Exercise Definition and 578 Threads

By that I mean, are there any weight-lifters on PF? Women/men, squats/curls, anyone pretty into exercise and nutrition?

Dummit and Foote Exercise 1 on page 545 reads as follows: Determine the splitting field and its degree over \mathbb{Q} for x^4 - 2 . ------------------------------------------------------------------------------------------------------ I have started on the solution to this exercise as...

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+...

------------------------------------------------------------------------------------------------ 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...

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]

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...

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)...

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

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...

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...

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...

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...

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...

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...

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...

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)...

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...

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...

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...

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

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...

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...

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!

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...

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...

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...

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...

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...

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...

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.

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

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...

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...

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?

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...

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...

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...

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...

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...

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 ...

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...

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...

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.

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...

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...

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...

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...

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...

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...

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...