Questions tagged [problem-solving]

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.

1
vote
2answers
974 views

Finding Y coordinate of third triangle point when X coordinate and two other points are already known

Suppose you know the coordinates for points A and B of a triangle. We can refer to those coordinates as (Ay,Ax) and (By,Bx). Also, suppose you know the X coordinate for point C (Cx) but do not know ...
5
votes
2answers
165 views

List of not-especially famous problems in undergraduate level mathematics

I know lists of problems like these have been compiled before, but most tend to collect either extremely difficult problems ( like Collatz conjecture in a question about number theory ) or ...
0
votes
1answer
44 views

What branch of maths helps develop an effective problem solving mindset

I have started doing maths about 5 years ago , i didnt have a math science orientation , but i have developped a study program specially for elementary algebra and geometry as well as basic statistics ...
0
votes
0answers
19 views

Dimensions of Box after binding it in circular shape [on hold]

I want to input the diameter....for the attached picture example, lets say I enter .750 for the diameter of the dowel. Then, I will enter the quantity of the bundle which is 25. The formula would ...
2
votes
5answers
54 views

What is the solution to this equation: $e^x+2x=0$

I cant find any program that actually solves this type of equations and I cant find anything helpful about this type. What is the name of these equations and how do I solve this one? Thanks.
0
votes
1answer
43 views

Probability of each outcome, when Flipping a Hemisphere

Say I have a hemisphere (A solid sphere, cut exactly in half), and I have an experement in which, when flipped, it can land either as: Flat Face Up Flat Face Down How would one go about calculating ...
1
vote
1answer
27 views

Finding the root of an equation involving digamma functions

Is it possible to get an analytic solution for the equation \begin{align} \frac{1}{x} + 2\psi(2x) + \pi \cot(\pi x) = 0 \end{align} for $x\in(0,1)$ (using the Newton-Raphson method I get $x\approx 0....
0
votes
1answer
35 views

How to find the solution of a Numerical Reasoning Problem

There is a girl who likes number 100 but doesn't like 99, she likes 900 but doesn't like 850, she likes 2500 but doesn't like 2600. I have to find out which number she is going to like. The proposed ...
0
votes
2answers
46 views

Probability of randomly choosing all elements fulfilling a certain condition

Assume you have a bag containing $m$ marbles, of $c$ different colors, where the number of marbles of each color is equal to $\frac mc$. If $n$ marbles are drawn from the bag, without replacement, ...
0
votes
1answer
28 views

Problems to read/write the polynomial equation

Can't figure out how the i could get from that equation $$\tag{1} p(x)=\sum_{l=0}^n \left(\sum_{j=0}^n a_j\binom{j}{l}\tilde x^{j-l}\right)(x - \tilde x)^{j-l}$$ for that example: "For an ...
0
votes
0answers
22 views

Book recommendations for Problem Solving

I am looking for book recommendations that will teach me the art of problem solving. Learning theory is one thing but doing problems in limited time in a test is another. To increase thid skills I ...
0
votes
1answer
60 views

Solve using KKT conditions when number of variables is less than number of constraints

$$\begin{align} \text{minimize} \quad & f(x) = x_1^2 + x_2^2 +x_3^2 \\ \text{subject to} \quad & 2x_1+ x_2-5\leq 0 \\ & x_1+x_3-2\leq 0 \\ & 1-x_1 \leq 0 \\ & 2-x_2 \leq 0 \\ & ...
0
votes
1answer
31 views

Optimization problem for maximum profit

I have to write a linear program for the following problem: We have three products that are made in a factory: A, B and C, we are given the amount of energy every product needs (A ~ 1kWh, B ~ ...
0
votes
1answer
24 views

Right Circular Cylinder: Distance between axis and plan

B is a point in the top circle of a right circular cylinder. C is a point in the bottom circle of the given cylinder. The angle between [BC] and the base's plan of the cylinder is 45 degrees. The ...
0
votes
0answers
21 views

Understanding Intermediate steps in this Boundary value Problem

I have been trying to replicate a derivation from a scientific paper (for my understanding) which involves solving a Boundary value problem on the Stokes operator. The author jumps some steps while ...
-2
votes
1answer
19 views

intuition behind LCM method used to solve time/work aptitude problems

Below is a sample time/work problem. Rakesh alone can do a work in 10 days. Brijesh can do the same job in 15 days. If both Rakesh and Brijesh work together, then in how many days the work will get ...
3
votes
3answers
95 views

Congruence equations in the form $x^k \equiv b \bmod m$

In my textbook its described as finding $k\;$th roots moduluo $m$. How do you solve equations of this form as I can't find any examples anywhere? I am just looking for a step by step example so I can ...
0
votes
1answer
62 views

How can I find all solutions of this equation?

I am trying to solve the equaiton $n^3+2019 n=k^2$, where $n$ and $k$ be two positive integral numbers. I tried with Mathematica and get two solution $k = 78, n = 3$ and $k = 17498, n = 673$. How ...
0
votes
1answer
12 views

Determing power settings

A company has three machines which output at different wattages(35, 45 and 60). The 35-watt machine runs best at a power level of 45%. The 60-watt machine runs best at a power level of 60%. What is ...
0
votes
2answers
32 views

Basic “Punctuation” and “words” used in basic Mathematics

I live in a place where solving math problems is taught perfectly, but Punctuation and correct words are overlooked. I don't know to use comma, period, dash, paragraph change, etc and words like ...
0
votes
1answer
1k views

How many ways can you make change for a dollar?

This is a generic generating functions problem, and you are left with 1/(x-1)(x^5-1)....(x^50-1) however now I want to find the coefficient of the x^100 term of this expression... how can I do this or ...
0
votes
1answer
1k views

Convert $\sin 2x$ into terms of $\cos 2x$

I need to convert a factor of $\sin 2x$ into terms of $\cos 2x$, or any power of $\cos 2x$. Basically I need to solve an equation by substituting $r = \cos 2x$ and solve for $r$, but I am stuck with a ...
1
vote
1answer
790 views

what is wrong in my answer and what will be the correct solution for this probability question ?

A and B play a game where each is asked to select a number from 1 to 5. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial is - a)1/...
0
votes
1answer
25 views

Complicated transporting problem.

In the following problem, goods will be transported from farmers to stores. I know how to minimise the transport costs in such problems. The complication comes because the goods have to go to some ...
0
votes
1answer
23 views

Calculate the running and walking distance depending on speed and hours

So here's my problem I'm having: Say someone runs or walks 40 kilometers in a day in 8 hours. We don't know how many kilometers in specific the person was walking or running, though that's what we'd ...
0
votes
0answers
97 views

Simple ratio problem

I am currently working through some tests for graduate schemes and I am finding the maths tests relatively okay despite the time restrictions. However, I have come across one basic ratio question that ...
-3
votes
0answers
15 views

In a mathematics exam(UG engineering level), how do you know whether your answer is correct or not?

This is quite confusing for me. Whenever in an exam, I never know if my answer is correct or not. How can I be sure if its correct and satisfies all the condition?
2
votes
1answer
36 views

Solve a trigonometric equation where one constant can be negative

I previously posted a code-related questions on StackOverflow here but after doing some more investigation work into the code, I had an epiphany when looking at the actual Newton-Raphson section ...
0
votes
0answers
20 views

Constructing numbers with a limited “inventory” of numbers and operations where numbers are consumed upon use.

This might be way too specific, but I will give it a try posting it here nonetheless. There is a (multi)set of numbers that can contain the same number multiple times, and there is a set of "...
1
vote
2answers
71 views

Solving system of 10 equations involving some degree 2

Recently I was doing a pipe network problem without Hardy Cross Method (approximate method ) I have obtained 10 desired equations with 10 unknowns as shown in this image below highlighted by red pen. ...
0
votes
1answer
19 views

Solving mathematical economics problem

kindly I'm stuck in this problem instead of many attempts through net present value and other discounted cash flow methods, some one could give me a detailed information and answers on this problem : (...
4
votes
4answers
2k views

Difficulty in solving challenging trig equation

Find $\theta$ on $[0, 2\pi)$ such that $$\cos{\theta}^{\sin{\theta}^{\cos{\theta}^{\dots}}} = 2 + 2\sec^2{\theta}\tan^2{\theta} - \sec^4{\theta} - \tan^4{\theta}$$ I'm not sure on how to tackle this ...
5
votes
6answers
131 views

Find $a,b,c,d$ such that $2^a + 2^b + 2^c = 4^d$

Let $a,b,c,d$ be whole numbers that satisfy $$2^a + 2^b + 2^c = 4^d$$ What values of $(a,b,c,d)$ would make this equation true? Here is my work so far. Without loss of generality, assume $a\ge b\...
2
votes
2answers
39 views

Explicit solution to nonlinear ODE

I'm trying to find an explicit solution $u(t)$ of $$ \dot{u} = \frac{\beta}{\sqrt{\alpha t}-u},\quad u(0)=0 $$ where $\alpha>0$ and $\beta\in\mathbb{R}$ are given constants. I did not know how to ...
2
votes
2answers
77 views

Geometric argument showing that the sum of the series $\sum_{n = 1}^{\infty} n^{-1}(n + 1)^{-1}$ is $1$

I can't see the relationship between this telescopic series and the area under the curve for functions $f(x)=x^n$.
3
votes
2answers
52 views

Solve the equation: $x-a^2x-\frac{b^2}{b^2-x^2}+a=\frac{x^2}{x^2-b^2}$

Here is the equation: $$x-a^2x-\frac{b^2}{b^2-x^2}+a=\frac{x^2}{x^2-b^2}$$ The equation looks very simple. But, it's a little misleading (for me). $$x-a^2x-\frac{b^2}{b^2-x^2}+a=\frac{x^2}{x^2-b^...
0
votes
3answers
37 views

Word Problem - what percent of the women who apply are hired?

At a certain factory, twice as many men as women apply for work. If 5% of the people who apply are hired and 3% of the men who apply are hired, what percent of the women who apply are hired?
3
votes
1answer
46 views

Optimise allocation to minimise variance

Background I am trying to allocate customers $C_i$ to financial advisers $P_j$. Each customer has a policy value $x_i$. I'm assuming that the number of customers ($n$) allocated to each adviser is ...
0
votes
2answers
41 views

A simple but painful calculation.

$$S=(x_3-x_1)^2+(x_4-x_2)^2+(x_5-x_3)^2+(x_1-x_4)^2+(x_2-x_5)^2$$. $$S'=(x_3-x_1)^2+(x_4+x_2)^2+(x_5-x_2-x_3)^2+(x_1+x_2-x_4)^2+(-x_2-x_5)^2$$ Find $S$–$S'$? I thought that, I should manipulate the ...
0
votes
2answers
25 views

Absolute Value Problem Using Only Variables

I recently encountered this problem, and it does not make sense to me. It looks like Given $|a(b-cx)|=d$ , find the value of $|x-\frac{b}{c}|$ This was on a multiple choice test awhile ago, and I ...
0
votes
0answers
18 views

Calculating density of individuals within an area (tree stand density)

Any help greatly appreciated! I want to find the density of trees surrounding a sample point (measured in trees/m$^2$). The distance from the sample point to the three nearest trees has been ...
1
vote
0answers
51 views

Finding roots for $(1+c) \cos(ax)+(1-c) \cos(bx)=0$

Looking to find the analytic roots of $$(1+c) \cos(ax)+(1-c) \cos(bx)=0$$ where $a$,$b$, and $c>0$. Any ideas? For $c=0$ the answer is straight forward. P.S. The constants $a=A-B$ and $b=A+B$ if ...
0
votes
0answers
21 views

Compounding Formula (and its reverse)

I've written a program in which I'm using a compounding calculator to determine an output. But without a formula I'm having trouble reversing the calculation. Given a compounding problem whose ...
0
votes
1answer
23 views

Find solution to exact ODE: $(4bxy(x)+3x+5)\dot{y}+3x^2+8ax+2by(x)^2+3y(x)=0\hspace{0,5cm}a,b\in\mathbb{R}$

So I have this exact ODE $(4bxy(x)+3x+5)\dot{y}+3x^2+8ax+2by(x)^2+3y(x)=0\hspace{0,5cm}a,b\in\mathbb{R}$ I already managed to show that $F=2bxy^2+3xy+5y+x^3+4ax^2$. Now, how can I find the solution ...
2
votes
3answers
59 views

How to derive this relation that I found intuitively?

By intuition, I found that the result of evaluating the following expression $$ \frac{1}{M} \frac{\sum_{N=0}^M \frac{M!}{(M-N)!N!} N e^{cN}}{\sum_{N=0}^M \frac{M!}{(M-N)!N!} e^{cN}} $$ does not ...
0
votes
1answer
28 views

Word problem - How many times was the player at bat during the entire season?

Its the first time I am asking a question on a forum. I have been self-studying math for a month and now am stuck in word problem chapter. I searched a lot for a solution manual, but I didn't find any....
0
votes
0answers
39 views

Puzzles and exercises to improve mathematical intelligence and spatial thinking

In your childhood or adolescence, or maybe as an adult, have there been types of exercises or puzzles that you think have improved your mathematical intelligence and in particular the spatial thinking?...
1
vote
1answer
29 views

Word problem - Problem Solving

My kid is practicing word problem. I have an issue with the question which i m unable to produce any solution. Would be appreciated if any solution is provided. QUESTION: In the village there were ...
2
votes
1answer
75 views

Solving a set of multivariate polynomials; four equations, four unknowns, maximum degree 2

I am currently trying to solve a set of four polynomial expressions for a geometric purpose. in short they take on this form: $A_0=\frac{w_0^2+w_1 w_0+w_2 w_0+w_3 w_0+27 w_0+6 w_1+6 w_2+6 w_3+117}{\...
1
vote
1answer
28 views

Minimum quadratic formula value

I have recently been researching about quadratic equations, and came across the following formula for finding the minimum $x$ and $y$ values from a "Bivariate (two equation) quadratic": $$x = -(2BC-...