# 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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22. ### MHB What is the Minimum Number of Friends Needed for Unique Dinner Invitations?

Hello all, I am trying to solve this one: John has n friends . He wants to invite in each evening (365 days a year) three of his friends for dinner. What should be the size of n, such that it will be possible not to invite the same triplet twice ? What I did was: $\binom{n}{3}\leq 365$...
23. ### About work done through exercise (push ups)

Hello, everyone. I'm not sure if I did this problem right because there's no answer key. I got this question from a high school introductory Physics book. But it's jaded and I accidentally poured coffee on it, so I can't take a picture of the question. I copied it word for word though. This is...
24. ### B Is the Quotient Topology of Real Numbers Homeomorphic to Real Numbers?

Hello! I have two related exercises I need help with 1. Partition the space ##\mathbb{R}## into the interval ##[a,b]##, and singletons disjoint from this interval. The associated equivalence ##\sim## is defined by ##x\sim y## if and only if either##x=y## or ##x,y\in[a,b]##. Then...
25. ### How do I solve this physics exercise (Equilibrium)?

I tried to solve it and I got the following, is it correct?
26. ### How do I solve this physics exercise (moment)?

This is the image of the problem: I tried to solve it and I got the following is it correct? derive and equal to 0 because it is between an angle of 0 and 180° is this statement correct?
27. ### How to solve this balancing exercise? (towing a boat with two ropes)

This is the image of the problem I tried to solve it and I got the following is it correct?
28. ### Calculus Learning Calculus with Stewart: Exercise Sets Explained

Hello PF, After thinking, googling, and reading many threads here, I decided that I'm going to start learning calculus using Stewart. The problem is that the book puts too many exercises after each section, in addition to those at the end of each chapter. What's the difference between these...
29. ### Special relativity - Trivial exercise with spacetime interval

For a observer on Earth, a rocket takes Mike from Earth to Pluto with a speed of 0.82 c for 33.72 yr. Find the space-time interval for the two events such as Mike leaving the Earth and reaching Pluto considering Pluto is at rest relative to Earth for the observer on Earth. I confess that i am...

35. ### Scholarship exam exercise about complex numbers - Can't solve

Hello, I have this (I am solving scholarship exams)math problem and I don't quite know what to do with it , Could You please help? The exercise is about complex numbers and it says: Calculate in the algebraic form(a+bi) I thought on applying substitution since -1=i^2 and z is the real part but...
36. ### Capacitor exercise -- Calculate the force needed to withdraw the dielectric

First, I think that I need to calculate the capacitance. It is ## C=\epsilon_0*\frac{l*w}{d}-x*\frac{w*\epsilon_0}{d}+\epsilon*\frac{x*w}{d} ##. After that I should calculate the potential energy. It is ##U=\frac{1}{2}*C*V^2 ##. After that I should take its gradient to get the force. So ##\vec F...
37. ### Finding Spring Constant & Energy w/ Doubt in Exercise

Summary:: Doubt in a spring exercise Text of the exercise "a mass of ##m = 0.4 \ \text{kg} ## is attached to a spring and it oscillates horizontally with period ##T = 1.57 \text{s}##; the amplitude of the oscillation is ##d = 0.4 \text{m}##. Determine the spring constant, the total energy of...
38. ### MTW Exercise 22.7 -- Calculate the law of local energy conservation for a viscous fluid with heat flow

I've come to a grinding halt with this and I can't see a way forward. Can someone please take a look at what I've done so far and let me know if what I have done is OK and then if it is, give me a hint on how to proceed. First up, Is ## u \cdot \nabla \cdot T = u_\alpha...
39. ### I Physics of exercising and forces felt

Let's imagine an ideal scenario where you're lifting your own weight in its entirety. Let's say a woman weighing 100 lbs. Suppose she's doing an idealized handstand and pushup from that position. So she's lifting 100 lbs. Let's say ideally all of the forces are on her arms only. Do these forces...
40. ### Exercise 16, chapter 3 (Tetrad) in Carroll

My attempt at solution: in tetrad formalism: $$ds^2=e^1e^1+e^2e^2+e^3e^3≡e^ae^a$$ so we can read vielbeins as following: \begin{align} e^1 &=d \psi;\\ e^2 &= \sin \psi \, d\theta;\\ e^3 &= \sin⁡ \psi \,\sin⁡ \theta \, d\phi \end{align} componets of spin connection could be written by using...
41. ### Force diagram for integrated exercise

Hello, Can someone help me out with this one. I solved the exercise but didn't get the right answer so I went searching on internet for solutions. It seems something was wrong with my force-diagram. In my force diagram I had another force included excerted by the wire on the post, since the...
42. ### Group exercise for rotations of regular n-gon objects

The doubt is about B and C. b) n = 4, $C = {I,e^{2\pi/4}} n = 5,$C = {I,e^{2\pi/5}} n = 6, \$C = {I,e^{2\pi/6}} Is this right? c) I am not sure what does he wants...
43. ### Estimator Exercise Homework Solution

Homework Statement:: 1) ##X## is number of success out of ##n## trials where ##p## is the probability of success. 1a) Show that ##\mathrm{E}\left[\hat{P}\right]-p=0##, where ##\hat{P}=X/n##. 1b) Find the standard error of ##\hat{P}##, then give calculate the estimated standard error if there...
44. ### Exponential distribution probability exercise

1) Since I want at least ##6## flights to come within ##2## hours, then the time interval between each should be, at worse, ##2/6=1/3## hours, and the probability is ##P(X\leq1/3)=1-e^{-1/3}##. 2) The probability that at best 5 airplanes arrive at the airport is...
45. ### Interesting exercise: Torque, radiation, momentum and equilibrium

t is Torque I is the inertia moment P is the power c is the constant light speed r is the spot distance to the fiber p is the torsional constant theta is what we want In the equilibrium $$t = 0$$ $$F\Delta T = \frac{E}{c} = \frac{P\Delta T}{c} => *F* = \frac{P}{c} (1)$$ This will be the...
46. ### Understanding Pascal's Law: Why is Force Greater in One Cylinder Than the Other?

Answer : Using Pascal's law, this is my answer : ##\color{blue}{\boxed{\vec F_a = \vec F_c < \vec F_b}}##. Reasoning : Forces ##F_a## and ##F_c## are equal because the pressures required at the two cylinders for case (c) is the same as that required in (a). It doesn't matter how many of those...
47. ### I Inequality from a continuity exercise

I am reading from Courant's book. He gave an example of the continuity of ##f(x)=5x+3## by finding ##\delta=\epsilon/5##. He then said that ##|x-x_0|## does not exceed ##|y-y_0|/5##, but I don't see how he came up with this inequality. I know that ##|x-x_0|<\epsilon/5##, and that...
48. ### MHB Exponential functions (calculator exercise)

Hi there, I have tried to do these questions but I don't understand. Any help would be appreciated!
49. ### Comp Sci PSPice Lab Exercise - Differentiator (Circuit)

Look, this is a weird one, but I really need help. This is the Electronics Laboratory, that is supposed to be hands-on, but with Corona it got cancelled. However, they announced that we'd do it through the internet, had us download PSPice, and now we basically have to try and "translate" the...
50. ### Calculating Exercise: Get Expert Help Here!

Hello everybody is anyone here who knows how I can calculate this exercise?