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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4
votes
2answers
70 views

What is the value of $n$ for which $n!=2^{25} \times 3^{13} \times 5^6 \times 7^4 \times 11^2 \times 13^2 \times 17 \times 19 \times 23 $

What is the value of $n$ for which $n!=2^{25} \times 3^{13} \times 5^6 \times 7^4 \times 11^2 \times 13^2 \times 17 \times 19 \times 23 $ The way I am approaching this problem is just to find the ...
0
votes
3answers
53 views

Let $V = \text{span}(\{\vec{v}_1,\vec{v}_2,\vec{v}_3\})$ be a $3$ dimensional subspace of $\mathbb{R}^4$. Prove that $V^{\perp}$ has dimension $1$.

Let $V = \text{span}(\{\vec{v}_1,\vec{v}_2,\vec{v}_3\})$ be a $3$ dimensional subspace of $\mathbb{R}^4$. Prove that the orthogonal complement of $V$ has dimension $1$ My approach: Set $A = ...
5
votes
1answer
51 views

Show that all the cards contain the same number.

Natural numbers from $1$ to $99$ (not necessarily distinct) are written on $99$ cards. It is given that the sum of the numbers on any subset of cards (including the set of all cards) is not divisible ...
1
vote
0answers
22 views

Finding positive integers with the same digits [duplicate]

Find the three smallest positive integers $K$ (two digits or greater) with the following properties: 1) $K=\frac{(n)(n+1)}{2}$ for some $n$ 2) Each digit of $K$ is the same. I was able ...
0
votes
2answers
34 views

Can we deduce anything given the equation of a curve and the fact that it has symmetry with $y=x$?

Question: The line $y=x$ is a line of symmetry to the curve with equation $$y=\frac{px+q}{rx+s}$$ where $p,q,r,s \neq 0$. Which of the following must be true? $p+s=0$ $p+q=0$ ...
-1
votes
1answer
10 views

One of the values of $z$ verifying

How to solve this equation of argument of complex number knowing that one of the values of $z$ verifying $\left|z+1\right|^2+\left|z-1\right|^2=2\left|z+i\right|^2$
0
votes
1answer
28 views

Finding the dimension of a vector space, and determing if it is the subspace of a parent space.

How could one determine the dimension of a some space which is the subspace of a particular vector space (or consider it a subspace of a particular space to begin with), say for instance given some ...
1
vote
1answer
66 views

Find a basis for the subspace determined by the given line.

Find a basis for the subspace of $\mathbb{R}^3$ determined by the line $x=-3t .\ y=2t ,\ z=t$. It seems to me that a basis for this subspace would be simply $\{t(-3,2,1)\}$, but could it really ...
0
votes
0answers
24 views

Determination of Bond prices

Two 1000 dollar face value bonds are both redeemable at par, with the first having a redemption date 3 years prior to the redemption date of the second. Both are bought to yield 11 percent convertible ...
0
votes
0answers
49 views

How to determine whether expression is positive or negative?

Given expressions $|x - 3 + y|$ and $|x + 3 + y|$ how can I determine, whether are those positive or negative, and determine their value in the intervals of: $y < -x - 3$ $y \in [-x - 3, 3 - x)$ ...
0
votes
1answer
23 views

Can a certain board be covered in Tetrominoes

Prove that a $15x8$ board cannot be covered by $2$ L-tetrominoes and $28$ skew tetrominoes. This is a coloring proof and I have tried a variety of colorings, from stripe colorings to other unique ...
0
votes
1answer
21 views

Diophantine equations: $x_1y_1+x_2y_2 = x_3y_3+x_4y_4$

Given 3 diophantine equations: $$x_1y_1+x_2y_2=x_3y_3+x_4y_4$$ and $$x_1+x_2 = x_3+x_4$$ and $$y_1+y_2 = y_3+y_4$$ We're interested in solutions to this system of equations when all variables ...
1
vote
2answers
42 views

A coin is tossed three times. Given that at least one head appears, what is the probability that exactly two will appear?

The "at least" confuses me. But I am assuming one head will appear. Making P(first head) = 1. Correct answer: 3/7 I start with the formula: P(A and B) = P(A) • P(B|A) Fitting the conditions into ...
0
votes
0answers
15 views

Class-participation problem modeled with game theory

I'm taking a class and the teacher has set up a system of class-participation to encourage us, the students, to, well, participate more actively. The system is as follows: each student is given 20 ...
0
votes
1answer
22 views

Creating a structure to show 2 formulas do not satisfy a 3rd using first order logic

A = (∀x∀y∀z(P xy → (P yz → P xz))) B = (∀x∀y(P xy → (P yx → x = y))) C = (∀x∃yP xy) → (∃y∀xP xy) I want to show that {A, B} does not imply C by constructing a structure. What I've done so far is ...
1
vote
1answer
38 views

Struggling a bit with Combinatorics Order in which to do this question?

n P 4 = 84 n C 2 Now I'm not even sure if the 84 is multiplying by the N choose 2? I don't understand. Ive done all the practice questions my teacher gave me and this came up on the homework and Ive ...
1
vote
0answers
65 views

Distribution of sum of $n$ i.i.d. symmetric Pareto distributed random variables

Let $X$ be a random variable which follows the symmetric Pareto distribution. For a fix, real parameter set $\alpha > 0$ and $L>0$, its PDF is defined as $$ p_X(x) = \left\{ ...
2
votes
1answer
60 views

If $x^2-3x+9=0$, can we say $(x+3)(x^2-3x+9)$ is also $0$ hence $x^3=-27$?

I was solving this question If $\dfrac x3 + \dfrac 3x = 1$ then find the value of $x^3$. I solved it as. Cube both sides and substitute $x^3$ with $t$, $$ \dfrac{t}{27} + \dfrac{27}{t}=-2$$ ...
0
votes
0answers
16 views

Uniqueness of a solution

Let $f_i(x_1, x_2, ..., x_n)$ for $i=1,...,n$, be real-valued differentiable functions with the following properties: 1) $f_i(x_1, x_2, ..., x_n)=0$ if $x_i=0$. 2) $f_i(x_1, x_2, ..., x_n)=1$ if ...
5
votes
1answer
69 views

How can I improve my problem solving abilities so that I stop missing the obvious?

I'm a generally good math problem solver. I get decent scores on contests, top of my class in math courses, and have a pretty wide array of knowledge from which to relate concepts in order to solve ...
3
votes
1answer
37 views

Does this seemingly elementary question require König's theorem?

Question Let $f:\;\mathbb{R}\to\mathbb{N}$ and let $X_n$ be the set of reals mapped to the integer $n$. Show that for some $n,\;X_n$ has cardinality of the continuum. This is straightforward if we ...
1
vote
1answer
23 views

Determining outstanding balance on a loan

A loan of $17,000$ dollars is to be repaid in annual installments of $2,100$ dollars, the first due in one year, followed by a final smaller payment. If the effective rate of interest is $8.8$ ...
0
votes
0answers
33 views

Bases & Congruence's decimal problem

This is a question for a university assignment I have. I'm not after more of a "how-to". ...
0
votes
0answers
45 views

How to mathematically calculate this?

I want to know "energy price" to conduct panel data analysis. But I cannot find it on database of all web-sites. On all database, enegy price is unavailable. And according to my reseach, it's said ...
0
votes
2answers
32 views

Prove one group is the subgroup of another under a specific condition

Suppose that $H$ and $K$ are subgroups of a group $G$. Now for some $g_1,g_2 \in G$, $Hg_1 \subset Kg_2$. Prove that $H \subset K$ I tried to write the condition given as $H \subset Kg_2g_1^{-1}$ ...
0
votes
1answer
73 views

Basic probability question, choosing between two options for every stage

Suppose that two players are playing a game, players select between two choices: Scenario 1: player $1$ chooses option $1$ with probability $60\%$, option $2$ with $40\%$ player $2$ chooses option ...
2
votes
0answers
32 views

Known classic problem or not?

There is a set of positive whole numbers without null. I have to find the minimal number of subsets of the original set so, that the the sum of two numbers in a subset can't be the value of a number ...
0
votes
1answer
28 views

Solving problems involving powers

How to reach from $1+𝐸𝐴𝑅= [1+𝑇×𝐴𝑃𝑅]^1/​t $ the power is (1/T) to $$APR = \frac{\ (1+EAR)^T - 1 \ }{T}$$ $$1+EAR=[1+T\times APR]^{1/T}\\ APR=\frac {(1+EAR)^T-1}T$$ and the same goes ...
1
vote
1answer
77 views

Solutions of diophantine eq: $x^4-2x^3y+2xy^3+y^4=2s^2$

I'm examining solutions of this diophantine equation: $$x^4-2x^3y+2xy^3+y^4=2s^2$$ It looks like all the solutions are of the form $(x,y,s) = (t,\pm t, \pm t^2)$ where $t$ is any integer. But how do ...
0
votes
1answer
125 views

Who is a mathematician? [closed]

My first question in Math SE. Basically the question itself, who is a mathematician? Is it someone who solves problems on his leisure time or as a part of a job or even as a hobby? who researches ...
2
votes
1answer
62 views

Diophantine equation: $y^2=1+12x+16x^2$

The diophantine equation $$y^2=1+12x+16x^2$$ only has solutions $x=0, y=\pm1$ according to wolfram alpha. How would I go about proving these are the only solutions? Similarly the equation ...
0
votes
1answer
30 views

Showing S is a subset of A by structural induction.

I have a problem similar to: Let S defined recursively by (1) 5 ∈ S and (2) if s ∈ S and t ∈ S, then st ∈ S. Let A = {5^i| i ∈ Z+}. prove that S ⊆ A by structural induction. I've only done ...
0
votes
1answer
47 views

Series expansion at infinity

I am trying to find to generalize the limit that involves all rational functions such as $\sum_{n=0}^{l}\frac{{a}_{n}{x}^{n}}{{b}_{n}{x}^{n}}$. I believe the best way of generalizing all of them is ...
0
votes
0answers
13 views

Potential Reward Average

I'll try to get straight to the point. I'll be offering a reward system as part of a marketing scheme and it will be for a select amount of users who opt-in. What will be calculated is the overall ...
0
votes
1answer
22 views

Invariance Dealing with Infected Squares

Twelve 1x1 cells of a 10x10 square are infected. Two cells are called neighbors if they share at least one vertex (thus an inner cell has 8 neighbors). In one unit time, the cells with at least four ...
5
votes
3answers
138 views

Is it possible for extremely ingenious but elementary proofs for famous problems to exist?

As Erdős put it, "Mathematics is not ready for such problems." when faced with the great conjecture of Collatz. So is it impossible altogether for simple but ingenious proofs for famous problems ...
0
votes
0answers
37 views

Optimality criterion for unconstrained convex optimization problems

Consider a general convex optimization problem: \begin{equation*} \begin{aligned} & \underset{x}{\text{minimize}} & & f_0(x) \\ & \text{subject to} & & f_i(x) \leq 0, \; i = 1, ...
0
votes
3answers
42 views

Odd and even coins

Two friends are playing a coin game. You need to give to your friend, one coin that has an even value and another coin that has an odd value. For example, a dime would be the even value ...
0
votes
1answer
22 views

Invariance problem dealing with the sums of units digits

We may write all the digits from 1 to 9 in a row in any order we like, and then we write plus signs between some digits (as many plus signs as we like). Finally, we evaluate the obtained expression. ...
0
votes
1answer
24 views

Into how many regions do they divide the plane? [duplicate]

Suppose that n lines in general position are given in a plane. (General position means that no two lines are parallel, and no three lines have a common point.) Into how many regions do they divide the ...
0
votes
1answer
20 views

Annuities-calculating interest

Janet receives a $ 10,000 life insurance benefit. If she uses the proceeds to buy an n-year annuity immediate, the annual payout will be 1613.36. If a 2n-year annuity due is purchased, the annual ...
1
vote
1answer
62 views

28 soldiers puzzle

A leader ordered his 28 soldiers to protect the castle , the castle has 4 walls or sides. He wants 9 soldiers to guard each wall. How can the be possible ?
0
votes
0answers
20 views

Calculate time needed to transmit 10 packets over 3 links

So very easy problem, but it really bugs my head and I am not sure if I am solving it in a right way. Imagine we have Sender and Destination endpoints and two routers in between: ...
1
vote
3answers
69 views

Is there an exact answer to this equation?

$$\frac{1}{x} +\ln(x)\ln(\ln x)=1$$ The solution to this equation is approximately $x \sim 5.13425\ldots$ but is there an exact answer?
0
votes
2answers
58 views

Finding the general term of a sequence (if there's any)

I would like to know if it's possible to find an expression for the following sequence $\;\{a_n\},\;n=0,\,1,\,2,\,3,\,\dots\;$ $1, 3 , 7, 13, 21...$ Someone would like to explain me what I have to ...
0
votes
1answer
34 views

Let F0 = 0, F1 = 1, F2 = 1, . . ., F99 be the first 100 Fibonacci numbers (recall that Fn = Fn−1 + Fn−2 for n ≥ 2).

Let F0 = 0, F1 = 1, F2 = 1, . . ., F99 be the first 100 Fibonacci numbers (recall that Fn = Fn−1 + Fn−2 for n ≥ 2). how many of them are divisible by 3
1
vote
1answer
25 views

How does this textbook compute the Nash Equilibrium of the two person zero sum game?

In Tamer Basar Noncooperative Game theory pg $33$ there is a $2 \times 3$ game (zero sum game) $A = \begin{bmatrix} 1 & 3 & 0 \\ 6 & 2 & 7 \end{bmatrix}$ (each element is a cost, ...
0
votes
1answer
143 views

Prove inequality $\sqrt{\frac{2a}{b+a}} + \sqrt{\frac{2b}{c+b}} + \sqrt{\frac{2c}{a+c}} \leq 3$ [duplicate]

How to prove the following inequality : $$ \sqrt{\frac{2a}{b+a}} + \sqrt{\frac{2b}{c+b}} + \sqrt{\frac{2c}{a+c}} \leq 3 $$ with $a>0,\ b>0$ and $c>0$.
0
votes
2answers
50 views

Mathematical Induction Problem solving [duplicate]

$1^3$ + $2^3$ + $2^3$ + ... + $n^3$ = ($1 + 2 + 3 + ... + n)^2$ I start with $P(1)$ and get $1 = 1$. Then I do it with $P(n+1)$ and I get stuck. $1^3$ + $2^3$ + $2^3$ + ... + $n^3$ + $(n+1)^3$ = ...
0
votes
1answer
68 views

Solve differential equation relating to air cannons

I made my own air cannon at home and would like to determine its launch velocity. I worked out the following differential equation: $$\frac{d^2}{dt^2} x(t) = \frac{A}{m} \left(\frac{P_0V_0}{V_0 + ...