Exercise Definition and 543 Threads

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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?

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 ]...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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}}...

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?

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)...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

I am reading An Introduction to Rings and Modules With K-Theory in View by A.J. Berrick and M.E. Keating (B&K). In Chapter2: Direct Sums and Short Exact Sequences we find Exercise 2.1.6 part (iii). I need some help to get started on this exercise. Exercise 2.1.6 reads as follows: I am...

I've been doing some long bike rides (50+ miles) on routes which include long (several miles) of low to moderate grades, or short distances of 3 to 8% grades. I've experience what smelled like ammonia or amines while exhaling through my nostrils, or while drinking and breathing heavily. I've...

Homework Statement Hi! My problem : There is given substance for which (dV/dT)_p =ap^2,where V-volume,T-temperature,p-pressure,a-const. How much the entropy S will increase if T=const and pressure changes from p1 to p2?Homework Equations The Attempt at a Solution So 1) Mathematically the...

our teacher gave us this exercise but no one could solve it. he said : I hang the weight of 100 g in a spring. it elongates 1 cm. then i hang a 200 g in the spring. it elongates 2cm . what is the original length of the spring? i tried solving it but it just didn't go right.. how do i solve it??

Homework Statement Homework Equations V= iR Kirchoff's law for voltage The Attempt at a Solution On the left-most part of the circuit , I did use KVL (voltage law) and I ended up with Vs = i0 (R1+R2) which basically boils down to i0(2R) since R1 = R2 =R3 ... I'm not even...

Homework Statement We have Vz=6.8 V and Iz=5 mA,rz=20 Ohm,Izk=0.2 mA, R=200 Ohm and the source V= 9 volt a)Find the output voltage when we have the input voltage with the nominal value of 9 Volt. b)Find for the nominal value of the voltage,which is the maximum load current for which the...

I am trying to capitalize the first letter of every word in a sentence. Example. "hey what's up" would be "Hey What's Up". here is my code but nothing is changing the sentence. I thought everything was right. public static String cap(String aString) { String[] sentence = aString.split("...

Exercise 2.1.6 (i) of Berrick and Keating's book An Introduction to Rings and Modules reads as follows:Let $$M = M_1 \oplus M_2$$, an internal sum of right $$R$$-modules, and let $$\{ \sigma_1 , \sigma_2, \pi_1 , \pi_2 \}$$ be the corresponding set of inclusions and projections. Given an...