Maximum Definition and 1000 Threads

Homework Statement An unstable particle of mass M = m1 + m2 decays into two particles of masses m1 and m2, releasing an amount of energy Q. Determine the kinetic energies of the two particles in the CM frame. Given that m1/m2 = 4, Q = 1 MeV, and that the unstable particle is moving in...

Hello, It's been a while since I did this in college and I cannot remember a few steps. I am trying to calculate the maximum force my designed shaft can handle before bending/shearing. My shaft material is C1018 steel rod, with a yield strength of 53.7 KSI and an ultimate strength of 63.8 KSI...

Homework Statement Find the required value of the load to achieve maximum power transfer for Z = 12+24 ohms Homework Equations ZL = Zs [b]3. The Attempt at a Solution [/b As the question does not state whether or not the phase or magnitude of the load can or cannot be varied. I...

Here is the question: I have posted a link there to this topic so the OP can see my work.

$n\in N$ $n^2 - 2112 $ is a multipler of $n+10$ please find :$max(n)$

Hi, I am not sure how to solve the following high school algebra problem. As shown in the attached file, I have plotted the first three equations, but I don't know what to do with the fourth equation. Find the minimum and maximum values of the objective quantity. 2X + Y ≤ -8 3X - 2Y...

Homework Statement Hey guys, I am having problems with finding the maximum charge of a capacitor. From the experiment we are given R=100 Ohms, and Capacitance = 330 uF We are asked to find the maximum charge the capacitor has. Time to half charge was 0.0235 sec. Voltage is 4V Homework...

Homework Statement A damped oscillator has a displacement x as a function of time t given by x = e-t cos(∏t). Find the time at which the displacement is a maximum, when it is a minimum, and also nd the time when x is a point of inflection. Homework Equations x = e-t cos(∏t) The...

Hello, If I have a shaft that has a section area of .0562 in. sq. and a material yield strength of 60KSI. And I will have the force applied at the top of the shaft pushing down. The shaft will be in a cantilever configuration where the force will be applied .125" from the base of the shaft...

Homework Statement A projectile is fired at 30 km/h at the angle θ in x direction of an x-y plane. Ignoring the effects of air resistance, find the maximum range and the value of θ that gives this range Part A: write down the initial horizontal and vertical components of the velocity Part...

Homework Statement One often stated advantage of ethanol/water as a recrystallization solvent is that the mixture behaves like ethanol at reflux and like water at room temperature or below. Assuming that 24 mL of the solvent is used per 1 g of crude product and recrystallization and recovery...

Homework Statement The bar 1 in the figure has a cross-sectional area of 0.75 in^2. If the stress in this bar must be limited to 30 ksi (30,000 psi) determine the maximum load that P that can be supported by the structure. Homework Equations σ = F/A τ = Fd The Attempt at a...

Homework Statement An ball is launched at a 45 degree angle with an initial speed v0. What is its speed at its max height? Homework Equations n/a The Attempt at a Solution This problem does not contain any calculations. I was wondering if somebody could explain how the speed at...

"Consider a solution of the diffusion equation ##u_{t} = u_{xx}## in {0 ≤ x ≤ L, 0 ≤ t ≤ ∞}. a) Let M(T) = the maximum of u(t,x) in the closed rectangle {0 ≤ x ≤ L, 0 ≤ t ≤ T}. Does M(T) increase or decrease as a function of T? b) Let m(T) = the minimum of u(t,x) in the closed rectangle {0 ≤ x ≤...

Homework Statement A rocket is launched straight up with constant acceleration. Four seconds after liftoff, a bolt falls off the rocket. The bolt hits the ground 8 seconds later. Three seconds after the bolt falls off, the rocket's engines fail. How high does the rocket go before it begins...

Homework Statement In a damped harmonic oscillator, show that |R(\omega)|^2 = \gamma at full width half maximum. 2. My attempt at a solution This is another one of those questions that I feel like I am almost there, but not quite, and it's the math that gets me. But here goes: For a...

1. Homework Statement A 2-kg mass attached to a spring oscillates in simple harmonic motion and has a speed of 5 m/s at the equilibrium point. What is the maximum potential energy of this oscillating mass? 2. Homework Equations I know that the potential energy is: Ep = 1/2 kx2 k = mω2

Homework Statement The Entropy of a probability distribution is given by, S = -k_B \sum _{i=1}^N p(i)\ln{p(i)} I've shown that the extremum of such a function is given by, S' = k_B \ln{N} (which is a positive quantity) Now I want to show that this is a maximum by showing that S' - S...

Please delete this post.

Homework Statement A person of mass mp stands on a scale in an elevator of mass me . The scale reads the magnitude of the force F exerted on it from above in a downward direction. Starting at rest at t=0 the elevator moves upward, coming to rest again at time t=t_0. The downward acceleration...

Homework Statement P-type silicon can be doped in the range from 5x1014 cm-3 to 1020 cm-3. Determine the maximum possible number of minority electrons in a neutral P-type region if the device area is limited to AD = 1 cm x 1 cm and the thickness of the P-type region is limited to tP=100 μm...

Homework Statement Given f(t) = integral {(x^2 + 12x + 35)/(1 + cos^2 (x)) dx}. At what value of t does the local max f(t) occur? (A more aesthetically-pleasing version of the question is attached as TheQuestion.jpg.) Homework Equations Differentiating (I think). The Attempt at a Solution I...

Homework Statement A particle is projected with an initial speed u from a point at a height h from the horizontal plane. Find the equation for maximum range of the particle. Homework Equations R=u^2sin2θ/g H=(usinθ)^2/2g The...

Homework Statement Assuming that the rock launched by a catapult is released from ground level, show that the theoretical maximum range is: R=2Mh/m, where M = mass of counterweight m = mass of rock h = height counterweight falls Homework Equations Ep=mgh Ek=(mv^2)/2 The Attempt...

I would like to calculate the maximum distance, crest, a guitar string will travel at it's center when plucked in order to determine how high the string needs to be on the fretboard to avoid striking parallel frets and thus avoiding "fret buzz". Example: 0.762 mm string thickness with...

Hi, I've got a simple question regarding the maximum of the spectral energy density in Planck's black body radiation. It turns out that if you calculate which frequency has the most power associated with it (i.e. maximize R(\nu)), then you do it with wavelength as well, and compare, they're not...

Hello! I would like to know what is the maximum flux density that can be used in a core for DC generator without taking the core in it's saturation point now a days?

Homework Statement So the question states that we have a hollow metal sphere of radius 2cm that is charged up. We take the breakdown field of air to be 1MV/m. We are asked to: a) Calculate the maximum amount of charge which can be placed on the sphere. b) Calculate the maximum potential on...

Homework Statement Given that V(t) = π*cos(πt/1.6 + π/6), at which time after t = 0 s is the kinetic energy first at a maximum? The answer is 1.33 seconds. Although, when I put it in the calculator, 1.33s is at a minimum. How would you do this by hand? Step by step work would be appreciated...

Homework Statement A ray of photons coming from a laser with a wavelenght of 589.59nm meets a ray of sodium atoms (A=23) coming from the opposite direction. What is the maximum speed the sodium atoms can have in order to absorb photons? The Attempt at a Solution I thought about...

I've prove everything except for the fact that E is bounded below. It would appear that you would need to know something about the functions taking a minimum value as well to show this using my method, so perhaps there is another way of thinking about things to show a lower bound?

Hello, I hope this is the right section to post this question. While analysing the asymptotic value of a ratio of a bessel and a hankel function, I reduced it to something of the form [(1 + β/n)^ n * (1 + n/β)^ β] / 2^(n+β) ; n and β are integers and greater than 1 how do I show that...

$a,b,c,d,e \in R$ $a+b+c+d+e=8$ $a^2+b^2+c^2+d^2+e^2=16$ $find :\,\, e_{max}$

I have a 1.5m beam with a uniformly distributed load of 57kn/m acting over 1.2m of the beam (0.6m from the centre of the beam in both directions). I require the maximum moment and the deflection of the beam. I know the maximum moment equation wl^2/8 and the deflection formula 5wl^4/384EI...

WHat is the permissible maximum transmission ratio of a Spur gear pair? I read somewhere that it is 1:5. What wil happen if this is exceeded?

Homework Statement A particle is projected from a point o with initial velocity u up a plane inclined at an angle 60° to the horizontal. The direction of projection makes an angle ∅ with the horizontal. The maximum perpendicular height is H. prove that H = u^2( sin^2(∅) ) / g Homework...

Homework Statement The maximum shear force of a set of bolts is 1000 kN. The ultimate shear stress is 750 MPa and the safety factor is 3. The diameter of each bolt is 20 mm. a) What is the maximum working shear stress in each bolt? b) The cross sectional area of each bolt? c) The maximum...

Homework Statement Let f be an analytic function on the disc |z|<1 and satisfies |f(z)|≤M if |z|<1. Show that |f(z)| \le M \left| \frac{z-a}{1-a'z} \right| when |z|<1 where a' is the complex conjugate of a Homework Equations This section uses maximum modulus principle, but I really don't...

The question asks me as follows: "What is the maximum number of comparisons required for a list of 6 numbers? Is the correct answer as follows: The maximum number of comparisons required for a list of 6 numbers is 5 comparisons. If this is not right, then can somebody please help and explain...

I am struggling in college at the moment and I don't know where else to turn. Any assistance or advice would help, thank you (a) A firm’s short-run production function is given by Q = L2e-0.01L where Q = output and L = labour. Find the value of L that maximises the average product of labour...

Homework Statement FIND MAXIMUM DEFLECTION AND ITS LOCATION (PLEASE SEE THE FIGURE)... THANKS Homework Equations The Attempt at a Solution

It appears the maximum value of x = 0.999... . But 0.999... = 1. But max value of x cannot be 1 based on the criteria. What is the maximum value of x then? It's puzzling me.

Block 1 has a mass of 2kg and is moving to the right on a frictionless surface at 10m/s. Block 2 is ahead of Block 1, has a mass of 5 kg, and is moving to the right at 3m/s. Block 2 also has a spring attached to its left end, which has a spring constant of 1120 N/m. When the blocks collide...

this is a problem in the topic of Concavity and the second Derivative Test The deflection $$D$$ of a beam of length $$L$$ is $$D=2x^4-5Lx^3+3L^2x^2$$, where $$x$$ is the distance from one end of the beam. Find the value of $$x$$ that yields the maximum deflection The answer to this is...

Hello, I have a doubt about the distribution of random variables that maximize the differential entropy in a set of inequalities. It is well known that the Normal distribution maximizes the differential entropy. I have the following set of inequalities: T1 < I(V;Y1|U) T2 < I(U;Y2) T3 <...

Homework Statement A rectangle has its base on the x-axis and its vertices on the positive portion of the parabola $$ y=2-3x^2 $$ What is the maximum possible area of this rectangle? A. (8/27)*181/2 B.(2/9)*181/2 C. (4/15)*301/2...

Hello everybody! Given a topological space ##X## and two functions ##f,g:X\rightarrow \mathbb{R}##, it is rather easy to prove that ##x\rightarrow \max\{f(x),g(x)\}## is continuous. I wonder if this also holds for infinitely many functions. Of course, the maximum doesn't need to exist, so we...

Hi, What is the material which would develop powerful vibration for a sustained period when they are stroked with another material(may be the same or a different material).

Can someone help me as a am racking my brain. I have been given this question; Two oil pipes with circular cross-sections are subject to the constraint that the sum of their diameters is 1m. By using careful reasoning find the diameters that give the maximum and minimum possible combined...

A non-conducting sphere of radius R = 7 cm carries a charge Q = 4 mC distributed uniformly throughout its volume. At what distance, measured from the center of the sphere does the electric field reach a value equal to half its maximum value? My attempt: Emax= q(4mC)/7 r= 7/2 cm = 3.5...