The Challenge (originally known as Road Rules: All Stars, followed by Real World/Road Rules Challenge and occasionally known as The Real World/Road Rules Challenge during this time), is a reality competition show on MTV that is spun off from two of the network's reality shows, The Real World and Road Rules. Originally featuring alumni from these two shows, casting for The Challenge has slowly expanded to include contestants who debuted on The Challenge itself, alumni from other MTV franchises including Are You the One?, Ex on the Beach (Brazil, UK and US), Geordie Shore and from other non-MTV shows. The contestants compete against one another in various extreme challenges to avoid elimination. The winners of the final challenge win the competition and share a large cash prize. The Challenge is currently hosted by T. J. Lavin.
The series premiered on June 1, 1998. The show was originally titled Road Rules: All Stars (in which notable Real World alumni participated in a Road Rules style road-trip). It was renamed Real World/Road Rules Challenge for the 2nd season, then later abridged to simply The Challenge by the show's 19th season.
Since the fourth season, each season has supplied the show with a unique subtitle, such as Rivals. Each season consists of a format and theme whereby the subtitle is derived. The show's most recent season, Double Agents, premiered on December 9, 2020. A new special limited-series, titled The Challenge: All Stars premiered on April 1, 2021 on the Paramount+ streaming service.
As a Bedouin schiek you own twenty-five horses. You want to find the three fastest. You have no clock or other device that measures time. Your racing field is wide enough that five horses can race unimpeded, so you can race five at a time and see how they place. You don't want to abuse your...
TL;DR Summary: How to find integrals of parent functions without any horizontal/vertical shift?
Say you were given the equation :
How would you find : with a calculator that can only add, subtract, multiply, divide
Is there a general formula?
Hello All,
Not sure if this belongs in general math but lets start here and see where it takes us.
In mathematics, a combination is a way of selecting items from a collection where the order of selection does not matter.
As an example , say we have digits 1 to 10. And we want to select 3...
Chatgpt is actually pretty good at generating math problems. It's awful at solving them. I guarantee every question posted here cannot be solved by chatgpt, but maybe can be solved by a human? My plan is to spend a couple minutes getting a question I think it's cool and then posting it here -...
Deadline April 18, 2022
Competition Eligibility at: https://www.drivendata.org/competitions/93/nasa-mars-spectrometry/rules/
HeroX Challenge page: https://www.herox.com/MarsSpectrometry
Brief article:
https://www.space.com/nasa-mars-habitable-herox-competition
Good Luck, and have Fun!
Tom
OK, I'm stuck on a problem implementing this map.
(It'll be built in HTML with JavaScript and CSS and is interactive but that's just context - this is really about map-colouring.)
The function of the map is to help users see at-a-glance what regions/counties of the province are serviced by...
This month's challenges will be my last thread of this kind for a while. Call it a creative break. Therefore, we will have a different format this month. I will post one problem a day, like an advent calendar, only for the entire month. I will try to post the questions as close as possible to...
Hi! I can't solve this. Please someone give me a hint and help? I'm unsure what equation to use. Thank you!🙏🙏🙏
An artillery crew demonstrates its skill by firing a shell at an angle of 49 deg and then lowering the gun barrel and firing a second shell at a smaller angle of 20 deg in such a way...
Summary: Gamma function. Combinatorics. Stochastic. Semisimple Modules. Topological Groups. Metric spaces. Logarithmic inequality. Stochastic. Primes. Approximation theory.
1. (solved by @julian and @benorin ) Let ##f## be a function defined on ##(0,\infty)## such that ##f(x)>0## for all...
To get you started I will derive the Lorentz force law from the QED Lagrangian \begin{equation}\mathcal{L} = \frac{i}{2} \bar{\psi}\gamma^{\mu}D_{\mu}\psi + h.c - \frac{1}{16\pi}F_{\mu\nu}F^{\mu\nu} ,\end{equation}D_{\mu} = \partial_{\mu} + ieA_{\mu}, and then, I let you do the same to a SM-like...
Summary: countability, topological vector spaces, continuity of linear maps, polynomials, finite fields, function theory, calculus
1. Let ##(X,\rho)## be a metric space, and suppose that there exists a sequence ##(f_i)_i## of real-valued continuous functions on ##X## with the property that a...
The phenomenon of diffusion is a transport phenomenon based on the thermal motion of molecules, a process in which molecules are transported from a region of high concentration to a region of low concentration by Brownian motion.
Let's assume that there is a car, the road under the wheels is...
Hello MHB, I saw one question that really tickles my intellectual fancy and because of the limited spare time that I have, I could not say I have solved it already! But, I will most definitely give the question more thought and will post back if I find a good solution to it.
Here goes the...
Summary:: Group Theory, Lie Algebras, Number Theory, Manifolds, Calculus, Topology, Differential Equations.
1. (solved by @Infrared ) Suppose that ##G## is a finite group such that for each subgroup ##H## of ##G## there exists a homomorphism ##\varphi \,:\, G \longrightarrow H## such that...
Hi all
I've long been a fan of the nrich site for maths and in recent years it has started to add a section on physics here. I also like IsaacPhysics although I haven't used it much in the past year so am still trying to get used to the new layout.
I'm looking for other resources along this...
Trying this out for fun, and seeing if people find this stimulating or not. Feedback appreciated! There's only 3 problems, but I hope you'll get a kick out of them. Have fun!
1. Springey Thingies:
Two damped, unforced springs are weakly coupled and obey the following equations of motion...
Summary: Lie algebras, Hölder continuity, gases, permutation groups, coding theory, fractals, harmonic numbers, stochastic, number theory.
1. Let ##\mathcal{D}_N:=\left\{x^n \dfrac{d}{dx},|\,\mathbb{Z}\ni n\geq N\right\}## be a set of linear operators on smooth real functions. For which...
Just for fun! :smile:
Feel free to have a go at any of the problems.
Problem 1
A spherical ball of radius ##a## and centre ##C## rolls on the rough outer surface of a fixed sphere of radius ##b## and centre ##O##. Show that the radial spin ##\boldsymbol{\omega} \cdot \mathbf{c}## is conserved...
The sequence $\{a_n\}$ and $\{b_n\}$ are such that, for every positive integer $n$, $a_n>0,\,b_n>0,\,a_{n+1}=a_n+\dfrac{1}{b_n}$ and $b_{n+1}=b_n+\dfrac{1}{a_n}$. Prove that $a_{50}+b_{50}>20$.
Summary: Differential Equations, Linear Algebra, Topology, Algebraic Geometry, Number Theory, Functional Analysis, Integrals, Hilbert Spaces, Algebraic Topology, Calculus.
1. (solved by @etotheipi ) Let ##T## be a planet's orbital period, ##a## the length of the semi-major axis of its orbit...
Let $x$ be a real number such that $\dfrac{\sin^4 x}{20}+\dfrac{\cos^4 x}{21}=\dfrac{1}{41}$. If the value of $\dfrac{\sin^6 x}{20^3}+\dfrac{\cos^6 x}{21^3}$ can be expressed as $\dfrac{m}{n}$ where $m$ and $n$ are relatively prime positive integers, find the remainder when $m+n$ is divided by 1000.
Summary: Calculus, Measure Theory, Convergence, Infinite Series, Topology, Functional Analysis, Real Numbers, Algebras, Complex Analysis, Group Theory
1. (solved by @Office_Shredder ) Let ##f## be a real, differentiable function such that there is no ##x\in \mathbb{R}## with ##f(x)=0=f'(x)##...
If $x\in \left(0,\,\dfrac{\pi}{2}\right)$, $0\le a \le b$ and $0\le c \le 1$, prove that $\left(\dfrac{c+\cos x}{c+1}\right)^b<\left(\dfrac{\sin x}{x}\right)^a$.
Summary: Linear Programming, Trigonometry, Calculus, PDE, Differential Matrix Equation, Function Theory, Linear Algebra, Irrationality, Group Theory, Ring Theory.
1. (solved by @suremarc , 1 other solutions possible) Let ##A\in \mathbb{M}_{m,n}(\mathbb{R})## and ##b\in \mathbb{R}^m##. Then...
Find all triples $(a,\,b,\,c)$ of real numbers such that the following system holds:
$a+b+c=\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\\a^2+b^2+c^2=\dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{1}{c^2}$
Do you consider writing a program that takes 3 integer inputs and orders them in ascending order (accounting for same numbers) difficult?
You can only use if statements (if, else if, else). I know there is some thing called "sort" that does the tedious work for you but do you find this simple...
Let $x_1,\,x_2,\,\cdots,\,x_{2014}$ be the roots of the equation $x^{2014}+x^{2013}+\cdots+x+1=0$. Evaluate $\displaystyle \sum_{k=1}^{2014} \dfrac{1}{1-x_k}$.
Hi, my question is that what is the main challenge of high energy physics? what is the best theory that maybe explain it and why it would not be accepted?
Summary: Circulation, Number Theory, Differential Geometry, Functional Equation, Group Theory, Infinite Series, Algorithmic Precision, Function Theory, Coin Flips, Combinatorics.
1. (solved by @etotheipi ) Given a vector field
$$
F\, : \,\mathbb{R}^3 \longrightarrow \mathbb{R}^3\, ...
Summary: Diffusion Equation, Sequence Space, Banach Space, Linear Algebra, Quadratic Forms, Population Distribution, Sylow Subgroups, Lotka-Volterra, Ring Theory, Field Extension.
1. Let ##u(x,t)## satisfy the one dimensional diffusion equation ##u_t=Du_{xx}## in a space-time rectangle...
So I am working on a project where I have a tank, which has a volume of electrolyte liquid inside it. This is coupled to a battery which charges it, and gives it energy. I will have a copperband arround it, so i can measure a potential voltage from the electrical field.
So what I need to...
Let $a,\,b$ and $c$ be real numbers such that $\sin a+\sin b+\sin c\ge \dfrac{3}{2}$. Prove that
$\sin \left(a-\dfrac{\pi}{6}\right)+\sin \left(b-\dfrac{\pi}{6}\right)+\sin \left(c-\dfrac{\pi}{6}\right)\ge 0$.
Summary:: Functional Analysis, Algebras, Measure Theory, Differential Geometry, Calculus, Optimization, Algorithm, Integration. Lie Algebras.
1. (solved by @julian ) Let ##(a_n)\subseteq\mathbb{R}## be a sequence of real numbers such that ##a_n \leq n^{-3}## for all ##n\in \mathbb{N}.## Given...
Summary: group theory, number theory, commutative algebra, topology, calculus, linear algebra
Remark: new solution manual (01/20-06/20) attached
https://www.physicsforums.com/threads/solution-manuals-for-the-math-challenges.977057/
1. Given a group ##G## then the intersection of all maximal...
1. (solved by @nuuskur ) Let ##K## be a non-empty compact subset of ##\Bbb{C}##. Construct a bounded operator ##u: H \to H## on some Hilbert space ##H## that has spectrum ##\sigma(u) =K##. (MQ)
2. Let ##f,g:[0,2]\to\mathbb{R}## be continuous functions such that ##f(0)=g(0)=0## and...