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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3
votes
4answers
57 views

Find $\min\big\{ \lfloor xy + \frac{1}{xy} \rfloor \,\Big|\, (x+1)(y+1)=2 ,\, 0<x,y \in \mathbb{R} \big\}$

I am invited to calculate the minimum of the following set: $\big\{ \lfloor xy + \frac{1}{xy} \rfloor \,\Big|\, (x+1)(y+1)=2 ,\, 0<x,y \in \mathbb{R} \big\}$. Is there any idea? (The question ...
1
vote
4answers
86 views

Solve $16x^{-3}=-2$

Solve $16x^{-3}=-2$. My working: \begin{align} 16x^{-3}&=-2\\ \frac{1}{16x^{3}}&=-2\\ \frac{16x^3}{16x^3}&=-32x^3\\ 1&=-32x^{3}\\ -32x^{3}&=1\\ -32x&=\sqrt[3]{1}\\ ...
4
votes
2answers
46 views

Frogs and switches - problem solving strategies

The question is pretty simple, consider 1000 switches and 1000 light bulbs, every time we press a switch it's light bulb changes it's state(ON to OFF and vice versa). We start with all the light bulbs ...
0
votes
1answer
82 views

Pigeonhole question about distinct sums

How do I show with the pigeonhole principle that no seven positive integers not exceeding $24$ can have sums of all subsets different. As observed by Ross Millikan, the simplest possible approach ...
0
votes
3answers
37 views

Solving a function for a variable, confusion

I have the function $f(t) = -4.9t^2+25t+3$, where $f(t)$ is a the height of a grapefruit after $t$ number of seconds. I need to find out how long the grapefruit is in the air, so I know i need to ...
1
vote
1answer
47 views

Local extension of smooth funtion to a embedded manifold

I'm trying to proof the following problem from Lee's Book: Suppose $M$ is a smooth manifold and $S\subseteq M$ is a smooth submanifold. Show that $S$ is embedded if and only if every $f\in ...
0
votes
0answers
25 views

Finding zeros of a piecewise function

Is there a general strategy for solving $$0 = \sum_i \left\{ \begin{array}{lr} f_i(x) \text{ if }p_i(x) \\ g_i(x) \text{ otherwise} \end{array} \right.$$ for $x$? To what ...
2
votes
0answers
34 views

Get function definition from an equation

My question: I have to find a function $g$ fulfilling the equation $$2\frac{t_k \cdot t_0 - 1}{t_k-t_{-1}} = g(t_k) + g(t_{k+1}) + t_{k+1}\cdot g(t_k)g(t_{k+1})$$ Whereby $t_{n+1}=t_n + h$ with $t_0, ...
1
vote
2answers
78 views

Partitioning positive divisors of 100!

Is it possible to partition all positive divisors of 100! (including 1 and 100!) into 2 subsets so that each subset has the same number of integers and the product of all the divisors making up the ...
0
votes
0answers
36 views

Is it possible to find out how many results were unexpected?

During a school year Andrew was given 40 mathematical problems as part of his assessment, one problem per week. As a result of marking he could receive 2,3,4 or 5 marks for each problem. Andrew called ...
0
votes
1answer
43 views

Perimeter problem involving different sized sticks?

Could you please help me find the answer to this question. I think it has something to do with grouping or pairing some numbers.I would appreciate easy-to-understand solutions. Thank you. There are ...
0
votes
3answers
53 views

How to solve $h(i) = \frac{i^2}{(n-i)^2+i^2}h(i-1) + \frac{(n-i)^2}{(n-i)^2+i^2}h(i+1)$

$h(i) = $P(reach n eventually| the initial state = i) $h(0) = 0$ $h(n) = 1$ 0 and n are stopping time. For $ 0 < i < n$, $$h(i) = \frac{i^2}{(n-i)^2+i^2}h(i-1) + ...
1
vote
1answer
57 views

Two rows or two columns with the same number of plusses

I have tried drawn numerous tables in attempt to explain this and understand that the number of cells must be even however, I am not sure how to create this proof. I appreciate your support. Each ...
1
vote
1answer
96 views

Solve All Sequence (Rubik's Cube)

Can you prove/disprove that there is a solve-all sequence of moves to complete the Rubik's Cube from any solvable-position? If so, can you explain how long it is? If not, explain why not. Just to be ...
1
vote
1answer
55 views

Prove that $a_i\leq 0$ for $i=1,2,…,N-1$?

Let $a_0,a_1,...,a_N$ be real number satisfying $a_0=a_N=0$ and $$a_{i+1}-2a_i +a_{i-1}=a_{i}^{2}$$ for all $i=1,2,...,N-1$. Prove that $a_i\leq 0$ for $i=1,2,...,N-1$. I saw the problem in ...
0
votes
2answers
72 views

How should a programmer store and solve simultaneous algebraic equations?

I need to store and solve simultaneous algebraic equations (no trig, no calc, no logs) as part of a larger program. I am not yet committed to a particular language, so long as it's a free one. For ...
0
votes
0answers
65 views

A Challenging Problem of Spherical Rectangle

Find out the area (in sq. units) covered by a spherical rectangle, having length & width (each as a great circle arc) of 15 & 4 units respectively, on a spherical surface with a radius ...
1
vote
1answer
46 views

Can problem solving be axiomatized? [closed]

Is it possible to develop a set of axioms for solving any problem, that are certain to work? Similar to problem solving strategies or proof strategies, though a set of steps that work indefinitely if ...
0
votes
1answer
83 views

How to find the minimum value of this integral?

I am struggling to find the solution to this problem. If anyone could help to explain how to solve this problem to me, it would be really appreciated. Let $$ f(x)=-\sqrt{3}x+(1+\sqrt{3}) $$ $$ ...
0
votes
1answer
16 views

For probabilities in sets, why multiply together for the complement but not for the normal probability?

For the birthday problem, the probability that a set of n birthdays (where n=1) contains your birthday is 1/365. The complement is that there is a 364/365 chance that it does not contain your ...
0
votes
1answer
13 views

Find caluclation to equal this value?

How can I find the calculation needed to reach the given value? This is related to programming but I don't see how I can do this myself. ...
0
votes
0answers
17 views

Ratio and rate using of SI units

When you have been given the ratio and rate of 4kg:500g do you change the values both to grams making it (8g:1g) or do you keep them in the SI units that they are placed in (1kg:125g) and for what ...
0
votes
1answer
33 views

Problem Analysis - Answer but no procedure - Differential Eq.

I stumbled with this problem in a notebook that has been bothering me...The answer is written but there's no explanation nor a steb-by-step procedure or anything. If you know how to analyse the ...
0
votes
1answer
27 views

What is the name for an ODE with an integral as a side condition?

My question: I have to find a function $y: \mathbb R \rightarrow \mathbb R$ fulfilling $$y^\prime(t) = f(t, y(t)),\ \int_{-\infty}^\infty y(t) dt = c$$ with a given $c \in \mathbb R$. What is the ...
0
votes
3answers
42 views

If |G|>1 is not prime, there exists a subgroup of G which is not G or {e}

Question: Prove the following: if|G|>1 is not prime, then $G$ has a subgroup other than $G$ and {e} We know that $\langle g \rangle$ is a subgroup of $G$ by previous part of the question and $G$ is ...
3
votes
2answers
53 views

Property of the solution for a specific system of non-linear equations.

We are stuck on a proof, and would appreciate any help: Let $\gamma >1$ be a known scalar and let $g,h=1,...,G$ and $s=1,...,S$. Let $\pi _{gs}$, $\beta _{s}$ and $y_{g}$ be known variables with ...
0
votes
1answer
40 views

Problem Analysis - Answer but no procedure - Finding Trajectories.

I stumbled with this problem in a notebook that has been bothering for the whole day(actually 3)...The answer is written but there's no explanation nor a steb-by-step procedure or anything. If you ...
0
votes
3answers
47 views

Problem Analysis - Answer but no procedure

I stumbled with this problem in a notebook that has been bothering for the whole day(actually 3)...The answer is written but there's no explanation nor a steb-by-step procedure or anything. If you ...
0
votes
0answers
46 views

Where does the problem statement say sides are *equal*?

In the book How To Solve It, Part I, chapter/section 19, Pólya's hypothetical teacher poses the following problem to prove to the hypothetical student: Two angles are in different planes but each ...
0
votes
2answers
17 views

The additive inverse for negative values only (otherwise zero)

I want to create a formula that only applies the additive inverse for negative values because I am trying to come up with a simple formula whereby two numbers are entered and if the second is larger ...
0
votes
1answer
34 views

What is a Single Objective Optimization problem?

I can't find any definition of this problem on the Internet. Could you help me by providing some definition?
0
votes
2answers
20 views

The Monthly Cost of the Third House Given the Total Rent Receipts of 186,390 in a Year.

This is how I solved this problem but I have some reservations regarding my answer. 1st house = x ; 2nd house = 3x ; 3rd house = [3x + x] - 2610 12(x) + 12(3x) + 12(4x - 2610) = 186,390 96x = ...
0
votes
1answer
60 views

Age Word Problem with 4 Variables

Simon is nine years older than Jairus. Simon is four times as old as Joter was three years ago. Joter is eighteen years younger than Marshall. How old is Jairus? The choices are as follow: 10 / ...
1
vote
2answers
22 views

Determining the Number of Adult Tickets from a Ratio of 4 is to 5

The ratio of adult tickets to student tickets for the play was 4:5. If the sum of the adult tickets and one half of the student tickets is 260, how many adult tickets were sold? The choices are as ...
1
vote
2answers
50 views

Show if $0 \le a <b$ implies $0 \le a^{\frac{1}{n}}<b^{\frac{1}{n}}$

Given that $0\le a<b$ show that $0\leq a^{1/n}<b^{1/n}$ Is this proof by induction? Show it's correct for $n=1$ Assume true for $n=k$, then $0\leq a^{1/k}<b^{1/k}$ holds for some $k$, ...
1
vote
2answers
63 views

How do you calculate P(A/B), when event B occurred after event A?

There's really only one question I can't begin to handle when it comes to probability, literally. It's not the only type of question I struggle with, though it's the type of question where I can't ...
0
votes
1answer
29 views

Isolate points of a metric space with some properties?

Suppose that all dense subspace of a metric space $(X,d)$ is open. Prove that the set of the isolate points of $X$ is dense in $X$. My Idea: all isolate points of $X$ are in any dense subspace, ...
0
votes
2answers
38 views

Is there a method or algorithm to solve “in what base is the equation true” questions?

I have been given some exercises in which I'm given some equation that doesn't hold in base ten, and I need to figure out in which base the equation does hold. For example: $\sqrt{41} = 5$ which I ...
1
vote
1answer
184 views

Does there exist continuously differentiable function $f:\mathbb{R}\longrightarrow\mathbb{R}$?

Does there exist continuously differentiable function $f:\mathbb{R}\longrightarrow\mathbb{R}$ such that for all $x\in \mathbb{R},\,\,f(x)>0$ and, $f'(x)=(f\circ f)(x)$? I see this question in ...
2
votes
1answer
54 views

What is the answer of this problem solving question?

You need to order 4 plastic cups for each of the 800 runners. Plastic cups are sold in 2 different pack sizes and you must choose one type of pack only. A pack of 500 costs £12.50 or a pack of 800 ...
0
votes
1answer
44 views

Wrong ILP solution with LPSolve (simple example)

I added the following example into LPSolve and found a strange issue. I don't want S1 and S2 to overlap within certain margins. ...
0
votes
1answer
104 views

Math Exercises, Highschool Student

I really want to improve my problem solving skills.. However I have found that most of the exercise books (lots of problems) are above my curent level (e.g. Olympiad and College) I am currently in ...
0
votes
1answer
52 views

Finding subgroups of a group from specific order

Given the following group: $$ \left<\left\{ \begin{bmatrix}a & b \\0 & c \end{bmatrix} \mid a,b,c\in \Bbb Z_{5},a,c \neq 0 \right\} ,\:\: * \right> $$ where ∗ is multiplication. ...
1
vote
2answers
68 views

List of N items, randomly putting them in order, showing the procedure ends.

On a bookshelf, there are N tomes of the encyclopedia in random order. Every hour, a librarian takes a tome which is not in place and puts it in its place, and we must show this process will stop ...
3
votes
3answers
132 views

Examples of open problems solved through short proof

Are there good examples of reasonable open problems in mathematics that had an 'obvious' solution via application of a theorem already known/not yet found in mathematics but could have been found with ...
1
vote
0answers
30 views

Techniques for computing (approximate or exact) partial sums for functions

Clearly there are several ways of computing the partial sum formulas of many summations, but is there a technique that can compute any partial sum. For example with $\sum_{x=0}^{n} \frac{1}{x}$, ...
3
votes
4answers
46 views

Prove $F^2_{n+1} - F_nF_{n+2} = (-1)^n$

This is a question about Fibonacci sequences, a sequence in which the previous terms build up upon the current term (e.g. $F_1 + F_2 = F_3$ where $F_1 = F_2 = 1$). How would I go about proving ...
0
votes
1answer
68 views

Finding the Compound Interest on 7500 Dollars at 4% per annum for 2 Years

Find compound interest on 7500 dollars at 4% per annum for 2 years, compounded annually. The choices are as follow: $512 $552 $612 $622 I tried to solve this problem by: C.I. = 7,500(.02) = ...
1
vote
1answer
22 views

Experiments with random selection: when to respect order?

I have a hard time imagining experiments of this nature without noting the arrangements (I draw that ball with my left hand, the other with my right. I draw that ball first, the other second) so I'm ...
0
votes
1answer
36 views

Help establishing restrictions for consistency on a linear system.

I'm having trouble wrapping my head around this problems, and others similar to it. I can typically solve systems of linear equations, but some give me trouble, especially dealing with unknown ...