Initial Definition and 1000 Threads

In a scientific paper (Neural Networks: A Systematic Introduction, page 86) about the Perceptron Algorithm I found: A good initial heuristic is to start with the average of the positive input vectors minus the average of the negative input vectors. In many cases this yields an initial vector...

Homework Statement A 2.45 kg aluminium pan at 155 C is plunged into 3.58 kg of water. If the entropy change of the system is 162 J/k, what is the initial temperature of the water? Homework Equations Q = mcΔT ΔS=mcln(T_2/T_1) Q_water + Q_Aluminium = 0 c water = 4184 J/kg*K c aluminium = 900...

Hi, I am trying to solve an ODE, however, the initial conditions are not known. From PDE examples, which are quite different, I see that some examples have initial conditions given by functions, and not by constants, i.e:: y(0) = x^2 I may have not modeled the problem correctly yet, however, I...

Homework Statement a block B of negligible mass is connected to a particle of mass 1 kg with a non-stretchable string. Now the hanging particle is given a velocity root(8gH) horizontally when system is at rest. Find the initial acceleration of block B. Homework Equations 3. The Attempt at a...

Hi guys. Just wanted to see if I could get a point on this problem I'm having. I'm using a book to learn Python3 and I'm using SublimeText as an editor. The book initially told me to configure Sublime for Python3 by typing this into a blank Sublime file: { "cmd": ["/usr/local/bin/python3"...

Imagine a moving rigid body B1 like a golf clubhead impacts with a stationary elastic body B2 like a golfball. Imagine that the initial velocity of the golfball at time T1 is zero, and the final velocity of the golf ball at time T2 is some value. Imagine that time T1 is when the clubhead first...

Homework Statement I've been asked as a part of some school project to find the Fourier transform, and time evolution of the following initial wavefunctions: 1. ##\Psi(x,0) = Ae^{\frac{-x^2}{2\sigma ^2}}## 2. ##\Psi(x,0) = Be^{\frac{-x^2}{2\sigma ^2}}e^{\frac{ipx}{\hbar}}## What physical...

Dear Every one, Two cars approach an extremely icy four-way perpendicular intersection. Car A travels northward at 12 m/s and car B is traveling eastward. They collide and stick together, traveling at 40.1° north of east. What was the initial velocity of car B (in m/s)? (Enter the magnitude...

Homework Statement A mass hangs from a light string of length 45cm attached at its other end to the ceiling. If the mass is given an initial speed of 5m/s, what is its speed when it reaches point A in its circular path (see Figure 1)? https://imgur.com/a/ERdlD Homework Equations ##E_i = E_f##...

Consider the integral $$ G(x) = \int_0^\infty \frac{e^{-xt}}{1+t}dt$$ which is convergent for x>0. For large x, it is dominated by small t so expand: $$G(x) = \int_0^\infty e^{-xt}\sum_{m=0}^{\infty}(-t)^mdt$$ From here my notes say to take out the summation and write: $$G(x) =...

Homework Statement In an experiment similar to Thomson’s, we use deflecting plates 5 cm in length with an electric field of 1.0×10^4 V/m. Without the magnetic field, we find an angular deflection of 30°, and with a magnetic field of 8×10^-4 T we find no deflection. What is the initial velocity...

I am not sure how to approach a problem involving the friction coefficient when only given initial velocity, final velocity, and distance traveled. I could combine the friction and kinematic equations, but I am only familiar with doing that for one velocity... Here is the specific problem I had...

Homework Statement A power plant operator on a bicycle is pedaling at uniform acceleration of "a", when his initial velocity "u" m/s. After 6.2s, and 9.3s, the bicycle had moved 23.5m & 39.7m respectively. Find the value of "u" & "a". Homework Equations s=ut+1/2at^2The Attempt at a Solution...

I'm asking many questions on inflation, I hope this is the last one... If inflation is correct, our observable Universe would have been a tiny homogeneous patch before inflation started (if it started at all). The length of that initial patch is estimated to be of the order of 1 Hubble length...

The prefix is a bit irrelevant This is on renormalisation. How do they cancel out? Isn't it adding? So the mass experimental = m + (c2correction) so how do you cancel out the m and correction? I'm new to this area (just finished watching lectures by Richard Feynman, specifically a 4 lecture...

Imagine that we have a closed plastic bottle filled with water and then we punch a hole with area A in its cap. How can I find the initial velocity the water will he "fired" with if we squeeze the bottle applying stress S? Assume that we know all about the bottle (moduli, change in volume etc...

Why we take initial velocity of dropped object downwards as 0 and 25m/s when the object is thrown 25m/s upwards ? What is then initial velocity cause when t=0 both object dropping and moving upwards had 0 velocity - in other words when object came to motion at both places it had some velocity?

I'm currently reading class notes from an introductory waves course, written by the professor himself. I'm stuck in the Fourier analysis part, because he gives the formulas for the nth mode amplitude of a standing wave with fixed ends and then states some properties which I can't really make...

Homework Statement A high-energy photon collides with a proton at rest. A neutral pi meson is produced according to the reaction ##\gamma + p \to p + \pi^{0}##. What is the minimum energy the photon must have for this reaction to occur? (The rest mass of a proton is ##938\ \text{MeV/c}^{2}##...

Homework Statement Use the van der waals constant for ##H_2## and ##O_2## to calculate the initial slopes of the plots of compressibility factor Z versus P. Homework EquationsThe Attempt at a Solution Using virial expansion for van der waal gas in terms of ##P## I get ##Z = 1 +...

OK, I understand the idea of neutron bombardment of fissile material causing the nuclei of this material to split, thereby releasing more than 1 neutron, which then go on to bombard other nuclei, such that if more than 1 neutron per reaction ends up causing further reactions, the rate of...

My question here is a simple one. Most tension springs come with an initial tension requirement for spring action. Is it that tension springs are usually used for measuring through some range while compression springs are usually energy absorbers that such a difference is built into them? Also...

Homework Statement A flute player hears four beats per second when she compares her note to a 587 Hz tuning fork (the note D). She can match the frequency of the tuning fork by pulling out the "tuning joint" to lengthen her flute slightly. What was her initial frequency? Homework Equations Not...

Homework Statement I would like to know the initial voltage across the capacitor terminals in the following diagram. Homework Equations when a capacitor is connected to a DC source for a long time, it acts an open circuit. The Attempt at a Solution for t < 0, we get the diagram below and I...

The problem states: Typical chemical fuels yield exhaust speeds of the order of 103 m/s. Let us imagine we had a fuel that gives v0 = 3 × 105 m/s. What initial mass of fuel would the rocket need in order to attain a final velocity of 0.1c for a final mass of 1 ton? I derived the equation in the...

Hello everyone. So I have a test coming up and I am struggling with the concept of figure out what the initial phase or angle of a transfer function is. For instance, consider the following transfer function: L(s) = 4/s(.4s+1)(s+2) So the initial angle for L(s) is -90 degrees. Is there a...

the function y_p is a particular solution to the specified nonhomogeneous equation. Find the unique solution satisfying the equation and the given initial conditions. $y'' + 7y' = 7x$ $y_p=\frac{1}{2}x^2-\frac{1}{7}x$ $y(0)=y'(0)=0$ $r^2+7r=0$ $r=0$ $r=-7$

Hi For a book I'm writing, i try to write a very very very detail proof of self-buckling. I did it almost by taking inspiration of: https://en.wikipedia.org/wiki/Self-buckling But i really really don't get how we arrive to, that when, x=0 as we obviously must have: \dfrac{\mathrm{d}^2...

Homework Statement A uniform rod (mass 'm', length 'l') held horizontally above the ground. It is released from its supports and struck vertically upwards at one end. With what impulse should the rod be struck if it is to return to exactly its starting position and orientation? Homework...

Homework Statement Vo = 5m/s W to the left = 6N Ffriction = 2N F to the left = W - Friction = 4 N m = 1kg g = 10 m/s^2 Ramp length = 10m sin a = 3/5 cos a = 4/5 Homework Equations F = ma Vt ^2 = Vo^2 + 2as Vt = Vo + at The Attempt at a Solution Outside force (1) to cancel acceleration from...

Homework Statement On a particularly hot day at the racetrack, Dale Earnhardt's famous no. 88 Chevy impala (m = 1600 kg ) speeding at 200 mph (89 m/s) blows a gasket and the engine begins to deaccelerate. The car is shifted to neutral and coasts toward the pit lane. Neglecting all sources of...

I'm stuck on this idea. How are initial radioactive isotope quantities assumed in radiometric dating? There are current abundances for all isotopes, but wouldn't these abundances have been different in the past (much higher)? I honestly can't grasp how radioactive isotopes with short half lives...

Homework Statement A 10kg block moving at 1 m/s hits another 10kg stationary block. Those two blocks (now stuck together) collide with another 10kg stationary block. What percent of the original energy is lost after the two collisions? Homework Equations m1v1 + m2v2 = (m1+m2)v3 Kinetic energy...

Homework Statement A softball is hit with an initial velocity of 29 m/s. at an angle of 60 degrees above the horizontal and impacts the top of the outfield fence 5s later. Assuming the initial height of the softball was .5 m above (level) ground, what are the balls horizontal and vertical...

Homework Statement Homework Equations $$\frac{dy}{dx}=f(x)~\rightarrow~dy=f(x)dx~\rightarrow~y=\int f(x)dx$$ $$F=ma,~a=\frac{dv}{dt}$$ The Attempt at a Solution $$-\frac{mgR}{s^2}=mv\left( \frac{dv}{ds} \right)\rightarrow~v^2=\frac{2gR}{s}+C$$ $$v_0(s=R)=\sqrt{2gR}\rightarrow~C=2g(R-1)$$...

Hi! I would like to submit a model glider to a CFD wind tunnel so I can determine what would be its optimum glide ratio and forward speed at this incidence. I am not supposed to know in advance the range of speed this glider can fly (between stall and structural damage), so the speed I will...

Question: If you charge a capacitor circuit and then separate the capacitor, does voltage increase beyond the initial source? It seams counter intuitive that if you plug a 9 Volt battery into two metal plates and pull the plates apart that you'll get massive voltage spikes, but that's what the...

Solve the initial value problem for $y$ as a function of $x$ \begin{align*}\displaystyle \sqrt{16-x^2} \, \frac{dy}{dx}&=1, \, x<4, y(0)=12 \end{align*} assume the first thing to do is $\int$ both sides

Homework Statement Determine the initial acceleration of the 15-kg block if (a) T = 23 N and (b) T = 26N. The system is initially at rest with no slack in the cable, and the mass and friction of the pulleys are negligible. I have attached a picture of the problem. The Attempt at a Solution a)...

Homework Statement [/B] Derive an expression for vc(t) in the circuit of Figure P4.13 and sketch vc(t) to scale versus. I attached a screen shot of the circuit for this problem. time. Homework Equations V = IR V = V0exp(-t/tau) The Attempt at a Solution [/B] I am trying to find the...

Homework Statement A rock is thrown horizontally from a tower point A, and hits the ground 3.5 s later at point B. A line from A to B makes an angle of 50 degrees with the horizontal. Compute the magnitude of a initial velocity u of the rock. The Attempt at a Solution I started looking at the...

Homework Statement A Solve the following initial value problem: ##\frac{dx}{dt}=-x(1-x)## ##x(0)=\frac{3}{2}## B. At what finite time does ##x→∞## Homework EquationsThe Attempt at a Solution ##\frac{dx}{dt}=x(x-1)## ##\frac{dx}{x(x-1)}=dt## Partial fractions...

Homework Statement A fireworks rocket is launched vertically upward, and explodes into two equal-mass pieces at the top of its trajectory. The pieces hit the ground at t1 and t2 seconds after the explosion. What is the rocket’s launch speed? Assume no air resistance. Homework Equations v1 =...

In E6, the product 27 x 27 contains the (conjugate) 27. In SU(3), something similar happens with 3 x 3, which decomposes as 3 + 6. I was wondering, how usual is this? Do we have some lemmas telling when a product N x N is going to "recover" the original N, or its conjugate, inside the sum?

Homework Statement Solve the initial value problem: ##\frac{dx}{dt} = x(2-x)##, ##x(0) = 1## for ##x(t=ln2)##. Homework EquationsThe Attempt at a Solution I moved the right side to the left and multiplied both sides by dt to get: ##\frac{dx}{x(2-x)} = dt## Integrating gave me...

Homework Statement dv/dt = 9.8 - (v/5) , v(0) = 0 (a) The time it must elapse for the objet to reach 98% of its limiting velocity (b) How far does the object fall in the time found in part (a)? Homework Equations (dv/dt)/(9.8-(v/5)) The Attempt at a Solution I'm a little overwhelmed by this...

Homework Statement A stone is dropped from the top of a tall building. It accelerates at a rate of 9.81m/s^2. How long will the stone take to pass a window that is 2.0m high, if the top of the window is 20.0m below the point from which the stone was dropped? I've already solved the initial...

Homework Statement Deriving an s-domain equation for the following inputs a) &b) The Attempt at a Solution I understand how to derive the equation for an input with zero initial conditions (part a) but I'm not sure what to do when there are non-zero initial conditions (part b)

Homework Statement A ball is thrown upwards. Its velocity at 3/5 its max height is 16.0m/s What is its initial velocity? What is its max height? Homework Equations vf^2 = vi^2 -2g(yf-yi) define up as positive The Attempt at a Solution I ran through numerous attempts on paper but can't...

NOTE: The subject should say Inelastic Collision 1. Homework Statement A 980kg sports car collides into the rear end of a 2300kg SUV stopped at a red light. The bumpers lock, the breaks are locked, and the two cards skid forward 2.6m before stopping. The police officer, estimating the...