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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Time and distance problem

A train starts from Jammu for Srinagar at 13:30 and reached at 17:30.Another train starts from Srinagar at 15:30 and reaches Jammu at 19:00.At what time both train will meet??. I have solved this ...
0
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2answers
27 views

Given $f(x)=x^2-4x+3$, find the points on the curve $y=f(x)$ where the tangent to the curve passes through -6.

Given $f(x)=x^2-4x+3$, find the points on the curve $y=f(x)$ where the tangent to the curve passes through $(0,-6)$. State the equations of the tangents at these points. Hi everyone, I tried to find ...
3
votes
1answer
38 views

Algebraic solution for the value of $x$.

I solved this problem the fifteen years ago without numerically solving equations of degree 4, I was happy in a substitution that I avoid directly attacking equations of degree 4. Today my nephew, ...
0
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2answers
27 views

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 ...
1
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1answer
35 views

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 ...
23
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3answers
2k views

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\\ ...
0
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0answers
35 views

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 ...
4
votes
0answers
45 views

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 ...
-1
votes
0answers
31 views

Solve Equation with max integer [closed]

Solve please $\dfrac{\left[\sqrt{x-[x ]}\right]}{(x+3)(x+4)}\ \geq0$ edit
4
votes
1answer
106 views

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 ...
0
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2answers
45 views

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 ...
0
votes
2answers
62 views

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 ...
0
votes
1answer
455 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 ...
4
votes
1answer
70 views

Studying for grad school qualifying exams; need a little help on how to effectively study higher math. [closed]

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 ...
0
votes
2answers
49 views

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. ...
1
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0answers
34 views

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 ...
1
vote
2answers
48 views

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 ...
-2
votes
3answers
578 views

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 $5$, ...
2
votes
3answers
44 views

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: $(-3,2) , (4,2), (0,-4)$
1
vote
2answers
39 views

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? ...
0
votes
1answer
41 views

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 ...
0
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2answers
546 views

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: ...
1
vote
1answer
64 views

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
0
votes
1answer
32 views

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 $n \in \mathbb{N}$. ...
0
votes
1answer
50 views

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 ...
4
votes
2answers
53 views

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 ...
1
vote
1answer
33 views

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 ...
1
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2answers
42 views

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 ...
4
votes
4answers
10k views

Missing dollar problem

This sounds silly but I saw this and I couldn't figure it out so I thought you could help. The below is what I saw. You see a top you want to buy for $\$97$, but you don't have any money so you ...
9
votes
2answers
100 views

Favourite problem books at university level

As background let me start by stating what I perceive to be the point of problem books, or to put the matter in perhaps more acceptable way, how I define problem books. A large majority of textbooks ...
1
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3answers
54 views

Find m. $y=e^{mx},m\in\mathbb R,\frac{d^2y}{dx^2}-3\frac{dy}{dx}-4y=0$

If: $$y=e^{mx},m\in\mathbb R$$ Find m if: $$\frac{d^2y}{dx^2}-3\frac{dy}{dx}-4y=0$$ Differentiating and substituting gives: $$m^2e^{mx}-3me^{mx}-4e^{mx}=0$$ Dividing across by $e^{mx}$ and solving ...
3
votes
2answers
104 views

How many positive integers from set $\{1,2…,10^{30}\}$ can't be represented as 2nd, 3rd, or 5th power of some positive integer?

An interesting problem I ran across. My guess is that it can be solved somehow using inclusion-exclusion principle. It would be a fun thing to learn how to do this, so I could use that knowledge in ...
-1
votes
1answer
60 views

Checkers Board Problem

Here we consider a checkerboard expanded to size 12 × 12 instead of the ordinary 8 × 8 checkerboard. a) How many squares on this board contain more than a third of the total number of dark small ...
0
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0answers
24 views

Solving for the growth rate in a growing annuity formula

Firstly, If there is a better forum for this question, please help direct me. I looked in the quantitative finance forum, but someone already asked this and the question was closed because "its too ...
4
votes
2answers
55 views

How can I solve this nice rational equation

I am trying solve this equation $$\dfrac{3x^2 + 4x + 5}{\sqrt{5x^2 + 4x +3}}+\dfrac{8x^2 + 9x + 10}{\sqrt{10x^2 + 9x +8}} = 5.$$ Where $x \in \mathbb{R}$. I knew that $x=-1$ is a given solution. But I ...
6
votes
2answers
530 views

$\text{Let }y=\sqrt{5+\sqrt{5-\sqrt{5+\sqrt{5-…}}}} $, what is the nearest value of $y^2 - y$?

I found this question somewhere and have been unable to solve it. It is a modification of a very common algebra question. $\text{Let }y=\sqrt{5+\sqrt{5-\sqrt{5+\sqrt{5-...}}}} $, what is the ...
-1
votes
1answer
81 views

How to solve $\log_2(x) +3 = \log_3(x+2)$ [closed]

Hi Math Stack Exchange Communities, I am new here. I have a question regarding logarithm solving. Let's say I have this equation: $$\log_2 (x) +3 = \log_3 (x+2)$$ How can I solve this kind of ...
0
votes
2answers
34 views

primitive polynomials and their factorisation

A polynomial with integer coefficients is called primitive if its coefficients are relatively prime. For example, $$3{x^2} + 7x + 9$$ is primitive while $$10{x^2} + 5x + 15$$ is not. (a) Prove that ...
0
votes
1answer
54 views

Prove that any integer greater than or equal to $7$ can be written as a sum of two relatively prime integers, both greater than $1$.

Prove that any integer greater than or equal to $7$ can be written as a sum of two relatively prime integers, both greater than $1$.For example, $22$ and $15$ are relatively prime, and thus $37 = 22+...
-1
votes
1answer
36 views

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 ...
1
vote
1answer
26 views

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 ...
2
votes
3answers
645 views

Solve $x^4+3x+20=0$ by Ferrari's method

Comparing the equation $$x^4+3x+20=0$$ With the equation $$(x^2+\lambda)^2-(mx+n)^2=0$$ we get $m^2=2\lambda,$ $-2mn=3,$ $n^2=\lambda^2-20$ Now, $4m^2n^2=9\Rightarrow 4(2\lambda)(\lambda^2-...
1
vote
1answer
407 views

Solving system if equations containing trigonometric functions with Ti-Nspire

In trying to solve the following system of equation: $20000\times9.81+a\cos b=0$ $a\sin b=6.17\times20000$ Find $a$ and $b$ . It gives me something containing "n2" in bold and I don't know why? $...
0
votes
2answers
35 views

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 ...
-1
votes
1answer
32 views

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 ...
3
votes
0answers
67 views

Does this equation have no solutions?

The question is this : The source from where I got this question was devoid of any answers to it, so I came here, this is how I proceeded : LHS : $((((({(x)^x})^{2x})^{3x})^{....x^2})^2 = (((((x)^...
1
vote
0answers
55 views

Multiple choice excercise with more than one answer correct

Q. Consider the function $$F(z)=\int_{1}^{2} \frac {1}{(x-z)^2}dx, {\text {Im}(z) \gt 0}$$ Then there is a meromorphic function function $G(z)$ on $\Bbb C$ that agrees with $F(z)$ when ${\text {Im}(...
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votes
2answers
58 views

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 ...
1
vote
1answer
55 views

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 ...
0
votes
1answer
48 views

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 ...