Maximum Definition and 1000 Threads

Hello! (Wave) We are given the function $g: \mathbb{R}^{2016} \to \mathbb{R}$ with $g(y)=\sqrt{10 y_1^2 + 10^2 y_2^2+ \dots+ 10^{2016} y_{2016}^2} where y=(y_1, \dots, y_{2016})$. I have found that the maximum of this function over the set $\{ y=(y_1, \dots, y_{2016}) \in \mathbb{R}^{2016}...

Homework Statement Homework Equations number of alpha hydrogens= number of no bond resonating structures The Attempt at a Solution option 1: 3 option 2: 6 option 3: 8 option 4: 9 So the answer should be 4, right?

Homework Statement 2 boxes containing the same number of moles of 2 ideal identical gases with the same adiabatic index (this is given as gamma), at the same initial temperature Ti but with different volumes, V1 and V2 are brought together. Find the maximum mechanical work that can be obtained...

Homework Statement Find the maximal power on resistor R. Homework Equations [/B] The Attempt at a Solution I used Thevenin theorem. I found that Z_t=5+j10 , and U_t= 10-j10. The maximum power happens in this case when $$R=|Z_t| = 5 \sqrt{5}$$ , and I get that P=6.18, while the answer is...

Hi - Can anyone help me out with a question. The answer seems obvious, but maybe so obvious that I'm jumping to wrong conclusions! Just been reading Guy Martin's book "When your dead, your dead" (good read by the way) and one of his stories is about breaking the world speed record for a wall of...

Homework Statement Determine the maximum kinetic energy of a uniform rod of mass 0.5Kg and length 0.75 that has an angular displacement of 5 degrees. Homework Equations y = rsin (x) where x is the angular displacement The Attempt at a Solution Using conservation of energy ETotal = EMech +...

I would like to know the maximum voltage that a metal sphere can hold from applying negative charge to it. My thoughts are that the maximum voltage is the breakdown voltage of the surrounding medium (air in this case). I assume that at that voltage, electrons would arc from the sphere to the...

Homework Statement A 5V battery rated at 1800mAh has a soucre resistance of 10 Ohms. What is the maximum power that can be extracted from the battery? Homework EquationsThe Attempt at a Solution I understand that had the battery not had any source resistance then the power out would have been...

Homework Statement After happily working my way through the earlier parts of this question, I'm pretty much at the end of my tether with the last two parts. Please find the diagram attached: A) Determine the value of the angle θ (measured from vertical) when the angular velocity of link AB a...

If an object is an infinite distance from a black hole and falls directly to the black hole without being affected by any other force, what is its velocity at the event horizon?

What is the maximum practical or theoretical pressure at which x-rays can be produced, as in a Crookes tube or cathode ray tube? I know Crookes tubes operate at 0.1pa and lower, but I need to know if I am at risk of producing x-rays with high voltage (60kv+) discharges at medium vacuum, as low...

The problem gives you a function describing the position of a particle moving along an x axis: x(t) = 12t2 - 2t3 With this function, one must determine the maximum positive coordinate reached by a particle and the maximum positive velocity. The first step to the problem is to take the...

Hello (Smile). I have been stuck on this question for a while. A company charges $550 for a transistor set on orders of 50 or less sets. The charge is reduced by $5 per set for each order in excess of 50 sets. Find the largest size order company should allow so as to receive a maximum revenue...

I have a flat steel bar (30 mm width, 5 mm thick, 1100 mm long). The bar has a load applied in the centre of 100N. the bar is fixed at both ends with a single concentrated load P applied mid-span the maximum yield stress is 250 MPa (250x10^6 Pa) How do I calculate the maximum load the bar can...

Hello everyone. So I have this one question which I thought was going to be pretty easy, but now I struggle with it. It says: 1. The question A rock is thrown vertically up in the air with an initial velocity of 0.75ms-1. What would the rock's maximum theoretical height be? I am currently in...

Hi, I'm familiar with the expression for calculating the built-in voltage of a p-n junction. How can I find the maximum built-in voltage before the semiconductor becomes degenerate (i.e., a bad metal) if I only know the material and the intrinsic carrier concentration at a given temperature...

Homework Statement Find the extremizing (maximum) value of the function f(x) = sin x / x using Newton's 1D method. Homework Equations [/B]The Attempt at a Solution I know the maximum point in this equation is (0, 1). When I differentiated the equation twice and used the formula above, I...

Hi everyone : I have a question: how to calculate the maximum work delivered by a turbine. Steam input T and pressure are given plus the outlet pressure only. Using Peng-Robinson equation of state. Adiabatic process. I tried to find outlet temperature by trial and error using Peng-Robinson EOS...

Homework Statement We have a wheel with [mass = 1.5 kg] and a [radius = 0.06 m]. The static friction thing between the ground and the wheel is 0.3 . WIth how much force can we pull the string spooled around the wheel without the wheel slipping. The string ends at the top of the wheel and we...

Homework Statement Hey guys, I have been struggling on this problem for a while now and was hoping I could get a little help What is wanted is the maximum value of Ro for maximum power. Homework EquationsThe Attempt at a Solution Knowing that the Maximum power transfer to Ro would be when...

Homework Statement [/B] A uniform stick is held horizontally and then released. At the same instant, one end is struck with a quick upwards blow. If the stick ends up horizontal when it returns to its original height, what are the possible values for the maximum height to which the center...

I have seen a video in which the time dilation due to velocity is explained by saying that light and light interactions inside a moving body must travel a longer distance in space, which reduces the passage of time. Video: This explanation is new to me, and in fact, I recently heard an almost...

Homework Statement So a generation with an internal resistance r delivers a voltage E. The generator is connected to a electrical circuit with a resistance R. The work W done each second in sending a current through a circuit with a resistance R is given by W =E^2*R/(R+r)^2. For constant r...

Homework Statement A platform (m = 5,0kg) is suspended from 4 steel cables whose length is 3,0m and diameter 2mm. a) How much further will the platform sink if a mass of 50kg is placed on the platform? b) What is the maximum load that the wires can hold before breaking? Homework Equations...

If I have to transfer 250 MWh through 3 phase aluminium tubular busbar what is the maximum current carrying capacity under normal condition at 80c temperature and voltage is 132kv at busbar from each 60mw 04 transformers 50hz 132/11kv stepup transformers connected on that busbar, this is not...

Hi, I'd like to know if there is a maximum matrix size after which radiation counting (using a scintillator/photomultiplier) on a flat paper sample doesn't improve or is not significant. Specifically this would refer to radiochromatograms, or chromatography strips of radioactive samples. If...

Find the maximum and minimum of $x^3+y^3+xy(x^2+y^2)$ given $x,\,y$ are two non-negative real numbers that satisfy $x+y+xy=3$.

Hello This is what I have attempted so far. But now I'm at utter loss at how to calculate the rest Can you help? Thanks in advance.

Homework Statement A box of mass m = 40kg is released from rest at thte top of a frictionless ramp. The ramp makes an angle theta = 45 degrees to the horizontal. After sliding fom the rigin a distance d = 2.00 m down the ramp, the box strikes a spring of force constant k = 500 N/m. The box...

A football is kicked from a tee to start the football game. If the ball is kicked at a 38 degree angle with an initial velocity of 27.1 m/s, Find the maximum height of the football as it flies through the air. I was using these equations: Voy = Vo(sine of theta) Vy = Voy + at y = 1/2(a)(t^2)...

If a string can handle a max tension of 85 N what is the largest mass that could be lifted with this string if it is lifted with an acceleration of 2.0 m/s^2 up on the moon? Let up be positive in value. Ft = - 85 N, a = 2.0 m/s^2, Fg = -1.6 m/s^2 Homework Equations F = ma -> Fg = mg -> Ft =...

What limits the speed of light to 3x10^8ms^-1? I was referred to Maxwells equations and have studied them but am not sure if this is the full answer and am unsure where Maxwell's relate anyway, the lectures I watched were unclear apart from relating to Ampere's Law. As much maths as possible...

Homework Statement Find the maximum and minimum values of f(x,y,z) = x^2 - 2x + y^2 - 4y + z^2 - 4z in the region x^2 + y^2 + z^2 <= 36. Homework Equations Lagrange multipliers The gradient of f = lambda * gradient of g <Fx, Fy, Fz> = lambda<Gx, Gy, Gz> Test for local extrema If Determinant...

I have tried to get some answers related to a humans ability to produce power and torque on cycling forums with mixed response. So I came to the experts to help me out! Basically some cyclist belief that the maximum torque a human can produce is solely limited by their body weight keeping them...

like in NH3, maximum number of Hydrogen bonds is 4 and general is 2 ... is it that in any molecule, max number of hydrogen bonds=Hydrogens with +∂ change + lone pairs with -∂ charge (enough polarization by F or O or N and chelated with Cl) now, if that was correct, hydrazine nh2-nh2 forms 6...

Homework Statement Let's take two spheres that are somewhat nearby. On one sphere, sphere A, there is Q units of charge. Now, we take some little bit of charge q off of sphere A, and put it on sphere B. What should the ratio q/Q be if we want the electrostatic force between the spheres to be a...

If $s,\,t,\,u,\,v$ are positive integers with sum $63$, find the maximum value of $st+tu+uv$.

Homework Statement The sinusoidal voltage output from the AC generator oscillates between 500 V and -500 V. The circuit for an ideal transformer is constructed with a generator, transformer and a 30 Ω resistor . The generator makes 4 loops with the transformer and the resistor makes 9 loops...

A simple pendulum, 2.0 m in length, is released by a push when the support string is at an angle of 25° from the vertical. If the initial speed of the suspended mass is 1.2 m/s when at the release point, to what maximum angle will it move in the second half of its swing? Let h1 be the...

Homework Statement A 2.49×104-kg rocket blasts off vertically from the Earth's surface with a constant acceleration. During the motion considered in the problem, assume thatg remains constant. Inside the rocket, a 14.5-N instrument hangs from a wire that can support a maximum tension of 37.3 N...

Homework Statement The question is showed as below. Homework Equations I don't know how to find i when the resistor is 4 ohm. I think it is quite difficult as the voltage is varying all the time. So how do I find the current? Thanks! The Attempt at a Solution

1. In general, dense fluids (such as water) produce a drag force that is directly proportional to the speed of an object moving through them. Suppose a boat is moving through the water and experiencing a fluid drag force of F=-8 v. Suppose the boat has a motor which can output up to 450 Newtons...

Hello, been thinking on this one for a little while, and can't seem to figure it out. Problem statement is: The cubic curve y = 8x^3 + bx^2 + cx + d has two distinct points P and Q, where the gradient is zero. Show that b^2 > 24c. It seems simple enough, but I can't logic it out. This...

I put basic on this because my maths skills are exactly that and I suspect the answer to this question will be fairly maths heavy. I understand that the equation to calculate the maximum height of a projectile (ignoring wind resistance) is Hmax = (Vf2 - Vi2)/2a But this only works over small...

Homework Statement Let's say you want to find the minimum and maximum observed frequencies of light observed on Earth from the sun, when considering the Earth's motion around the sun. How would you go about doing this if you assume Earth takes time X to complete a revolution around radius R...

Homework Statement :[/B] A projectile is given initial velocity 80 m/s ( V0 ) at angle 60° above the horizontal. Find the time it takes to reach to the highest point and find the maximum height. (g = -10 m/s2) Homework Equations :[/B] 1. y_{final} = y_{initial} + v_{y_{initial}}t + \frac...

Hello, The Gibbs free energy is the maximum amount of non-expansion work that can be extracted from a closed system; this maximum can be attained only in a completely reversible process. This maximum work is equal to H-TS. My question is this TS energy is what kind of energy? and from where it...

Hello! (Wave) If $f: \mathbb{R}^n \to \mathbb{R} (n \in \mathbb{N})$ and $D \subset \mathbb{R}^n$ then it doesn't generally hold that there exists a $\max_{x \in D} f(x)$, i.e. that there is a $\overline{x} \in D$ such that $f(\overline{x}) \geq f(x)$ for each $x \in D$. For example if $n=1$...

Homework Statement Initially your receiver is positioned at a distance of 8.4 cm from the goniometer and recording a maximum intensity. You move it through 10 minimums in the intensity and then stop at the next maximum intensity. The receiver is now a distance of 27.3 cm from the goniometer...

Homework Statement A weight W is supported by bar AO and cables AB, AC, and AD. Point A lies in the xy plane, if the bar and cables have the strengths listed below, determine the largest value W may have. Hint given: A FBD of joint A is recommendedto being this problem. Bar AO should be...