What is Exercise: Definition and 576 Discussions

Exercise is any bodily activity that enhances or maintains physical fitness and overall health and wellness.It is performed for various reasons, to aid growth and improve strength, preventing aging, developing muscles and the cardiovascular system, honing athletic skills, weight loss or maintenance, improving health and also for enjoyment. Many individuals choose to exercise outdoors where they can congregate in groups, socialize, and enhance well-being.In terms of health benefits, the amount of recommended exercise depends upon the goal, the type of exercise, and the age of the person. Even doing a small amount of exercise is healthier than doing none.

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  1. A

    Can Conservation of Energy Alone Solve Momentum Problems?

    Homework Statement Homework Equations Conservation of momentum: m1*v1 + m2*v2 = k Conservation of mech. energy 1/2 * m * v^2 + m * g * h = k The Attempt at a Solution Why can't i just use conservation of energy to solve this one? I know that the bullet contains all the kinetic energy before...
  2. A

    Why Is My Calculation for the Time to Drop an Object Incorrect?

    Homework Statement Homework Equations F = ma The Attempt at a Solution The gravity pulls on m with a force Fg: Fg = m*g This force is directly translated into pulling the total mass m+M with an acceleration a: (m+M)*a = Fg <=> a = Fg / (m+M) = m*g / (m+M) with this acceleration, we can...
  3. mcaay

    Lagrange Multipliers in Classical Mechanics - exercise 1

    Homework Statement The skier is skiing without friction down the mountain, being all the time in a specified plane. The skier's altitude y(x) is described as a certain defined function of parameter x, which stands for the horizontal distance of the skier from the initial position. The skier is...
  4. Math Amateur

    MHB Indexed Families of Sets .... Just and Weese .... Exercise 8 ....

    I am reading the book: "Discovering Modern Set Theory. I The Basics" (AMS) by Winfried Just and Martin Weese. I am currently focused on Chapter 1 Pairs, Relations and Functions ... and I am in particular focused on Cartesian Products and indexed families of sets ... I need some help with...
  5. patrickmoloney

    Relation between heat capacities and van der Waals equation

    Homework Statement Find the expression for c_p - c_v for a van-der-waals gas, with the equation of state \Bigg{(}p+\dfrac{a}{V^2}\Bigg{)}(V-b)=RT Homework EquationsThe Attempt at a Solution Basically I've proved c_p - c_v = \Bigg{[} p + \Bigg{(}\dfrac{\partial E}{\partial V}\Bigg{)}_T...
  6. K

    Exercise from Supergravity textbook

    Homework Statement In Ex. 2.4 from textbook Supergravity by Freedman and Van Proeyen one needs to prove the following identity $$ A^\dagger \sigma_\mu A=\sigma_\nu \Lambda^\nu{}_\mu $$ Homework Equations It is easy to prove the other identity in this exercise $$ A\bar{\sigma}_\mu...
  7. T

    MTW Exercise 20.5 -- prove ∇2Φ=4πρ

    Homework Statement I have a couple of issues with this problem, but first of all, I want to find out what I am missing in my attempt to prove ##∇^2Φ = 4πρ## Homework Equations See below The Attempt at a Solution [/B] If ##Φ = \frac {-M}{r}## Then ##Φ_{,i} = \frac {Mx^i}{r^3}## So ##Φ_{,ii}...
  8. Math Amateur

    MHB Ordering on the Set of Real Numbers .... Sohrab, Exercise 2.1.10 (c) ....

    I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with Exercise 2.1.10 Part (c) ... ... Exercise 2.1.10 Part (c) reads as follows:I am unable to make a meaningful start on...
  9. Math Amateur

    MHB Ordering on the Set of Real Numbers .... Sohrab, Exercise 2.1.10 (b) ....

    I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with Exercise 2.1.10 Part (b) ... ... Exercise 2.1.10 Part (b) reads as follows: I am unable to make a meaningful start on...
  10. Math Amateur

    MHB Ordering on the Set of Real Numbers .... Sohrab, Exercise 2.1.10 (1) ....

    Ordering on the Set of Real Numbers ... Sohrab, Exercise 2.1.10 (a) ... I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with Exercise 2.1.10 Part (a) ... ... Exercise 2.1.10...
  11. Math Amateur

    MHB Ordering on the Set of Real Numbers .... Sohrab, Exercise 2.1.12 ....

    I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with Exercise 2.1.12 Part (1) ... ... Exercise 2.1.12 Part (1) reads as follows: I am unable to make a meaningful start on...
  12. N

    Exercise about meiosis and mitosis

    Homework Statement A cell with 16 chromosomes undergoes meiosis. One of the then formed cells (at the end of meiosis 2) gets fertilized by an unknown gamete. The zygote formed from this fertilization undergoes mitosis 3 times. How much DNA-strands will there be at the end, only taking into...
  13. Math Amateur

    MHB Limits of Sequences .... Sohrab Exercise 2.2.7

    I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with a part of Exercise 2.2.7 Part (1) ... ... Exercise 2.2.7 Part (1) reads as follows:I have managed a solution to this...
  14. Math Amateur

    Limits of Sequences .... Sohrab Exercise 2.2.7 ....

    Homework Statement I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with a part of Exercise 2.2.7 Part (1) ... ... Exercise 2.2.7 Part (1) reads as follows: I have managed a...
  15. Math Amateur

    MHB Open and Closed Sets - Sohrab Exercise 2.4.4 - Part 3

    I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with a part of Exercise 2.2.4 Part (3) ... ... Exercise 2.2.4 Part (3) reads as follows: I am unable to make a meaningful...
  16. Math Amateur

    Open and Closed Sets - Sohrab Exercise 2.4.4 - Part 3 ....

    Homework Statement I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with a part of Exercise 2.2.4 Part (3) ... ... Exercise 2.2.4 Part (3) reads as follows: Homework...
  17. Math Amateur

    MHB Closed Sets - Sohrab Exercise 2.2.4 - Part 2

    I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with a part of Exercise 2.2.4 Part (2) ... ... Exercise 2.2.4 Part (2) reads as...
  18. Math Amateur

    MHB Density of the Irrationals in R .... Corollary 2.1.39 and Exercise 2.1.40 .... ....

    I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with Corollary 2.1.39/Exercise 2.1.40 ... Corollary 2.1.39/Exercise 2.1.40 reads as...
  19. Math Amateur

    MHB The Completeness Axiom .... and Sohrab Exercise 2.1.29 ....

    I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with Exercise 2.1.29 ... Exercise 2.1.29 (including the Completeness Axiom) reads as...
  20. Math Amateur

    MHB Some Properties of the Rational Numbers .... Bloch Exercise 1.5.9 (3)

    I am reading Ethan D. Bloch's book: The Real Numbers and Real Analysis ... I am currently focused on Section 1.5: Constructing the Rational Numbers ... I need help with Exercise 1.5.9 (3) ...Exercise 1.5.9 reads as follows: We are at the point in Bloch's book where he has just...
  21. Math Amateur

    MHB Field Extensions - Dummit and Foote - Exercise 13, Section 13.2 .... ....

    I am reading Dummit and Foote, Chapter 13 - Field Theory. I am currently studying Section 13.2 : Algebraic Extensions I need some help with Exercise 13 of Section 13.2 ... ... indeed, I have not been able to make a meaningful start on the problem Exercise 13 of Section 13.2 reads as...
  22. Math Amateur

    Field Extensions - Dummit and Foote - Exercise 13, 13.2 ....

    Homework Statement I am reading Dummit and Foote, Chapter 13 - Field Theory. I am currently studying Section 13.2 : Algebraic Extensions I need some help with Exercise 13 of Section 13.2 ... ... indeed, I have not been able to make a meaningful start on the problem ... ... As indicated...
  23. Math Amateur

    MHB Confirm/Critique Solution to Dummit and Foote, Section 13.2: Exercise 2

    I am unsure of my approach to Exercise 2 Dummit and Foote, Section 13.2 : Algebraic Extensions .. I am therefore posting my solution to the part of the exercise dealing with the polynomial g(x) = x^2 + x + 1 and the field F = \mathbb{F}_2 ... ... Can someone please confirm my solution is...
  24. Math Amateur

    MHB Help with Dummit & Foote Exercise 1, Section 13.2 - Algebraic Extensions

    I need help with Exercise 1 of Dummit and Foote, Section 13.2 : Algebraic Extensions .. I have been unable to make a meaningful start on the problem ... ... Exercise 1 of Dummit and Foote, Section 13.2 reads as follows: I have been unable to make a meaningful start on this problem ...BUT ...
  25. Math Amateur

    Basic Theory of Field Extensions - Exercise from D&F ....

    Homework Statement I am reading Dummit and Foote, Chapter 13 - Field Theory. I am currently studying Section 13.1 : Basic Theory of Field Extensions I need some help with an aspect of Exercise 1 ... ... Exercise 1 reads as follows: Homework Equations Relevant theorems for this exercise...
  26. Math Amateur

    MHB Basic Theory of Field Extensions - Exercise from D&F ....

    I am reading Dummit and Foote, Chapter 13 - Field Theory. I am currently studying Section 13.1 : Basic Theory of Field Extensions I need some help with an aspect of Exercise 1 of Section 13.1 ... ... Exercise 1 reads as follows: My attempt at a solution is as follows:p(x) = x^3 + 9x + 6 is...
  27. S

    Shankar Exercise 1.1.3 (Vector Spaces)

    <Mentor's note: moved from a technical forum, therefore no template.> I'm long out of college and trying to teach myself QM out of Shankar's. I'm trying to understand the reasoning here because I think that I am missing something... 1.1.3 1) Do functions that vanish at the endpoints x=0 and...
  28. TreeLover

    B An exercise related to the mass of the Milky Way, sort of.

    So, in preparation to the Portuguese Astronomy Olympiads, I've stumbled upon this problem (exercise): The sun, which is 8 kpc away from the centre of the Milky Way, has a rotation speed of approximately 220 kms-1 . Whereas a a star that is 15 kpc from the centre of the Galaxy orbits at a speed...
  29. L

    Prof. Shankar's (Phy I) Constant Motion Exercise 3 Question

    Hello everyone, this is my first post, so go easy on me! Thank you to those who are able to help. 1. Homework Statement The problem is taken from Professor Shankar's Fundamentals of Physics exercises (Problem 3). Romeo is at x = 0 m at t = 0 s when he sees Juliet at x = 6 m Romeo begins...
  30. P

    B Exercise for Students: Incorrect Special Relativity Analysis

    Based on an incorrect understanding of special relativity a) Pick a problem from a textbook, and come up with a different answer than the textbook does. Additionally, do one or both of the following: b1) Argue that the textbook answer is wrong and you are right b2) Argue that there is an...
  31. I

    MHB Solving Exercise - Proving f(1 + w) > f(1) + w*f(1)

    Hello :) Help please about the following exercise : The function f(x) comes up and is an convex which gets out from (0,0) and continues into the first quarter. Prove that for all w > 0, takes place f(1 + w) > f(1) + w*f(1). I have been trying for two days to solve it :\ Thanks a lot!
  32. L

    What is the equation of the tangent line to a circle passing through the origin?

    Homework Statement Equation: x^2+y^2-6x-2y+8=0 Find the center and the radius. (Help) : Find the equation of the tangent to the circle above that passes through the beginning of axis O (0,0)The Attempt at a Solution I found the center and radius and i believe the values are : C (3,1) and R...
  33. M

    Coordinate geometry - centroid (SL LONEY exercise problem)

    Homework Statement If G be the centroid of ΔABC and O be any other point, prove that , ## 3(GA^2 + GB^2 + GC^2)=BC^2+CA^2+AB^2## ##and,## ##OA^2 + OB^2 + OC^2 = GA^2.GB^2+GC^2+3GO^2## Homework Equations i m practising from S L LONEY coordinate geometry first chapter ... only the equation...
  34. FallenApple

    Quantifying the effects of physical exercise on cognition

    We all know that there's plenty of evidence showing that exercise does benefit cognition. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3951958/ The real question is how can I actually use this in practice to get real world results. So if I spend 8 hours a day studying a certain subject/trade...
  35. R

    Circle inscribed in a triangle exercise

    Homework Statement In the drawing you can see a circumference inscribed in the triangle ABC (See the picture in the following link). Calculate the value of X https://goo.gl/photos/CAacV2dJbUrywfXv92. The attempt at a solution It seems I found a solution for this exercise with the help of a...
  36. G

    MHB A Strange Probability Exercise

    Hello and I would like to thank you for your space in this website I'm from Greece and i have exams in next days I need some help with an exercise that I can not solve! There is a probability density function with the following type : P(Y=y/X=x)=f(y,x)= {n \choose y}* {x}^{y} *...
  37. B

    Help please with this precipitation exercise

    Knowing Ks=6⋅10−38 for Fe(OH)3 in neutral solutions, calculate the minimum pH of an acidic solution in order to completely dissolve 10 mg of Fe(OH)3. Data: Volume = 0.1 L. I set out the equation for the equilibrium constant. having first calculated the concentration or iron ions (9.35899*10-4...
  38. A

    Comp Sci More efficient way of doing this? (java exercise)

    Homework Statement Given 2 int arrays, a and b, of any length, return a new array with the first element of each array. If either array is length 0, ignore that array. front11([1, 2, 3], [7, 9, 8]) → [1, 7] front11([1], [2]) → [1, 2] front11([1, 7], []) → [1] Homework EquationsThe Attempt at...
  39. R

    What is the distance and mass of a binary star system with given parameters?

    Homework Statement In an visual binary star system,the apparent magnitude of the primary star is m=9.8 and its spectrral type is G2V.The angular semi-major axis is φ=0''.1 and the period of the system is 24y.Find the distance of the system r and the two masses.The Sun's absolute magnitude is...
  40. louisnach

    Exercise involving acoustics physics engineering

    Homework Statement A disturbance signal propagates in a ventilation duct with cross-sectional area A=0,04m2. The fundamental frequency of the disturbance signal is 250Hz and its spectrum consists of odd harmonics only. Choose the appropriate filter options for rejecting this particular...
  41. M

    Leptonic-Hadronic Tensor Multiplication Proof with Rest and Final Target Momenta

    Homework Statement Proof the leptonic-hadronic tensor multiplication, with ##p^\mu=(M,\textbf{0})## and ##p'^\mu=(E',\textbf{p}')## is rest target and final target momentum respectively, and ##k^\mu=(\omega,\textbf{k})##, ##k'\mu=(\omega' ,\textbf{k}')## is momenta of incoming and outgoing...
  42. J

    MHB Help with Practice Exercise: Seeking Guidance

    Hello! My professor distributed this problem as a practice exercise but I'm not sure how to go about it. Can someone point me in the right direction? Thank You!
  43. Kernul

    Tension Exercise on frictionless inclined plane

    Homework Statement A mass ##m_1## is attached to a second mass ##m_2 > m_1## by an Acme (massless, unstretchable) string. ##m_1## sits on a frictionless inclined plane at an angle ##\theta## with the horizontal; ##m_2## is hanging over the high end of the plane, suspended by the taut string...
  44. Kernul

    Simple Tension Exercise: Acceleration and Final Velocity Calculation

    Homework Statement A mass ##m_1## is attached to a second mass ##m_2## by an Acme (massless, unstretchable) string. ##m_1## sits on a frictionless table; ##m_2## is hanging over the ends of a table, suspended by the taut string from an Acme (frictionless, massless) pulley. At time ##t = 0##...
  45. W

    Question about torque (I think) and a gymnastic exercise

    Hi, I'm training an advanced calisthenics exercise called the planche. And I noticed a while ago that doing it with my legs apart (this is called "straddle planche") it's noticeably easier than if I put my legs together (this is called "full planche"). In fact the first is used as a transition...
  46. jamalkoiyess

    Exercising for Better Studying: Benefits & Tips

    Hello PF, I have heard many times and read in many places that good exercise for at least half an hour a day can be a booster to cognitive functions and helps with studying. And my university campus is huge so everyday just getting from one place to another stackes up into a 12000 steps a day of...
  47. Const@ntine

    Second opinion needed at UAV Exercise

    Homework Statement We're driving with a Uav of 80 km/h The duration Δt is 2 h 45 min On a rainy day, our Uav' is 65 km/h If the distance is the same, how much more is the duration of the drive? So, technically we want the result of Dt = Δt' - Δt Homework Equations Uav = Δx / Δt The Attempt at...
  48. M

    MHB Tackling a Difficult Triangle Exercise

    I am having a very difficult time comprehending this exercise and any direction would be appreciated. Feel completely lost! Not necessarily asking for the answer just want to know how to tackle this. This program will output a right triangle based on user specified height triangleHeight and...
  49. 4

    QFT for the Gifted Amateur Exercise 17.1

  50. Basti3018

    Bonding and Deformation exercise

    Homework Statement A Titanium alloy hast he following mechanical properties: ultimate tensile strength = 860 MPa, yield stress = 780 MPa, maximum strain = 15%, Young’s Modulus E = 120 000 MPa, density ρ = 4,5 g/cm3. To what percentage can the material be deformed elastically? Plastically? How...
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