# Tagged Questions

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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### What are the steps to do to solve this Algebraic problem?

A mixture of 12 ounces of vinegar and oil is 40 percent vinegar,where all of the measurements are by weight. How many ounces of oil must be added to the mixture to produce a new mixture that is only ...
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### How do I know if this equation can be solved symbolically?

Can these equations be solved symbolically for $x$? \begin{align} x &= \frac{p - p_m(x)}{p_m(x) - p_m(x)^2} \\ \\ p_m(x) &= \frac{e^x}{e^x + e^y} \\ \end{align} If not ...
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### Find a thousand natural numbers such that their sum equals their product

The question is to find a thousand natural numbers such that their sum equals their product. Here's my approach : I worked on this question for lesser cases : \begin{align} &2 \times 2 = 2 + 2\\ ...
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### What is the largest possible area that $PQRS$ could have?

In a $14\times 18$ rectangle $ABCD$, points $P,Q,R$ and $S$ are chosen, one on each side $ABCD$ as pictured. The lengths $AP, PB, BQ, QC, CR, RD, DS$ and $SA$ are all positive integers and $PQRS$ is a ...
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### Division of a square and value of a disk

I cam across this problem and I really don't know how to solve it. So you start with a square that has value 1. You divide this square in 4 so that each new square has a new value, as given by the ...
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### Solve Equation with max integer [on hold]

Solve please $\dfrac{\left[\sqrt{x-[x ]}\right]}{(x+3)(x+4)}\ \geq0$ edit
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### Chess tournament problem

$12$ chess players took part in a tournament. Each played against each other exactly once. After the tournament every chess player did $12$ lists of names. On the first list, the player only wrote ...
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### Determining values satisfying an inequality

I have the following inequality: $$\left\lceil \frac{\log((n-1)/6000)}{\log(3)} \right\rceil < \left\lceil \frac{\log((n-1)/3000)}{\log(3)} \right\rceil,$$ where $n$ is a positive integer, and I ...
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### How to solve the given problem of simple interest?

The problem statement is: What annual instalment will discharge a debt of 1092 due in 3 years at 12% simple interest? Now, what I know is Simple interest =( principal* Rate per annum*Time in ...
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### 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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### Studying for grad school qualifying exams; need a little help on how to effectively study higher math. [on hold]

This is entirely embarrassing to admit, but I'm realizing, one year into my doctorate program, I don't know how to effectively study math. I feel like a failure and a fraud for even having to come ...
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### What is the smallest number of coins I could have? [closed]

A country has 6 coins of the following denominations: 1 cent, 2 cents, 4 cents, 10 cents, 20 cents and 40 cents. Using the coins I have, I can pay exactly for any amount up to and including 200 cents. ...
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### Isosceles Triangle With Height Limiting To Zero, part 2

The figure shows an isosceles triangle ABC with ∠B=∠C . The bisector of angle B intersects the side AC at the point P. Suppose that the base BC remains fixed but the altitude |AM| of the triangle ...
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### Grade 10, waiting for the train.

At Berracan station, northbound trains arrive every three minutes starting at noon and finishing at midnight while southbound trains arrive every five minutes starting at noon and finishing at ...
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### Clearance in a semi-circular tunnel [closed]

A single-lane street 10ft. wide goes through a semi circular tunnel radius 9ft. How high is the tunnel at the edge of each lane?(Round off to 2 decimal places) This is our coming new lesson and I ...
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### How many eggs are there in the basket? [closed]

There is a basket of eggs. The remainder is $1$ when we put the eggs in groups of $2$. $2$ when we put the eggs in groups of $3$. $3$ when we put the eggs in groups of $4$. $4$ and $5$, ...
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### Find all the integer pairs $(r,s)$ that satisfy $s= (r^2 +3r +8) / (r^2 +r -2)$?

I have been trying to solve this question but struggling to see where to start. Examples I've seen that works are the pairs: $(-3,2) , (4,2), (0,-4)$
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### How would you work out these combinations?

If there are 16 different ice-cream flavours, how many combinations are there for a two scoop? If there are still 16 different ice-cream flavours, how many combinations are there for a three scoop? ...
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### Probability Average amount of rolls

I have a question regarding probability. I'll start by saying I've never taken a statistics or other similar course and was trying to work out this for a game. On average how many attempts will it ...
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### Solve $4 A (L^{3/4}) - wL (((24 - L) w)^{-3/4}) = -(((24 - L) w)^{1/4})$ for L? Using Mathematica

I'm trying to solve $$4 A (L^{3/4}) - wL (((24 - L) w)^{-3/4}) = -(((24 - L) w)^{1/4})$$ for $L$ using Mathematica, and it spits the following out: ...
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### Can someone suggest books on mathematics and problem solving which nurtures the reader? [closed]

Can someone suggest books on mathematics and problem solving which nurtures the reader like Alexander Soifer's books? Thanks in advance
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### Using induction on modified inequalities.

Here's the original problem: Prove by induction that $\left(\frac{1}{2}\right) \left(\frac{3}{4}\right) \cdots \left(\frac{2n-1}{2n} \right) \leq \frac{1}{\sqrt{n+1}}$ for all $n \in \mathbb{N}$. ...
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### Special Numbers [closed]

Q . Suppose that we state that a positive integer number 𝑛𝑛 is called “special” if the set {1,2,3, . . . ,2016} can be split into 𝑛 subsets, all of them with the same number of elements and the ...
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### How to find the average Kendall's distance between 2 rankings

Suppose I have 2 rankings: $1$, $2$, $3$ and $2, 1, 3$ then the Kendall's distance between the two is 1 since there is only one pairwise adjacent switch. My question is, suppose my 2 rankings each ...
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### Text problem with workers

I'm having an entrance examination in two days and I'm having problems with this math problem here. A group of workers works on two jobs in two days. The second job is 2 times smaller in volume ...
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### Problem: Using Cauchy's integral formula show…

I've stumbled upon a problem I can not solve in the book Mathematical Methods for Electrical Engineers by Thomas B.A. Senior(Page 171). The book gives the following instruction: Using Cauchy's ...
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### writing numbers as sum of at least two consecutive odd positive integers [closed]

Since 24 = 3 + 5 + 7 +9, the number 24 can be written as the sum of at least two consecutive odd positive integers. (a) Can 2005 be written as the sum of at least two consecutive odd positive ...
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### Prove that among any 12 consecutive positive integers there is at least one which is smaller than the sum of its proper divisors

Prove that among any 12 consecutive positive integers there is at least one which is smaller than the sum of its proper divisors. (The proper divisors of a positive integer n are all positive integers ...
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### Solving an equation

I have the following equation: $x_1^3 = \hat{x}_1^3 + e_1\delta(x_1,e_1)$ I have to find the function $\delta(\cdot)$ for which this equation holds. By definition: $e_1 = \hat{x}_1 - x_1$ So I am ...
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### solving equation using square root

I have a question here... Usually, for $x^2 = 4$ $x=\sqrt{4}$ $x=±2$ But if the question is like this : $y^2 = (x+2)(x+2)$ $y^2 = (x+2)^2$ If I want to find $y$ in term of $x$,I will put square root ...
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### Probability problem

I created this problem based on the following probability riddle here. You're a king, and you were given two groups of people, and a certain information about them. First group has 2 people. One of ...
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### Differential equation, Solution is a Bessel fucntion

this is my first post here. I knocked my head on a differential equation yesterday, this one: $$\frac{12 \nu}{x^2} \frac{S(x)''}{S(x)} = -\lambda^2$$ Where $nu$ is a constant. The book says the ...
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### Minimizing a strictly convex function with inequality constraint

So we've been learning about the Kuhn Tucker conditions in my non-linear optimization course and I've been having trouble with this problem: QUestion: description here Question: a strictly convex ...
### Homeomorphism from $S^1\backslash(0,1)$ to $\mathbb{R}$
I am trying to derive a bijection between $S^1\backslash{(0,1)}$ and the real line, but I am stuck on using the most obvious way Let the top point of the circle be $(0,1)$, and the blue line hits ...