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.

2,729 questions
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 ...
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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 ...
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 ...
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 ...
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.
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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 ...
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 $x\approx 0.... 1answer 35 views How to find the solution of a Numerical Reasoning Problem There is a girl who likes number 100 but doesn't like 99, she likes 900 but doesn't like 850, she likes 2500 but doesn't like 2600. I have to find out which number she is going to like. The proposed ... 2answers 46 views Probability of randomly choosing all elements fulfilling a certain condition Assume you have a bag containing$m$marbles, of$c$different colors, where the number of marbles of each color is equal to$\frac mc$. If$nmarbles are drawn from the bag, without replacement, ... 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 ... 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 ... 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 \\ & ... 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 ~ ... 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 ... 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 ... 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 ... 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 ... 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 ... 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 ... 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 ... 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 ... 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 ... 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/... 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 ... 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 ... 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 ... 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? 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 ... 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 "... 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. ... 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 : (... 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}$$I'm not sure on how to tackle this ... 6answers 131 views Find a,b,c,d such that 2^a + 2^b + 2^c = 4^d Let a,b,c,d be whole numbers that satisfy$$2^a + 2^b + 2^c = 4^d$$What values of (a,b,c,d) would make this equation true? Here is my work so far. Without loss of generality, assume a\ge b\... 2answers 39 views Explicit solution to nonlinear ODE I'm trying to find an explicit solution u(t) of$$ \dot{u} = \frac{\beta}{\sqrt{\alpha t}-u},\quad u(0)=0 $$where \alpha>0 and \beta\in\mathbb{R} are given constants. I did not know how to ... 2answers 77 views Geometric argument showing that the sum of the series \sum_{n = 1}^{\infty} n^{-1}(n + 1)^{-1} is 1 I can't see the relationship between this telescopic series and the area under the curve for functions f(x)=x^n. 2answers 52 views Solve the equation: x-a^2x-\frac{b^2}{b^2-x^2}+a=\frac{x^2}{x^2-b^2} Here is the equation:$$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^... 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? 1answer 46 views Optimise allocation to minimise variance Background I am trying to allocate customersC_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 ... 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 ... 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 ... 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 ... 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 ... 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 ... 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 ... 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 ... 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.... 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?... 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 ... 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}{\...
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-...