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. C

    Fibonacci Sequence converge exercise

    Let Fn denote the Fibonacci sequence. un is the sequence given by: un= Fn+1/Fn. Show that mod(un - \phi) \leq\frac{1}{\phi}mod(un-1-\phi) and therefore mod(un - \phi) \leq \frac{1}{\phin-1}[/itex]mod(u1-\phi) and then conclude un converges to \phi I have tried with the identity \phi = 1+...
  2. Math Amateur

    MHB Field Theory - Algebraic Extensions - D&F - Section 13.2 - Exercise 7, page 530

    ------------------------------------------------------------------------------------------------ 7. Prove that \mathbb{Q} ( \sqrt{2} + \sqrt{3} ) = \mathbb{Q} ( \sqrt{2} , \sqrt{3} ). Conclude that [\mathbb{Q} ( \sqrt{2} + \sqrt{3} ) \ : \ \mathbb{Q} ] = 4 . Find an irreducible...
  3. Math Amateur

    MHB Field Theory - Algebrais Extensions - D&F - Section 13.2 - Exercise 4, page 530

    Can someone help me get started on the following problem. Determine the degree over \mathbb{Q} of \ 2 + \sqrt{3} and of 1 + \sqrt[3]{2} + \sqrt[3]{2} Peter [This has also been posted on MHF]
  4. Math Amateur

    MHB Field Theory - Algebrais Extensions - D&F - Section 13.2 - Exercise 2, page 529

    Dummit and Foote Exercise 2, Section 13.2, page 529 reads as follows: ------------------------------------------------------------------------------------------------------------------ 2. Let g(x) = x^2 + x -1 and let h(x) = x^3 - x + 1 . Obtain fields of 4, 8, 9 and 27 elements by...
  5. Math Amateur

    MHB Field Extensions - Dummit and Foote Chapter 13 - Exercise 2, page 519

    Dummit and Foote Chapter 13, Exercise 2, page 519 reads as follows: "Show that x^3 - 2x - 2 is irreducible over \mathbb{Q} and let \theta be a root. Compute (1 + \theta ) ( 1 + \theta + {\theta}^2) and \frac{(1 + \theta )}{ ( 1 + \theta + {\theta}^2)} in \mathbb{Q} (\theta)...
  6. Petrus

    MHB Confused About Exercise 11 Answer Key

    Hello, in exercise 11, I get b is not and w is, but the answer key says b is and w is not...? I don't understand...have I misunderstood or is the answer key wrong? Regrds, |\pi\rangle
  7. Math Amateur

    MHB Field Theory - Dummit and Foote Ch 13 - Exercise 1, page 519

    I am studying Dummit and Foote Chapter 13: Field Theory. Exercise 1 on page 519 reads as follows: =============================================================================== "Show that p(x) = x^3 + 9x + 6 is irreducible in \mathbb{Q}[x] . Let \theta be a root of p(x). Find the...
  8. M

    Classical mechanics exercise, pion decay

    Homework Statement If anyone could help me with this classical mechanics exercise I would be very grateful! The exercise is as follows: The muon (μ) is a particle with mass mμ=207me, with me being the electron mass. The pion (∏) has a mass of m∏=273me. The pion can decay into a muon...
  9. T

    Calculating Probability for Transferred and Selected Balls

    Hello, Homework Statement Suppose we have two boxes, numbered 1 and 2. Box 1 contains 10 white and 6 numbered red balls, while Box 2 contains 8 white and 12 numbered red balls. We take out 2 balls from Box 1 and are transferred in Box 2. Then, we choose 1 ball from Box 2. a) Find the...
  10. tridianprime

    Calculus made easy by Thompson: exercise vii: 1

    Hello, I require some assistance with this problem. It reads: If, u=1/2x^3; v=3(u+u^2); w=1/v^2; Find dw/dx. It's clear that you should use the chain rule so I begin by calculating the derivative for each one. I get v^(-2); 6u+3; and 3/2x^2. I then have to multiply them but this is where...
  11. J

    Exercise on collisions and oscillations

    Hi, I tried to solve this problem myself and I'd like someone to check it :) Thanks already! A ball is rolling towards a block, which is connected to a spring. Assume no friction occurs. The initial velocity of the ball is 10 m/s. The spring constant is k = 5 N/m. Mass of the ball = 5 kg and...
  12. Math Amateur

    MHB Noetherian Rings - Dummit and Foote - Chapter 15 - Exercise 2a

    In Dummit and Foote Chapter 15 Exercise 2(a) on page 668 reads as follows: Show that the following ring is not Noetherian by exhibiting an explicit infinite increasing chain of ideals: - the ring of continuous real valued functions on [0, 1]I would appreciate help on this exercise. Peter...
  13. E

    Can Disjoint Sets Help Prove Subset Relations in Set Theory?

    I am currently reading vellemans how to prove it for the purpose of being able to construct a proof on my own. I would like to carry on this knowledge to also help me out with spivaks calculus So the problem is: Prove that if a and b\c are disjoint, then a\bigcapb\subseteqc. 1.goal...
  14. J

    How Do You Calculate Focal Length in a Two-Lens System?

    Homework Statement An object is placed at 25 cm to the left of a diverging lens. A converging lens with a focal length of 12 cm is located 30 cm to the right of the diverging lens. The two-lenses-system forms a real inverted image 17 cm to the right of the converging lens (see attachment)...
  15. B

    Please help with an exercise in mathematical methods for physicists

    Homework Statement Derive the equation of motion of a particle of mass m and charge q moving in three dimensional space under a Coulombic attraction toward a fixed center. I have the answer for a plane but a i need it for the space Homework Equations Mathematical Methods for...
  16. reenmachine

    Proof Exercise II: Real Numbers and Squares

    Homework Statement Suppose ##x## and ##y## are positive real numbers.If ##x < y## , then ##x^2 < y^2##. Homework Equations Assume ##x<y## with ##x,y \in ℝ^+##.This implies that ##\exists z \in ℝ^+## such that ##x+z=y##.We have ##y^2 = (x+z)^2 = x^2 + 2xz + z^2## , and this proves that if ##x...
  17. D

    Electrochemistry Exercise: Normal Potential of a Reaction

    Homework Statement Calculate the normal potential at 25 °C for the reaction: HA(aq) + e- → A-(aq) + 1/2H2(g) if the dissociation constant of HA is equal to 3.3*10-4 Homework Equations ΔG° = -RTlnK ⇔ -ΔG°/nF = RT/(nF)lnK ⇔ E° = RT/(nF)lnK The Attempt at a Solution Just...
  18. T

    Exercise 2.5 in Misner, Thorne and Wheeler

    If the squared length of a 4-velocity is -1, how can you have a component v0 =0? I've played with equation (2.35) and produced a result of v = γ(-u2, -u1, -u2, -u3), which doesn't have a squared length of -1. Can anyone help out? TerryW
  19. D

    Seemingly simple kinematics exercise

    Homework Statement Rigid body The plane rigid body ABCD shown in the figure has rectangular shape and slides along the orthogonal runners X, Y. The points A and B are always in contact with the ranners. Data: ω=3 rad/s (angular velocity counterclockwise); \Theta=30°; AB=CD=1m; AD=CB=0.5m...
  20. F

    Doubt about exercise with eigenvalues

    Homework Statement Given the endomorphism ϕ in ##\mathbb{E}^4## such that: ϕ(x,y,z,t)=(4x-3z+3t, 4y-3x-3t,-z+t,z-t) find: A)ker(ϕ) B)Im(ϕ) C)eigenvalues and multiplicities D)eigenspaces E)is ϕ self-adjoint or not? explain The Attempt at a Solution I get the associated matrix...
  21. evinda

    MHB Exercise in Probability - balls drawn from a box

    Hey! I need some help at the following exercise... We have a box with balls and 10% of them are red. If we choose at random 20 balls with replacement, which is the probability to pick more than 3 red balls? Thanks in advance!
  22. E

    Computer science student needing help in solving an exercise

    I even don't know if this is the appropriate place to post this questions, while as long as I know this place is considered for research topics and more advanced topics in physics. The point is that I need to write a MATLAB code for specific question, but first of all I need to solve it, and...
  23. F

    Exercise about work and forces

    Homework Statement An object, (mass=15 kg) is thrown up a 30° inclined plane, with initial velocity=4.6 m/s The coefficient of friction is μ=0.34. Find the work done on the object by the normal force, the resultant force, the weight and the friction, from the beginning until it stops (so not...
  24. F

    Help with a mechanical energy exercise

    Homework Statement A spring cannon is used to shot horizontally a marble mall, whose mass is 75g, from a platform located 1.2 m from the ground. If the spring compression is 25 mm, the ball hits the ground 4,2m from the base of the platform. Not taking friction into account, determine...
  25. Z

    MTW Exercise 19.3 last part

    hello In part 8) of this Ex, MTW mentions that the dominant non linear terms must be proportional to the square (M/r)2. The problem is that since I got the value : h00 = A0/r + 6Qijninj/r3 (Qij is the quadrupole moment) and following the translation of coordinates suggested by MTW which is...
  26. C

    Convolution exercise with block diagram and cases

    1. First of all, a block diagram is given where x(t) is the input and y(t) the output.The y(t) is asked when given the h(t) and x(t).We have in parallel h(t) and δ(t-1)*h(t) and those 2 go through a summer (the second one with minus and the first one with a plus) and give y(t). 2. I know from...
  27. F

    Troubles with a Dynamics exercise

    Homework Statement Two carts (1&2) on a flat surface, are pushed by an external force (##\vec{F}##), exerted on 1 (the carts are motionless and touching each other). Consider the two objects as particles and take no notice of any friction. F=12N; mass of 1 (##m_1##)=4,0 kg; mass of 2...
  28. Ackbach

    MHB Metric Space Exercise: Have Fun in an Hour or Two

    To all those who have studied metric spaces, take a look here. It's a fun little exercise, if you have a hour or two.
  29. mathbalarka

    MHB Can we express cos(pi/11) using radicals?

    This is the question I found long ago in another math forum. I thought that it would be a good sweat for everyone in order to find the answer : Find all the closed from of the roots of this solvable quintic 32 x^5 - 16 x^4 - 32 x^3 + 12 x^2 + 6x - 1 = 0
  30. C

    Art of Electronics Exercise 4.3 Operational inverter

    Homework Statement The circuits in Figure 4.14 let you invert or amplify without inversion, by flipping a switch. The voltage gain is either +1 or -1, depending on the switch position. http://tinypic.com/r/2hnql2c/6 http://tinypic.com/r/2hnql2c/6 Homework Equations Gain for the first...
  31. J

    Magnetic Resistance Exercise Bike Theory Question

    I am an electrical engineer disabled in a snow sking accident and am now a quadriplegic. I'd like to design an exercise arm bike and make it magnetically resisted because friction resisted is not conducive to minute changes in resistance. I have a magnetic resisted trainer for a road...
  32. J

    The Evolutionary Necessity of Exercise for Mind and Body Health

    By exercise I mean both physical and mental So are we evolved in such a way that we need to give it some sort of workout to keep it healthy? Why is this? I don't understand why our mind and body need a workout to keep it healthy? Why won't just proper food work? Why exercise is necessary?
  33. P

    Archived 'Kinematics - Vector Derivative' Exercise

    Homework Statement I'm studying for a Mechanics exam and I have a doubt on a 'Kinematics - Vector Derivative' exercise. I don't know how to begin and that's my main problem. Well, this is the exercise: Some data: This mechanical system comprises: - Body 1: A T-shaped arm, with...
  34. R

    Exercise combining Wave and Hydrostatic: Pulley and Submerged Ball

    Homework Statement One end of a horizontal string is attached to the wall, and the other end passes over a pulley. A sphere of an unknown material hangs on the end of the string. The string is vibrating with a frequency of 392 cycles per second. A container of water is raised under the sphere...
  35. K

    Bouncing ball exercise with time of contact with the surface given

    Hello. I have an exercise (not exactly homework, it's a physics contest that we are allowed to solve at home, using all possible help we can find) that goes like this: A ball with mass m = 0,10 kg falls vertically on a horizontal non-movable solid surface. Speed of the ball just before the...
  36. A

    Please correct my mistake in this limits exercise

    Homework Statement we have this function f(x)=1 if \frac{1}{x}\in Z ( aka integer) f(x) = 0 otherwise Prove that limit (as x approach 0) dosen't exist (use the definition of limit - trying to prove that limit as x approchaes 0 and x approchs 0+ will not work here)<-- hint given by the...
  37. tsuwal

    Metric Spaces: Exercise 1.14 from Introduction to Topology (Dover)

    Homework Statement X is a metric and E is a subspace of X (E\subsetX) The boundary ∂E of a set E is defined to be the set of points adherent to both E and the complement of E, ∂E=\overline{E}\cap(\overline{X\E}) (ignore the red color, i can't get it out) Show that E is open if and only...
  38. A

    KVL Exercise: Basic Homework Statement & Solution

    Homework Statement Click on the link https://www.diigo.com/item/image/2sb3i/yjim Homework Equations KVL Law Similar Example : https://www.diigo.com/item/image/2sb3i/orwa The Attempt at a Solution (a) In the left loop : -8-12+VR2 = 0 VR2 = -20 v (b) In the big loop ...
  39. M

    Finding an Idea for Exercise: Let's Explore Vector Spaces!

    Hello friends, I am looking for an idea to my exercise! let's E be a vector space, e_ {i} be a basis of E, b_ {a} an element of E then b_ {a} = b_ {a} ^ {i} e_ {i}. I want to define a family of vectors {t_ {i}}, that lives on E , (how to choose this family already, it must not be a...
  40. E

    Proving that V^{\bot} is a Subspace: Exercise 3.3

    This Exercise 3.3 from Advanced Calculus of Several Variables by C.H. Edwards Jr.: If V is a subspace of \Re^{n}, prove that V^{\bot} is also a subspace. As usual, this is not homework. I am just a struggling hobbyist trying to better myself on my own time. The only progress I've been able...
  41. S

    Avoiding a Wall with Circular Motion: A Physics Exercise

    Should the driver apply brakes or turn the car in a circle of radius 'r' to avoid hitting the wall? This question is in the excercise of circular motion chapter. In this question I don't uderstand from where to start. Some help would be greatly appreciated.
  42. F

    Simple exercise about integrals

    Homework Statement Let ## f: [0, a]## ---> ## \mathbb{R}## be positive and increasing. Prove that the function G, such that: ##G(x):= \frac{1}{x} \int_0^x f(t)dt## ## x\in (0,a)## is increasing. The Attempt at a Solution I know that if the first derivative of a function is positive, that...
  43. F

    Exercise with lagrange and derivatives

    Homework Statement Being a>0 and f:[a,b]--->R continuos and differentiable in (a,b), show that there exists a t ##\in## (a,b) such that: ## \frac{bf(a)-af(b)}{b-a}=f(t)-tf'(f)## The Attempt at a Solution For lagrange's theorem, we have: ## \frac{f(a)-f(b)}{b-a}= -f'(t) ## thought i could...
  44. T

    Exercise on dual / second dual spaces (functional analysis)

    Homework Statement Let (X,\|\cdot\|) be a reflexive Banach space. Let \{T_n\}_{n\in\mathbb{N}} be a sequence of bounded linear operators from X into X such that \lim_{n\to\infty}f(T_nx) exists for all f\in X' and x\in X. Use the Uniform Boundedness Principle (twice) to show that...
  45. C

    Angular momentum - Planet exercise

    Homework Statement Dear all, This is my first post and I need some help. The exercise I am trying to solve is this one: A star has a radius of 6 × 10^8 m and a period of rotation of 30 days. Eventually it becomes a neutron star with a radius of 10^4 m and a period of 0.1 s. If the...
  46. J

    Kibble book exercise about conservative forces

    Homework Statement Kibble book exercise 1, chapter 3. It is the following: Find which of the following forces are conservative, and, for those that are conservative, determine the corresponding potential energy function (a and b are constants, and a is a constant vector) ii) Fx= a*y...
  47. S

    Can I Use Submaximal Data to Estimate VO2 Max for a Conditioned Athlete?

    Homework Statement Alright, so I am a graduating senior studying Exercise science and physiology. I just had what we call "Client Testing" and ran my client (who was a collegiate athlete for the last four years and this year was her first year not competing or training) in the Bruce protocol...
  48. Julio Cesar

    Algebra based physics exercise practice

    1. "The problem statement" is more of a theory question based on physics. This would be my first post to this forum and I'm attempting to follow the rules as best I can. I guess the equation in question is T= 2∏√(m/k) 2. The above mentioned equation. According to my textbook author James...
  49. M

    How can I select ( identify) the exercise which I have solve in Dummit book ?

    How can I select ( identify) the exercise which I have solve in Dummit book ? and avoid these exercises which I have not to solve ? I talk about Identified book " Dummit and Foote "
  50. T

    Chain Rule Exercise: Find dg/dx + dg/dy

    Homework Statement Suppose g(x,y)=f(x-y,y-s) Homework Equations Nothing else The Attempt at a Solution Find dg/dx + dg/dy
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