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.

learn more… | top users | synonyms

2
votes
3answers
74 views

Finding roots of Equation involving trig. functions.

In a problem of classical mechanics, I encounter the following equation: $$\mu \sin^4 \theta + \cos \theta = 0 \qquad \mu > 0 \qquad \frac{\pi}{2} < \theta < \pi,$$ where $\mu$ is some ...
2
votes
2answers
53 views

Determine the angle of 3 drawn lines from each corner of 3 congruent squares

Three squares are drawn next to each other. Three lines are drawn from a corner as illustrated. Determine the sum of the three angles exposed (the exact number of degrees or radians):
1
vote
1answer
34 views

Problem solving: How far is the maximum distance?

The tires located on the front of the car wears out after $25000$ km, while the tires on the back wears out after $15000$ km. How far can you maximum ride with new tires if you can swap the tires ...
-1
votes
5answers
63 views

Christmas problem, the salesman with the nuts [closed]

At the Christmas market, a man was selling nuts in a market stall. The first person bought one nut, the next customer bought two nuts, the next bought four, and so on. That is, every new ...
3
votes
0answers
94 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
votes
2answers
86 views

A coin is tossed if a dice is rolled

I was given this question yesterday. A dice is rolled. If the number is even, a coin is tossed. If it is odd, the dice is rolled exactly once again and results are recorded. Find the probability ...
1
vote
1answer
95 views

Prove that 012345678910111213 etc is not a periodic sequence.

Prove that the sequence $012345678910111213...$ (all non-negative integers written one by one in natural order) is not periodic. I want to know the shortest and most elegant way to prove it. Can you ...
3
votes
0answers
34 views

Green's Theorem with respect to a given polar region.

Using Green's Theorem, compute the counterclockwise circulation $I$ of $\vec{F}=\langle-\sqrt{x^2+y^2},\sqrt{x^2+y^2}\rangle$ around the region defined by the polar coordinate inequalities $7 ...
2
votes
1answer
64 views

Solve matrix vector equation

Let $A$ be a real $n\times n$ matrix and $w,x$ real $n\times 1$ vectors. For fixed $A$ and $w$ solve the following for $x$: $(x^\top A x)w - (x^\top w) (A+A^\top) x = 0$ Any hints? I do not really ...
1
vote
1answer
65 views

Optimal strategy for unlocking Cho'gall (probability intuition question)

Right now there is an event occurring in Heroes of the Storm where a special hero (Cho'gall) is unlocked if you play with another player currently playing that hero. I ran into a bit of an intuition ...
1
vote
1answer
47 views

How do we integrate $xe^{x^2}$ in this differential equation?

Yeah I did try searching how to integrate $e^{x^2}$ and mostly I stumbled upon how a similar but not this function called Gaussian function $e^{-x^2}$ is un-integrable , now I was given to solve a ...
0
votes
0answers
40 views

Solutions of diophantine equation: $s^2 = (ad)^2+ (bc-ad+4ac)^2$

Given diophantine equation: $$s^2 = (ad)^2 + (bc-ad+4ac)^2$$ $s,a,b,c,d$ are all variables. They are all odd. a and b are coprime. c and d are coprime. How do you parametrize all the solutions? ...
1
vote
1answer
72 views

Quartic diophantine equation: $16r^4+112r^3+200r^2-112r+16=s^2$

Given this diophantine equation: $$16r^4+112r^3+200r^2-112r+16=s^2$$ Wolfram alpha says the only solutions are $(r,s)=(0,\pm4)$ How would one prove these are the only solutions? Thanks.
1
vote
0answers
34 views

Proof for a periodic function

I have to solve the following exercise: The function $f : \mathbb{R} \rightarrow \mathbb{R}$ is a periodic function with $P = 2\pi$ so that $f(x) = f(x + 2\pi)$ is true for all $x \in \mathbb{R}$. ...
0
votes
0answers
11 views

Point set in affine euclidian planes

Let $\cal{P}$ be an affine euclidian plane, $F_1$ and $F_2$ two points of $\cal{P}$. We consider the following set: $\cal{H}$ = $\{M \in \mathcal{P} \ |\ |MF_1 - MF_2| = F_1F_2\}$ I need to ...
0
votes
1answer
45 views

How to solve the quadratic form

I am a physicist and I have a problem solving this \begin{equation} Q(x)=\frac{1}{2}(x,Ax)+(b,x)+c \end{equation} In a book it says that: "The minimum of Q lies at $\bar{x}=-A^{-1}b$ and ...
0
votes
1answer
34 views

How can I use the solve() function inside of itself?

I'm trying to use the solve function recursively on my TI-89 calculator. Minimal example to demonstrate the concept: ...
0
votes
1answer
16 views

Mandelbrot set, inequality proof

If I have the relation $z_{n+1} = z_{n}^2 + c$. How can I show that $|z_{n+1}| > k |z_n|$ for some $k>1$, if $|z_n| > |c| > 2$? I have no idea how to proof this, any help will be good.
1
vote
2answers
30 views

There exist fractal with similarity dimension between 0 an 1?

How to prove that there exist a fractal with similarity dimension D = x, where x is between 0 and 1?
5
votes
1answer
96 views

Winning Strategy with Addition to X=0

Problem: Two players play the following game. Initially, X=0. The players take turns adding any number between 1 and 10 (inclusive) to X. The game ends when X reaches 100. The player who reaches 100 ...
1
vote
1answer
25 views

Game Dealing with Multiplication and Winning Strategy

Two players play the following game. Initially X=1. The players take turns multiplying X by any whole number from 2 to 9 (inclusive). The player who first names a number greater than 1000 wins. Which, ...
1
vote
2answers
199 views

Determine if a 4-tuple exists

Starting with 2,0,0,3, we construct the sequence 2,0,0,3,5,8,6,..., where each new digit is the mod10 sum of the preceding four terms. Will the 4-tuple 0,4,0,7 ever occur? Any help is greatly ...
1
vote
1answer
36 views

Working Backwards to Determine Winning Strategy

There are two piles of candy. One pile contains 20 pieces, and the other 21. Two players take turns eating all the candy in one pile and separating the remaining candy into two (not necessarily equal) ...
1
vote
1answer
17 views

Approaching concepts involving graphs in analysis

At least in undergraduate algebra, we can discuss the properties of algebraic structures and their elements without losing generality with notation such as let $G$ be a group and $g\in G$. In using ...
0
votes
1answer
25 views

Proper mathematical description for outer perfect shuffling

I was given the following problem: Consider a pack of $2 n$ cards, numbered from 0 to $2 n − 1$. An outer perfect shuffle is a shuffle of the cards, in which one first splits the pack in two ...
0
votes
1answer
101 views

Clarification on the intended meaning of a probability problem [closed]

I am just wondering if anyone can help with this question: A radio station held a competition where contestants were invited to pick a number from $1$ to $50$. If a contestant picked the ‘winning’ ...
1
vote
2answers
34 views

Prove diophantine equation $S^2+R^2+(r_1-r_2)^2 = 2R(r_1+r_2)$ has at most one solution

Given this diophantine equation: $$S^2+R^2+(r_1-r_2)^2 = 2R(r_1+r_2)$$ $S,r_1,r_2$ are variables. $R$ is a given constant. all values are positive integers. How do I prove that there's at most one ...
0
votes
4answers
59 views

Why is $\left(\frac{1}{2}\right)^{x} = \frac{1}{7}$ the same as saying: $(2)^{x} = 7$

Why is $\left(\frac{1}{2}\right)^{x} = \frac{1}{7}$ the same as saying: $(2)^{x} = 7$ Sorry for the really dumb question but I'd like to see the process of how this is achieved.
0
votes
3answers
41 views

How to solve for exponent when adding fractions raised to unknown exponent?

I'm sure this is probably an extremely simple problem but I'm stuck figuring this out. For example: $(\frac{1}{5})^{x} + (\frac{7}{10})^{x} = 1$ What would be the steps to solve for x?
1
vote
2answers
69 views

Number of Polynomials with Integer Coefficients that are bounded by $x^2$ and $x^4+1$

What is the number of polynomials $p(x)$ with integer coefficients, such that $x^2≤p(x)≤x^4+1$ for all real numbers $x$?
0
votes
0answers
77 views

Find a basis for the hyperplane and use the line to extend the basis for the hyperplane to a basis for $\mathbb{R}^4$

Suppose there is a hyperplane in $\mathbb{R}^4$ that is the solution set to the homogeneous equation $x+2y-3z+w=0$ and a line in $\mathbb{R}^4$ given parametrically by ...
1
vote
3answers
48 views

Finding a basis for the intersection of two vector subspaces.

Suppose: $V_1$ is the subspace of $\mathbb{R}^3$ given by $V_1 = \{(2t-s,t,t+s)|t,s\in\mathbb{R}\}$ and $V_2$ is the subspace of $\mathbb{R}^3$ given by $V_2 = ...
2
votes
2answers
30 views

Sultan's law involving outnumbering

A Sultan wanted to increase the number of women in his country, as compared to the number of men, so that men could have larger harems. (Sorry ladies!) To accomplish this, he proposed the following ...
0
votes
0answers
65 views

Finding a finite dimensional subspace of an infinite vector space.

How could one find a nontrivial example (a subspace which contains more than simply the zero vector) of an infinite dimensional vector space that contains a finite dimensional subspace and prove it's ...
3
votes
1answer
38 views

Determine how many paths exist from $A$ to $B$ that > travel only to the right and up.

In the picture below, you see a schematic of some of the streets in a certain town. Determine how many paths exist from $A$ to $B$ that travel only to the right and up. Two such paths are given ...
4
votes
2answers
71 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
54 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
29 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
73 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
26 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
55 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
24 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
22 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
45 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 ...