Exercise Definition and 578 Threads

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. Math Amateur

    MHB Gödel Numbering - Exercise 3.2.5 - Chiswell and Hodges

    I am reading the book Mathematical Logic by Ian Chiswell and Wilfred Hodges ... and am currently focused on Chapter 3: Propositional Logic ... I need help with Exercise 3.2.5 which reads as follows:Can someone please help me with reconstructing the formula of the Gödel number that is given...
  2. Math Amateur

    Thread: Artinian Modules - Cohn Exercise 3, Section 2.2, page 65

    I am reading P.M. Cohn's book: Introduction to Ring Theory (Springer Undergraduate Mathematics Series) ... ... I am currently focused on Section 2.2: Chain Conditions ... which deals with Artinian and Noetherian rings and modules ... ... I need help to get started on Exercise 3, Section 2.2...
  3. Math Amateur

    MHB Artinian Modules - Cohn Exercise 3, Section 2.2, page 65

    I am reading P.M. Cohn's book: Introduction to Ring Theory (Springer Undergraduate Mathematics Series) ... ... I am currently focused on Section 2.2: Chain Conditions ... which deals with Artinian and Noetherian rings and modules ... ... I need help to get started on Exercise 3, Section 2.2...
  4. E

    How to Calculate Grounding Resistance with Two Electrodes?

    Hi! I can't find the method of the solution to this question, it was an exercise on an exam.. There are two grounding electrodes buried in the ground. We make three measurments. First, we measure the first electrode's grounding resistance, which is: 6 ohms. Then, the second's: 7 ohms. Then the...
  5. P

    Solving an Exercise Involving Particle P Moving Along the X-Axis

    Hello. I have the following exercise, and I would like you to say to me if I have it right and how to proceed: "A particle P moves with constant speed v along the X axis of a reference system O, being x0 = 0 the position in t = 0. Describe the movement on another system O' with the same...
  6. sa1988

    My first exercise on Group Theory

    EDIT: I've just realized this is the 'Calculus and beyond' subforum - I saw 'beyond' and thought, "Well I've done all my calculus, and now I'm doing group theory, so this thread must go here!". But now I realize it surely belongs somewhere else. Sorry about that. Mods feel free to shift it to...
  7. KostasV

    I need your opinions on Zettili's solution of an exercise

    1. Homework Statement (Uploaded photo from Zettili Quantum Mechanics - Chapter 3 - Solved problems 3.4 and 3.5) Check at problem 3.4 the relation that he gives between operator A and state φn. Now check the relation that he uses in problem 3.5 between A and φn again. They are different while on...
  8. Kernul

    Calculate Velocity & Tension of 100g Block on 50cm Wire

    Homework Statement A block of 100g is attached to a wire inexstensible long 50cm. The block is left with a null initial velocity when the wire form an angle of 90° with the vertical. Calculate the velocity of the block and the tension of the wire when the block is at the position of...
  9. Ackbach

    MHB Solve Exercise 1.6 in Greenberg's Euclidean Geometry: Betweenness and Lying On

    Exercise 1.6 in Greenberg's Euclidean and Non-Euclidean Geometries: "Betweenness" and "Lying On" Undefined terms: point, line, lie on, between, and congruent. Postulate I. For every point $P$ and for every point $A$ not equal to $P$ there exists a unique line $\ell$ that passes through $P$ and...
  10. B

    [check exercise] Perturbation theory

    I have solved this exercise, but I'm not sure that it is good. Please, can you check it? A lot of thanks! 1. Homework Statement The hamiltonian is ##H_0=\epsilon |1><1|+5/2 \epsilon (|2><2|+|3><3|)## The perturbation is given by ##\Delta(|2><3|+|3><2|)## Discuss the degeneration of H0. Using...
  11. F

    Engineering Exercise about Thevenin equivalent circuit

    Hi all :) I'm trying to figure out the Thevenin equivalent of this circuit: I start by switching off every source and calculating the equivalent resistance: RTh = RN = (6 + 14) || 5 = 4 Ω Then I proceed with finding the voltage at 2. I note that the nodes between 1 and 2 form a...
  12. Math Amateur

    MHB Is that correct so far ... ?Yes, that is correct. Good job!

    I am trying to gain an understanding of the basics of elementary algebraic geometry and am reading Dummit and Foote Chapter 15: Commutative Rings and Algebraic Geometry ... At present I am focused on Section 15.1 Noetherian Rings and Affine Algebraic Sets ... ... I need help to get...
  13. Math Amateur

    MHB Elementary Algebraic Geometry: Dummit & Foote Ch.15, Ex.24 Coordinate Ring

    I am trying to gain an understanding of the basics of elementary algebraic geometry and am reading Dummit and Foote Chapter 15: Commutative Rings and Algebraic Geometry ... At present I am focused on Section 15.1 Noetherian Rings and Affine Algebraic Sets ... ... I need help to get...
  14. Math Amateur

    MHB Elementary Algebraic Geometry: Exercise 23, Sect 15.1 Dummit & Foote

    I am trying to gain an understanding of the basics of elementary algebraic geometry and am reading Dummit and Foote Chapter 15: Commutative Rings and Algebraic Geometry ... At present I am focused on Section 15.1 Noetherian Rings and Affine Algebraic Sets ... ... I need help to get...
  15. Kernul

    How Can I Find the Initial Velocity of a Ball Based on Angle and Window Height?

    Homework Statement A boy kicks a ball with an initial velocity v0 that forms an angle of 30° with the x. The ball, at the culmination of the trajectory, enters a window at a height of 9.8 m. Find the module of the initial velocity and the time used by the ball to reach the window. Also find the...
  16. S

    Exercise on Poisson distribution

    Homework Statement An experimenter measures the counting rate from a radioactive source as 10,150 counts in 100 minutes. Without changing any of the conditions, the experimenter counts for one minute. There is a probability of about 15 percent that the number of counts recorded will be fewer...
  17. J

    Gym exercise equipment analysis

    I need some help on the direction to go with this problem. This is a workarm on a leg extension machine and there's 300 pounds (max) coming from the weight stack attached via a cable on the cam. I need to find the total force exterted on this system to double check my results on an analysis...
  18. Math Amateur

    Affine Algebraic Curves - Kunz - Exercise 1 - Chapter 1

    I am reading Ernst Kunz book, "Introduction to Plane Algebraic Curves" I need help with Exercise 1, Chapter 1 ... Indeed ... I am a bit overwhelmed by this problem .. Exercise 1 reads as follows: Hope someone can help ... ...To give a feel for the context and notation I am providing the...
  19. Math Amateur

    MHB Affine Algebraic Curves - Kunz - Exercise 1 - Chapter 1

    I am reading Ernst Kunz book, "Introduction to Plane Algebraic Curves" I need help with Exercise 1, Chapter 1 ... Indeed ... I am a bit overwhelmed by this problem .. Exercise 1 reads as follows:https://www.physicsforums.com/attachments/4549Hope someone can help ... ...To give a feel for the...
  20. N

    Abstract Algebra: Dummit and Foote Exercise

    This isn't homework, I'm just trying to refresh my memory on cyclic groups. My question is, in this problem solution, how does ##{\sigma_i}^m=1## follow from ##\sigma_i## being disjoint?
  21. Kernul

    Is there something wrong with this code for checking and merging two vectors?

    The exercise is this: Assigned two vectors (V1 and V2) of integers. Check if within one of the two vectors (VY) there is a sequence of values in consecutive positions such that every element is included between two successive elements of a sequence of elements of the other vector (VX): VX [ i ]...
  22. C

    [Question]How to find lower bound for this exercise

    Homework Statement Apply the Central limit theorem to evaluate approximately the lower bound for the probability that the difference between the relative frequency p^ and p is less than 0.01, if n = 4500 Homework Equations This exercise do not give me the confidence interval? What function...
  23. shanepitts

    A simple astrophysics rough estimate exercise

    Homework Statement Homework Equations (mv2)/r=(GMm)/r2 --------(1) r≈8kpc≈2.47×1020m v≈220kms-1 The Attempt at a Solution Using equation (1) and solving for M I got M=(v2r)/G=(4.84×10102.47×1020)/6.67×10-11 M=1.79×1041 kg does this answer seem correct? P.S. This is not a homework...
  24. G

    Challenging exercise about polynomials

    Homework Statement If ##P,Q## are polynomials of ##\mathbb{Z}[X]##, and ##p## is a prime number that divides all the coefficients of ##PQ##, show that ##p## divides the coefficients of ##P## or the coefficients of ##Q##. Homework Equations ##c_n = \sum_{k=0}^{n} a_k b_{n-k} ## is the n-th...
  25. marcus

    Ceres/Mars as manufacturing outposts (analytic exercise)

    Note from mfb: This thread is a fork of our Dawn and Ceres thread, as we got multiple posts about potential missions to Mars and Ceres and further exploration. End note.Part of astrophysics is being able to calculate---things like the altitude of a geosynchronous satellite, for example. Even if...
  26. M

    What is a magnetic field? (fun mental exercise)

    Think of a charged particle moving parallel to a wire carrying a constant current. The magnetic field caused by the constant current exerts a force on the moving particle (say it moves towards the wire). Now, think of the same thing from a different reference plane. Think of a still particle...
  27. D

    MHB How Do Jane and Terry Divide 10.35 Miles of Treadmill Exercise in 3.5 Hours?

    This problem has me stumped Jane and Terry used two different treadmills to exercise. The total distance waled between them was 10.35 miles. Jane waled at a pace of 4.9 per hour and Terry walked the pace of 4.5 per hour. Their total time as 3.5 hours. This is how I would set it up, but not...
  28. Z

    How can I solve for a vector in a tensor equation involving dot products?

    Homework Statement I'm currently trying to work through some issues I'm having with tensor and vector analysis. I have an equation of the form $$\textbf{a} \bullet \textbf{b} = \textbf{c} \bullet \textbf{d}$$ where all quantities here are vectors. I want to solve for ##\textbf{b}## by finding...
  29. SmokeyMTNJim

    Exercise: who does more work weight lifter/marathon runner

    I was trying to identify which athlete does more work per rep/stride. I am trying to understand how a marathon runner can run sub 6 minute miles under aerobic conditions. To me this seems like a high intensity to I wanted to figure out who was doing more work, producing more force, or if you can...
  30. S

    Calculus by Apostol Exercise 2.8 number 30

    Homework Statement Homework EquationsThe Attempt at a Solution I have no idea on how to start proving this, but I know the theorem is stating that the integral of a translated periodic function is the same with the integral of the periodic function without translation, is this concept...
  31. J

    Can Euler-Lagrange Equations Explain Mirages?

    Homework Statement On very hot days there sometimes can be a mirage seen hovering as you drive. Very close to the ground there is a temperature gradient which makes the refraction index rises with the height. Can we explain the mirage with it? Which unit do you need to extremalise? Writer the...
  32. B

    Exercise proofreading about Fourier Series

    Homework Statement I have solved the following exercise, but I have obtained the half of the correct result! I can't understand where is the problem... ##f(x)=\begin {cases} 0, x \in[-\pi, 0]\\cos x, x \in[0, \pi]\end{cases}## 1) Find the Fourier Series (base: ##{\frac{1}{\sqrt{2 \pi}}...
  33. J

    Can pull up exercise increase height?

    Can pull up exercise (at a younger age, say, before 15 years old) increase height? My guess is yes, since weight lifting could decrease height (Or that is another myth?) If yes, by how much?
  34. B

    How to Solve a Convolution Exercise with Step-by-Step Instructions

    Homework Statement I have found the following exercise just solved, but I haven't understood some steps... f(t)=\begin {cases}1, t\in [-1,1] \\ 0, t\not \in [-1,1]\end{cases} We have to do the convolution f*f=\int^{+\infty}_{-\infty}f(\tau)f(\tau)f(t- \tau) d\tau=\int^{+1}_{-1}f(t- \tau)...
  35. S

    Calculus by Apostol Exercise 1.7

    Homework Statement A point (x,y) in the plane is called a lattice point if both coordinates x and y are integers. Let P be a polygon whose vertices are lattice points. The area of P is I + B/2 - 1, where I denotes the number of lattice points inside the polygon and B denotes the number on the...
  36. Math Amateur

    MHB Simple Exercise Involving the Algebra of Limits

    I need some help in understanding the reasoning and analysis in the solution to Exercise 4.5 in Robert C. Wrede and Murray Spiegel's (W&S) book: "Advanced Calculus" (Schaum's Outlines Series). Exercise 4.5 in W&S reads as follows: https://www.physicsforums.com/attachments/3918 The...
  37. Rampart

    How to Find Ibq and Vceq in a Common Base Amplifier?

    Homework Statement In the following common base circuit,β=100.If Vcc=15V, VEE=4V,RE=3.3KΩ, Rc=7,1KΩ find the Ibq and Vceq(they are related to the dc values of the Q point) Homework EquationsThe Attempt at a Solution Well ah...i mainly want to ask some things.However knowing that i must...
  38. T

    Physics based Calculus exercise books

    While still at an ongoing journey with calculus, would there be any book recommendations that will allow to apply calculus in physics/astrophysics based scenarios? Should one too complete a course in multrivariable calculus and get very comfortable with vectors before doing such problems, or is...
  39. itsjorge

    What is the gas pressure in state 3 if the efficiency is 0.40?

    Homework Statement An engine works with an ideal diatomic gas (γ=1.40) according to a thermodynamic cycle consisting in four processes that take the gas successively through the states 1, 2, 3 and 4. The processes 1 -> 2 and 3 -> 4 take place at constant pressure and the two other processes are...
  40. Coffee_

    The use of cross section in a particle collision exercise.

    1. Situation: I have no specific exercise in mind but just the general form. ''A beam of protons is colliding with a plate of a given particle density ##\rho## and thickness ##l##. The cross section is ##\sigma##. What should the thickness of the plate be such that the intensity of the outgoing...
  41. Luca_Mantani

    What Is the General Solution to the Dirac Field Theory Equation?

    Homework Statement [/B] This is an excercise that was given by my professor in a previous test: Consider the equation: $$ \displaystyle{\not} p =\gamma^\mu p_\mu= m$$ where the identity matrix has been omitted in the second member. Find its most general solution. Homework Equations The...
  42. J

    Calculating Probabilities in a Double-Elimination Tournament

    Homework Statement In Game 6 of a 6-team double-elimination tournament, Team 1, the top-ranked team, faces the loser of a previous game involving Team 2, the second-ranked team, against one of either Team 3, the third-ranked team or Team 6, the sixth-ranked team. This exercise tests the limits...
  43. E

    At What Distance Will a 10 km/s Bullet Fired Vertically from Earth Arrive?

    If a bullet is fired vertically from the surface of the Earth with initial velocity v = 10 km / s, ignoring air resistance, at which distance h from the center of the Earth would arrive? (The radius of the Earth is RT = 6360 km, and the mass of the Earth MT = 5.98x10^24 kg) I used the formula...
  44. burnst14

    Mouse Jumps Onto An Exercise Wheel

    Homework Statement The vertical exercise wheel in a mouse cage is initially at rest, but can turn without friction around a horizontal axis through the center of the wheel. The wheel has a moment of inertia I=0.0004kg m2 and radius R = 0.06m An extremely smart pet mouse of mass m = 0.03 kg runs...
  45. F

    Kinetic energy physics exercise

    I'm going through a physics exercise at high school level. A ball is dropped through a slide and when it reaches the bottom of the slide it will travel horizontally. Assuming there is no energy loss due to friction or air resistance draw a velocity time graph. I tried working it out, the answer...
  46. T

    Why Does Functional F Not Yield Expected Results in Merzbacher QM Exercise 9.8?

    I think I almost get there, but something's not right, and need your help. if F(ψa,ψb) is a complex valued (scalar) functional of the two variable vectors ψa and ψb with linearity properties. Show that F can be represented as an inner product F(ψa,ψb)=(ψa, Aψb), for every ψa,ψb and the previous...
  47. K

    Where can I find more challenging excercises?

    Ehi guys. I noticed that the excercises of my book are quite 'scalar', that is none of them require to use explicitly some vector properties, they're all funny special case. I want something more exciting. Do you have any suggestion? Thank you very much! Bye bye topic: kinematics, dynamic of...
  48. thegreengineer

    Derivative as a rate of change exercise

    Homework Statement A police car is parked 50 feet away from a wall. The police car siren spins at 30 revolutions per minute. What is the velocity the light moves through the wall when the beam forms angles of: a) α= 30°, b) α=60°, and c) α=70°? This is the diagram...
  49. PcumP_Ravenclaw

    Exercise on (ir)rational numbers

    Dear all, I have done question 1 of exercise 2.1 from the book Alan F beardon, Abstract Algebra and Geometry. Please answer some of my doubts. Q1. a) Show that √(2/3) is irrational. b) Use the prime factorization of integers to show that if √p/q is rational, where p and q are...
  50. T

    Help with MTW Exercise 6.9 - Yes/No Answer

    Can anyone help with the attached problem. A simple yes or no answer only is required, but if you want to point me in a particular direction...
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