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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Costruction of a sqaure grid from a given centre (lat,lon) and direction of the sides

Let us consider a point (longitude,latitude) on earth (location). My question is: how to construct a square grid around this point (taking this point as the centre of the square or intercept of the ...
1
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2answers
30 views

a lorry is loaded with 3 layers of 17 crates. Each crate contains 231 bananas. How many bananas are there in total? [on hold]

I need help on a question I can't simply get my head round! Please help!
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0answers
22 views

Challenging Mathematical Problem of Solid Angle by H.C. Rajpoot [on hold]

Calculate solid angle (in Ste-radian) subtended by a plane bounded by the straight lines x=-∞, x=14, y=6 & y=∞ in XY-plane at the point (8,-9,-5). posted by H. C. Rajpoot (29/01/2015)
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2answers
47 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 $k$, ...
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2answers
39 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
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1answer
28 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, ...
1
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1answer
24 views

Value(s) of the parameter $a$ that give explicit formula's

For what value(s) of the parameter $a$ is it possible to find explicit formula's (without integrals) for the solutions to $$\frac{dy}{dt}= aty +4e^{-t^2}$$ The answer is $a=-2$. I don't know how to ...
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2answers
27 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 ...
0
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2answers
57 views

Solving a system of three simultaneous equations

Given the system $$ \begin{align*} -2x + ay - bz &= -4 \\ x + bz &= 2 \\ 2x + y + 3bz &= b \end{align*} $$ The question asks to find conditions on $a$ and $b$ that the system has no ...
2
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1answer
147 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
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1answer
24 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 ...
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0answers
10 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. ...
-5
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1answer
47 views

Let $w=1+3i$. Investigate whether $|iw+w|=|iw|+|w|$. [closed]

Let $w=1+3i$. Investigate whether $|iw+w|=|iw|+|w|$. This is a question on complex numbers.
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votes
3answers
37 views

simplify the equation [closed]

I need help simplifying this equation. It is a fraction just in case the way I formatted it doesn't turn out right. $$ \frac{(4x + 3)^{1/2} − (x + 6)(4x + 3)^{−1/2}}{(4x+3)} $$
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votes
1answer
62 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
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1answer
46 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. ...
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2answers
45 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 ...
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0answers
42 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 ...
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0answers
20 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
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4answers
42 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 ...
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1answer
21 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) = ...
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0answers
12 views

A Fall in the Annual Rate of Interest From 8% to 7.75%

A moneylender finds that due to a fall in the annual rate of interest from 8% to 7.75%, his yearly income diminishes by $ 61.50. His capital is: The answer choices are as follow: $22,400 $23,800 ...
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1answer
30 views

Find Cyclic Group [duplicate]

Given the following : $$ \langle\Bbb Z^{*} _{91}, {*}\rangle,$$ where $*$ is multiplication, and $\mathbb{Z}^{*}_{91}$ is $\mathbb{Z}_{91}\setminus \{0\}$. ($\mathbb{Z}^{*} _{91}$ contains any ...
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1answer
14 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 ...
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0answers
37 views

Solutions that are easy to sketch but difficult?

I am wondering if there are any famous problems in math where everyone knew how the solution should proceed, but the sheer mental effort required to execute that solution was itself what made no one ...
0
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1answer
21 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 ...
0
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1answer
28 views

The Profit Gained by a Shopkeeper who Uses an 800gm Weight Rather than a Kilogram weight

A shopkeeper professes to sell his goods at $200 but uses a weight of 800gm instead of kilogram weight. Thus, he makes a profit of The choices are as follow: 20% 22% 25% None of these The ...
7
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2answers
59 views

For which $n, k$ is $S_{n,k}$ a basis? Fun algebra problem

Here it is a nice algebra problem I had some fun with Let $V$ be a vector space over $\mathbb R$ of finite dimension $\dim V = n$. Let $v = \{ v_1, \dots, v_n\}$ be a basis for $V$. Let $$S_{n,k} = ...
1
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1answer
23 views

What's the Total Number of Candidates who Applied for the Exam?

In an examination, 5% of the applicants were found ineligible and 85% of the eligible candidates belonged to the general category. If 4275 eligible candidates belonged to other categories, then how ...
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1answer
39 views

Find Cyclic Group [closed]

Given the following : $$ <\Bbb Z^{*} _{27}, *> $$ $$ <\Bbb Z^{*} _{35}, *> $$ $$ <\Bbb Z^{*} _{91}, *> $$ $$ < \Bbb Q^{*}, *> $$ $$ <\{ \begin{bmatrix}1 & ...
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votes
3answers
32 views

Cars A, B, C, and D travel in an infinite boundless flat plane [closed]

Cars $A$, $B$, $C$, and $D$ travel in an infinite boundless flat plane, each one at a constant speed and direction (though these constants are not all the same). It is given that cars $A$ and $B$ meet ...
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1answer
55 views

Solving equation with exponentials

How to solve $ {z = x^y, x = y^z, y = z^x }$ for $ x, y $ and $ z? $ Is some sort of triple Lambert W to be introduced? Done so far: Taking logs, $$ \log z = y \log x , \log x = z \log y , \log ...
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1answer
32 views

How to best approach a problem of this kind (problem solving and simple linear equations)

This is a common type of problem that appear on algebra tests to test problem solving abilities (this is not from a real test or homework). I am curious on how to best approach these kind of problems ...
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2answers
75 views

Trouble with Vakil's FOAG exercise 11.3.C

I'm having trouble with the exercise in the title, even with part (a), which asks to prove that if $X$ is a closed subset of $\mathbb{P}^n_k$ of dimension at least 1 and $H$ is a non-empty ...
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1answer
39 views

One hundred indistinguishable ants are dropped on a hoop of diameter 1

I have this question which I am not sure how to solve: One hundred indistinguishable ants are dropped on a hoop of diameter 1. Each ant is traveling either clockwise or counterclockwise with a ...
2
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1answer
29 views

Finding the best fit of 3 categories ( restaurants/meal/person analogy problem )

I have this problem that sounds tedious and long and I'm not sure if there exist an intuitive way to solve it. The problem is related to image recognition but I will try to give an analogy to it You ...
1
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1answer
93 views

Time & Distance : Pokemon Hunter and the Rogue Brook

I was working my way through some Puzzles in Discrete Maths by Rosen, when I came across the following question: A Pokemon Hunter is rowing upstream a brook As he passes under the ...
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23answers
8k views

An example of a problem which is difficult but is made easier when a diagram is drawn

I am writing a blog post related to problem solving and one of the main techniques used in problem solving is drawing a diagram. Essentially, I want to illustrate that some hard problems (for example, ...
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0answers
21 views

problem solving on work rate

please tell me this problem has insufficient data.. 5 men and 2 boys working together can do four times as much work as a man and a boy. working capacities of a woman and a boy are in the ratio ... ...
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1answer
20 views

Find the probability for … [duplicate]

Suppose we uniformly and randomly select permutations from the 20! Permutations of 1, 2, 3,..., 20. What is the probability that 2 appears at an earlier position than any other even number in ...
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1answer
24 views

Defining addition of vectors of different dimensions

While doing real data analysis I came up with a problem. I have given lots of efforts to solve it and could not succeed. Here is the problem: Suppose, we have a set of vectors ...
0
votes
1answer
36 views

how to reduce a fraction?

I solved expression and saw this solving, but I didn't see the way to reduce one. $$\begin{align}\frac{a+2\sqrt{ab}-3b}{ab(a - \sqrt{ab} - 3\sqrt{ab -3b})}=\frac{1}{ab}\end{align}$$ Can you show me ...
2
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1answer
30 views

Sequence pattern question

I have the following question. Let $S_1$ be the sequence of positive integers $1,2,3,4,5 , \ldots$ and define sequence $S_{n+1}$ in terms of $S_n$ by adding $1$ to the integers of $S_n$ which are ...
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2answers
36 views

Making up groups of Coins [duplicate]

In how many ways can a group of 100 coins be made up from 50,20,10,5,2 or 1 coin(s) respectively? An alternative way of phrasing this would be how many ways can a group of 100 coins be made from ...
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1answer
34 views

Polar coordinate system : Is radial coordinate is a function of angular coordinate?

In polar coordinate system: The polar coordinates $r$ is called the radial coordinate and $\theta$ is called the angular coordinate, often called the polar angle. I am confused when answering the ...
1
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1answer
40 views

How do you compare carsharing plans to calculate the cheapest?

Call hourly rate = HR. Assume that I can guess my monthly usage in hours, which I call $g$. Beware that the fixed fees are presented in different units of time, so first convert everything into ...
0
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1answer
67 views

Different ways to write $n$

What is a general formula $n(n)$ for this? We know that starting from below, we can see how many numbers a certain $n$ generates by counting the number of numbers contained in the column $n$ is in, ...
0
votes
1answer
51 views

Solution to $b\sin({\theta})\cos({\phi})+a\cos({\theta})\sin({\phi})=0$ for $\phi$

I'm looking for a solution to $b\sin({\theta})\cos({\phi})+a\cos({\theta})\sin({\phi})=0$ for the variable $\phi$. In the equation both $a$ and $b$ are real numbers; in particular, I have ...
5
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1answer
113 views

Prove Divisibility In Fibonacci Sequence Over A Prime Number

In The Fibonacci sequence which is defined as: Lets say we have the number $p$ which is an odd prime. Prove that: $F_{p-1} + F_{p+1} -1$ Is divisible by $p$. Prove that for any given $n$ real ...
3
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2answers
91 views

Is it possible to solve this equation with logarithms and exponents?

$$-\frac{1}{3}\log(4x-12)+6=\left(-\frac{1}{2}\right)^x $$ Out of all the logarithm laws I've learned (which is pretty limited), I have not found a way to solve for what x is yet. Can someone verify ...