Is this proposition posible? [duplicate]

In a board, you have $13$ White round pieces, $15$ Black round pieces, and $17$ Red round pieces. In each round you can choose two different color pieces and change them with two other pieces of ...
1
vote
1answer
21 views

Question about “linear programming problem” in reference to joint pmf

I'm working on a homework problem and I'm not totally sure what the question is asking... The question reads: "Consider the linear programming problem: maximize $Ax_1+Bx_2$ subject to $x_1+x_2\leq ...
1
vote
1answer
33 views

Modular arithmetic and using in well-ordering principle

I need to prove the following, but I do not know how to go about it. If $$ (*)\:\:\: x^{3} - y^{3}= 3^{n} $$ Then $$ x \equiv 0 (mod 3) \:\: and \:\:\: y \equiv 0 (mod 3)$$ In addition, ...
0
votes
1answer
20 views

Solve equation with two unknowns (maybe modulo)

Given the following equation: $$ x^{2} - y^{2}=17, \quad 0\neq x,y\in \mathbb N$$ I know for example that one solution is $x=9$, $y=8$, but I do not know how to get it.
59
votes
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. ...
3
votes
3answers
830 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 ...
2
votes
3answers
75 views

Finding roots of a quartic

How do I find the roots of the equation $$(x+3)^5-(x+1)^5=7$$ I tried opening it up, it turns into a ugly quartic which doesn't factor. I don't know what to do next. Please help me out.
3
votes
1answer
39 views

Find a seven digit number which describes itself

Find a seven digit number which describes itself. The first digit is the number of zeros in the number. The second digit is the number of ones in the number, etc. For example, in the number 21200, ...
0
votes
1answer
324 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 ...
2
votes
2answers
121 views

Fundamental Matrix

Determine $\phi(x,0)$ for $A(x)=\begin{pmatrix} -1 & \cos(x) \\ 0 & -1\end{pmatrix}$, where $\phi(x,0)t_{0}$ is a solution of $\frac{d}{dx}t(x)=A(x)t(x)$. I am not entirely sure as to ...
2
votes
1answer
42 views

Possible values of $\gcd(a+b, a\times b)$

Main Question: Let $N \in \mathbb{N}$. What are the possible values of $\gcd(a+b, a\times b)$ given that $\gcd(a,b) = N$? Fact 0. If $\gcd(a,b) = N$, then $N \leq \gcd(a+b, a\times b) \leq ...
0
votes
1answer
26 views

Set of vectors to span.

Find a set of vectors that span the subspace $W$ of $V$: 1) $V = P^3(\mathbb{R})$ (polynomial degree 3) $W = \{p|p(1) = p(3) = 0\}$ 2) $V = \text{span}(\{\sin x, \cos x, \sin 2x, \cos 2x\})$ ...
60
votes
12answers
15k views

Dividing 100% by 3 without any left

In mathematics, as far as I know, you can't divide 100% by 3 without having 0,1...% left. Imagine an apple which was cloned two times, so the other 2 are completely equal in 'quality'. The totality ...
0
votes
1answer
30 views

Simple probabilistic expression

For the following expression: $$ \prod_{i=0}^{n-1} \frac{2n-i}{3n-i} $$ I'm trying to get a simple expression, unsuccessfully. Many thanks, Jonathan
2
votes
6answers
790 views

Different ordered triples $(a,b,c)$ of non-negative integers

How many different ordered triples $(a,b,c)$ of non-negative integers are there such that $a+b+c=50$? I tried to list the possibilities but the list is way too long, I know how to find the ordered ...
0
votes
2answers
15 views

Number of unique Team parings given 10 players and 2 teams

I yammer a wee bit too much, feel free to skip to TLDR unless you want more background as to why I care about this problem. I was just thinking that it would be a fun to figure out the best 5 players ...
1
vote
1answer
76 views

Is there a solution to the equation x^x^x^x^x^x^… = 2?

I have been asked the following brainteaser, is there a solution to the equation: $$ x^{x^{x^{...}}} = 2$$ (x to the power of itself an infinite number of times) I am not sure about how to approach ...
-1
votes
0answers
12 views

Solving For A Given Equation With Exponents

I'm unable to solve the following equation. The question asks: The population $p$ at time $t$ years is assumed to be: $p= {2800ae^{0.2t} \over 1+ae^{0.2t}}$ where $a$ is a constant. Given that $p ...
3
votes
3answers
814 views

Missing dollar problem

This sounds silly but I saw this and I couldn't figure it out so I thought you could help. The below is what I saw. You see a top you want to buy for $\$97$, but you don't have any money so you ...
4
votes
5answers
60 views

If $9\sin\theta+40\cos\theta=41$ then prove that $41\cos\theta=40$.

I tried it this way: $$ 40\cosθ+9\sinθ=41 $$ $$ 9\sinθ=41-40\cos\theta $$ Squaring both the sides: $$81\sin^2\theta=1681+1600\cos^2\theta-2\cdot 40\cdot 41 \cos\theta$$ $$81-81 ...
2
votes
2answers
60 views

How to solve trigonometric equations with a domain involving negative values of $x$?

I don't seem to understand the concept of a negative domain when solving trigonometric equations on "another interval" For example: Solve $\cos x=-\sqrt{3}/2$ given that the domain is $-\pi \le ...
1
vote
2answers
74 views

How to solve a algebraic equation?

My maths teacher gave me this equation and I really don't know how to solve this: $$\overline{abc}+\overline{ab}+\overline{bc}+\overline{ac}+a+b+c=29,$$ where $a$, $b$, $c$ are digits. I need to ...
3
votes
1answer
21 views

$y = ln(p+qe^x)/x$, solve $x$

$y = \ln(p+qe^x)/x$ $p$ and $q$ are constants. Express $x$ in terms of $y$. I believe I have to use Lambert W function, but I'm stumped. Thinking help is needed. Thank you very much!
4
votes
1answer
40 views

Normal distribution - how to solve P(-b<X<b)=0.95

$X\sim N(2,3^2)$ How do you find $b$ where $P(-b<X<b)=0.95$ other than trial and error? You can't directly transform to $z$ because if you find an appropriate $z$, transforming back will give ...
0
votes
1answer
17 views

Mgf of double exponential RV

In class the other day we were talking about a double exponential RV $X$ with a pdf $f(x)=\frac{1}{2}e^{-|x|}$ for $-\infty<x<\infty$. The professor noted that the mgf was $M(t)=\frac{1}{1-t^2}$ ...
0
votes
0answers
34 views

What's the solution set $S \subset \mathbb{R}^2$ of this equation?

I see that $(1,1)$, $(2,4)$ and $(4,2)$ are in $$S= \{(x,y) \in \mathbb{R}^2: \, x^y = y^x\}$$ My question is: The set $S$ contains many others elements? Thanks for any suggestions and helpful ...
-2
votes
0answers
47 views

Very difficult word problem

I tried using derivatives to find the critical points but didn't have any success. I would like to know how to approach the problem. Nigel owns a fruit stand. He is also a gambler. This Tuesday he ...
1
vote
2answers
43 views

Probability of Game Series

A world series is a best of $7$ series between team $A$ and team $B.$ It takes $4$ wins to win the series. How many ways can a team win the World Series? I said: Suppose that a World Series is ...
0
votes
0answers
32 views

What kind of math do I use to solve this problem?

Nigel owns a fruit stand. He is also a gambler. This Tuesday he has a special deal, and naturally it involves some risk. Instead of the usual markdown, he offers the following: in a black bag there is ...
0
votes
0answers
16 views

Do you have a specific method to solve logiqual sequences or do you rely on intuiton?

I'm preparing a presentation on Logical Sequences. Here's one : $2, 6, 12, 20, 30,42, [?]$ The goal is to find the following number in the sequence. In this particular case, a possible answer is ...