# What is 2017: Definition and 169 Discussions

2017 (MMXVII) was a common year starting on Sunday of the Gregorian calendar, the 2017th year of the Common Era (CE) and Anno Domini (AD) designations, the 17th year of the 3rd millennium, the 17th year of the 21st century, and the 8th year of the 2010s decade.
2017 was designated as International Year of Sustainable Tourism for Development by the United Nations General Assembly.

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1. ### Ball hitting racket - Momentum Question (ENGAA 2017)

Please scroll-sown to Question 52: https://www.undergraduate.study.cam.ac.uk/files/publications/engineering_s1_qp_2017.pdf The correct answer is 'B'. This is the working I did: F = (change in momentum) / (change in time) change in momentum = mv - mu, where v = final velocity and u = initial...
2. ### Ball's motion after one bounce off the ground - SUVAT Question (ENGAA 2017)

Please scroll-down to the end (Question 54): https://www.undergraduate.study.cam.ac.uk/files/publications/engineering_s1_qp_2017.pdf I have also been referring to unofficial worked solutions (http://www.engineeringadmissionsassessment.com/2017-solutions.html), but I didn't understand how it...
3. ### Friction between a mass and a conveyor belt (ENGAA 2017)

Please scroll-down to Q50: https://www.undergraduate.study.cam.ac.uk/files/publications/engineering_s1_qp_2017.pdf The correct answer is 'B', or 'mgsin(Θ)'. I put 'E', or 'μmgcos(Θ)'. There are unofficial worked solutions which I have been referring to when I have attempted the question and...
4. ### Ghost in the Shell (1995 & 2017)

I watched Ghost in the Shell 1995 the other night. It was cartoon. At first I was hesitant being just cartoon. But found it so intriguing, then I rewatched again the 2017 live version staring Johansson Scarlett. I noticed the 1995 cartoon version was more well-received (Tomato score 96%) than...
5. ### Trouble Connecting to Default Instance in SQL Server 2017 (Win10)

Hi All, Trying to do some querying in my (local) SQL Server. Thing is I am having trouble accessing my default instance, though no trouble accessing the one named instance I have. I have been to Stack Overflow , read up, posted a few things, then told to read again after it all failed. I get a...
6. ### 2017 Article on Qubit Flipflops

I found this interesting article on theory work done to create qubit flipflops that can be adjusted via electric fields making them easier to integrate into existing computing systems...
7. ### I 2 second delay at the merger of two neutron stars in August 2017

Some new papers appeared about processes in the collision of the two neutron stars, measured in August 2017. Is now more clear, why 2 second delay between gamma rays and gravitational waves happens?
8. ### Is Dec. '17 work paid Jan. '18 taxable for 2017?

If I worked Dec. 2017 and didn't get paid until January 2018, is that taxable income for a 2017 tax filing? Anyone know? Thanks.
9. ### Science Facts Discovered in 2017

A reference article to other articles on science facts that were discovered this year 2017. Some were theorized and finally proven, others were discovered totally by chance. Which ones most impressed you? http://www.sciencealert.com/23-science-facts-we-didn-t-know-at-the-start-of-2017
10. ### MHB Is the Putnam Solution for Var(fg) Inequality Correct?

Here is this week's POTW: ----- For any continuous real-valued function $f$ defined on the interval $[0,1]$, let \begin{gather*} \mu(f) = \int_0^1 f(x)\,dx, \, \mathrm{Var}(f) = \int_0^1 (f(x) - \mu(f))^2\,dx, \\ M(f) = \max_{0 \leq x \leq 1} \left| f(x) \right|. \end{gather*} Show that if $f$...
11. ### MHB Movie Reviews of 2017: My Take on the Year's Hits and Flops

I go to the movies quite a bit. I've always loved the experience and find it's fun to go into a new world for 1-3 hours. Usually I have at least one movie that gets me super excited each year, but this year was a big flop unfortunately. These are the ones I saw accord to my purchase history. I...
12. ### MHB Prove Inequality: (x^2+y^2+z^2)(x+y+z) + x^3+y^3+z^3 > 4(xy+yz+zx)

Here is this week's POTW: ----- Prove that $(x^2+ y^2 + z^2)(x + y + z) + x^3+ y^3+ z^3> 4(xy + yz + zx)$ for all $x,\,y,\,z > 1$. ----- Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to...
13. ### MHB What is the Riemannian distance between two points in the open unit disk?

Happy Holidays, everyone! Here is this week's POTW: ----- Consider the open unit disk $\Bbb D\subset \Bbb C$ with Riemannian metric $ds^2 = \dfrac{\lvert dz\rvert^2}{(1 - \lvert z\rvert^2)^2}$. Find a formula for the (Riemannian) distance between two points in $\Bbb D$, and use it to find the...
14. ### MHB Integers as Roots of Polynomial: Find Possible Values | POTW #293 Dec 19th, 2017

Here is this week's POTW: ----- Suppose $n \ge 0$ and all the roots of $x^3+ax+4-(2\times 2016^n)=0$ are integers. Find all possible values of $a$. ----- Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out...
15. ### MHB Problem Of The Week # 293 - Dec 14, 2017

Here is this week's POTW: ----- What is the greatest common divisor of the set of numbers $\left\{16^n+10n-1 \;|\; n=1, 2, 3, \dots\right\}?$ ----- Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to...
16. ### MHB How Can You Minimize This Complex Fraction Given the Constraints?

Here is this week's POTW: ----- Minimize \frac{2x^3+1}{4y(x-y)} given x\ge -\frac{1}{2} and \frac{x}{y}>1. ----- Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to...
17. ### MHB How Is the Infinite Product of a Recurrence Sequence Solved?

Here is this week's POTW: ----- Let $a_0 = \dfrac52$ and $a_k = a_{k-1}^2 - 2$ for $k \geq 1$. Compute $\displaystyle\prod_{k=0}^\infty \left(1 - \frac{1}{a_k} \right)$ in closed form. ----- Remember to read the...
18. ### MHB What is the solution to this week's POTW?

Here is this week's POTW: ----- If $\phi : A \to B$ is a local homeomorphism from a compact space $A$ to a connected Hausdorff space $B$, show that $\phi$ is surjective and the fibers of $\phi$ over the points of $B$ are finite sets. ----- Remember to read the...
19. ### MHB What Is the Minimum Value of This Complex Fractional Expression?

Here is this week's POTW: ----- Find the minimum value of $\dfrac{1}{a-b}+\dfrac{1}{b-c}+\dfrac{1}{a-c}$ for all reals $a>b>c$, given $(a-b)(b-c)(a-c)=17$. ----- Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to...
20. ### MHB How many pages are in the first 5 chapters of the novel?

Here is this week's POTW: ----- A novel has 6 chapters. As usual, starting from the first page of the first chapter, the pages of the novel are numbered 1, 2, 3, 4, . . . . Also, each chapter begins on a new page. The last chapter is the longest and the page numbers of its pages add up to...
21. ### Bali Mount Agung Eruption 2017

Some experts are saying the big eruption could happen tonight! :nb):frown: http://www.cnn.com/2017/11/27/asia/bali-volcano-agung-eruption/index.html Here is a live video feed
22. ### MHB Can You Solve the Existence of $x$ in this Trigonometric Equation?

Here is this week's POTW: ----- Prove that there exists $x\in \Bbb{N}$, where $1\le x \le 89$ such that $\sqrt{3}\tan x^\circ-1=\sec 20^\circ$. ----- Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how...
23. ### MHB Problem Of The Week # 290 - Nov 24, 2017

Happy Thanksgiving, for those of you in the USA! Here is this week's POTW (not a Putnam this week!): ----- If $a_0\ge a_1 \ge a_2\ge \cdots\ge a_n\ge 0,$ prove that any root $r$ of the polynomial $$P(z)\equiv a_0 z^n+a_1 z^{n-1}+\cdots+a_n$$ satisfies $|r|\le 1$; i.e., all the roots lie...
24. ### MHB What is the maximal function of a finite Borel measure on $\Bbb R^n$?

Here is this week's POTW: ----- Suppose $\mu$ is a finite Borel measure on $\Bbb R^n$. Define the maximal function of $\mu$ by $$\mathcal{M}\mu(x) = \sup_{0 < r < \infty} \frac{\mu(B(x;r))}{m(B(x;r))}\quad (x\in \Bbb R^n)$$ Here, $m$ denotes the Lebesgue measure on $\Bbb R^n$. Show that if...
25. ### NASA’s new visualization of the 2017 hurricane season

"How do you observe the invisible currents of the atmosphere? By studying the swirling, billowing loads of sand, sea salt and smoke that winds carry. A new simulation created by scientists at NASA’s Goddard Space Flight Center in Greenbelt, Md., reveals just how far around the globe such aerosol...
26. ### MHB Can You Solve High School POTW #289's Trigonometric and Polynomial Equation?

Hi MHB, The High School POTW should be number 289 this week, but due to the fact that I was a bit late carrying out my duty over several weeks, I fell behind a week, and so I will make it up by posting two POTWs this week. I sincerely apologize for this, and I hope our members can take up...
27. ### MHB Solution to Quadratic Expression with Three Distinct Real Numbers

Here is this week's POTW: ----- Fill in the blank: If $a,\,b$ and $c$ are three distinct real numbers, then the quadratic expression \frac{(x-b)(x-c)}{(a-b)(a-c)}+\frac{(x-c)(x-a)}{(b-c)(b-a)}+\frac{(x-a)(x-b)}{(c-a)(c-b)} is identically equal to _____. ----- Remember to read the...
28. ### MHB This proves the claim.

Here is this week's POTW: ----- Prove that every nonzero coefficient of the Taylor series of $\left(1 - x + x^2\right) e^x$ about $x=0$ is a rational number whose numerator (in lowest terms) is either $1$ or a prime number. ----- Remember to read the...
29. ### Relativity Wheeler, Thorne and Misner Gravitation Book Revised in 2017

The classic book on General Relativity by Wheeler, Thorne and Misner is now out: https://www.amazon.com/gp/product/0691177791/?tag=pfamazon01-20 I got to use preprints of the book while doing an independent study of General Relativity in 1973. It brings back fond memories of being tortured by...
30. ### MHB How Do You Solve POTW #287 Involving Integer Equations?

Here is this week's POTW: ----- Positive integers $a,\,b, \,c, \,d$, and $e$ satisfy the equations $(a + 1)(3bc + 1) = d + 3e + 1\\ (b + 1)(3ca + 1) = 3d + e + 13\\ (c + 1)(3ab + 1) = 4(26 − d − e) − 1$ Evaluate $d^2 + e^2$. ----- Remember to read the...
31. ### MHB Problem Of The Week # 288 - Nov 09, 2017

Here is this week's POTW: ----- Let $f$ be a polynomial with positive integer coefficients. Prove that if $n$ is a positive integer, then $f(n)$ divides $f(f(n)+1)$ if and only if $n=1$. Assume $f$ is non-constant. ----- Remember to read the...
32. ### MHB Tricky Trigonometry: Evaluating Cosine Cubes Without a Calculator

Here is this week's POTW: ----- Without using a calculator, evaluate $\cos^3 \left(\dfrac{2\pi}{7}\right)+\cos^3 \left(\dfrac{4\pi}{7}\right)+\cos^3 \left(\dfrac{8\pi}{7}\right)$. ----- Remember to read the...
33. ### MHB How Does Morphism Affect Prime Spectra and Module Support?

Here is this week's POTW: ----- Given commutative rings with unity $R$ and $S$, let $\phi : R \to S$ be a morphism of rings. It induces a morphism $\phi^* : \operatorname{Spec}(S) \to \operatorname{Spec}(R)$ of prime spectra such that $\phi^*(\mathfrak{q}) = \phi^{-1}(\mathfrak{q})$ for all...
34. ### MHB Hence the original sum equals $\pi^2/16$.

Here is this week's POTW: ----- For each positive integer $k$, let $A(k)$ be the number of odd divisors of $k$ in the interval $[1, \sqrt{2k}\,)$. Evaluate $\sum_{k=1}^\infty (-1)^{k-1} \frac{A(k)}{k}.$ ----- Remember to read the...
35. ### MHB How Do You Prove the Root Constraints of a Quadratic Equation Given a Summation?

Here is this week's POTW: ----- One of the roots of the quadratic equation $x^2-kx+2n=0$ is equals to $\dfrac{1}{\sqrt{1}}+\dfrac{1}{\sqrt{2}}+\cdots+\dfrac{1}{\sqrt{n}}$, where $n$ is a positive integer. Prove that $2\sqrt{2n} \le k \le 3\sqrt{n}$. ----- Remember to read the...
36. ### MHB Problem Of The Week # 286 - Oct 24, 2017

Here is this week's POTW: ----- Show that for each positive integer $n$, all the roots of the polynomial $\sum_{k=0}^n 2^{k(n-k)} x^k$ are real numbers. ----- Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to...
37. ### MHB What are the real numbers that give positive integer roots for a cubic equation?

Hello, MHB Community! (Wave) anemone has asked me to fill in for her this week. :) Here is this week's POTW: Find all real numbers $k$ that give the three roots of the cubic equation $5x^3-5(k+1)x^2+(71k-1)x-(66k-1)=0$ are positive integers. Remember to read the...
38. ### MHB How Does Grouping Terms Simplify the Infinite Series in This Week's POTW?

Here is this week's POTW: ----- For any positive integer $n$, let $\langle n\rangle$ denote the closest integer to $\sqrt{n}$. Evaluate $\sum_{n=1}^\infty \frac{2^{\langle n\rangle}+2^{-\langle n\rangle}}{2^n}.$ ----- Remember to read the...
39. ### MHB What is the norm of a linear operator in $\mathscr{L}^p(0, \infty)$?

Here is this week's POTW: ----- Find the norm of the linear operator $T: \mathscr{L}^p(0, \infty) \to \mathscr{L}^p(0, \infty)$ defined by the equation $$(Tf)(x) = \frac{1}{x}\int_0^x f(t)\, dt$$ Here it is assumed that $1 < p < \infty$. Note: The space $\mathscr{L}^p(0,\infty)$ consists of...
40. ### MHB Can You Prove This Reciprocal Sequence Sum is Less Than 4?

Here is this week's POTW: ----- Consider the sequence $\{a_k\}_{k\ge 1}$ is defined by $a_1=1$, $a_2=\dfrac{1}{2}$ and $a_{k+2}=a_k+\dfrac{a_{k+1}}{2}+\dfrac{1}{4a_ka_{k+1}}$ for $k\ge 1.$ Prove that $\dfrac{1}{a_1a_3}+\dfrac{1}{a_2a_4}+\dfrac{1}{a_3a_5}+\cdots+\dfrac{1}{a_{98}a_{100}}<4$...
41. ### B Einstein Proven Right by 2017 Eclipse? Investigation

Did the 2017 eclipse prove Einstein was right or the jury is still out? I can't find any references to the new measurements and what they proved (or did not).
42. ### MHB Why is $X$ connected if $A$ and $X/A$ are connected in a topological group?

Here is this week's POTW: ----- Let $X$ be a topological group; let $A$ be a subgroup of $X$ such that $A$ and $X/A$ are connected. Show that $X$ is connected. ----- Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines...
43. ### What's the interest level in M6+ seismic events based on response rates?

another couple of M6 events from my seismograph M 6.3 - 36km SSW of Putre, Chile M 6.7 - Bouvet Island region on my seismogram below, the P arrival for the M6.3, Chile event is approx 0652UT the P arrival for the M6.7, Bouvet Is event is approx 1907UT cheers Dave
44. ### 8 Oct 2017, 3 significant Earthquakes

3 respectable events within 10 hours M 6.1 - 153km NW of Pangai, Tonga M 6.3 - Balleny Islands region M 6.6 - 60km E of Buldir Island, Alaska The first 2 events are on this map. The third event, the M 6.6 in the western Aleutian Islands, is the other end of the pacific from me. The largest...
45. ### MHB Can You Prove the Minimum Value of a Trig Expression Given Certain Conditions?

Here is this week's POTW: ----- Let that $a,\, b,\,c$ be three angles with $0<a,\,b,\,c<90^\circ$ that satisfy $\sin a+\sin b+\sin c=1$. Prove that $\tan^2 a+\tan^2 b+\tan^2 c \ge \dfrac{3}{8}$ ----- Remember to read the...
46. ### MHB How Do You Solve the Alternating Series in POTW #283?

Ackbach has asked me to step in for him for a while. Here is this week's POTW: ----- Evaluate the sum of the alternating series $$\sum\limits_{n = 1}^\infty \frac{(-1)^{n-1}}{n^4}$$ ----- Remember to read the...
47. ### Gravitational Waves: The 2017 Nobel Prize Surprise?

Big surprise? awarded to Rainer Weiss, Barry Barish and Kip Thorne for their detection of gravitational waves. https://phys.org/news/2017-10-nobel-physics-prize-awarded-scientists.html
48. ### What breakthrough technology might be awarded the 2017 Nobel Prize in Chemistry?

The 2017 Nobel Prize in Chemistry is being announced tomorrow! I really can't wait to see what it will be awarded for, because it is always interesting and sometimes unexpected. I think it might be awarded for works on nanotechnology, because it is currently a hot field. It might be displayed...
49. ### 2017 Nobel Prize in Physiology or Medicine

This morning, the 2017 Nobel Prize in Physiology or Medicine was awarded to Jeffrey C. Hall, Michael Rosbash and Michael W. Young for their discoveries of molecular mechanisms controlling the circadian rhythm. https://www.nobelprize.org/nobel_prizes/medicine/laureates/2017/press.html
50. ### Is arXiv down, or is it just me? (Sun 1 Oct 2017)

Can't get to some papers. No response at all from the site. Most other sites are working for me. Anyone else have insight?